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CRC Handbook of Sample Size Guidelines for Clinical Trials [1 ed.]
 9781138105393, 9781315150864, 9781351366250, 9781351366243, 9781351366267, 9781138558427

Table of contents :

1. How to use the sample size tables 2. Identification of parameters 3. References 4. Design and analysis of randomized clinical trials 5. Formulation of the therapeutic question 6. One sided vs. Two-sided question 7. Design of the clinical trial 8. Statistical considerations 9. Conduct of the trial 10. Analysis and reporting of the trial 11. Crucial elements 12. Binomial comparison 13. Kaplan-meier comparison (large sample) 14. Logrank test 15. References 16. Derivation of the statistical results 17. Derivation of the large sample distribution of the logrank statistic 18. Derivation of the large sample distribution of the kaplan-meier statistic 19. Difference between kaplan-meier curves 20. Exponential survival 21. Application of the logrank test when survival is exponential 22. Exponential survival with a poisson accrual process 23. Extension to the two-sample problem 24. Exponential survival with "up-front" accrual 25. Proportional hazard models and the exponential distribution 26. Consideration in planning a trial under proportional hazards: putting it all together 27. Losses to follow-up and sample size adjustment 28. Interpretation of the tables 29. Multi-treatment trials 30. Type a 31. Type b 32. Type c 33. Type d 34. Stratified logrank test 35. Advice on stratification 36. Intuitive justification why the logrank test and kaplan-meier estimation for actual accrual process behave in the limit in the same way as the fixed binomial assumption 37. Alternate standard error for the kaplan-meier estimator 38. Connection between kaplan-meier with binomial 39. References 40. Figures. Appendix i: a review of mathematical statistics. Appendix ii: tables. Index.

Citation preview

CRC Handbook of Sample Size Guidelines for Clinical Trials

Author

Jonathan J. Shuster, Ph.D. Professor of Statistics, University of Florida Gainesville, Florida and Co-Principal Investigator Pediatric Oncology Group Statistical Office St. Louis, Missouri

CRC Press Taylor & Francis Group Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an informa business

First published 1990 by CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 Reissued 2018 by CRC Press © 1990 by Taylor & Francis CRC Press is an im print of Taylor & Francis Group, an Informa business No claim to original U.S. Government works This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attem pted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as perm itted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transm itted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without w ritten permission from the publishers. For permission to photocopy or use material electronically from this work, please access www. copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organiza-tion that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. A Library of Congress record exists under LC control number: 92049333 Publisher’s Note The publisher has gone to great lengths to ensure the quality of this reprint but points out that some imperfections in the original copies may be apparent. Disclaimer The publisher has made every effort to trace copyright holders and welcomes correspondence from those they have been unable to contact. ISBN 13: 978-1-138-10539-3 (hbk) ISBN 13: 978-1-315-15086-4 (ebk) Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com

PREFACE This book is primarily designed as a guide for physicians and biostatisticians working in clinical trials, where the primary objective is survival (or disease-free survival or progression-free survival etc). It will also be useful as a supplement to text material in courses dealing with biostatistics. To project patient needs of a trial, the physician needs to provide “ planning parameters” . These include endpoints (eg 3 year survival); minimum difference the trial is to be sensitive to (eg 50% control vs 65% experimental); patient accrual rate (eg 55 patients per year are expected to be accrued); precision measures (“ ALPHA” = probability of falsely concluding experimental therapy has efficacy given that it has none: typically .05) (“ POWER” = probability of correctly concluding the experimental therapy has efficacy when the minimum difference is as above: typically .8 or .9 depending on the field); and anticipated rate of patient losses for non­ study related reasons called “ LOSSES TO FOLLOW-UP” . This Handbook is organized into three Chapters, an Appendix, and Tables. CHAPTER 1, “ //ow to Use the Sample Size Tables” , is designed for users who simply want to know how many patients they need. This section is therefore a “ Cookbook” approach, including a worksheet for obtaining the appropriate sample size for the trial. CHAPTER 2, “Design and Analysis o f Randomized Clinical Trials’

is a non-technical discussion of the

major elements of such trials. This section may be helpful for the user wishing to write a clinical protocol or a clinical research grant. A blueprint for protocol construction is included. CHAPTER 3, “Derivation o f the Statistical Results” , contains a heuristic derivation of the statistical methods presented in CHAPTER 2. One full year of Calculus-based Mathematical Statistics is sufficient background to understand the material in CHAPTER 3. In addition, this Chapter contains some simple results on multiple comparisons and stratified analysis (in non­ technical language). APPENDIX I contains a fairly detailed review of Mathematical Statistics, thereby making the text self-contained with respect to CHAPTER 3. Summary of What you need to read:

1.

Cookbook: Give me the sample size needed. (CHAPTER 1)

2.

Clinicians: Help me write my Research Protocol. (CHAPTERS 1 and 2. For a discussion of “ losses to

follow-up” , the reader might also consult Section 3.10 of CHAPTER 3. If the study has more than two treatments, see Section 3.12 of CHAPTER 3. Although that Section is far more technical than CHAPTER 2, most clinical investigators should be able to follow the main ideas. If after reading CHAPTER 2, “ stratification” is contemplated, see Section 3.13 of CHAPTER 3.) 3.

Biostatisticians: Entire text material. Extensions and Limitations: While the major scope of this Handbook is for two treatment randomized trials, CHAPTER 3 (Section 3.12) does contain methods for the design and analysis of trials involving three or more treatments. This Handbook is limited in scope to therapeutic comparisons involving survival (or disease-free survival or progression-free survival, etc) as the primary endpoint. Analysis of prognostic factors are not discussed.

NOTE: In any Clinical Trial, it is in everyone’s best interest that a team of researchers be assembled at the planning stage. This team should consist of clinical researchers, a biostatistician, and computer scientists. Laboratory researchers are often important members of the team.

THE AUTHOR Jonathan J . Shuster, P h.D ., is currently a Professor in the Department of Statistics, University of “Florida, Gainesville, Florida. He serves as Co-Principal Investigator of the Statistical Coordinating Center of the Pediatric Oncology Group, which at any time has at least 75 active multi-center clinical trials in childhood cancer. Apart from cancer, he has participated in major collaborative projects in Ophthalmology and Urology. He has published over 80 articles in methodologic research and in medical applications. His major statistical research interests include the design and analysis of clinical trials and of large epidemiologic studies. Dr. Shuster has served on numerous NIH Study Sections including the Epidemiology and Disease Control Study Section #1 (1986— 90). He served as Chair of that Study Section for the 1989— 1990 fiscal year. It is largely through service on these study sections that Dr. Shuster recognized the need for this book. In addition to his research efforts, Dr. Shuster has been active in teaching. He has taught service statistics courses to students in the health sciences, as well as elementary, intermediate, and advanced courses in statistics. Dr. Shuster received his Ph.D. degree from McGill University, Montreal, Canada in 1969. Since then, he has been at the University of Florida. As of the spring of 1990, he had received nearly $10 million in grants, mostly from the National Institutes of Health. The author wishes to express his appreciation to many kind friends who directly contributed to this project, most notably to Dr. Jim Boyett, to Dr. Dick Scheaffer, and especially to Dr. Jeff Krischer. This book is dedicated to Isobel and Samuel Shuster, parents of the author, on the occasion of their golden wedding anniversary.

TABLE OF CONTENTS Chapter 1 HOW TO USE THE SAMPLE SIZE T A B L ES............................................................................................................. 1 1.1. Identification of Param eters......................................................................................................................................2 References................................................................................................................................................................................ 5 Chapter 2 DESIGN AND ANALYSIS OF RANDOMIZED CLINICAL T R IA L S.......................................................................9 2.1. Formulation of the Therapeutic Question............................................................................................................... 9 2.1.1 One Sided vs. Two-Sided Q uestion......................................................................................................... 9 2.2.

Design of the Clinical T ria l.................................................................................................................................... 11 2.2.1. Statistical Considerations.......................................................................................................................... 12

2.3.

Conduct of the Trial................................................................................................................................................. 20

2.4.

Analysis and Reporting of the T ria l...................................................................................................................... 21 2.4.1. Crucial E lem ents.................................................................................................................................... 21 2.4.2. Binomial Com parison............................................................................................................................... 22 2.4.2.1. Large Sample M ethodology.................................................................................................22 2.4.2.2. Confidence Intervals...............................................................................................................23 2.4.2.3. Numerical Example (Test).................................................................................................... 24 2.4.2.4. Numerical Example (One-Sided Confidence Interval).................................................... 25 2.4.2.5. Numerical Example (Two-Sided Confidence Interval).................................................... 25 2.4.2.6. Small Sample M ethodology................................................................................................. 25 2.4.3 Kaplan-Meier Comparison (Large Sam ple)........................................................................................... 28 2.4.3.1. Assumptions Underlying Kaplan-Meier Curve.................................................................. 28 2.4.3.2. Calculation of the Kaplan-Meier Curve........................................................................... 29 2.4.3.3. Numerical E xam ple...............................................................................................................30 2.4.3.4. Standard Error..........................................................................................................................31 2.4.3.5. The Kaplan-Meier Comparison of Two T reatm ents........................................................32 2.4.3.6. Confidence Intervals for Difference in Fixed-Term S urvival........................................ 33 2.4.4.

Logrank T e st...............................................................................................................................................34 2.4.4.1. Important Observations With Respect to the Logrank T e st.........................................36 2.4.4.2. Numerical E xam ple............................................................................................................ 36 2.4.4.3. Footnotes to Numerical Example and the Logrank T e s t.................................................38 2.4.4.4. Proportional Hazards and the Logrank T e s t..................................................................... 39 References........................................................................................................................................................................... 40 Chapter 3 DERIVATION OF THE STATISTICAL RESULTS.................................................................................................... 51 3.1. Derivation of the Large Sample Distribution of the Logrank Statistic........................................... ...........53 3.2. Derivation of the Large Sample Distribution of the Kaplan-MeierStatistic..................................................63 3.2.1.

Difference Between Kaplan-Meier Curves.......................................................................................... 85

3.3.

Exponential S urvival.............................................................................................................................................86

3.4.

Application of the Logrank Test When Survival is Exponential...................................................................93

3.5.

Exponential Survival with a Poisson Accrual Process....................................................................................98

3.6. Extension to the Two-Sample Problem ..............................................................................................................110 3.7. Exponential Survival with “ Up-Front” Accrual.............................................................................................. 114 3.8. Proportional Hazard Models and the Exponential Distribution...................................................................... 117 3.9. Consideration in Planning a Trial Under Proportional Hazards: PuttingIt All T ogether.......................... 120 3.10. Losses to Follow-Up and Sample Size Adjustment......................................................................................... 128 3.11. Interpretation of the Tables.................................................................................................................................. 130 3.12. Multi-Treatment T ria ls ......................................................................................................................................... 130 3.12.1. Type A .....................................................................................................................................................131 3.12.2. Type B .....................................................................................................................................................132 3.12.3. T y p e C .....................................................................................................................................................133 3.12.4. T y p e D .....................................................................................................................................................136 3.13. Stratified Logrank T e st............................................................................................................................................137 3.13.1. Advice onStratification......................................................................................................................... 139 3.14. Intuitive Justification Why theLogrank Test and Kaplan-Meier Estimation for Actual Accrual Process Behave in the Limit in the Same Way as the Fixed Binomial Assum ption............................................... 140 3.15. Alternate Standard Error For the Kaplan-Meier Estim ator.............................................................................141 3.16. Connection Between Kaplan-Meier With Binomial.........................................................................................144 References.............................................................................................................................................................................145 FIGURES 1. Codes for T ab les..........................................................................................................................................................6 2. Worksheet for Sample Size D eterm ination.............................................................................................................7 3. Modifications of Figure 2 .......................................................................................................................................... 8 4. Simple Randomization for 1200 P atients.............................................................................................................. 43 5. Random Length Permuted Blocks of Four or Six Patients.................................................................................44 6. One-Sided P-Values for Normal Curves................................................................................................................45 7. Two-Sided P-Values for Normal Curves; Ignore Sign of Z + V S — ............................................................. 46 8. Values for W in One-Sided Confidence Intervals for ApproximatelyNormally Distributed Estim ates......................................................................................................................................................................47 9. Values for W in Two-Sided Confidence Intervals for Approximately Normally Distributed E stim ates..................................................................................................................................................................... 4 7 10. 11.

Survival in Randomized Pediatric Cancer Trial Entries are in Days with+ to Indicated Survivors____ 48 Survival Com parison................................................................................................................................................. 49

Notation Chart........................................................................................................................................................................ 52 APPENDIX I A REVIEW OF MATHEMATICAL STA TISTICS......................................................................................................147 Expected Value of a Function of a Random Vector (D efinition)............................................................................... 155 Special D istributions.......................................................................................................................................................... 162

Transformations (Continuous Variables) (Consequence)............................................................................................ 169 Statistical Inference............................................................................................................................................................ 189 Sample Size Determination.............................................................................................................................................. 197 The Poisson Process.......................................................................................................................................................... 201 References........................................................................................................................................................................... 210 APPENDIX II T A B L E S..............................................................................................................................................................................211 TABLE TABLE TABLE TABLE TABLE TABLE TABLE TABLE INDEX

1: 2: 3: 4: 5: 6: 7: 8:

ALPHA ALPHA ALPHA ALPHA ALPHA ALPHA ALPHA ALPHA

= = = = = = = =

0.005 0.005 0.01 0.01 0.025 0.025 0.05 0.05

and POWER and POWER and POWER and POWER and POWER and POWER and POWER and POWER

= 0 .8 0 ....................................................................................................213 = 0 .9 0 ....................................................................................................293 = 0 .8 0 ....................................................................................................373 = 0 .9 0 ................................................................................................... 453 = 0 .8 0 ....................................................................................................533 = 0 .9 0 ....................................................................................................613 = 0 .8 0 ....................................................................................................693 = 0 .9 0 ....................................................................................................773 853

1 Chapter 1 HOW TO USE THE SAMPLE SIZE TABLES Introduction It is vital th a t a clinical trial has a reasonable chance of achieving its objectives. Sm all negative studies could be harm ful, as they m ight not have had adequate power to find im p o rtan t differences. Researchers m ight falsely conclude from the com pleted trial th a t a new therapy lacks efficacy. Freim an et al (1978) reviewed a large num ber of published negative studies and concluded th a t the vast m ajority were not adequately sensitive to clinically m eaningful differences. T o avoid this problem , clinical trials m ust be well designed, and m ust have sufficient num bers of p atients to answer the study question. In order to use the sam ple size tables, the user m ust supply several values called param eters. The worksheet, Figure 2, will be helpful. Before getting too form al, let us have a glance a t a “Statistical C onsideration” of a research protocol. At first, it probably will look quite technical, but we shall unravel the details.

STATISTICAL CONSIDERATION “Historically, the In stitu te has been able to accrue 125 patients per year w ith newly diagnosed X-disease. Based on our prior studies, the three year survival rate is expected to be about 60% on the standard therapy (or control therapy). In order to detect a 15% im provem ent under the experim ental therapy (three year survival of 75%), a t “alpha” = .05 (one-sided) and 80% “power” , a sam ple size of 204, half random ly assigned to each treatm en t, will be needed. T his calculation assum es exponential survival w ith all patients followed to death or term ination point of the study. Allowing for a 10% loss to follow-up, a figure consistent with past history, a revised sam ple size of 227 (1.8 years of accrual) is needed. P atien ts will be followed until death, loss to follow-up, or the com pletion of the study (up to 4.8 years). T he logrank test will be used to make the treatm en t com parison.”

CRC Handbook o f Sample Size Guidelines fo r Clinical Trials

2 1.1

Identification of Parameters

(1)

M inim um Planned Follow-up: At how m any years will the key survival com parison be m ade? 3 years

(2)

Annual Accrual 125 P a tie n ts per year

(3)

Expected Accrual thru M inimum Follow-up 125 X 3=375 (This param eter is used in tables)

(4)

P C O N T = P lanning value for survival thru the m inim um follow-up period

(In this case

3

years) under the CON TRO L treatm ent. .6 (ie 60%) (This param eter is used in tables)

(5)

D E L = P lanning value of im provem ent under the experim ental treatm en t a t the endpoint (ie a t three years in this case.) .15 (ie 15%) (This param eter is used in tables)

(6)

A L PH A =C hance of falsely concluding experim ental therapy is superior to the control, when in fact it is equivalent to the control. In m ost studies, a value of .05 (ie 5%) is used. T here is no special reason to pick this value other than standardization. For further discussion, see C hapter 2, especially as to one-sided versus two-sided tests. See also the footnote a t the conclusion of the chapter. .05 (ie 5%) (This value is used in the tables)

P O W E R = C hance of correctly concluding th a t the experim ental therapy is superior to the control, when in fact the planning values (4) and (5) are correct. T he m ost com m on values for power are 80% and 90% depending on the field. T his is discussed further in C hapter 2 and in the footnote a t the end of this chapter. .80 (ie 80%) (This value is used in the tables)

F A C T (for factor). T his asks the following question. Consider a typical day before and after the endpoint. A value of FA C T is the ratio of the instantaneous death rate after the endpoint to th a t before the endpoint. The exponential distribution implies a value of 1.0. If you consider patients cured after three years, you would use a value of 0. However, the tables can be used for interm ediate situations. For exam ple, you m ight consider th a t the typical day m ore than three years out carries half the risk of the typical day less th an three years out. In th a t case, you would use a value of FA C T = .5 (or 50%). A value of FA C T = B IN is for comparison only. T his gives the sam ple size required if you only looked the “B inary” event of surviving three years or not surviving three years. T he com parison would ignore tim e of death and all d a ta collected after the patient had m ade it to the three year point. T his comparison is distinct from the logrank test and carries a different sam ple size. T his alternate and less powerful test is discussed in C hapter 2 under the nam e “Kaplan-M eier.” If you browse through the tables, you will note th a t for m any situations, the F A C T = .00 and FA C T = B IN sam ple size requirem ents are very close. W hen FA C T = .00, no deaths are expected after the endpoint. FA C T = 1.0 (Exponential) (This value is used in the tables)

SUMMARY (3)

E X PE C T E D ACCRUAL TH RU MINIMUM FO LL O W -U P=375

(4)

PCC)NT=.60

CRC Handbook o f Sample Size Guidelines fo r Clinical Trials

4 (5)

DEL=.15

(6)

A LPH A =.05 (One-sided)

(7)

PO W E R = .80

(8)

FA C T = 1.0

T o look up the sam ple size, we sta rt from ALPHA and PO W E R . These are coded as follows: To look up the sam ple size, on the basis of (6) and (7), we shall employ the TA BLE 7. T his is arranged in order of increasing expected accrual (3). Once the chart for A LPH A =.05, PO W E R =.8(), and E X PE C T ED ACCRU AL=375 is located, locate the P C O N T =.60 row and the D E L =.15 colum n. T he following six sam ple sizes:204,211,220,231,245, and 235 correspond respectively to FA C T=1.0,.75,.50,.25,.00, and BIN. Since our FA C T = 1.0, we use

Sam ple Size= 204

T he statistical section inflated the sam ple size to adjust for 10% losses to follow-up, for a total of 227 patients. By dividing by the accrual rate of 125 patients per year, this m eans th a t the accrual is expected to take 1.8 years, (22 m onths) and the study will require 4.8 years to complete.

*** Footnote on one-sided vs two-sided tests. In situations where you wish to com pare two treatm ents, neither of which can be viewed as a control, you should run a two-sided test. Basically, you proceed exactly as above but replace the value of ALPHA by A L PH A /2. If the above study consisted of two experim ental therapies, we would use A LPH A=.025. (TABLE 5) For the 45% vs 60% com parison, we would use PC O N T =.45 and D EL=.15, with FA C T=1.0. T his would require 282 patients. For the 60% vs 75% com parison, we would use P C O N T =.60 and D EL=.15 with FA C T = 1.0. T his would require 250 patients. T o be safe, we take the larger of these two num bers, 282. Allowing for 10% loss to follow-up, the final sam ple size would be 313 (2.5 years of accrual).

5 *** F u rth er Reading. T he sam ple size results of this handbook are sim ilar to those of Schoenfeld (1981), R ubinstein et al. (1981), and especially Lachin (1981, where his equations (25) and (26) are employed). A nother interesting m ethod is due to Halpern and Brown (1987), who offer a com puter program which can sim ulate the properties of the logrank statistic under any survival distributions provided by the user. Finally, a m ethod of Sposto and Sather(1985) is useful in some applications. T h a t m ethod yields sim ilar results to those of this handbook.

REFERENCES 1. Freiman, J. A ., Chalmers, T. C ., Smith H ., and Keubler, R., The importance of beta, the type II error and sample size in the design and interpretation of the randomized controlled trial, N. Engl. J. Med., 299, 690, 1987. 2. Halpern, J. and Brown, B. W ., Designing clinical trials with arbitrary specification of survival functions for the log rank or generalized Wilcoxon test, Control. Clin. Trials, 8, 177, 1987. 3. Lachin, J ., Introduction to sample size determination and power analysis for clincial trials. Control. Clin. Trials, 2, 93, 1981. 4. Rubinstein, L. V., Gail, M. H ., and Santner, T. J., Planning the duration of a comparitive clinical trial with loss to follow-up and a period of continued observation, J. Chron. Dis., 34, 469, 1981. 5. Schoenfeld, D ., The asymptotic properties of nonparametric tests for comparing survival distributions, Biometrika, 68, 316, 1981. 6. Sposto, R. and Sather, H. N ., Determining the duration of comparitive clinical trials while allowing for cure, J. Chron. Dis., 38, 683, 1985.

CRC Handbook o f Sample Size Guidelines fo r Clinical Trials FIGURE 1. Codes For Tables

ALPH A =.005 and P0W E R = .8() TABLE 1 A LPH A =.005 and PC)W ER=.90 TABLE 2 A LPH A =.01

and P 0W E R = .8() TABLE 3

A LPH A =.01

and P O W E R = .90 TABLE 4

A LPH A =.025 and PO W E R = .80 TABLE 5 A LPH A =.025 and PO W E R = .90 TABLE 6 A LPH A =.05

and PO W E R = .80 TABLE 7

A LPH A =.05

and P0W E R =.9Q TABLE 8

7 FIGURE 2. Worksheet For Sample Size Determination One-Sided Studies 50% assigned to each treatm ent.

*

(I)

Expected Annual Accrual

(2)

E ndpoint (? Year Survival) M inim um Planned Follow-up

(3)

Expected Accrual th ru M inim um Follow-up

(4)

PC O N T (C ontrol Planning Survival Probabilty to E ndpoint)

(5)

DEL (Planned im provem ent in Survival to E ndpoint under

_

_(Patients) ___(Years)

_ _

_(Decimal) _(Decimal)

E xperim ental T reatm ent) (6)

A L PH A = Probability of concluding experim ental therapy superior

_

_(Decimal)

_

_(Decimal)

_

^(Decim al)

when it is equivalent to control (7)

P ow er= P robability of correctly concluding experim ental therapy superior when DEL is as in (5)

(8)

F A C T = R a tio of instantaneous death rate after the endpoint to th a t before the endpoint

From (6) and (7), use FIG U R E 1 to identify table code. Next, use (3) to identify chart. CO N T and DEL identify row and column. T his identifies six sam ple sizes, one for each of five values of F A C T and one for binary comparison. (9)

Identify Initial Sam ple Size

_______ (P atients)

(10)

E stim ated Fraction to be Lost to Follow-up

_______ (Decim al)

(II)

S ubtract num ber in (10) from 1.0

_______ (Decim al)

(12)

Final Sam ple Size (9) divided by (11)

_______ (P atients)

(13)

Accrual Period (12) divided by (1)

_______ (Years)

(14)

T o tal Study D uration (2) + (13)

_______ (Years)

CRC Handbook o f Sample Size Guidelines fo r Clinical Trials

8

FIGURE 3. Modifications of Figure 2

1:

FO R T W O -SID ED TESTS

(A)

Replace ALPHA by A L PH A /2 in (6).

(B)

Replace

PC O N T by the lower of the two planning survival probabilities in (4)

(C)

Replace

DEL by the difference between the two planning survival probabilities in

(5). (D)

Proceed

as in Figure 2. (You m ay have to do this twice if the planning survival

probability is known for one of the experim ental therapies while the other is planned a t from DEL worse to DEL better. If this is the case, do both calculations and use the larger of the two sam ple sizes.)

2:

F O R UNEQUAL P A T IE N T ALLOCATION (ie not a 50-50 random ization) (Valid for allocations from 33% to 67%)

(A)

Find the sam ple size as if the allocation was 50-50 using FIG U R E 2 (and FIG U RE 3-1 if needed)

(B)

A djust as Follows Allocation 2:1(67%) or 1:2(33%),M ultiply result in (A) by 9/8 Allocation 3:2(60%) or 2:3(40%),M ultiply result in (A) by 25/24 Allocation X:Y,M ultiply result in (A) by (X + Y )(X -fY )/(4X Y ) Note th a t this sam ple size is always higher th an a 50-50 allocation.

9 Chapter 2 DESIGN AND ANALYSIS OF RANDOMIZED CLINICAL TRIALS

This Chapter is a concise, non-technical introduction to the design and analysis of randomized clinical trials. For more detail, at a non-technical level, the reader is referred to the following excellent references: Pocock (1983), Buyse et al. (1984), and Meinert (1986). While the Tables of this volume apply to very specific types of trials, they are in fact applicable to the majority of major definitive trials run today. We shall discuss clinical trials in a more general framework, but restrict our analytic considerations to randomized trials. We shall discuss the trials under each of their four basic steps:

1. Formulate a therapeutic research question 2. Design a trial to answer this question 3. Conduct the trial as planned 4. Analyze the data and report the results

2.1 Formulation of the Therapeutic Question This part of the trial is more medical than statistical. The question might be, for example, “Can Beta-Blocker X improve survival of newly diagnosed myocardial infarction patients over that of the standard Beta-Blocker Y?” This is the type of question which can form the starting point of a clinical trial. Note that there are two competing therapies proposed for this trial. While this book is devoted to two treatment trials, Section 3.12 provides extended use for more complicated questions involving three or more competing therapies. Note that the research question is very loosely worded at this point. There will be considerable work to convert this question into a truly testable hypothesis.

2.1.1. One-Sided vs. Two-Sided Question An important component of your research question is whether your question is "one-sided" or "two-sided". The following discussion will help make this determination.

10

CRC Handbook o f Sample Size Guidelines fo r Clinical Trials When you conduct a clinical trial, you will usually put on trial one of the following statements 1. One-Sided Statement: The new (test) therapy is superior to the standard; or 2. One of the two therapies is superior to the other, but you have no vested interest as to which.

Sample One-Sided Questions Drug companies, developing a new drug, are generally interested in one-sided questions. Their product may only be marketable if they can prove beyond a reasonable doubt that their product is superior to the standard. The competing therapies have asymmetrical interest. Again, if any scientific researcher is considering the efficacy of adding a toxic agent to a standard regimen, and comparing this to the standard regimen alone, a one-sided question results. After the study is over, one would use the new therapy only if it proved to be significantly better than the standard. Whether the efficacies were not signifi­ cantly different or the toxic agent had significantly reduced the efficacy, one would make the management decison not to use this toxic agent for future patients.

Sample Two-Sided Questions There may be two standard therapies that are in widespread use, but no one really knows which is superior. The scientific issue here is simply, which is the better therapy? Interest is symmetric. In some diseases, ther may be no known effective therapy. One might wish to test two new experimental therapies. Here too, a two-sided question is clear. One-sided questions need fewer subjects than two-sided questions of equal precision. The "Zone of proof beyond a reasonable doubt" is concentrated in the zone where the test outperforms the control treatment. The two-side< question must create two such zones, one corresponding to superiority of each treatment. Consequently, the region of superiority of each given treatment must be smaller in the two-sided question corresponding to the one-side question o the same precision. The one-sided vs. two-sided question must be spelled out in advance as a vital part of the research question. Clearcut rationale for asymmetric interest must be given. In point of fact, most trials conducted in the medical school environment should be two-sided, unless there is a compelling reason for asymmetry.

11 2.2 Design of the Clinical Trial In order to conduct a valid clinical trial, it is vital to develop a complete plan for its conduct. A manual of operations, called a “Protocol”, should be written with the following elements:

A. Objectives of the Study (What you hope to accomplish.) B. Background Information (Literature review of prior therapy and outcome. Include your own experience as well.) C. Rationale (Why you feel you have good prospects to achieve your objectives.) D. Patient Eligibility (A Precise definition as to who can participate in the trial.) E. Treatment Plans (Full description of how patients will be treated under each competing therapy. This must include contingency plans for complications.) F. Off-Study Requirements (Full description of events that place the patient off study. For example, patient may go off study at time of recurrence of disease, allergic reaction to the drug, or death.) G. Data Submission Requirements (This describes the schedule of follow-up, the medical tests required and their timing, and the description and timing of the data form submission.) H. Statistical Consideration. (This describes the actual design, including the endpoint of the study, whether stratifica­ tion and randomization will be used, plans for interim and final analysis, and sample size projections. If the study is a “masked design”, this is also discussed in this Section.) I. Study Monitoring (A committee called the Data Safety and Monitoring Committee should be listed along with their meeting schedules and responsibilities.) J. Appendix (This should include blank copies of all data forms and the informed consent form. Instructions on forms completion should also be included.) K. Database Documentation (While this may not be a formal part of the protocol, it is a critical element of the design. A protocol cannot be compromised by turnover in computer staff.)

This author was once sent a computer tape of a trial completed some six years earlier, in order to re-analyze the data. Unfortunately, the senders lacked documentation of the data. Despite our best efforts, we could not crack the code with enough confidence to complete any analysis.

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2.2.1 Statistical Considerations In planning a trial, there are a number of issues that need to be considered in (H) above. First, the eligibility conditions define the ‘T arget Population”. This is the hypothetical pool of past, present, and future patients with well defined characteristics. Note that the actual patients who participate in the study are considered to be a representative sample from this target population. Our ultimate conclusions will be directed to the target population not to the sample. Of course, we use the sample data to make an inference about this target population. Such inferences are subject to sampling error, since only a portion of the target population has been sampled. This is much like the use of voter surveys to project election results. Answers to the following question are needed to formulate the statistical consideration.

W hat is the single p rim ary variable upon which the m ajor comparison will be based? It is essential to pin down a primary variable up front. If this is not specified, the data may be analyzed in a wide variety of ways, leading to investigator selection bias. Each analysis carries a sampling error, and hence the more analyses one performs, the greater the cumulative error effect. To control this, a primary single analysis should be specified. Others can be done, but as strictly secondary analysis. Example primary variables might be three year remission, five year survival, two year peak intra-ocular pressure below 23 mm hg, etc. As mentioned in the Introduction, there are two types of primary variables considered in this Handbook. The first type is “Censored Survival Data”. Time is measured from entry onto the study until failure, termination of the study, or loss to follow-up. The last occurs if the patient exercises his or her option to quit the study. The only survival information available are (1) the time from entry to last follow-up and (2) the patient status at last follow-up. The data are censored (or more precisely, right censored), since for survivors, we do not know their true survival times, although we do know that they survived at least a given number of days (eg 655+ days). The second type of data in which these sample size tables can be used is binary data (yes/no). For example, a study on operative deaths (whether or not the patient died during surgery), is not concerned with time of death, but only whether or not the patient survived the surgical procedure. Unlike the censored survival situation, follow-up is short and equivalent for all patients. In a censored survival study, involving a three year patient accrual phase plus a two year minimum follow-up (a five year total study), patients have a potential follow-up of from two to five years. The risk of a study death among earlier

13 entries is higher than that among later entries, since the early entries are at risk longer. This needs to be taken into account in the analysis. The operative death problem is quite different. The only data used in that analysis is whether or not the patient survived surgery.

Will the study be randomized? This is a controversial topic. Let us suppose that you plan to compare two therapies. You may have consider­ able experience with one of the therapies (the “control” or “standard”) and little experience on the other (the “experi­ mental” or “test”). You may ask, “Why not simply recruit patients to the experimental regimen and compare these to the existing control patients?” This is called an “Historical Control Study”. There are both advantages and disadvan­ tages of such a strategy. Historical control studies often require fewer patients than randomized studies, and hence can often be completed in less time and at less cost than concurrently controlled studies. Unfortunately, however, historical control studies cannot be viewed as definitive scientific evidence about the relative merits of the competing therapies. You cannot adequately attribute differences (or lack of differences) in outcome with differences in efficacy. Subtle changes in any of the following can hopelessly confound the results of an historical control trial: Changes in referral pattern, changes in personnel, changes in diagnostic techniques, changes in concomitant care, changes in public awareness programs, etc. In addition, the trial may have been motivated by disappointing results under the standard therapy. Disappointment is more likely when the sampling error under the historical control is negative than it would be if the sampling error is positive. In other words, suppose the true success rate is 60% under the standard. A 50% observed success rate in your sample of 50 historical patients could provide greater motivation to conduct a study than a 70% observed success rate. One advantage of historical control studies, not often mentioned in publications, is the issue of gaining informed consent. It is very difficult to approach a patient in order to gain consent for randomization. Uncertainty in a physician can undermine the confidence of the patient. However, in truth, the same uncertainty is generally present in the historical control study, although it is often downplayed. Finally, historical control studies are fully justified if the historical control success rate is virtually zero. In such cases, you are unwilling to subject patients to a hopeless therapy. Even here, however, there is no unanimous agreement among scientists. For example, in 1986, randomized studies were conducted in AIDS patients, using a

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control known to offer no hope for survival. Surprisingly, there was a strong moral argument for the randomization. Since only a limited number of patients were approved for initial testing of new agents, a randomized design could treat as many patients as a non-randomized design. Further, by careful interim comparison of treatment vs. control patients, the randomized study offers the best way to study non-fatal events. For additional information on randomized vs. historical controls, see Zelen (1983), Shuster et al. (1985), Pocock (1983), Gehan (1978 and 1982), Peto et al. (1976), Diehl and Perry(1986), and Dupont (1985). These articles present all sides of the issues. In summary, a randomized study is recommended very strongly, except perhaps when the historical success rate is near zero. However, if you consider a randomized study and determine that the required sample size is too large, an historical control study might be considered. Prior to doing so, however, the possibility of running a randomized study with additional institutions should be seriously considered. Note: Randomization is a more complex topic than one might at first believe. It is important that the investiga­ tor cannot predict what therapy the next patient will be assigned. The purpose of randomization is threefold. First, it prevents unconscious bias in treatment assignment as compared to non- randomized assignment. Second, the frame­ work of statistical analysis relies on randomization. Finally, a properly set up randomization procedure offers an audit trail of treatment assignments. This protects the investigator if the results of a study are questioned by a review group or by journal editors.

Random ization M ethods Some randomization techniques are discussed in Pocock (1983, Chapter 5). Figure 4 presents a table of randomized treatment assignments, based on “simple randomization”. Each successive entry is an independent flip of an unbiased coin (50% probability of heads). Heads represents treatment 1, while tails represents treatment 2. Figure 5 represents an alternate design, with “random length permuted blocks”. The following is the mechanism for Figure 5. First, a balanced coin is flipped. If the coin is heads, then we generate a random “word” consisting of three l*s and three 2 ’s. Each of the possible 20 words consisting of three l ’s and three 2 ’s has an equal chance of occurring. If the coin lands tails, then we generate a random word consisting of two l ’s and two 2*s. Each of the following six equally likely words is drawn: 1122,1212,1221,2112,2121,2211 This procedure is repeated, until the figure is completed. These figures provide the serial assignment of treatments for successive patients.

15 Simple randomization (Figure 4) is very simple to employ, but may lead to rather substantial differences in the number of patients assigned to each therapy. To illustrate, after 813 randomizations in Figure 4, there are 443 patients assigned to Treatment #1 and 370 assigned to treatment #2, for a net difference of 73 patients. This is the peak differ­ ence over the 1200 patient assignments. The random length permuted blocks procedure keeps the numbers well balanced throughout the study, while it is quite unpredictable to the investigator, especially if the exact mechanism of randomization is masked. Randomization is discussed further under stratification and institutional balancing below.

Will the study be stratified? Are there key “risk factors” that need to be balanced “prospectively” or “retrospectively”? There is always concern that a randomized design will place a disproportionate number of poor risk patients on one of the treatments. If one has historical information about such risk factors, they might be planned for in two ways. First, we may wish to stratify the trial prospectively. That is, we shall define patient subgroups according to the risk factors, and essentially run independent trials within each subgroup. Using random length permuted blocks within each subgroup, we can maintain good balance of the treatments across each stratum. This is a good design feature, but it comes at a price. Over stratification can reduce the precision. Peto et al. (1976) estimate that the effective sample size of the study is reduced by one for each stratum you create, as compared to the luckily perfectly balanced randomized trial. For example, a trial stratified on age group (4 levels), sex (2 levels), smoking history (3 levels), and serum cholesterol (3 levels) would create 4 X 2 X 3 X 3 = 72 strata. Clearly, a poorly designed study could be so heavily stratified that there would be very few patients in any one stratum. The purpose of stratification is to compare like patients with like patients. However, stratification limits the possibility of comparison, as the following example illustrates. Suppose that there are 100 patients, 50 in stratum 1 and 50 in stratum 2. Suppose that 50 are assigned to each treatment. The un-stratified design allows 50 treatment #1 patients each to be compared to 50 treatment #2 patients (2500 comparisons). The stratified design eliminates half of these, namely patients in different strata and different treatments. Clearly, there is a trade-off. We recommend only very limited stratification, based on important proven risk factors, be made. The second method to deal with stratification is to adjust for the risk factors retrospectively in the analysis. This method is discussed in CHAPTER 3.13. The reader is further referred to Peto et al. (1977). No within-stratum balancing is done, but imbalances are corrected for in the analysis.

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If the study is a multi-center study, will institutional balancing be used? When conducting a multi-institutional study, especially if it is conducted by a large number of institutions, each with a relatively small number of patients, one should consider balancing the randomization within institutions. While it seems that this might create too many strata, especially if the study is also stratified according to risk factors, a method called “Marginal Balancing” can be used to avert this problem. Basically, marginal balancing, as discussed in Shuster et al. (1985), works as follows. Assign the patient according to prior assignments for the institution and stratum as follows:

Priority #1: Check how many patients have been assigned to each treatment at this institution. If the difference between the number o f assignments exceeds the maximum allowable margin, (say 2), assign the treatment that has beer assigned less often at that institution. For example, if at X-Hospital, 7 patients are on Treatment #1 and 4 patients are on Treatment #2, and the maximum allowable margin for randomization is 2, the next patient at this institution must receive Treatment #2. Priority #2: Applies only if Priority #1 has not forced a treatment assignment. For the patient’s stratum, check the number of patients assigned to each treatment. If the difference exceeds the maximum allowable margin for randomization, assign the less used treatment. (Note that the stratum maximum margin need not match that of the institution.) Priority #3: Applies only if Priorities #1 and #2 have not forced a treatment assignment. Assign treatment according to the next unused entry on the random length permuted block assignment sheet. (For example, Figure 5.)

Bookkeeping: After each patient assignment, it is necessary to update the number of patients assigned to each therapy by institution and stratum. In addition, the assignment should be recorded on the random length permuted blocl assignment sheet by crossing off the first available entry matching the assigned treatment This will be the next entry if Priority #3 applies. Marginal balancing keeps institutions and strata balanced. It also keeps the overall study balanced because of the permuted blocks. One of the advantages of marginal balancing is that the study can be analyzed as if it was a single institutional study. In other words, one can ignore the stratification effect of institution in the analysis. This is espe­ cially important in studies conducted by a large number of institutions with a large number of strata. In practice, the

17 “error” one makes in treating the study as a single institutional study is in the conservative direction. That is, there will be a slight tendency to underestimate the significance of the differences between the treatments (overestimate the “Pvalues”). However, this error is rarely of practical significance. Marginal balancing is also important for non-statistical reasons in studies where some institutions contribute small numbers of patients. Each institution should gain experience on both therapies. Without institutional balancing, there is more than a 12% chance that an institution contributing four patients will place all four on the same treatment.

If the study is multi-institutional, will centralized randomization be employed? Centralized randomization is strongly recommended for all multi-center trials. Clearly, if marginal balancing is used, a central office must have up-to-the-minute information on all prior treatment assignments. There are more important considerations, however. The integrity of the study is best insured through centralized randomization. No patient can get onto the study without contact with the central office. Eligibility can be verified by standardized criteria prior to acceptance of the patient. Without centralized randomization, the study is open to the possibility that early failures may never be placed on the study. Individual investigators may overlook the important task of forwarding the information on such patients to the central office. With centralized registration and randomization, patients must be put on study before starting treatment. Registration and randomization need not be done at the same time. Some studies will have both treatments identical for the first 6-12 weeks, followed by a divergence. All participants should be registered at the time of treatment start, but a callback for randomization should occur at the time when the treatments diverge. This callback will in fact improve the precision of the comparison, since the major comparison will be based on outcomes after the divergence point. Failures before the divergence point are not part of the study question, although they are vital to the estimation of the efficacy of each therapy. The treatment differences must occur after the diver­ gence point, but the overall success rate of each therapy is measured from the start of treatment. You have the luxury of using all patients (regardless of assigned therapy) to assess the efficacy of the therapy from its starting point to the divergence point.

Will the study be masked (blinded)? It is a good experimental technique to mask the identity of the treatment from both the patient and the investi­ gator. (The more common term is blinded, but as one with experience in ophthalmic trials, your author considers that

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designation is a bit short sighted.) Masking is an especially important consideration if (1) patient psychological factors may be involved, (2) the response measurements involve subjective judgement on the part of the physician or the patient, or (3) the treatment can be put in a masked form, ethically and logistically. Contra-indications for masking include possible discomfort to the control patient; the need for the physician to perform expensive and/or painful medical tests to monitor one of the treatments and its side-effects; and the ability to mask the therapy. It would be unethical to perform sham surgery on a patient in order to mask the true procedure. Some masking is better than no masking. For example, if it is unethical to mask the treating physician, it might be possible to have the critical observations made by a colleague who is indeed masked as to the treatment identity. A vital consideration in masked studies is that the master code, indicating who got each treatment, be securely main­ tained. More than one masked study has failed because the master code was lost! If such a loss occurs, nothing can be done to recover.

What methods of analysis will be used? This will be discussed further in Section 2.4. However, the statistical section must spell out the exact statistical details as to what methodology will be used. This needs to be specified in the protocol, as a protection to the investigators. Journal reviewers can sometimes criticize a study on the basis that it was not analyzed according to the design of the study. The best protection against this contingency is to submit a copy of the protocol with the manuscript. Often, the protocol itself undergoes peer review, and hence, there is strong support for your analysis.

What patients will be included in the analysis? In most studies, there will be some severe violations of the protocol, often for reasons beyond the control of the investigators. The question one might pose is, “Will the major comparison be based on all compliant patients, or on all eligible patients?” There is now fairly unanimous agreement that the most convincing scientific analysis is based on all eligible patients. Once a patient is deemed to meet the entry requirements, that patient is included in the major analysis, whether or not the patient complies with the assigned protocol. This is often called ‘T h e intent to treat principal”. Many journals have published policy that the major analysis must consist of all patients who meet the eligibility conditions, whether or not they comply with the protocol. Two important editorials supporting this point are

19 Zelen (1983) and Simon and Wittes (1985). As soon as subjective judgement is allowed to enter the picture, the potential for bias arises. Other analysis can be done as secondary evidence. However, severe bias can be induced by eliminating non-compliant patients. Compliance can have a strange relationship to treatment, apart from merely a disproportionate number of non- compliers within the two treatment groups. Non-compliers on one treatment may be at increased risk, while non-compliers on the other treatment may be at decreased risk. The “intent to treat principal” also implies that patients are analyzed on the treatment to which they were assigned, even if they actually received the other therapy! This may seem to be invalid at first glance, but it is the only way to prevent bias. The argument is that the Intent to Treat Principal closely resembles the real world application of the treatment. Poor compliance to a protocol will adversely affect its success. It is vital to keep track of compliance, but the major analysis should not utilize compliance. For additional detail on this topic, see Shuster et al (1985), Simon and Wittes (1985), and Haynes and Dante (1987).

What are the plans for interim analysis? When conducting a long-term trial, there is considerable motivation to look at the results to date to see if the question can be answered early. Such a plan for example led to the early closure of the Multi-Institutional Osteosar­ coma Trial of Link et al. (1986). That protocol specified times for interim analysis as well as conditions which would lead to early termination of the study. It needs to be pointed out that the decision to close a study early should be based on very compelling evidence. Generally speaking, the more interim analyses that are conducted, the greater the risk of false-positive results. If interim analyses are to be conducted, they should be conducted at a very small P-value as compared to a one-time final analysis. This can be put into a formal statistical methodology called “Group Sequential Methods” or in a more informal way, where the critical P-value is a small fraction of the final planning P-value. (eg .005 for interim analysis vs. .05 for the final planned analysis.) For more information on this topic see Armitage (1975), O ’Brien and Fleming (1979), and Tsiatis and Rosner (1985). In any case, the protocol should spell out exactly when interim analyses will be conducted, and how decisions based on interim analyses will be made. If an interim analysis does in fact suggest that the study be terminated, the decision should not be made until the data have been reviewed carefully by the “Data Safety and Monitoring Commit­ tee”. See Section 2.2.(I) discussed earlier.

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2.3 Conduct of the Trial Once the trial is opened to patient accrual, there are many elements which are required to ensure that the trial meets its objectives. Each institution must obtain annual approval from its Institutional Review Board (IRB) in order to register patients on the study. In order to place any patient on the trial, informed written consent must be obtained. The risks and benefits of the competing therapies must be explained as well as the objectives of the study. If the trial is randomized, the patient should know this before the treatment is assigned. There are some pre-consent randomization designs. See Zelen (1979 and 1982), Smith (1983), and Fletcher (1985) for more details. Such designs are highly controversial as these references point out. The vast majority of studies assume randomization after consent, unless the patient is incapable of giving informed consent, Abramson et al. (1985). The patient becomes part of the trial as soon as consent is obtained. Further, once treatment is assigned, the patient is a part of that treatment group, regardless of whether or not the patient complies with the therapy. The investigator is ethically bound to follow the therapy as prescribed in the protocol, unless there is overwhelming evidence that violating the protocol is in the patient’s best health interest. The patient assumes no legal commitment to follow the protocol, but does so in the spirit of physician-patient relationship.

D ata Submission It is the responsibility of each investigator to fully comply with all data submission requirements of the trial. Even the world’s most outstanding statistician is limited by the quality and quantity of data submitted by the investiga­ tors. Even small amounts of missing data can bias a study.

Interim Analysis A well -written protocol has provisions for interim analysis. However, it is important that while the trial is accruing patients, this information should be restricted to the Data Safety and Monitoring Committee. Investigators should not see interim treatment comparisons while patient accrual is ongoing. The committee is charged with the responsibility of determining if randomization remains ethical. With open reporting, selection bias could result from individualized analysis on the part of the investigators. In some situations, it may be important to mask the treatment comparisons until all patients have completed

21 therapy. For example, suppose that Treatment A consists of two years of Beta-Blocker X, while Treatment B consists of two years of Beta-Blocker Y, from the time of myocardial infarction. If an unblinded interim analysis shows a trend in favor of B, some investigators may want to switch their A patients to B. This could compromise the entire trial. The decision to switch or not switch should be in the hands of the Data Safety and Monitoring Committee, not the individ­ ual investigator.

Protocol Am endm ents Once a protocol is actively accruing patients, amendments should be resisted. However, even the most carefully written protocols are not immune to unexpected results. For example, one might encounter toxicities, that had not occurred in pilot studies. Counter measures would have to be written into the protocol. If the counter measure has efficacy implications on one or both treatments, then the amendment may have the effect of forcing the investigators to start the accrual process over. The patients already accrued would not be used in the comparison of the treatments. Each amendment has to be sent back to the IRBs for approval. In addition, the Statistical Consideration and Consent Form will need modifications to incorporate these amendments. Amendments must be handled with as much precision as the original protocol.

2.4 Analysis and Reporting of the Trial Upon completion of the accrual phase and minimum projected follow-up on all patients, the final analysis phase begins. The first step is to acquire all possible delinquent and missing information. Next, the analysis is com­ pleted as prescribed in the Statistical Consideration. Finally, the results of the trial are submitted for publication in a refereed medical journal.

2.4.1. Crucial Elements The analysis described in the statistical section must be employed in the analysis. The sample size calculation only applies to the statistical methods detailed in the protocol. Definition of P-value: The methodology of the statistical consideration provides an ordering of the possible outcomes in terms of how well they support a difference between the treatments (one-sided or two sided as specified in

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the design.) The P-value is interpreted as follows: Suppose that you repeated this study in another universe where the treatments were in fact equivalent. What is the maximum probability of observing evidence of a difference in this repetition that is as least as convincing as that observed in the actual trial? (The answer is the P-Value.) For example, suppose that the observed success rate of the test treatment was 46/84 while that in the control treatment was 34/81. The statement, which we shall discuss in more detail below is, “P = .05 one-sided.” That is, if we repeated our protocol in a population where the success rates are equal, then there is at most a 5% chance of observing a difference of 12.8% or more in favor of the test treatment. (46/84-34/81 = .128=12.8%).

Methods of Analysis of Clinical Trial Data We shall discuss three methods of analysis of clinical trial data. These include Sections 2.4.2, Binomial Comparison; 2.4.3, Kaplan-Meier Comparison, and 2.4.4, Logrank Comparison.

2.4.2 Binomial Comparison The Binomial Comparison is applied to trials where the outcome is binary: Success or Failure. The following properties must be satisfied, at least conceptually, in order to apply this methodology: PI: Trials are “INDEPENDENT”. That is, the outcome of a given patient is not influenced by the outcome of any other patient. This methodology should not be used for matched studies, since the outcome of one patient will have more predictive value on the matched patient than it would on any other patient. P2: The “Success Probability” within a given treatment is the same from patient to patient. That is, without knowing the patient characteristics in advance, the probabilities of success in the first, second, th ird ,... patients assigned to the given treatment are equal. For censored survival studies where patients enter serially and where the study is analyzed at a fixed point in time, this assumption is violated. Early entries are at risk for a longer period than later entries, and hence, have lower success rates than later entries. Of course, the success rate of each treatment need not be the same.

2.4.2.1

Large Sample Methodology Let Nl=SampIe Size for the Standard or Control Therapy

23 Sl=Num ber of Successes in the Control Sample Fl=Num ber of Failures in the Control Sample Pl= Sl/N l= Fraction of Successes in the Control Sample. Let N2=Sample Size for the Test Therapy S2=Number of Successes in the Test Sample F2=Number of Failures in the Test Sample P2=S2/N2=Fraclion of Successes in the Test Sample. The difference in Success rates is P2-P1. We also need a quantity called the “Estimated Variance of P2-P1”, denoted by:

V={P1(1-P1)/N1}+{P2(1-P2)/N2}

The test statistic for which a decision about the therapies is based is:

Z=(P2-P1)/SE

where

SE=SQRT(V)

(SQRT=Square Root)

The approximate “P-value” associated with Z is obtained from FIGURE 6 for one-sided comparisons and from FIGURE 7 for two- sided comparisons. The intuitive interpretation of the P-value is given in Section 2.4.1.

2.4.2.2 Confidence Intervals Another more descriptive way to report the above information is via a CONFIDENCE INTERVAL. A “One­ Sided Confidence Interval” is reported for DEL, the true target population difference in success rates, as: DEL >P2-P1-W SE

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where W is selected from Figure 8 according to the desired confidence. The intuitive interpretation of the Confidence Interval is given below Figure 8. A “Two-Sided Confidence Interval” is reported as:

P2-P1+W SE >DEL >(P2-P1)-W SE

where W is selected from Figure 9 according to the desired confidence. The intuitive interpretation of the Confidence Interval is given below Figure 9.

2.42.3 Numerical Example (Test) Suppose that the Control therapy had Nl=81 patients of whom SI =34 were successes and FI =47 were failures. We have P I =34/81=0.420. Suppose further that the Test therapy had N2=84 patients of whom S2=46 were successes and F2=38 were failures. Hence, P2=46/84=0.548. To calculate V, note that l-Pl=l-.420=.580 and l-P2=l-.548=.452.

V= {(.420)(.580)/81} + {(.548)(.452)/84}={.2463/81}+{.2477/84} =0.00304+0.00295=.00599

SE=SQRT(V)=.0774 and P2-P1=.548- .420=.128

Hence, Z=.128/.0774= 1.653

From Figure 6, this translates to a P-Value of slightly less than 0.05, for a one-sided test. Had this been a two­ sided study, we see from Figure 7 that the two-sided P-value is slightly less than 0.10. Finally, if the Experimental and Test labels had been reversed so that the Experimental group had 34 successes in 81 patients while the Control group had 46 successes in 84 patients, the One-Sided P-Value would have been approximately 0.95.

25 2 .4 2 .4 Numerical Example (One-Sided Confidence Interval) If one was to construct a 95% One-Sided Confidence Interval for DEL, the target difference in success rates, one would employ FIGURE 8:

DEL >. 128-1.645 {.0774}=. 128-. 127=.01

That is, DEL> .01 with 95% confidence. Notice that the value of Zero, the point of equal efficacy, lies just outside the confidence interval. (Had the Pvalue been greater than 0.05, Zero would have appeared within the confidence interval. The two-sided confidence interval will illustrate this.)

2.42.5 Numerical Example (Two-Sided Confidence Interval) Had this been a two-sided question, a 95% two-sided confidence interval would be obtained from Figure 9 as follows:

.128+ 1.96{.0774} >DEL >.128-1.96{.0774}

That is .28 >DEL > -.02 with 95% confidence. Had this been a two-sided experiment, the outcome would not have achieved statistical significance at the conventional .05 level. However, we are highly confident that the Test treatment ranges from trivially inferior to vastl> superior. The value in the confidence region most favorable to the control treatment represents only a 2% advantage to the control. The confidence interval allows a management decision to prefer the test treatment for future patients, despite the fact that conventional significance of the two-sided trial was not achieved. The P-Value alone does not allow this type of management logic.

2.4 2 .6 Small Sample Methodology In order to apply the Large Sample Methodology, the following rules of thumb are often used:

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Each of the following four quantities arc greater than 5.0:

N1(S1 + S2)/(N1 + N2) = “Expected Successes for Control” N1(F1 + F2)/(N1 + N2) = “Expccted Failures for Control” N2(S1 + S2)/(N1 + N2) = “Expected Successes for Test ” N2(F1 + F2)/(N1 + N2) = “Expected Failures for Test ”

The term “Expected” refers to the idealized distribution of the actual patient results to the two groups, where the success rate would be the same in both treatment groups.There is nothing magic about the number 5.0. However, the approximations seem to be “adequate” at this number of patients. Generally speaking, if a randomized clinical trial is designed to be sensitive to clinically relevant differences, the approximations made for large samples will be valid. However, in very small trials with low power, exact methods are needed. The two most widely used methods are Fisher’s Exact Test and the Exact Unconditional Z Test. We shall discuss these briefly. For more detail, the reader should consult Armitage (1971), Suissa and Shuster (1985), and Shuster (1988).

Fisher’s Exact Test In the numerical example above, imagine that we have a deck of cards, distributed as follows: 80 Cards are labeled SUCCESS and 85 Cards are labeled FAILURE, for a total of 165 cards. Now suppose that we randomly distribute the cards to two players called Control and Test (81 to Control and 84 to Test). What is the probability of dis­ tributing 46 or more successes to the Test player? In other words, if we repeated the experiment on a different target population, where in fact the control and test therapies were equivalent, and if we happened to again get a total of 80 Successes and 85 Failures, what is the likelihood of obtaining evidence at least as convincing as that observed in favor of the test therapy? The answer is P=.068. (The approximation had P=.05 one-sided) Note that this is not a true P-value, since the additional proviso is made that in the replication of the experi­ ment, you must match the total number of successes with that observed (80). We call such a P-Value “an Exact Conditional P-Value” to remind us that it was calculated under an added artificial condition.

27 A two-sided analogue of Fisher’s Exact Test is also possible. The observed difference in success rates was P2-P1=.128. If we had seen 44 successes in 81 controls and 36 successes in 84 test (keeping the total successes at 80), then the difference in success rates would have been .115; while the difference between 45/81 vs 35/84 is .139. On a two­ sided basis, if the test group is dealt either (A) 46 or more successes or (B) 35 or fewer successes, the evidence in favor of a difference would be at least as strong as that observed (.128).The probability that either (A) or (B) occurs in redeals is:

P=.120 (Conditional) vs P=.10 (2-sided approx.)

The P-value requires the same condition in the replication of matching total successes to that observed. Thus, this is not a true P-value, but rather a conditional one.

Exact U nconditional P-Value The Exact Unconditional Z-test works as follows. The observed Z value was 1.653. What is the probability that if we had 81 independent success/failure observations for control and 84 success/failure observations for test, with the success rate identical for both control and test, that we would observe a Z-value of at least 1.653? The answer may depend on the value of that common success rate. The exact unconditional Z-test maximizes this probability over all possible identical values for the success rates (from 0 to 1). According to the definition, this yields the P-value. A microcomputer program (including hardware requirements), to perform the calculations is described in Shuster (1988). The one-sided version considers values above the observed Z of 1.653 in favor of the test treatment, while the two­ sided version considers values above the observed value of 1.653 in favor of either treatment The exact unconditional P-values are .057 (vs approximation of .05 one-sided) and .108 (vs approximation of .10 two-sided). These agree remarkably well. As Suissa and Shuster (1985) point out, the Exact Unconditional Z-Test generally outperforms Fisher’s Exact Test. (Requires fewer patients for trials.)

CRC Handbook o f Sample Size Guidelines fo r Clinical Trials

28

2.4.3 Kaplan-Meier Comparison (Large Sample) The Kaplan-Meier (1958) methodology is designed to estimate the probability of surviving for a given number of years, utilizing “Censored Survival Data”. Unlike the Binomial methods above, the Kaplan-Meier technique recog­ nizes the possibility that patients' times at risk will be unequal. However, the Kaplan-Meier technique makes the very important assumption that the prognosis of a patient who withdraws from the study is the same as that of a patient of the same “age” who remains on the study. This means for example, that the prognosis of a patient who was lost to follow-up after 6 months on the test therapy is the same after the six month point as that of a patient still on the test therapy at six months. It is therefore clear that in many studies, the validity of the Kaplan-Meier method rests heavily on obtaining virtually complete follow-up on all patients. Note that the above assumption is reasonable for patients whose follow-up is short, but current. For example, it is reasonable to assume that if a patient entered the study six months before it was to be analyzed he/she has the same outlook post six months as that of a patient who entered the study on the first day the study opened, four years prior to the analysis. For each treatment, the Kaplan-Meier curve provides an estimate of the true probability of surviving at least Tdays. The true probability represents the hypothetical target population of all past, present, and future patients who meet the eligibility conditions of the study. The estimate is based on the sample of patients assigned to the given treatment. It is subject to sampling error, since the actual sample assigned to the treatment is assumed to be a concep­ tual random sample from the target population. It also could be subject to selection biases, if the sample of patients cannot be viewed as a conceptual random sample from the target population. A good example where selection bias can occur, is where there is selective participation by some institutions in a multi-center trial. For example, institution X agrees only to place their advanced patients on a study.

2.4.3.1

Assumptions Underlying the Kaplan-Meier Curve P I. All observations are “INDEPENDENT”. That is, the outcome of a given patient is not influenced by that

of another. P2. Given the treatment assignment, the survival probability distribution of each patient over time is the same from trial to trial. In other words, patient prognosis on the test treatment is the same for early entries in the trial as later entries. The same holds true within the control treatment.

29 P3. The loss to follow-up rate is very small. Otherwise, we assume that patient losses are not in any way influenced by the patient’s prognosis. Failure of this assumption is especially serious if one of the therapies is more toxic, leading to vastly differing withdrawal rates between the treatments. Comment: Withdrawals for toxicity probably violate this assumption. It is therefore vital to keep track of study losses to toxicity.

2 .4 3 2 Calculation o f the Kaplan-Meier Curve The Kaplan-Meier curve starts at DAY 0 at a value of 1.00(100%). On each succeeding day, we compute the value from the preceding day as follows:

Let

R=Number of patients left at risk on that day(At Risk) F=Number of patient failures on that day (Deaths)

KM=KM (on previous day) X (R-F) / R

(1)

The estimate is easily justified intuitively as follows. The estimate is built on a day-to-day basis, using the data for each day. To survive 100 days, a patient has to survive day 1, day 2,...., day 100. The logical estimate of the probability of surviving a given day, assuming that the patient was alive at the start of that day, is (R-F)/R, the ratio of the number of patients who survived that day to the number at risk on that day. The Kaplan-Meier estimate for day 100 is simply the product of the (R-F)/R values for days 1,2,3,...,100. An analogy to successive taxes will further motivate the multiplication. Imagine that you wish to send $1000 to a relative in Angola. The money is routed as follows. First it goes to Canada, which extracts 1%. Next, it goes to Cuba, which takes 13% of the balance. Finally, it goes to Angola, which charges 16% of what is left. We see that 99% survives the first taxation; of that, 87% survives the second taxation; and of that, 84% survives the final levy.

Surviving Gift=$1000X.99X.87X.84=$723.49

CRC Handbook o f Sample Size Guidelines fo r Clinical Trials

30

1. Canada: 1% of $1000.00 tax ; 99% of $1000=$990 survives 2. C u b a: 13% of $990.00 tax ; 87% of $ 990=$861.30 survives 3. Angola: 16% of $861.30 tax:84% of $861.30=$723.49 survives.

Note that the KM value in (1) stays the same as the previous day, unless at least one failure occurs. We shall demonstrate the curve concept for the Control Treatment (See Figures 10 and 11).

2.43.3 Numerical Example: See Figures 10 and 11.

Control Kaplan-Meier Curve On Day 1, F=2 and R=186 and hence (R-F)/R=184/186. On Day 2, only 184 patients are at risk, two having been lost on day 1. For Day 2, F=1 and R=184 and hence (R-F)/ R= 183/184. On Days 3-6, no failures occurred and hence (R-F)/R=1.000. On Day 7, F=1 and R=183, and hence (R-F)/R= 182/183. On Days 8-11, no failures occurred and hence (R-F)/R= 1.000. On Day 12, no failure occurred, but one survivor had only 12 days of follow-up. Here too, F=0 and hence (R-F)/ R =1.000. On Days 13-15, no failures occurred and hence (R-F)/R=1.000. On Day 16, F=1 and R=181, and hence (R-F)/R=l80/181. This process continues to day 3454. On Day 1, KM=184/186=.98925. On Day 2, KM=.98925X183/184=.98387. On Days 3-6, KM stays at .98387, but on Day 7, KM=.98387X182/183=.97850 On Days 8-15, KM stays at .97850, but on Day 16 KM=.97850X 181/182=.97309 This process continues to day 3454.

31 Wouldn’t a computer be nice? There are many excellent programs for both mainframe computers and micro­ computers.

2.4 3 .4 Standard Error A second important quantity relative to the Kaplan-Meier Curve is the “Standard Error”. This latter quantity is used to obtain confidence intervals for fixed term survival as well as for comparison of fixed term survival for two competing treatments. There are several forms of the standard error, but the most convenient is due to Peto et al (1977, Statistical Note 6). For a given day,

SE=KM SQRT {(1 -KM)/RX}

(2)

With KM as in (1) above. RX is the number at risk at the start of the following day. [Some users replace RX by the value of R from (1). However, in nearly all cases, the alternate SE is virtually identical to that of (2).] One-sided and two-sided approximate confidence intervals can be obtained (using W from Figures 8 and 9 respectively) for a single fixed term survival as: TrueSurvival >KM-(W SE) One-Sided Upper (Figure 8)

True Survival Rj for all j

(T reatm ent 2 Superior)

H ^ : Pj < Rj for all j

(T reatm ent 1 Superior)

or

or a two sided alternative ha

:

ha

°r

ha

-

W hen m ixed behavior occurs under H A, some P- < R. while other P- > R., the logrank test A J J J J m ay not have good perform ance. S tructurally, we com pute the following quantities relevant to T reatm en t 1: O = 51 Fj

X =

^2 Ej

where (Fj + Gj)Nj

(observed failures on T reatm en t 1),

(i-i:

(expected failures on T reatm en t 1),

( 1 .2 :

54

CRC Handbook o f Sample Size Guidelines fo r Clinical Trials

If Nj + Mj = 1, then the j ^ 1 term in (1.4) is defined as zero. The logrank statistic is

7 - O- X Z~

SE

(1

which under m ild regularity conditions is asym ptotically standard norm al under H q. Note: If we interchange the definition of T reatm ent 1 and T reatm ent 2, all we do is change the sign of Z.

T he P-value is obtained from (1.5) and Figure 6 or Figure 7, depending on the A lternative Hypothesis.

Large Sam ple Result (Logrank) If the assum ptions below hold, then Z given in (1.5) is asym ptotically standard norm al.

A ssum ptions: N.M .p .Q.

M

?

(b)

No day is a “wipeout.” There exists a positive num ber S < 1 such th a t Pj > 1- 6

for all j.

T his is equivalent to bounding the failure rates away from one,

(

Plan of the Proof: Step 1: Representation of Numerator of Z.

(M.F. - N.Gj) Prove

° - X = g

j

j

with

and

Fj

Binom ial w ith Param eters Nj and Qj

Gj

Binomial w ith P aram eters Nj and Tj

{ * j} ’ { ^ j } m utually independent.

Step 2: -

N( ° ’ ■)

where

See A93 for a definition of convergence in distribution ( 5 ) . Step 3: If Y is binom ial with param eter Q and sam ple size N, then for P = 1 - Q

E {Y (N -Y )} = N(N-1)PQ and V a r|Y (N -Y )} < N(N-1) 2 PQ.

Step 4: Show

Step 5: Com plete the proof. Show th a t Z, defined in (1.5) converges in distribution to the standard norm al.

56

CRC Handbook o f Sample Size Guidelines fo r Clinical Trials

Proof of Step 1: 0 - X = £ F . -E E . j j

- 'P F V j J j

(F: + G.)N. J J__J Nj + Mj

- v / F . . (Fi + G^

TP

f (N; + i t

i\

Ni +Mj J - (Fj + Gj)Nj | Nj + Mi

J

(M ^ G j)

“V

Now

Nj + Mj *

K 0)

Fj is Binomial with param eters Nj and Qj Gj is Binomial w ith param eters Mj and Tj

from the model assum ed in the introduction to C hapter 3. This completes Step 1.

Proof of Step 2: Let us represent the Fj and Gj as Bernoulli Random Variables, and apply the central lim it theorem for Bernoulli variables.

N. J F. = £ Y J i = i 1Ji Mi G = T Y.. J i = l IJ2 ,J

with Y-- = 1 or 0 depending respectively on whether for treatm ent £, the i ^ p atient trial on 1J£ day j results in a failure or survival. From (1.8),

57 Nj ••

x

M jYij,

J 1=1

J

Mi Nj Y ij 2 > :> :s . . i ,

J

J 1=1

J

, x

J

Using (1.9) and the null hypothesis Qj = T j we have

NJ

M.Q.

Mj

E ( 0 - X ) - £ £ n . + M- ' J i= l

J

J

J i= l

N.T.

N. + MJ

J

NiMi = S N T T l T j (Qj - Tj ) = 0: Nj V ar(0 - X ) = £ £

m2

^

------- ----- o PjQ ; + £ £

j i = i (Nj + Mj)2

J •>

2

------- ------o RjT:

j i = l (Nj + Mj)2

J J

fM ?N . + N?M>1

(PiQi=RjTi) N.M.

- ? N 7 + l T j PjQ j

2 = V*.

^From (1 .7 )j

W e wish to apply the C entral Lim it Theorem for Bernoulli Variables: (C ondition 2), See A107 Let ijk

Mi -J— Nj + Mj

k =

-NJ ’ Nj + Mj

k =

1

2

From (1.9) N,

Mj

O - X ^ E b i j , ^ + S | > 8 2 Yii2 with Nj

Mj

58

CRC Handbook o f Sample Size Guidelines fo r Clinical Trials

Now

V ^—►oo.

^Assumption (a)j

T o apply condition 2 of A 107 we m ust show ^

—►0 where

Nj

Mj

W = E E lb.,^13 Qj + E E |b ij 2 l3 Qj. J 1=1 J 1=1 J

3

Nj Nj

N .M ?

l ^ i i l Qi = E 3 Qi Q: E E lbiiil £ — ... l j ~ 7T5

Now

ji= l

‘J 1

J

j

and

j ( ^ + M j)

3

E E |bii 2 l3Qi = E — ji= l

^

j

Mj Nf

L J — s Qi-

Nj + M j)

T hus Nj , Mj , N,Mj(N? + M?)Q. W = E E I b y / Q j + E E |bij 2 l3Qj = E J ' ' I ->■ J 1=1

J 1=1 J(Nj 4-M j)

Now since (Nj + Mj)^ > N? + M?

NjMjQj

From assumption (b), P.

w

T h a t is, since V

o

^

-

— oo

>

i

iv

1-6

1 - f with 6 fixed. Hence

N-M-Q.P. J

J J J

^ (Nj +

Mj)

2

— v

“ 1-

6

59 ^The other condition

V

2

postulates are clearly satisfied since Qj < 6 (bounded away from one) and

s '•)

T his com pletes the proof of step 2.

Proof of Step 3: Let Y be binom ial w ith sam ple size N and param eter Q. Let P = 1-Q. For now, let N > 1.

e ( y ( n -y

))

= £ y ( N - y ) ( y ) Q y P N' y

= N (N -l)P Q IE (N ;2 ) Qy- y N- 2 M y -1)

'N - 2 W 'DN-2-j

= N(N-1)PQ.

(1.11)

Note: if N = l, form ula (1.11) holds since both sides equal zero. Sim ilarly, if for now N > 2,

E(Y(Y-1)(N-Y))

= N(N-1)(N-2)PQ2 x f ( Nj'3)QJPN"3’J

= N (N -1)(N -2)PQ 2.

e ( y ( n -y )( n - y - i ))

(1.12)

= n ( n - i )( n -2) p 2q E ( Nj 3) o ip N' 3'-i

= N(N -1)(N -2)P 2 Q.

(1.13)

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CRC Handbook o f Sample Size Guidelines fo r Clinical Trials

If N = 1 or 2 (1.12) and (1.13) hold since both sides are zero. If for now N > 3, E (Y (Y -1)(N -Y )(N -Y -1))

= N (N -l)(N -2)(N -3)P 2 Q 2 X:4 ( N: 4 )Q iP N"4' j

= N(N -1)(N -2)(N-3)P 2 Q2 .

(1.14)

If N = 1, 2, or 3 (1.14) holds since both sides equal zero.

e ( y 2( n - y )2) =

E{Y(Y-1)(N-Y)(N-Y-1)} + E{Y(Y-1)(N-Y)}

+ E{Y(N-Y)(N-Y-1)} + e | y ( n -y )}.

(1.15)

The above is obtained by writing

Y 2 (N-Y ) 2 = Y ( N - Y ) |( Y - l ) + l ||( N - Y - l ) + l |.

Substitution of (1.11) - (1*14) into (1.15)

e { y 2 (N-Y )2 } = N(N -1)(N -2)(N-3)P 2 Q 2 + N (N -1)(N -2){PQ 2 + Q 2 p } + N(N -1)PQ

= N(N -1)(N -2)(N-3)P 2 Q 2 + N (N -1)(N -2)PQ (P+Q ) + N(N -1)PQ

= N(N -1)(N -2)(N-3)P 2 Q 2 + N(N-1) 2 PQ.

|^E jY (N -Y )|J2 = N2(N-1)2P 2Q2.

Hence subtracting (1.17) from (1.16) yields:

(1.16)

(1.17)

61 V a r{ Y (N -Y )} = N (N -l){(N -2)(N -3) - N (N -1)}p 2 Q 2 + N(N - 1 )2 PQ

< N(N-1) 2 PQ .

(1.18;

T his com petes the proof of step 3.

Proof of Step 4: Under the null hypothesis (Fj + Gj) are independent binom ials w ith respective sam ple sizes

(Nj + Mj) and respective param eters Qj. F rom (1.4) and (1.11) successively,

e (se 2 )

N i M i E ll F ^ G i K N i + M i - V G , ) } j

(Nj + Mj) 2 (Nj + Mj - 1 )

~

Nj Mj (N j + Mj ) ( Nj + Mj ~1)P jQ j

j

(Nj + Mj)2 (Nj + Mj - 1 )

N iM iP iQ i

9

(1'19

=

from (1.4) and (1.18) successively,

j

(Nj + Mj)4 (Nj + Mj - l )2

N ^ N j - f M j K N j + M j- D 'P jQ j j

(N j + M j)4 (N j + Mj - l ) 2

N?M 2

< £

Now since

Nj-—-—~ Mj -----< .25,

(Nj + Mj)2

. .. J .VT5 P A

62

CRC Handbook o f Sample Size Guidelines fo r Clinical Trials 2

V ar(SE ) < .25 £

NiMiP iQi 2 ^ ^ = .25V2.

(1.20)

From Chebyshev’s Theorem A51, (1.19) and (1.20), we have

SEZ -

1

> €

= p [ | SE 2 - V2 | > fV 2]

< V ar(S E > < _ J _ _ ( 2y 4 4 0 0 by (1.7) and assum ption (a). T h a t is, from the definition of covergence in probability

T his com plete the proof of step 4.

Proof of Step 5: From step 2, we have

From step 4 and Appendix A98, V

P

Hence by Slutzky’s m ultiplicative theorem , Appendix A 105,

T his com pletes the proof.

o.

3.2

Derivation of the Large Sample Distribution of the Kaplan-Meier Statistic Refer to the T reatm ent 1 colum n of the N otation C hart.

Large Sam ple Results

Assum ptions: (a)

T he sam ple size on day j, Nj are non-increasing: N i - N 2 > Ng > ...

(b)

No day is a “w ipeout” . There exists a positive constant 6 < 1 such th a t Pj, the probability of surviving day j is: Pj >

(c)

1

- 6

for all j .

There is a m inim um hazard on any given day. There exists a constant c > 0 such tha Qj > c

for all j.

Note th a t c can be sm all.

(d)

—►0.

(e)Nk Dk _

(See N otation chart item 10)

oo.

Conclusions: Si - Si

(1)

r)

- I j j - * H N(0,1). uk

(S tandard Norm al)

CRC Handbook o f Sample Size Guidelines fo r Clinical Trials

64

Note: T he lim iting process can involve Qj (the probability of failure on day j given patient was alive a t the sta rt of day j), k (the day num ber at which survival is evaluated), as well as Nj (the num ber of patients a t risk at the sta rt of day j.) is given in item 9 of the N otation C hart,

in item

8

,

in item 10, and

in item 11.

T he arrow represents the lim iting distribution (approxim ate distribution). See A ppendix A93.

Plan of Proof: Step

1:

Show th a t V

Sk = Hk + Ik-

where

*k = S k i / V W and

with

S 0 - S 0 - 1.

pP

Step 2: Show

-5 N(0, 1).

(Standard Norm al)

Step 3: Show

Step 4: Show S

Step 5: Show

S —-

5 N(0,1).

(Standard Norm al)

65 Step 6: Show S S —g — -

N(0,1). (Standard Norm al)

Before form ally conducting the proof, some rationalization m ight be in order. First, C entral Lim it Theorem s apply to sums. Hence, we would like to write ^S^ - S j^ as a sum . T he astute reader m ight ask, “W hy not take logs?” This would work if each Pj was asym ptotically norm al. However, m ost of the applications will have a large Nj and a sm all Qj (Pj near one). In these situations, the Pj m ay not be well approxim ated by norm ality. The decom position in Step

1

is m otivated as follows.

Lem m a (Product Difference to Sum m ation): Let Aq =

1

and

j A. = a 1 a 2 - a. = f j a ;> J J i= l

Bq =

1

and

B. = b^b 2 ’**bj =

j

b.

i= l

with each b. ^ 0. T hen k A- j ( a r b i) j= i

j

Proof: By adding and subtracting common term s,

Ak "Bk= (alb2"'bk ' bib2 "bk) + (V2V"«>k ' alb2" bk) + ( a j a j a j ^ - bij - a ^ b g ^ ) + ••• + ( a ja 2 - a k -

_

k

/V k

■ j ? i ^ Bj

Aj - l Bk \ '

Bj - 1

CRC Handbook o f Sample Size Guidelines fo r Clinical Trials

66

, , v _ ?kk b r * ' bk bj + l ' ' bk = b r -b. ~ TT ’ r - bj ~ BJ

The term

which produces the above sum.

Now

Aj = ajAj_i

and

Bj B. , = t^. j-i ^

S ubstitution in the sum yields

Ak - Bk = Bk £ ^ ( v bj)-

T he com pletes the proof of the Lemma.

Proof of Step

1:

F irst, we apply the Lem m a with

aj = Pj

bj = Pj

Aj = Sj = n P j

Bj = sj = n P j -

T his yields

k S. Sk - s k = s k j 5 1^

B ut since Sj = Sj

this further reduces to

( V

pj>-

Now since Sj ^ = Sj_^ + ( S j e q u a t i o n (2.1) can be rew ritten as

. sk - sk

k (Pj - P: = ks .k=1£ — Fj ^ +

T5-

k

sk E1 k .=

= Hj^ -h Ij^.

S. j - S-_1 )(P .-P j) J bJ.JPj S P

(See S tatem ent of Step 1).

This com plete the proof of Step 1.

Proof of Step 2 : T o prove norm ality, we shall apply the C entral Lim it Theorem for Bernoulli variables, See A107. Note th a t (Pr

Pi ) = -(Qi - Q j)

where

Qj =

1-

Now

H,

Pj and Qj =

1

- Pj.

k (Q: - Q;) K

= - S. E

P

J= 1

k

*j

Nj (YH - Q=)

—"^ k E £ Kj = l i = l

(N P )

where Y - i = l...N j, j = l ...k are independent Bernoulli random variables with

P(Y jj = 1) = Qj

P(Yjj = 0) = Pj = 1 - Qj.

Let v i = v “ ( :T ! r ) ' where

68

CRC Handbook o f Sample Size Guidelines fo r Clinical Trials N = NkDk-

From (2.2), 2 *12 = Ek ENj bfjP.Q . K

j= ii= i

1J J J

where h ^ bi j - - N jP jDk Hence

9

vk=

NS? k

j

Q:

E E ~r~

k

j = l i = l Nj Pj NS? k

ND r

= N. Note th a t under our assum ption (e), N =

o > oo and hence —►oo.

We next show th a t |by| is bounded.

^Tn s ,,

|b:;l = ,------ k—

^ j Pj Dk

^ k DkSk

W Nk < N j Pj J W Sk ( W )J n^ -

Now since

—►oo

Pj >

1 - 6

by assum ption (b)

69 and hence there exists B > 0:

I V

Thus, |b--| < /i ij

F urther, the Qj =

1

c\ t>

throughout the lim iting process,

(1-0)13

- P- < 1 - ^ < 1 are bounded away from one. ^A ssum ption (b)^. T o obtain

condition 2 of the C entral Lim it Theorem , (A107) we m ust show

k

Ni

E £ lbjjl Q:

j= li= l

J

J

— 3-------- 0 .

Vk

Now k Nj |b j.| 3 Q.n 3 / 2 S? k y ' y' *J J vj

Qj

________ kJ

^uses Vk =

- NV J D 3 j = l N ?P? g3

^

Q.

^ , ,2 k 3 2 rT F (1-*) 2 N. ? j = l Nj Pj \ D u kJ=

(Since Ni ^ Nk ’ p i ^ J k J

- 6>

Sk D k _ Sk (l-« ) 2 Nk D 3 ( K ) N k Dk

* 0.

Hence, from Appendix A107

>fNH,

#

However, since

o

= N, (as shown above)

d

^Since N ^D ^ —►oo per assum ption (e)

CRC Handbook o f Sample Size Guidelines fo r Clinical Trials

70

*

Dk v k

Dk

and hence

£

-

N(0,1).

Dk

T his completes step 2.

Proof of Step 3: F irst note th a t 1^ is a linear com bination of term s

Bj = (SH - sj - l) ( V pi> W e shall use the independence of P p

P ^ to obtain the means, variances, and covariances of

B’s. See A45 and A46.

(a) Proof:

E(Bj) = 0 E(Bj) =

j

- S j_ ^ E ^ P j - P ^ .

(Sj _j and Pj are independent)

Since P j is the binom ial estim ate o f Pj, (a) is clear.

(b)

Var(Bj) = Var(Sj_j)Var(Pj)

Nj

Proof:

Note that E ^ . j ) = E (P 1...P ..1) = E (P j) ••• E fP j.j) = P x ' P j . j = Sj_r

Var(Bj) = E(B?)

(Since E(Bj) =

o)

= E [ ( s j . i - S j . i ) 2 ( p j - pj ) 2 ]

(Independence)

71 = V ar(Sj

NoW

V a r^ J

1 )V a r(p j

).

(2.4)

= e ( p 2, P 2, .... P ? j ) - { e ^

=

e(p

2) . "

e(p

? i ) - S?

)

}

2

i

= n {pi + ^ } - sfisince

V a r^ P ^ =

- ^E ^P jJJ 2

(2-5) implies

E( p i ) = [ E ( p i ) ] 2 + V ar( p i ) = p i + ^ p .Q .

Also

V ar( Pj ) = "N T-

(2-6)

Upon substituting (2.5) and (2.6) in (2.4), the result (b) holds.

(c)

Cov (B j, Bj) = 0.

i * j

Proof: Since

E(B.) = E(Bj) = 0

C°v(Bj,Bj ) = E(BjBj ). Now if j < i,

C o.(B ,, Bj) = E [(S ,., ■ S|. 1)(P j - P ,)( s j _, -

- P j) ]

= E ( P ,- P ,) E [(S H - Si.i) ( S H • S j-i)(P j - P j)],

72

CRC Handbook o f Sample Size Guidelines fo r Clinical Trials

since (s^ ^ - S-

^ - Sj

- P j) depends only on P j ,

Pj j and is therefore independent of

P-. Now E ^Pj - P .) = 0 and hence Cov(B-, Bj) = 0.

T he result follows in a sim ilar fashion if i < j. Next, we shall evaluate the mean and variance of 1^.

,

„ X

( §H - sj - l X f j ' pi )

kj5 .

W

i

k B. = Sk — 1p k £^ C j = 2 bj - l j

since S 0 = S 0 = 1 and Bj = (Sj j -

- P j).

Using linear com binations per A45 and the fact th a t Cov (Bp Bj) = 0

E (Ik ) k

k E(B.) = Sk £ g - i . = j = 2 bj - l Pj

0

, k Vat(B-) V ar(Ik ) = SI ' Z j = 2 SfA P f

M

=s

9

k

si’j - i

j= 2 Since

j-i sh

V ar(Ik ) = S£ £ K j= 2

= ,D

j' 1 r

w-

Q;

n {i + — 1 Ni P , i= l

Now applying the Lem m a on converting products to sums, we see

3 .

Y i

(2.8)

73 j' 1 ( Qj ", H n l 1 + n t p :} ' 1 = . £ A i-i 1=1 i r 1=1

w here

Q; : i i

(2.9)

n t

Aq = 1

Ai ~ J ? 1{ 1 + Nf p J < A i

1 J .

104

CRC Handbook o f Sample Size Guidelines fo r Clinical Trials = (s+t-X) v Q(s+t-x).

S ubstituting these into (5.9), the first expression for

= q E(vjwj)’

yields (after cancellation)

by< 5-8> -

Hence, E ( ( Vj - QJWj ) 2 )

= E ( VJ2 ) - 2QE( v j w j ) +

q 2 e ( W j2)

= E ( v f ) - 2 Q E ( v j Wj ) + 2Q

= e ( vJ ) .

o However, Vj takes on only values of 0 or 1. Hence Vj = Vj. T h a t is, from (5.6) and (5.4)

!( ( v j * s w i ) J ) =

e ( vj )

* 1*4

{

Sum m ary for Step 2. We have shown the following properties of the Vj and Wj given the num ber of arrivals in the tim e interval from 0 to s

O .V J = Q E(W j) - 1 - j j j {0 0 .

(It does not m a tte r w hether A is fixed and s —>0 0 , or s is fixed and A —*>0 0 , or w hether sim ply A s—>oo on any p a th .) T hus As Since

L

CRC Handbook o f Sample Size Guidelines fo r Clinical Trials

108

4A -s[£-Q ] = { < n [E -Q] } and since (Appendix A98),

Slutzky’s M ultiplicative Theorem , A105, and step 4 yield

4 A i [ E - Q ] H N ( 0 , B2).

T his com pletes Step 5.

Proof of Step 6: Let b 2 = e|

N

(5.16)

- affIEnlJ2 -

Now since from Step 5:

J S (£ -

q

) ^

N(0, B2),

as A s—*oo F

P

Q

(5.17)

N

Now given n,

F = XJVj

(See Definition of Vj in Step 1)

is a sum independent identically distributed random variables. From (5.10), (5.1), and (5.2)

109 (5.18)

Since Vj is Bernoulli, VaKV.) = E (V .){l - E(Vj)}.

Given n is sufficiently large,

^

{ I - E (Vj)} ^

N( ° ’ V ar(V .)),

and hence E - E(V.) I

0.

T h a t is, from A95, F

P i

nE(Vj)

from (5.18), b 2f

p

,

(5.19)

nQ 2

From Step 4, F /(N Q )

1. Application of A98 and A101 to (5.17) and (5.19) yields,

(5.20)

From Slutzky’s M ultiplicative Theorem A105 and (5.20)

110

CRC Handbook o f Sample Size Guidelines fo r Clinical Trials

|L [ E - q J has the same asymptotic distribution as

which is N(0, 1) from Step 4. T his completes the proof.

3.6

Extension to the Two-Sample Problem Here the accrual rate is A /2 to each treatm ent, G is the num ber of failures on T reatm en t # 2 ,

M is the to tal tim e on test for T reatm ent # 2 . T is the daily failure rate on T reatm ent # 2 . W e have by the one sam ple results (halving the accrual rate):

[E - q ] B . N(0, B2)

with

J(.5A)s [ h - T ] £ N(0. C2 )

with C2 = T 2[ l - i i {e-T t - e - T (S + t)} ] ' 1

Hence

[(n * i ) - (Q • T>] ° N(°- ®2 + c2)-

Since from A142, each accrual process is independent, and A 108 can be applied.

Ill Now from the previous section, Steps 5 and 6

B /(.5A s) _p F /N 2 and C2/(.5 A s ) _p G /M 2

Hence from the Appendix A103,

(B2 + C 2)/(.5A s) P l (F /N 2) + (G /M 2)

'

By applying A109, the following “Block” holds: Results for Poisson E ntry, E xponential Survival

Proof: From item 9 of the N otation C hart a t the beginning of C hapter 3,

(15.2)

Now, by applying the lem m a on converting a difference of products to a sum (Section 3.2) with

and bj = Pj, we have

(15.3)

Now,

(15.4)

143 Now from the actual accrual process,

Nj+i =Y Fr wj where Nj = N um ber of P atients a t risk a t sta rt of day j, Fj = Failures on Day j,

W j= C om peting “w ithdraw als” on Day j.

T he W j include p atients who are alive with tim e of risk j, as well as those who quit alive on day j.

N .-F .

N .-F .-W ,

Pj =

N.

.

------ = “ N T '

( 15-5)

As long as the Wj are sm all percentages of Nj, approxim ate equality holds. By sub stitu tin g (15.5) into (15.4) we have

c -M bj - l i=J

N.

“ 1

N. J

S ubstituting (15.6) in (15.3) yields

1 - Sk > N k + 1 E j V j

(15.7)

( 1 ~ ^ k) > E — Nk + 1 - j NjPj

(15-8) V '

Hence

T h a t is,

144

CRC Handbook o f Sample Size Guidelines fo r Clinical Trials

■>;

- *

. 0

J J

and approxim ate equality holds as long as the w ithdraw al rates are sm all fractions of the Nj.

Sum m ary: The use of Dj£ instead of

is conservative. The form ula will underestim ate the precision of

the estim ator S^, b u t only slightly if the fraction of com peting w ithdraw als is sm all.

3.16

Connection Between Kaplan-Meier and Binomial Note th a t if there are no censored patients to day k, under actual accrual. N j ^ j = Nj - Fj and

Pi -

Nj '

T his yields from the N otation C hart:

s - n s “ “ jS i "j

_ N2 N3 -N l V .2 T o evaluate D £, note hat

and hence

Nk+1 _ Nk+1 Nk " N1 '

( 16 .1)

145 1

i

Nr Nj + i "

A

= j£= (l \f rV - -i N : j)/

j = l PjNj

Nj+ l N j

i

PjNj

_

j.

- N j + 1 - Nj

i

i

_ N i - Nk + i

_ N k + r Ni _

N i Nk + i

Hence .o .o k Q: D = s j = i pj Nj _ Nk + i 0, we obtain the result by successively letting t = ± y y a r^x ) *

Note th a t this implies C o v f x ,, X9) - 1 < P = ------- — — —— r ^ h (V a H X j) V ar(X 2 ) } 5

A51. (k)

Chebyshev Theorem (Consequence)

. . . 2 Let X be a random variable w ith m ean /i and variance 0

p [ | x - H > *]
t (x - # A

(x )d x

> f 2 p [ i x - /i|> < ]. o , Divide both sides by e to obtain the result.

161 A52. (1)

“Consistency of X ” (Consequence)

If X p X2, ... are independent, identically distributed random variables w ith m ean /i and o variance

0

P [ |X n - H > e]] —+ 0

_

as n —>oo

(x1 + - + xn)

where X n = -----------^---------- -. In lay term s, this is the “Law of Averages” . Proof: From A47 and A48 above, E (X) = /i

n-2 V ar(X ) =

and

By Chebyshev’s Theorem (k) P [jX —fi\ > e] < —►0 e

as n —>oo. n€

MOMENT GENERATING FUNCTIONS (Consequences) Mx (t) = E (etX )

A53. (a)

If two cum ulative distributions differ, then they have different m om ent generating functions. (The m om ent generating function uniquely identifies the distribution. In fact, we only need to identify the m om ent generating function in an open interval about t = 0 .) See Fraser (1976, pages 544-546).

A54. (b)

Provided the m om ent generating function is defined in a neighborhood of t = 0, then E (X n ) = tKm

m

£ }(1)

(The n ^ derivative of M ^ (t) with respect to t is taken, and then t —►O.) See Fraser (1976, page 233).

CRC Handbook o f Sample Size Guidelines fo r Clinical Trials

162

ASS. (c)

M x (t) = 1 + § j= l

J‘

See Fraser (1976, page 233).

A56. (d)

If X j, X 2,

Xn are independent random variables with respective m om ent generating

functions Mx (t)

j = l, ...,n

and Y = E a ft

j= l J J w ith a j’s constant. T hen Y has m om oment ent generating gener* function M y (t) = f t Mx .(a.t) j= l J J Proof (d): e

E(e

= e

tv

)

tEa-Xn ta-X. J J = n e J J j= l

n = II j= l

/ ^a i ^ i \ e ) V '

^

independence

n

=

n M y (a.t)

by definition.

j=i Aj J

SPECIAL DISTRIBUTIONS BINOMIAL DISTRIBUTION (Discrete) A57. (a)

P robability Mass Function of the binomial distribution

f(x) = (S )p X( l - p ) n -X

where

x = 0, 1,

(*) =

a! = a (a -l).

0! = 1

..1

n

0 0 0 and p —►O with n p —^A>0 ( $ ) p X( l - p ) n - X —

x =

0 , 1 ,2

,...

CRC Handbook o f Sample Size Guidelines fo r Clinical Trials UNIFORM DISTRIBUTION (Continuous) A65. (a)

P robability Density Function of the uniform distribution.

f(x) = b^TA

A 6 6 . (b)

a 0 and let X have the exponential distribution. P [ X > t] = l - F ( t )

= e “ At

_ P [ X > t + s ] _ e ~ A(t + s) " P [X > s ] ~ e -A s

T he exponential distribution would im ply th a t an s-year old individual has the same outlook as a newborn, in term s of future life. The “H azard R ate” defined as



=nSkj

"

x> °

A e ~ Ax > e-A x - A

H (x)dx is the instantaneous probability of failure between x and x + d x , given survival of at least x. A76. C onstant H azard implies exponentiality, since if f(x) = A l-F (x )

rt f(x)dx _ •* 0 1 —F(x) -

x>0

CRC Handbook o f Sample Size Guidelines fo r Clinical Trials

166

l o g { l - F ( 0 ) } - l o g { l - F ( t ) } = At Now F(0) = 0 for a survival distribution, and hence l- F ( t) = e-A t

GAMMA DISTRIBUTION (Continuous) A77. (a)

P robability Density of gam m a distribution, xor a

=

— 1

—Ax

r(a)---

x>0, a>0, A>0

r ( a ) = / § 0x “ - 1« - x dx

Note: if a is an integer, n r ( n ) = (n — 1)!

A78. (b)

Mean and Variance ft = (a /A ) j

0

1

0

••

0

1

1

...

0

1

1

0

0

det(K ) = 1 f y (y lt •••. y n ) =

An e x p |- A ( x j + ••• + xn )}

= An e x p |- A y n |

Now the range of the y ’s is obtained from the range of x ’s as 0

< Xj < x j + x 2 < x 1 -fx 2 + x j . ..

° < yi < y2
0 , there exists a num ber N = N(e) such th a t whenever n>N ,

|An —A| < €.

In other words, you challenge me with a tiny num ber e. I find a large N such th a t |An —A| < e for all n > N . T his can be done for every e > 0 . Exam ple:

An =

1 /n

A =0

N( 0 p ( |X n - C | > e ) —»• 0 as n —> oo In other words, regardless of w hat sm all “challenge num ber” e you provide, the probability th a t Xn is w ithin € of C goes to one.

A93. Convergence in D istribution (Definition) Let X j, X 2, ... be a sequence of random variables with respective cum ulative distributions F l ( x ). F 2 (x )> •••> Fn (x)> ••• W e say th a t F n —►F in distribution if

CRC Handbook o f Sample Size Guidelines fo r Clinical Trials

172

Fn(x) ~ 1> F(x)

at every continuity point of x.

This is denoted by Fn 2 F or Xn S F.

A94. Convergence in D istribution (Consequence) Let X p X2, ... be a sequence of random variables with respective cum ulative distributions F j(x ), F 2 (x), ... and respective M oment G enerating Functions M x(t), M 2 (t), ... Suppose th a t M „(t) -

M (t)

in a neighborhood of t= 0 and M (t) is the M om ent G enerating Function of F(x). Then F n -&F. The proof is beyond the intended scope of the book. Interested readers m ight refer to Fraser (1976, pages 248 and 558-560.)

Convergence in P robability (Consequence) A95. (i)

A96. (ii)

A97. (iii)

If

v — P x Xn

and

Yn = cX„

Then

Y n £ cx

If

Xn - x

and

Yn - 0

then

X „Y n £ 0

If

vXn — P x

then

if Y n = 1/X n Y „ £ (1/x)

c constant

and

x^O ,

173 A98. (iv)

p

If then

Xn —►x

and g is continuous a t x

g(Xn ) £ g(x)

Proofs: (i)

If c = 0, then Yn = 0 = cx for all n and the result is im m ediate If c ^ O P [lYn - c x | > f ] = P j j x n —x| > j |j j -* 0 T h a t is, Yn

(ii)

since Xn £ x

cx

The event th a t |Xn Yn |< e contains the intersection of the events |Xn —x| < e and

(event An )

|Yn |


P (A „)-P (B „)

Now

P (A n ) —*1

since Xn £ x

and

P (B n ) —*0

since Y n -^0.

Hence P (A n Bn ) —>1. P [|X n Yn | < f] > p (A „ B n ) - l as n - o o .

(iii)

T his is an im portant special case of (iv).

(iv)

Given e > 0 , there exists a 6 > 0 such th a t whenever |y —x | < 6 , |g (y )—g (x )|< c . Above is the definition of continuity. Therefore, the event th a t |g(Xn ) —g (x )|< c contains the event An , th a t |Xn —x | < 6 . But p [An] = P [lx n"*x l
1

(Convergence in P)

CRC Handbook o f Sample Size Guidelines fo r Clinical Trials

174

Convergence in Probability (Consequence) Let Xn

A99. (v)

x and Yn -5- y. Then

Xn + Y n £ x + y

A100.

(v i)X n - Y n ^ x - y

A101.

(vii)

Xn Y n £ xy

A102.

(viii)

Xn /Y n

(v)

T he event th a t |Xn + Y n —x —y |< e contains the event th a t both |Xn —x | < | and

x /y

if y ^ O

Proofs:

|Yn - y | < | .

P [ |X „ - x |< § , |Yn —y | < | ] = p[|Xn - x | < £ ] - P [|X n - x | < | , | Y „ - y | > | ]

P[|Xn - x | < | ] - P[|Yn - y | > j

> i.e.,

p [ |x n+ Y n - x - y | < f] ^ l

(vi)

p By (i), —Y n —►—y. Apply (v) to get desired result.

(vii)

Xn Yn - x y = Xn (Yn - y ) + (Xn - x ) y Now by (ii),

X n (Yn - y ) £ 0

and by (i),

(Xn - x ) y — 0

Hence, by (v)

Xn Yn —xy

0

-

1 - 0 = 1 as n - o o .

175 ... (viii)

A103.

Proof:

.. By (iii)

1 P 1 ^ ----- ►y- Results hold by (vii) above. Yn J

Convergence in Probability (Consequence) if

An 4s £

i

d„

1

w ith

An , B jj , C q ) Dn ^ 0

Bn

Let e > 0 , 6 > 0 . T hen there exists N ^ > 0 and N 2 > 0 ,

„ > Ni => p[ J-< < ( h S) < i +«] > i - 1

n > N 2 => p [ l - c

< ( g j ) < 1+e] > 1 -

n > m a x (N 1, N2) =!> P [ B n ( l - e ) < A n < Bn ( l + e f ] > 1 - | P [D n( l - t ) < Cn < Dn( l + « ) ] > 1 - |

T he event

‘- < £ r § < 1 + ' includes the intersection of the events B n (l —e) < An < Bn (l+ e ) with

Dn ( l —e) < Cn < Dn ( l+ e )

P[ ‘ - ‘ •=

and hence

< 1+‘] > * - '•

Since c and 6 are arb itrary , the desired result holds. A104.

Convergence in D istribution (Consequence) Slutzky’s Theorem Let X p X2, ... be a sequence of random variables with cum ulative distributions

176

CRC Handbook o f Sample Size Guidelines fo r Clinical Trials F j, F2,

with Xn S F.

. . P Let Y n be a sequence of random variables with Yn —►0. T hen if Zn = Xn + Yn , and if we denote the cum ulative distribution of Zn by Gn , then Zn ° F

(G n S F)

Note: We shall prove the result under the m ild restriction th a t F(x) has “isolated discontinuities.” T h at is, a t each point Xq such th a t F has a ju m p a t Xq, there exists an h > 0 such th a t F is continuous in the intervals (xq —h, Xq) and (xq, Xg+h). Continuous distributions and discrete distributions over the integers have this property. [A discrete distribution over the rational num bers is pathological, and does not have this property.]

Proof:

Let x be a continuity point of F and let An be the event th a t Xn < x —6 Bn be the event th a t Y n < S Cn be the event th a t Xn + Y n < x. Since Cn contains the intersection of An and Bn G „(x ) = P (C „ ) > P (A „B „ ) > P(A n ) - P (A n Bn ) > P (A n ) - P (B 0 ) G n W > F „ ( x - < ) - P (Y „ > 6) Sim ilarly, if

( 1)

A j is the event th a t Xn > x + i B^ is the event th a t Yn > —S C j is the event th a t Xn + Yn > x

Cj5 contains the intersection of A j and B j and hence

l - G n ( x ) > l - F n ( x + i) - P (Y „ < - S ) i.e.,

G „(x ) < F n (x+ «) + P (Y „ < - S )

(2)

177 Com bining (1) and (2) we have F n (x-tf) - P(Y n > £ ) < G n (x) < F n (x+ «) + P (Y n < - « ) .

(3)

Since discontinuities are isolated, we can restrict our a tten tio n to 6 < h, where F is continuous in the interval (x —h, x + h ). In (3), as n —>ooF n (x + 6 ) —►F (x + 6 ) F „ (x -« ) -

F (x -« )

by convergence in distribution. Also,

P (Y n >(5) and P (Y n < - 6 ) - > 0

since

p Y n —►0.

Hence:

n 1- ^ o o { F n (X''5) ' P (Yn > * ) } =

and

F (x - 0

n *-i?oo{F n (x + i ^ + P ^Yn -

= F (x + i )‘

Let e > 0 be arbitrary. T hen there exists N j = N ^(c, 6 ) and N 2 = N 2 (e, 6 ) such th a t whenever n > N ^ G n W > F„(x-«) - P (Y „ > « ) > F(x-«) - £ and whenever n > N 2 G n (x) < F n (x + 6 ) + P (Y n < - 6 ) < F (x + 6 ) + c. T h a t is, whenever n > M ax(N j, N2) F ( x - S ) - e < G n (x) < F (x+ 6) + c. Finally, from the continuity of F a t x, there exists

6

q such th a t

whenever

|F (x) - F(y)| < * |x - y | < «0 From (4), we have whenever

F(x) - 2 c < G n (x) < F(x) + 2c. Since c is arb itrary , we conclude th a t G n (x) T his com pletes the proof.

F(x)

as n

oo.

(4)

178CRC Handbook o f Sample Size Guidelines fo r Clinical Trials A105.

Slutzky’s Theorem for Products (Consequence) Let Xn S

f

and Yn £

1

then Zn = Xn Y n B F Note: We shall prove the result under the sam e isolated discontinuity assum ption as the previous result. Proof:

It is clear th a t X nY n = Xn + Xn (Yn - l) If we can show Xn (Y „ -l) £

0

the desired result is im m ediate from the previous result. 6 and c.

Suppose we are challenged with two sm all num ber,

F irst, since F is a proper distribution we can find a real num ber B such th a t both B and -B are continuity points of F and F(B) - F(-B) > 1-6 Let An be the event th a t - B < X n < B and Bn be the event th a t |Yn - l | < e/B . T he event th a t |Xn (Yn- l ) |< e contains the intersection of An and Bn . P (A n B „) = P(A n ) - P (A n Bn ) > P (A n ) - P (B „ ) > Fn(B ) - F n (-B) - P (B n ) — F(B) - F(-B)

as n — > 0 0

> 1- 6 . i.e., since we can m ake 6 as close to zero as we wish, and since |Xn (Yn - l ) |< f whenever An Bn holds, |X „(Y n - l ) | -

0

.

T his com pletes the proof.

A106.

C entral L im it Theorem for Independent, Identically D istributed Random Variables

179 Let X |, X2,

Xn • • be independent, identically distributed random variables with o

mean /i, variance a , and moment generating function M ^(t).

1 Then Zn =

£

N(0,1) where X n = (X 1 + ^ +

and N(0)1) ;s the

standard normal distribution.

Proof.

It is seen from A56 and A40 that Zn has moment generating function

MznW = [Mx ( 4 s ) ] Dexp[; i ^ ] -

We need to show (See A94 and A85) that

Mz (0) —►e

e2 /2

in a neighborhood of 0 — 0.

That is, we must show Kn (0) = log M^n (0)

^

Kn (tf) = n log

m a neighborhood of 0 = 0.

^

(0)

(1)

By Taylor’s Theorem, there exists 6*: |0 * |< |0 |

Kn W - Kn (0) + 9K{,(0) + ^ K " (0 ) +

From (1), and the fact that Mx (0) = E^e^^n j = 1, we see that Kn (0) = 0

(2)

180

CRC Handbook o f Sample Size Guidelines fo r Clinical Trials 1

M " {0 /(a < H )} to l

(4)

t\



Mx { 0 /(* V “ ) } 1

1

s

|

1

M$['{0/(>0.

Proof. Let Kn (0) = log E (e*Zn) the log of the moment generating function of Zn . It is readily seen by independence that

bjO/Vn Kn W = E (lo g

j=H

(1-Pj) + Pje

To prove normality, we need to show that



l\

■ vn |

183 K n (0) —►^*2

35 n —►oo

in a neighborhood of 0 = 0. By Taylor’s Theorem, there exists a $* such that |0*| < \$\ with

Kn (0) - Kn (0) + 0K{,(O) + ^ K " (0 ) +



b?pj ( l - p )

K X (0) = E J o 1= 1 Vn

*

1

...

n

(2)

-b j5 / V n

J --------- ^ b J T v -----------•

(4)

fb -0/V n ^ _

{ (i-P j ) . >

+ P |} 2

, 9 - 2 M /V n b- p-(l-p-) e

-b .0 /V n n

b?p.(l-p.)e

K n"(0) = 2 E -J-J-- ------------ Z --- U -- trTv----- ' j =1 v 3/m - u jJ ; n{(l-Pj)e

13 +Pj}3

Clearly, Kn (0) = 0 ^Substitute 0 — 0 in (1) By substituting 0 = 0 in (3), we see that

-y /V n (1 - Pj) e

0 + Pj

= (1 - p j)e =

Hence

1.

K^fO) = 0. Similarly, from (4),

n

Kn ( 0) = E

j= l

n b?p-(l - p.) y2 J J -2- J- = ^ 8 = 1 -

V2

V2

„3fn

J=1 „ j Y J /V n + _ Pj}\22 J V n {(l-Pj)e

+ Pj

CRC Handbook o f Sample Size Guidelines fo r Clinical Trials

184

To prove Condition 1, consider in (5)

_____ - Zp

~ 1 - /3 under H ^,

with S, a function of the parameters of the distribution under H^ satisfying the implicit sample size equation: (1). [KEY EQUATION]

(Z Q and Z p are generally the upper (100a)% and (100/?)% points of the standard normal distribution,

but this derivation holds in general.) Then

That is, if S is given as per the (1) [key equation], then the rejection region 9 > 0q -f- Za SE

has approximate Type I Error a and Power 1 - (3.

198

CRC Handbook o f Sample Size Guidelines fo r Clinical Trials

Proof: This is simply a straight forward substitution for S in (b):

~ e. *

(z * + z , ) ( s e - s)

“I

r s E 1 --------------k ----------- > - 2 p \

(under h a )

0 - 0 , + (Za + Z^)S = P

- - V SE------- P

a + Z l3) > - Z l}

- 0, + ( 0 , - 0n) = PL

SE

-P

>

(Za 4- Z^)S — 0^ - 0 q

Z“

l g - 9o

(under H ^)

SE

That is, the Type I and Power requirements are approximately met when equation (1) holds.

Note: S is the asymptotic standard deviation of the statistic under H ^, and may contain nuisance parameters. [SE usually has the same form as S, except population values under

(from S) are

replaced by consistent estimators to obtain SE.]

A131

Extension to the two-sided test For the two-sided test, we can replace a by a /2 can utilize the equation

S =

iy * o i Za /2 + Z/J

This implies two calculations, one for each alternative

Ha : 0 =

= eQ + A

(A > 0)

and

HA : 6 =

- A

(A > 0)

199 The larger resulting sample size would be used.

A132

Example 1: Two Sample Independent Binomial with Equal Sample Sizes The following notation will be used: Treatment 1

Treatment 2

Failure Rate

Q

T

Sample Size

N

N

Failures in Sample

F

G

Q = F /N

T = G /N

Estimated Failure Rate 6= Q -T

Hq : 0 = 0 HA : 6 = ° l > 0 0 = Q -T

SE =

Q (l-Q ) , T (l-T ) N N

For large N, we know (i)

0- 0 SE

N(0,1)

0

under H .

Oi)

(Hi)

under H

e - ey - g g -1 -------

N(0,1)

under H* — A

The approximation (a) of A130 follows from (i), while from (ii), (iii) and Slutsky’s theorem (A104), we have the approximation (b) of A130.

200

CRC Handbook o f Sample Size Guidelines fo r Clinical Trials To obtain the sample size, we use

S =

9 l ' 0O

Squaring both sides yields

Q (l-Q )

T (l-T ) = (gj - gp )2 =

N

N

(Q-T )2 (Z 0 + Z ^ )2(Za + Z ^ )2

That is, each sample size must be

A133

N =

[Q(i-Q )+ T (l-T )](Z a + Z j9)2 (Q-T)2

The two-tailed version of this formula appears in Pocock 1983, page 125.

A134

Example 2: Let Q = .7 T = .5 in example 1, with a = .05 and (3 = .20 (80% power), then

N= H i +

+

M >2 =

71

( « h « « ..„ ,« )

(•2 )

How good are these approximations? The exact binomial probability that the left hand term in assumption (a) exceeds 1.645 is 5.2% under Hq (common Q = T = .7), while the exact binomial probability that the left hand term in assumption (b) exceeds -.84 is exactly 79.5% under H ^. These are very close to the asymptotic values of 5% and 80% respectively. For an exact approach to the two sample binomial problem see Suissa and Shuster (1985).

201 In the binomial example, we used a standard error valid under Hq and H ^. We did not pool the proportions in the calculation.

A135

Summary of Sufficient Conditions to Apply the Sample Size Methodology

(0 - 6}

(1)

SE

*S “ yn'Ptoticadly normal under Hq, 0 = 0q.

(0 - 0}

( 2)

(3)

^

(4)

SE

(5)

S

£

is asymptotically normal under H ^, 0 = 0 y

1

under HA -

is calculated from the data. is calculated from the parameters under H ^.

Note: This methodology will be employed to derive the sample size requirements for clinical trials, analyzed via censored survival analysis.

A136. THE POISSON PROCESS INTRODUCTION The Poisson Arrival Process is a logical model for patient accrual. The arrival rate (accrual rate), A, represents the expected number of patients to be accrued per unit time. The number of patients accrued in t units of time has a Poisson Distribution, with mean (At). Finally, conditional on the accrual of exactly n patients to time t, the n accrual times are uniformly distributed over the interval from 0 to t. This will be an appropriate model for the accrual process of many clinical trials. First, there is a time scale, denoted by t. The Poisson process is simply a count N(t) of the number of patient entries

202

CRC Handbook o f Sample Size Guidelines fo r Clinical Trials

up to time t. Let us assume that we have a very large population of K patients. Assume that for a small interval of time of length A t that the number of entries is binomial with sample size K and probability of incidence of disease AAt K ‘ That is, the expected number of entries is A A t, which is proportional to the length of A t.

A137

A is called the arrival rate or accrual rate We shall further assume that the number of entries in non-overlapping intervals are

independent events. This may seem artificial, but is generally a reasonable assumption. The number of patients who develop the disease and leave the population will be a negligible fraction of K. The net effect of other departures and arrivals will also generally be a negligible fraction of K.

PLAN OF DERIVATION OF PROPERTIES

A138

(1) Divide the time scale from 0 to t into M intervals 0, A t, 2A t, ..., M At = T

A139

M = T /A t.

(2) Prove that as K —►oo and A t —► O the probability that every interval has no more than one

arrival goes to one. Hence, we can consider (in the limit) that each interval will have either 0 or 1 arrival.

A140

(3) Prove that as K -+oo and A t-* 0 P[N (t) = x ] -> ( A t ) V A t/x!

that is, N(t) is Poisson with mean At.

x = 0, 1, ...

203 A l 41

(4) Prove that the waiting time between arrivals is exponential with parameter A.

A142

(5) Suppose we have a Poisson Process (with arrival rate A) where arrivals are assigned by

independent flips of a fair coin to treatment 1 and treatment 2. Then the two processes N^(t), the number of patients assigned to Treatment 1 by time t and N 2 (t), the number of patients assigned to Treatment 2 by time t are independent Poisson Processes with common arrival rates A /2.

A143

( 6) In a Poisson process, given that r entries occur by time t, the entry times are uniformly

distributed over the time interval from zero to t.

Proofs: Prior to proving the results, two lemmas will be derived for later use.

A 144

Lemma A:

v2 Let 0 < |y| < 1. Then there exists z : |z| < |y| and lo g (l+ y ) = y ------- ----- ~ 2 (l-fz)

Proof:

This is simply Taylor’s Theorem applied to the second derivative

f(y) = lo g (H y )

f( 0) = 0

f'(y) = rjy

f'(o) = 1

f"(y) = ~~~2 (i+y) Taylor’s theorem states that there exists a z : |z| < |y| with f(y) = f(0) + yf'(O) + ^ f " ( z )

204 A145

CRC Handbook of Sample Size Guidelines for Clinical Trials Lemma B: A Let A n —>00 and B n —>oo with ^

Proof:

►1 as n —►oo

Since Bn —>-oo, there exists N such that whenever n > N , |x /B n |
N so that logs are defined, and x /B n is bounded away from -1. Let Y n = logW n = An log(l +

*>n

From Lemma A (A144), there exists zn : |zn | < |x /B n |

Y

- ^

-

°

—►x

Anx 2 2B 2 ( l + z n)2

since An/ B n —»1

We show that second term of (*) goes to zero. Recall that Bn —>oo and An /B n —>1. Hence

which implies

2 B i ( l+ z n)2

That is, Y n = log(W n) That is

W n = eY" — ex .

x.

205 We now return to the major derivation of results.

Proofs: (Main results) First, we shall prove (2), that in the limit, multiple entries in any interval become impossible. For a given interval, the probability of zero or one entry is obtained from the binomial distribution as

K

K A A ti K 1

K -l

By independence, the probability of 0 or 1 entry in all M intervals is

Now A t = T /M and hence

We apply Lemma B to each term

ATNMCK-1) _ V " KM/

-AT e

(See A136)

206

CRC Handbook o f Sample Size Guidelines fo r Clinical Trials Since M (K-l) and M K—*oo with

—►1.

Also f ,1+ , ( (KJ-l)A T llM _ eAT S^ KM j {

since M —>-oo, M h>oo with — (K -l) KM

1>1.

That is, CM —►e ~ ^ e ^ = 1. Thus (2) holds. In the limit, we can ignore the possibility of multiple arrivals. This will help prove (3). The probability of zero and one arrivals respectively in a single interval are

PQ = ( l -

^ ) K and P x = A A t(l -

K' l .

The probability of r arrivals to time t is simply binomial

D r= ( y y y - ' p ]

K(M-r)

(K -l)t

‘ ( “ X 1 - 4# 1) . M K-r,

= n > - m

m

T r+ 1 is -AT g (T j, . . . , T r+ 1) = Ar+1e r+1

0 < T j < T 2 < ••• < T r+ 1 .

Let U be the event that exactly r arrivals have occurred by time t. The conditional density of (T j, ..., T r) given U is

T |m

g(

/t° ° 8( T i . - , T r + 1 )dT r+1

•••' rl ) -------------- p (U)------------'

Once the T j, ..., T r with T r < t are fixed, U occurs only i f T r + i > t.

210

CRC Handbook o f Sample Size Guidelines fo r Clinical Trials P(U) = P(Exactly r arrivals to time t)

_ (At) e----

/ t° ° g (T P

(Poisson Process).

T r + 1 )dT r+1 = A t + 1 J ™ ' ' A T ' + 1 d T t + l

= Are'At

Hence, the conditional density of T^,

g (T j,

T r given U is

T r|U) = r!tr

0 < T j < ••• < T r < t

That is, the ordered arrival times are uniformly distributed from zero to t. (This conditional density does not depend on the values of the T ’s provided they are ordered as above.) This completes the discussion of the Poisson Process.

REFERENCES 1. Fraser, D. A. S., P robability and Statistics: Theory and Applications, Duxbury Press, Boston, 1976. 2. Hogg, R. V. and Craig, A. T., Introduction to Mathematical Statistics, Macmillan, New York, 1978.

3. Mendenhall, W., Scheaffer, R. L., and Wackerly, D. D., M athematical Statistics with A ppli­ cations, Duxbury Press, Boston, 1986.

4. Mood, A. M., Gray bill, F. A., and Boes, D. C., Introduction to the Theory o f Statistics, McGrawHill, New York, 1974. 5. Suissa, S. and Shuster, J. J., Exact unconditional sample sizes for the 2 x 2 binomial trial, J. R. Statist.

Soc .. Ser. A, 148, 315, 1985.

211

APPENDIX II

TABLE OF CONTENTS

TABLE 1: ALPHA = 0.005 and POWER = 0.80............................................................ 213 TABLE 2: ALPHA = 0.005 and POWER = 0.90............................................................ 293 TABLE 3: ALPHA = 0.01 and POWER = 0.80 ............................................................ 373 TABLE 4: ALPHA = 0.01 and POWER = 0.90............................................................ 453 TABLE 5: ALPHA = 0.025 and POWER = 0.80 ............................................................ 533 TABLE 6: ALPHA = 0.025 and POWER = 0.90............................................................ 613 TABLE 7: ALPHA = 0.05 and POWER = 0.80.............................................................693 TABLE 8: ALPHA = 0.05 and POWER = 0.90............................................................. 773

213

TABLE 1: ALPHA= 0.005 POWER= 0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 30

DEL=.10

DEL=.15 1 .0 .75

.50 .25

.00 BIN

***

245 245

2 tt 248

”"265 409

142 143

0 .1

***

"386

388 393

444 584

“ ■204'

387

205

o to

0 .1 5

498 499

502

S09

----- 250

254

508

736

251

261

580“

5ff5

755

581

595

865

282 283

287 298

631 634

639 653

"879 970

300 303

*•*

656 659

666 685

980 1052

307 311

***' *#*

656 661

669 ” 1053“ 694

1110

**♦ ***

636 641

652 1 1 0 T 684

*♦* ***

59'fi 60 5

***

54"fi 557

"«* ' ***

489 500

*** •••

*** ***

0 .2 5 "'* * * '

***

0 .3 0 .3 5 0 .4 0 .4 5 0 .5 0 .5 5 0 .6 0 .6 5 0 .7 0 .7 5 0 .8 0 .8 5

***

" « * ' 425 *** 439 *** *** «* *** '« * *** '« * *** *** ***

.00 BIN

1 .0 .75

DEL=.25

DE1=.30

.50 .25

.00 BIN

1 .0 75

.50 .2 5

.0 0 BIN

1 .0 .7 5

.50 .25

.00 BIN

REQUIRED NUMBER OF PATIENTS

PCONT=*** 0 .0 5

.50 .25

1 .0 .75

FACT=

DEL=.20

155 216

lo o 101

ld l 103

109 138

78 78

79 81

84 97

64 65

65 66

69 72

206

236 289

134 135

136 140

T55

211

176

99 100

101 104

113 119

78 79

80 83

89 86

307

158 159

162 168

193 208

113 114

117 122

137 138

87

351

88

90 95

105 98

368 403

173 175

179 188

226 234

122 124

127 134

157 153

92 94

97 103

117 107

308 322

419 444

182 185

190 202

252 255

126 129

133 142

172 164

95 97

101 108

127 113

318 336

459 475

T84”

195

272

188

209

269

127 130

136 147

183 171

95 98

102 111

133 117

305

318

309

341

488 496

182 186

194 212

2SS 278

135 149

189 175

93 97

102 111

136 119

294 300

311 338

506

175

507

181

211

281

125

133 147

192 175

90 94

100 110

136 117

276 284

512 507

166 172

183 206

292 278

T14119

128 143

190

329

171

85 89

96 107

134 113

280 315

506 496

T54

174"

161

198

286 269

107 112

121 137

184 164

80 84

91 102

126 107

522 ~ 1107"

-231 ' 259

490

141

162

274

579

241

297

475

149

187

255

104

113 129

174 153

73 78

84 95

120 98

236 276

462 444

127 136

149“ 173

2$5 234

89 95

104“ 119

160 138

66 71

77 87

109 86

212 251

ll3 121

134“

403

157

230 208

79 85

93 107

142 119

59 63

68 77

95 72

80 92

120 97

1145

619

1134""

659

1157

574

"I134-

623

1145

— 235" 264

1110

466 —1057“ 530 1052

' “ 205' 217

144 146

297

129

'

T20

36'2

409

"983

180

379

478

970

192

'302

354

186

372

223

351

117“ 138

68

167

98 106

198

424

'8 8 2 865

155

321

176

73

248

300

'7 5 7

130 " 159

267

366

736

311 289

62 89

99 116

161 138

-1 9 8

m

217

305

ICTT 166

235

" 607 584

190 409

'

142

'

192

423

i'90~ 292

" " n r-

'105

129

239

115

155

216

CRC Handbook of Sample Size Guidelines for Clinical Trials

214

TABLE 1: ALPHA= 0.005 POWER= 0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 40

DEL=.10 FACT=

DEL=.15

1 .0 .75

.5 0 .25

.00 BIN

PCONT=***

1 .0 .75

.50 .25

DEL=.20 .0 0 BIN

1 .0 .75

DEL=.2 5

.50 .25

.0 0 BIN

1 .0 75

.50 .2 5

DEL=.30 .00 BIN

1 .0 .7 5

.50 .25

.00 BIN

REQUIRED NUMBER OF PATIENTS

0 .0 5

*♦* ***

245 246

247 249

265 409

143 143

144 147

155 216

101 101

102 104

109 138

78 79

80 81

84 97

45 65

66 67

40 72

0 .1

**•

387 388

390 395

444 584

205 206

208 213

236 289

135 136

138 142

155 176

100 101

102 106

113 119

79 80

81 84

80 86

0 .1 5

••• ***

490 501

504 513

400 736

251 253

2 56 265

307 351

159 161

164 171

193 208

114 116

119 124

137 138

88 90

92 96

105 08

0 .2

••• **•

" 5OT 584

588 —755” " 601 865

283 286

291 304

368 403

175 178

163 193

226 234

124 126

13o 137

157 153

04 96

100 105

117 107

0 .2 5

•* •

434 637

643 662

679 970

303 306

313 330

419 444

185 188

194 207

252 255

120 132

137 146

172 164

07 100

104 111

127 113

0 .3

••• • **

459 664

472 697

080 1052

311 316

324 346

459 475

186 192

200 217

272 269

130 134

140 152

183 171

96 101

106 114

133 117

0 .3 5

•** ***

661 666

477 710

1056 1110

309 315

326 353

488 496

ray 192

201 221

285 278

129 133

141 154

189 175

97 100

106 115

136 110

0 .4

••• ♦ **

641 649

663 704

1108 1145

300 307

32l 353

506 507

181 187

106 220

292 281

125 130

139 153

m 175

94 98

104 114

136 117

0 .4 5

••• ***

405 615

633 683

1134 1157

284 293

309 345

512 507

172 180

102 216

292 278

119 125

134 150

190 171

69 94

lb o 111

134 113

0 .5

**• ***

557 569

591 651

1134 1145

244 275

293 333

5o4 496

161 170

183 208

286 269

112 119

128 144

164 164

84 89

95 106

128 107

•**

500 515

542 611

1109 1110

241 253

274 315

370 ' 475

149 158

172 197

274 255

104 111

120 136

174 153

78 82

60 00

120 08

***

439 457

490 564

1059 1052

217 230

252 294

462 444

134 145

159 183

255" 234

05 101

110 125

160 138

71 75

81 00

100 86

••• ***

379 399

435 513

983 970

192 206

226 269

423 403

121 130

143 166

230 208

85 91

99 112

142 119

43 67

72 80

95 72

*#•

~ T Z I' 344

36i 457

882 865

147 181

20l 240

372 351

lb 6 114

126 146

198 176

73 78

34 97

120 97

0 .7 5

*** *♦*

267 290

324 398

757 ' 736

132 154

173 206

311 289

89 96

ld 6 123

161 138

0 .6

***

217 237

269 332

607 584

' "1 1 5 125

140 166

239 216

*»*

144 183

2b8 256

432 409

0 .5 5 0 .6 0 .6 5 0 .7

0 .8 5

"

215

TABLE 1: ALPHA= 0.005 POWER* 0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 50

DEL*.10 FACT=

DEL=.15

1 .0 .75

.50 .25

.0 0 BIN

PCONT=***

1 .0 .75

.50 .25

DEL=.20 .00 BIN

1 .0 .75

DE1=.25

DEL*.30

.50 .25

.00 BIN

1 .0 75

.50 .25

.00 BIN

1 .0 .75

.50 .25

.00 BIN

REQUIRED NUMBER OF PATIENTS

O.05

*** ***

244 244

247 250

245 409

143 144

145 147

155 216

101 102

103 105

109 138

79 79

80 82

84' 97

45 65

66 67

69 72

0 .1

*** ***

386 389

391 398

444 584

205 207

209 215

234 289

136 137

139 144

155 176

100 102

103 107

IT 3 119

80 81

82 85

89 86

0 .1 5

••• ***

500 502

506 517

609 736

252 255

259 268

307 351

160 163

166 173

193 208

" IT S 1 117

120 126

137 138

90 91

94 97

10$ 98

0 .2

*** **•

583 586

591 608

755 865

28J> 288

294 309

368 403

177 180

186 196

226 234

12? 128

132 140

157 153

101 107

117 107

0 .2 5

•** ***

634 640

648 671

879 970

305 310

318 337

419 444

187 191

198 212

252 255

131 135

140 150

172 164

99 102

106 113

127 113

0 .3

••• ***

452 668

678 709

980 1052

314 320

331 355

459 475

191 197

205 222

272 269

133 137

144 156

183 171

100 104

109 117

133 117

0 .3 5

*** ** •

665 672

686 725

1056 1110

314 321

334 364

488 496

191 197

207 227

285 278

132 137

145 158

18$ 175

99 103

109 118

134 119

0 .4

••• ***

647 656

674 722

1108 1145

305 314

330 364

5d6 507

186 “ 205“ 193 227

292 281

129 135

143 158

192 175

97 101

107 117

136 117

***

612 624

705

li'3 4 1157

291 302

320 358

512 507

178 186

2dd 224

292 278

124 130

139 155

190 171

93 97

104 114

134 113

0 .5

•** **•

564 580

608 676

1134 1145

272 284

305 347

£o4 496

168 177

191 216

286 269

117 124

133 149

184 164

88 92

99 109

128 107

0 .5 5

••• *•*

5T1 529

542 637

1109 1110

250 264

286 330

490 475

156 166

180 205

274 255

109 116

125 140

174 153

81 84

92 102

120 98

075"

**T ***

453 ” '511 474 592

1059 1052

227 242

265 308

442 444

143 152

167 191

255 234

100' 106

1T5 130

160 138

74 78

84 93

109 86

• **

394 418

458 541

983 970

203 218

240 283

423 403

128 137

"T 5T 174

230 208

89 95

ld 3 116

142 119

66 69

75 82

95 72

0 .7

*** **♦

338 363

404 485

882 865

178 192

213 252

372 ■ 351

■ T 1 2 ' 133 121 153

198 176

77 82

89“ ' 120 100 97

0 .7 5

••• • **

283 309

348 423

"757 736

151 164

183 216

311 289

0 .8

••• *•*

232 255

289 353

607 584

123 133

149 174

239 216

0 .8 5

*•* ***

179 196

223 271

432 409

0 .4 5

0 .4 5

94 102

112 127

161 138

'

"'

~

■ 96 98

'

CRC Handbook of Sample Size Guidelines for Clinical Trials

216

TABLE 1: ALPHA= 0.005 POWER= 0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 60

D E L = .15

D EL=.10 FACT=

o':i 0 .1 5 072 0725 0 .3

**

24*"' 245 409 251

'143 144

148

146 ” 155 216

101 102

103 105

** **

366 390

397

206 208

211 217

136 138

140 145

** **

5ff2

508 "~"6'09' 521

736

254 256

261 ~ 33 7'

504

271

351

162 164

** **

" 585 588

595“ 614

865

287 291

298 313

368 403

** **

439 643

653 679

870 970

308 313

322 343

419 444

** **

644 ' 6ff5~~ 980 672 720 1052

318 324 318 326 311 321

1.0 .75

**

400

444 584

"

694

ITT"" ** **

"752 663

487" ' 1108 "

rr~45" ** **

719 633

075' ' **

•*

"574 591

** **

0 .4 0 .6 5 077' 0 .7 5 0 /8

o:s5

.50 .25

.00

BIN

1.0 .75

.50 .25

65 66

67 "“ 59 72 68

.00

BIN

739 739

1056 1110 1145

457 " 1134 ’ " 297

i r a ' 113 107 119

80 81

83 85

86

168 175

193 208

117 119

122

'1"37

127

138

91 92

05 98

105 98

179 183

188 199

226 234

127

134 142

157

130

153

97 100

103 108

117 107

190 194

202 216

252 255

133 137

142 152

172 164

101 104

108 115

127 113

334 ~ 459' 362 475

195 200

209 227

272 269

136 140

i"47 158

183 171

102 106

111 " 133 119 117

341

488

372

496

194 201

212 232

285 278

135 141

149 161

189 175

102 106

m 120

136 119

338 374

506 507

190 198

211 233

292 281

133 139

14? 161

192 175

100 104

110 119

136 117

329

512 507

183

206 230

292----278

128 134

158

190 171

96 100

107 116

134 113

579"

1109 "

542

661

1110

** •*

466 490

617

1052

** *•

409 435

566

970

-** **

“ JIT-

A7T~ 'TOT" "

187

223

381

508

201

**

**

TOO 326

34T ~ 7 5 7 " ' 444 736

159

**

246 269

305 370

'

983

'■ '

607

'

584

190 ■■23T" 432 409 284



369

236 289

"

192

89

280

315

506

—174

198

28'4

293

358

496

183

223

269

121 128

137 153

184 164

91 95

102 111

128 107

259 274

297 “ 49 0 ' 342 475

162 472

187 212

274 255

1 13 120

129 144

174 153

84 89

95 104

120 98

236 252

276 320

442 444

149 159

173 197

255 234

104 110

119 133

160 138

77 81

87 95

86

212

251" 294

423 403

134 143

107 119

142 119

77

208

93 99

68

179

72

84

351

126

138 157

198 176

80

262

86

9^ 102

120 97

102 225

311 289

106

116 131

161' 138

155

239 216

228

865

”■

101 102

'522

53TT" 1059

84 97

155 '

1134 1145

’'

81

176

497

208

309

107” “- -?9 -

82

627

«

1.0 75

80

1157

**

.00

BIN

138

724

**

1.0 .75

BIN

REQUIRED NUMBER OF PATIENTS

' 469 677

0 .5 5 '

.50 .25

246 247

.00

BIN

** **

07 "35

.00

.50 .25

PCONT=***

0.05

.50 .25

1.0 .75

D EL=.30

D E L = .25

D E L = .20

173 129 140

181

117

99

15T" 230

'

109

05 72

217

TABLE 1: ALPHA= 0.005 POWER= 0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 70

DEL=.10 FACT=

DEL=.15

DEL=.20

DEL=.25

D EI=.30

.50 .25

.0 0 BIN

1 .0 75

.50 .25

.0 0 BIN

1 .0 .75

.50 .25

.00 BIN

102 102

104 105

109 138

79 80

8l 82

84 97

66 66

67 68

69 72

137 139

T4T" 146

155 176

102 103

105 108

113 119

81 82

83 86

89 86

307 351

163 165

170 177

193 208

118 120

123 128

137 138

91 93

95' 99

105 98

301 317

368 403

181 185

190 201

226 234

128 131

136 143

157 153

98 101

104 109

117 107

311 316

326 348

419 444

192

205 219

252

103

255

135 139

145 ~ 172

197

154

164

106

HD 116

127 113

980 1052

321 329

341 369

459 475

198 204

213 230

272 269

138 143

150 161

183 171

104 108

ll3 120

133 117

702 752

1056 1110

322 332

348 380

488 496

198 205

211 237

285 278

138 144

152 164

189 175

104 ' 113“ 108 122

136 119

658 670

694 754

1108 1145

316 327

346 383

506 507

195 203

217T” 292

13'6

150

281

142

164

192 175

IU2~~ 112

238

106

121

136 117

••• ** •

626 642

672 742

1134

304 317

338 379

512 507

188 197

211 235

292 278

131 138

"147

1157

161

190 171

98 103

109 118

113

**♦ *•*

583 602

638 717

1134 1145

287 301

325 368

506 496

179 189

203 228

286 269

_ 125

l4 l 156

184 164

93 98

104

128

132

113

107

••• ***

532 555

595 682

1109 1110

267 282

307 352

490 475

167 177

192 217

274 255

117 123

133 147

174 153

87 91

97 106

120 98

••• • **

478 504

548 638

1059 1052

244

285 330

462 444

154

255 234

138

79 83

89

114

122 136

160

164

179 202

'107

261

97

109 86

0 .6 5

*** ** »

423 451

496 587

983 970

220 236

261 303

423 403

139 149

162 184

230 208

96 102

110 121

142 119

70 74

79 85

95 72

0 .7

••• «**

368 396

441 528

882 865

194 210

232 271

372 351

122 131

nr~ 161

198 176

83 88

95 104

120 97

0 .7 5

••• *•*

313 341

383 462

757

166 180

199 232

311 289

103 110

119“ ” 161

0.8

••• ***

258 283

319 385

607 584

155

161 186

239 216

0 .8 5

••• ***

199

T45295

432 409

1 .0 .75

.50 .25

.00 BIN

••• ***

246 “ 249 247 252

265 409

144 145

146 149

155 216

***

389 391

394 403

444 584

207 209

212 218

236 289

*** **♦

505

“ 511 525

609 736

255 258

263 274

***

586 590

598 620

755 865

289 293

*** “ 6 41 *** 646

657 687

879 970

*** ***

669 676

691 730

*** ***

673 683

*** ***

PCONT=*** 0. 05 0 .1 07T5 0.2

f f .1 5 0 .3 0 .3 5 0 .4 0 .4 5 0 .5 0 .5 5 0 .6

1 .0 .75

.50 .25

.00 BIN

1 .0 .75

REQUIRED NUMBER OF PATIENTS

218

736

146

134

138

154

CRC Handbook of Sample Size Guidelines for Clinical Trials

218

TABLE1: ALPHA* 0.005 POWER= 0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 80

DEL=.10 FACT=

DEL=.15

0.1

.0 0 BIN

1 .0 75

.5 0 .2 5

102 103

104 106

109 138

80 80

236 289

138 140

142 146

“ 155'' 176

265 276

307 351

164 167

T71 178

291 295

304 320

366 403

183 186

679 970

313 319

330 352

319" 444

740

960 1052

324 333

346 374

710 763

1056 1110

326 337

353 386

1 .0 .7 5

444

0 .3 5

***

0 .5 5 0 .6 0. 65

69 72

102 104

106 109

113 119

81 82

84 86

89 86

193 208

119 121

124 129

137 138

92 94

96 " '1 0 5 " 100 98

193 203

226 234

130 133

"137

'' I T T

100

144

153

102

105 110

117 107

194 199

207 221

252 255

137 141

146 155

172 164

104 107

111 117

127 113

459 475

200 207

217 233

272 269

140 145

152 163

183 171

106 109

114 121

133 117

466

201 209

221 240

285 278

141 146

154 166

169 175

106 110

115

496

123

136 119

198 207

220 242

292 281

139

153

145

167

192 175

104 108

114 123

136 117

190 171

100 105

ll'l

164

120

134 113

126

155 216

39o 392

395 405

444 584

208 210

213 220

504 507

513

609 736

256 259

566

601 625

755

593

865

1 643 650

662 695

672 681

69V

1 .0 .7 5

'677 689

529

'

'

***

677

704 768

1108 1145

321 333

353 390

506 507

444

633 651

683 758

1134 1157

309 323

345 387

507

202

216 239

292 278

134 141

506 496

183 193

208 232

286 269

144 158

184 164

95 100

106

135

115

107

172 182

197 221

274 255

120 127

136 149

174 153

89 93

99 107

120 98

159

255

11

C

169

183 206

234

117

125 138

160 138

81 85

90 98

109 86

72 75

60 86

“ 95" 72

557

444 ***

512

"

T 7 2

'

150'

57T

651

613

734

1134 1145

293 309

331 377

**»

542 568

611

274 290

315 “ 170"

700

1109 1110

361

475

444 444

4^0 518

564 657

1059 1052

252 269

294 339

462 444

4*'»

435 465

513 606

963 970

228 244

26? 311

423 403

143 153

166 187

230 208

99 105

123

177 119

381 411

437 546

682 865

201 217

240 278

372 351

126 135

146 164

198 176

86 90

97 106

120 97

173 186

206 238

311 289

106 113

123 136

161 138

140 151

166 190

239 216

' 4n

r '

4*4

0 .7

67 68

147 149

v n > '1 **•

***

0 .5

66 66

144 145

'

0 .4 0 .4 5

84 97

.00 BIN

REQUIRED NUMBER OF PATIENTS

4**

0 .3

81 82

265 409

*4 4

*?"*"

.0 0 BIN

249 253

444

0 .2 5

.50 .25

247 248

***

4T»'

1 .0 .75

.00 BIN

*44 0.2

.50 .25

DEL=.30 .0 0 BIN

.50 .25

44#

0 .1 5

DEL=.25

.50 .25

1 .0 .75

PCONT =* * * 0 .0 5

DEL=.20

444 444

0 .7 5

494

326 354

396 477

757 736

0 .8

*r*'' • 44

269 294

332 398

607 584

0 .8 5

4 J*

208 227

256 304

432 409

**4

"

'

126

i n

"



219

TABLE 1: ALPHA= 0.005 POWER= 0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 90

DELs. 10 FACT=

DEL=. 15

1.0 .75

.50 .25

.00 BIN

O.i 0 .1 5 0.2

0.25

.50 .25

.00 BIN

68

69 72

138 140

143 147

155 " ' 176

103 104

106 109

113

289

119

82 83

84 86

89 86

307 351

165 168

172 180

193 208

119 122

125

137 138

93 95

97 100

105 98

184 188

194 205

226 234

131 134

139 145

157

100

153

103

106 110

117 107

252 255

138 142

148

172 164

105 108

112 118

127 113

183 171

107 111

116 122

133 117

216

*** ***

390'

397

444

407

584

211

214 221

236

393

*** ***

50'5 508

515

609 736

" "257"

532

267 278

***

590“ ' '605 ”"755

261

' 795 '

306

368

865

298

323

403

643” ' 0 .6 5

.0 0

1 .0 .75

DEL=.1 0

BIN

266 266

266 790

141

141

141

141

141

321

454 1009

204 204

204 204

“ 204

141

141 "1 4 1

373

141

141

954

329

“ 329

1637

329

"329 329

1829 2590

579 579

2665 2665

2665 3423

3391 3391

3415 3454

21579 22665 24665 22040 23477 28614

4016 4b4b

112329 126148

24102 25579 28415 24727 26727 31813

88629 95204 124727 91204 102915 136266

BIN

.0 0

.50 .2 5

DEL=.15

1 .0 75

15516 15665

071

0 .3 5

.50 .25

.0 0

BIN

tt* ♦ ** ***

0 .7 0. 75

1

45'4" “ 757"

.50 .25

BIN

.0 0

102 102

102 102

102 191

204

521

204

204

275

579 579

579 744

290 290

290 290

290 368

766 766

766 766

938

756

391 391

391 391

391 447

3454 4137

954 954

954 954

954 1102

454 "1 5 4 454 454

477 513

4079 4102

4141 4732

H 02

lio 2

1102

1102

1102 1235

516 540

540 540

540 566

4516 4540

4602 4665

47d4 5208

1227 1227

1227 1227

1227 1340

579 ' 579 579

579

579 606

25891 27766 31454 26704 29227 34268

4891 4954

5016 5079

5165 5565

1329 1329

1329 1329

1352 1414

602 602

602 602

632

90540 98391 134040 93516 107641 143408

27016 29227 33704 27954 30977 35979

5165 5227

5329 5391

5477 5803

1391 1391

1391 1 7 1 5 1391 1459

64l 641

641 641

641 645

90016 99266 140204 93579 109852 147574

27516 30040 35165 28602 32040 36946

5329

5477 5579

5665 5922

"1415 1415

i7rr1 7 5 4

641—" 641

5391

1415

1474

641

641

641 645

98141 1 7 3 1 4 1 '“ 27754 30204 35829 91727 109891 148765 28641 32391 37169

5540 5641

5727 5922

1415

5454

1415

1415 1415

1454 1459

641 641

641

641 632

5665

602 602

602 602

602 606

579 579

579 579

579 566

9540

5352

—5296” 5454

5803

1391 1391

1391 1391

1415

5579

5102"

5266 5391

5477 5565

1329 1329

1329 1329

1352

4977 5079

5165 5208

1227 1227

1221 1227

1235

540 540

540 540

540 513

7576

4727 4732

1102 1102

1102 1102

ll 0 2 1102

A ll

477

A ll 477

477 447

954 954

954 954

954 938

39l 391

391 391

391 368

290 290

290

290 275

26891 “29790 35665 28165 32079 36648

78977 91141 139290 83790 104040 142218

25891 28829 34704 27165 31141 35384

5165

73204 85602 78204 98477

132516 134480

24454 27329 32915 25727 29540 33375

4891

66727 78915 71665 91204

122540 123767

22602 25290 30352 23790 27329 30622

4391 4477

59602 71016 64266 82227

109391 110078

20329 22704 26977 21352 24454 27126

£1665 61766 55829 71391

93079 93413

42727 5b915 46165 58391

4790

4641

~'3S7I” 4016

1414 1340

1266

4141 4137

17540 19516 22829 18415 20891 22885

3266 3290

3329 3391

3423

766 766

766 766

766 744

73641 73773

14227 15665 17891 14891 16641 17900

2477 2516

2540

2602 2590

540 540

540

2579

540 521

32227 37852 34602 42641

51141 51156

1022 T 11040 12204

1602 1641

1641 1641

1665 1637

0 .9 5

18766 21227 19852 23016

25579 25563

5204 5329

0 .9 8

'7641 7891

8790 8779

(3.85

**•

• **

8141 8454

10602 11540 12172

5454 " 5727 5579

5699

64l

602

5352

83852 95352 142829 88391 107891 146979

4079

b.8

213

204 " 204T

3954

b.9

1 .0 .7 5

REQUIRED NUMBER OF PATIENTS

0 .0 1

0 .3

1 .0 .7 5

.50 .25

PCONT

0 .2

DEL=.05

1 .0 .7 5

3454

540

290

373

TABLE 3: ALPHA= 0.01 P0WER=0.8 EXPECTED ACCRUAL THRU MINIMUM F0LL0W-UP=3Q

DEL=.1 0 FACT=

DEL=.15

1 .0 .75

.50 .25

.00 BIN

*•*

2 ll 211

212 214

228 352

123 123

124 126

133 186

*** **•

“332 333

334 339

382 502

176 176

178 182

203 248

*** **•

429 430

432 439

523 633

215 217

219 226

•••

"499 500

504 514

649 743

243 245

• •• ” 544 "" 551 *** 546 565

755 833

••• T r e *** 568

"57'5“ 594

••• ***

566 570

PCONT=*** 0 .0 5

0.1

DE1=.20

•••

1 .0 .75

.50 .25

.00 BIN

1 .0 .75

DEL=.25

DEL=.30 .00 BIN

1 .0 .75

.50 .25

.00 BIN

68 70

72 83

55 56

56 57

60 62

.50 .25

.00 BIN

1 .0 75

.50 .2 5

88 89

44 118

67 68

85

REQUIRED NUMBER OF PATIENTS 86 87

” 115 ' 118

77

116

121

133 151

86

87 90

98 102

68 68

7d 72

74

264 302

136 138

140 146

166 179

98 99

101 106

I i"5 119

75 77

74 82

90 84

248 258

317 346

150 152

156 164

194 201

105 107

110 117

135 131

80 82

85 89

101 92

259 262

267 280

360 382

158 160

165 176

217 219

109

1T5

ITS

112

124

141

83 85

88 94

109 98

342 904

266 269

275 293

395 409

160 164

170 183

237" 231

111 114

119 129

15 7 " 147

83 86

90 97

114 101

579 603

908 954

264 268

"777

42(3 426

' 1'58

299

llO 186

245 239

109 113

119 130

163 151

82 85

89 98

111 102

• • • ' 549 *** 554

565 597

952 984

255 261

271 297

435 435

167 185

251 241

105 110

117 129

165 151

W

158

82

88 96

117 101

•••

538 " 974 577 994

241 248

261 290

446 435

145 151

161 181

251" 239

lOo

fT3

105

126

163 147

79

84 94

98

501 548

975 984

223 231

246 279

435 426

136 143

TO 175

246 231

94 99

107 121

141

71 74

80 89

110 92

0. 5T~ *** “ 425 ' 437 **• 436 512

953 954

203 212

229 264

42l 409

T 25

147

132

165

235 219

65 69

75 84

103 84

0 .6

0.15 0 .2 0 .2 5 0 .3 0 .3 5 0 .4 0 .4 5

• **

5I"7 524

0 .5

*** **•

475 484

163

153

''8 7 "" 100

158 150'"

114

131

74 84

92 105

119

59' 63

68 76

94 74

52 56

60 68

82 62

371 385

411 471

910 904

'" l'fll 192

2 l0 245

397 382

113 121

153

219 201

••• ***

"318

353 426

845 833

160 171

189 224

353 346

lOl

71

108

119 139

197

334

179

75

83 94

122 102

••• ***

266 286

316 379

758

139 150

157

743

199

320 302

95

105 122

17l 151

61 65

72 81

103 83

••• »**

222 240

259 329

650 633

117 127

143 171

26*7 248

14 80

0 .3

•** ***

178 195

222 274

521 502

95 103

116 139

205 186

0 .8 5

*** ***

136 150

171 ' 372

0 .5 5 0 .7 0 .7 5

211

352

sb

132

88

138

103

118

113

92

***

•••

73

138”

CRC Handbook of Sample Size Guidelines for Clinical Trials

374

TABLE 3: ALPHA= 0.01 P0WER= 0.8 EXPECTED ACCRUAL THRU MINIMUM F0LL0W-UP= 40

DEL=.10 FACT=

DEL=.20

DEL*.15

1 .0 .7 5

.5 0 .2 5

.0 0 BIN

211 211

212 215

228 352

123 123

124 127

133 186

0 .1

333 334

336 341

382 502

176 177

180 184

203

0 .1 5

430 431

434 443

523 633

217 218

222 230

0.2

501 503

507

245 247

252 264

317

521

649 743

346

546 549

556 574

755 833

262 265

272 288

568 573

581 606

"T42

M

904

269 274

570 576

587 619

908 954

***

554 562

576 616

***

524 533

PCONT =*** 0. 05

1 .0 .75

.50 .25

.0 0 BIN

1 .0 .7 5

.5 0 .25

.0 0 BIN

87 87

88 90

94 118

68

116

133 151

86 ' 89

248

117

264

138

I“42"'' 166

139

148

154

159 168

360 382

160 164

169 181

217 219

164

175

303

395 409

168

189

234 231

268 274

285 310

420 426

163

176

2'4'5 "

168

193

952 984

261 268

2ar 310

435 435

552 600

974 994

248 257

272 304

440 435

464 495

518 574

975 984

231 242

259 294

0. 55

434 450

477 540

953 954

212 224

0.6

385 402

433 501

9l0 904

192 205

334 354

387 457

845 833

286 307

T4D 409

758 743

240 260

293 356

195 214

243

150 165

0 .3 0 .3 5 0 .4 0 .4 5 0. 5

H*

0. 65 0.7 0. 75

***

0 \8 0 .8 5

***

1 .0 75

.50 .2 5

.0 0 BIN

1 .0 .7 5

.50 .25

68

69

73

■'56

”57

70

83

56

58

62

98 "

68

70

” 77

69

73

74

77 '

80" ' 90 83 84

.00 BIN

REQUIRED NUMBER OF PATIENTS

119 123

0. 25

DEL= .3 0

DEL=.2 5

87

91

'97 '

103

179

100

108

119

194 201

— 107

113

'1 3 5

109

119

112 115

119 128

114 117

123 133

113 117

T24

239

135

151

158 " T 7 4 164 193

251 241

110 115

122 134

"T S 5 " 151

l5 l 158

169 190

251 239

105 111

118 132

163 147

435 426

143 150

162 184

246 231

99 105

113 127

243 280

421 409

132 140

152 174

235 219

92 98

224 261

397 382

121 129

' 141

219 201

171

203"

184

239

363 346

108 116

147

" '1 5 0 ' 162

180 213

320 302

95 102

650 633

127 138

'154 183

267 248

80 86

521 502

103 112

125

297

205 186

188 229

372 352

148

302

" " T52~

102

"T18"

78

'60

” 82 '

87

"TEX

131

84

91

92

148 141

'85'" 87

97

98

157 147

86 88

93

114 101

163

85 88

93 101

“ TT7—

82

"TT7

86

91 100

79 83

88 97

115 98

158 141

74 " 78

8? 93

'1 1 0 92

106 119

150 131

69 73

78 87

103 84

84 90

98 110

138 119

63 67

72 79

94 74

197 179

75 81

88 99

122 102

56 59

63 70

82 62

112 129

171 151

65 70

'7 6

94 108

l3 8 118

162

128

'

85

103 83



91

100

'

"1137 ' "

102 101

'

375

TABLE 3: ALPHA= 0.01 POWER= 0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP=5Q

DEL=.10 FACT=

DEL=.15

1 .0 .75

.50 .25

.0 0 BIN

1 .0 .75

.50 .25

DEL=.20 .00 BIN

1 .0 .75

DEL=.2 5

DEL= .3 0

.50 .25

.0 0 BIN

1 .0 75

.50 .2 5

.0 0 BIN

1 .0 .7 5

.50 .25

.00 BIN

REQUIRED NUMBER OF PATIENTS

PCONT=*** 0 .0 $

•••

211 212

213 216

228 352

123 124

125 127

133 186

87 88

89 90

94 118

68 68

69 70

73 83

56 57

57 58

60 62

0 .1

*** ' •**

334 335

337 344

382 502

177 179

181 186

203 248

117 118

120 124

133 151

87 88

90 92

98 102

69 70

71 73

74

' 78"

T1

79

84

90 84

***

431

437

433

448

523' 633

218 220

224 233

264 302

139 141

144 151

166 179

100 102

104 109

118 119

•**

502 505

511 527

"549 743

247 250

255 268

317 " 346

154 157

161 171

194 201

109 111

115 121

135 131

83 85

88 93

101 92

• ••

546 552

560 583

755 833

264 269

276 294

360 382

163 167

173 185

217 219

n r - " 122

08

117

130

141

87 89

93 98

109 98

*** *»*

572 577

588

842 904

273 278

288 310

395 409

167 172

179 194

234 231

116 120

126 136

T57 147

88 91

45 102

"114

617

908 954

273 280

292 319

420 426

167 172

182 199

243

127 138

1*3 151

87 91

93

239

116 121

103

117 102

435 435

163 170

180 200

251 241

119

138

151

85 89

94 102

117 101

25l 239

109

123 136

163 147

82 86

9l

"115

115

100

98

118

158

131

141

78 82

87 95

110 92

72 76

ffl

103

89

84

66 69

74

94

81

74

66 72

82 62

0.T5- ***“ 0 .2 0 .2 5 0 .3 0 .3 5 0 .4 0 .4 5

•••

574

***

581

595 633

*•*

560 569

586 633

952 984

266 275

290 320

53T

565 620

974 994

"235

"" 282

440

265

316

435

533 596

975 984

239 251

270 306

435 ...........1 4 8 " 426 157

164 190

246 231

104 109

421

235

9 102

111 123

150 131

89 94

102 114

138 119

9l 102

122 102

79 88

103 83

***

543 0 .5

••• ***

492

507

447

157 ' 1 7 6 " 164 197

1

464

495 565

953 954

221 234

254 292

409

138 147

159 181

219

***

348 418

4!>3 526

910 904

202 215

236 274

397 382

127 135

148 169

201

• ••

349 371

408 483

” 343

214 251

363 " 346

114 122

134

197

833

181 194

153

179

79 84

0 .7

••• *•*

302

361 433

75^ 743

" ”159 " 172

191 224

320 302

io o 108

118 135

17i 151

” " 69 73

0 .7 5

••• ***

650 633

136 147

164 192

267 248

b4

278

312 378

91

94 112

138 118

••• *•*

210 229

260 316

n o 119

133

205

502

154

186

••• ***

162 177

20l

O .i

0.65

0 .8 0 .8 5

***"

325

255

242

521 372 352

"

219

'

114" ~TZl ' 165 "

••• ***

0 .5 5

'

77

"

"

58 61

101

CRC Handbook of Sample Size Guidelines for Clinical Trials

376

TABLE 3: ALPHA= 0.01 POWER= 0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 60

DEL=.10 FACT=

DEL=.15

1 .0 .7 5

.50 .25

.00 BIN

0 . 0$

***

212 212

214 217

228 352

124 124

126 128

133 186

0.1

♦**

334 336

339 346

382 502

178 179

182 188

0 .1 5

***

***

432 434

439 451

5TT ~ 633

219 222

0.2

*** ***

504 507

514 533

649 743

0 .2 5

•••

551 556

565 591

0 .3

• • • ' 575 • »« 581

594 627

0 .3 5

•••

0 .4 0 .4 5 0 .5 — 0 .5 5 0 .6 0 .6 5 0 .7 0 .7 5 0 .8 0 .8 5

D E U .3 0

.0 0 BIN

1 .0 75

.5 0 .2 5

.0 0 BIN

1 .0 .7 5

.50 .25

.00 BIN

88 88

89 91

94 118

68 69

70 71

73 83

56 57

57 58

60 62

203 248

118 119

121 125

133 151

88 89

90 93

98 102

70 70

72 74

74

226 235

264 302

142

146 152

166 179

101 103

106 110

ll8 119

79 80

82 85

90 84

248 252

258 272

155 159

164 173

194 201

ir o

ri7

346

113

123

135 131

85 87

89 94

92

755

267'

833

272

280 299

360 382

165 169

176 188

217 219

116 119

124 132

148 141

88 91

94 100

109 98

842 904

276 282

293 317

395 409

170 175

183 198

234 231

T l? 123

129 138

157 147

90 93

97 103

114 101

603 ' "908 646 954

277 285

299 326

420 426

170 176

186 203

245 239

119 124

130 141

163 151

89 93

98 105

117 102

• • • ” 565 *** 576

597 648

952 984

271 281

297 329

435 435

" 167 " 185

251 241

117 122

129 141

165 151

88 91

96 104

117 101

***

538 552

577 637

974 994

261 272

290 325

***

501 518

548 616

$75 984

259

•••

***

.50 .25

DEL=.25

.50 .25

PCONT=***

1 .0 .75

DEL=.20 .0 0 BIN

1 .0 .7 5

REQUIRED NUMBER OF PATIENTS

579 587

317

11

101

174

205

440 435

161 169

181 —251" " 239 202

113 118

126 139

15T 147

84 88

94 102

115 98

27$ 316

435 426

154 162

175 196

231

107 113

121 134

158 141

80 84

89 97

110 92

279 " 264

421 409

144 152

165 186

235 219

lbO 106

ITT 126

150 131

75 78

84 91

lo 3 84

*** " 457'' *•* 477

517 ' " 9'53‘" ' 586

954

243

302

*** •**

411 433

471 548

910 904

210 224

245 284

397

132 141

153 174

219 201

92 98

105 117

138 119

68

382

72

76 83

94 74

w

***

363 387

376 504

843 833

189 203

224 260

363 346

ll9 128

139 158

197 179

83 88

97 104

122 102

60 63

68 73

82 62

••• ***

316 340

377

758

rc7— 199

320

454

743

180

232

302

105 112

122 1 7 1 " 151 138

72 76

82 90

103 83

*'**" **•

269 293

32$ 397

650 633

ITS"

171

711 -- ■- * r

154

199

248

*** ***

222 243

274

521

331

502

116 125

13$ 160

205 186

*** ***

171 188

211 253

372 352

94

103 115

138 118

377

TABLE 3: ALPHA= 0.01 POWER= 0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 70

D E L :.10

DEL=.15

DEL=.20

DEL=.25

DEL=.30

.50 .25

.0 0 BIN

1 .0 75

.50 .2 5

.0 0 BIN

1 .0 .7 5

.50 .25

88 89

89 91

94 118

69 69

70 71

72 83

57" 57

58 58

" 60 62

203 248

119 120

122 126

133 151

88 89

91 93

97 102

70 71

72 74

77 74

228 238

264 302

141 144

147 153

166 179

102 104

HJ7“ 111

118 119

79 81

83 86

90 84

250 254

261 275

317 346

137“

166 175

194 201

112 114

118 ' 135 124 131

86 88

90 94

101 92

269 275

264 303

360 382

i'67'

833

172

179 190

2 l7 219

118 121

126 134

148 141

90 92

'"95" 101

98

600 437

842 904

279 286

298 322

395 409

1*72 178

186 201

234 231

121 125

131 140

157 147

' 9f 94

98 104

114 101

m ' 583 *** 592

611 657

908 954

281 290

304 333

420 426

17 3 '" T 7 0 ~ 180 207

245 239

l2 l 126

133 143

163 151

91 95

99 106

117 102

*** "'3 7 1 *** 583

606 662

952 984

274 287

304 336

435 435

171 179

190 ' 2 5 1 208 241

119 125

132 ' 145 143 151

90 93

98 105

117 101

3*7“ 653

974 994

267 279

296 333

440 435

166 174

186 206

251 239

116 121

129 141

163 147

87 90

94 103

115 98

*** ' 509 *** 528

561 633

975 984

253 266

287 325

435 426

158 167

179 “ 244 200 231

110 116

124 136

158 141

82 86

91 99

110 92

0. 55

*** ♦**

526 604

953 954

234 250

272 311

421 409

146 157

170 191

235 219

103 109

117 ' 150' " ' 129 131

77 ' 80

85 92

103 84

0 .6

*** “ *22 ~ 487 *** 446 567

910 904

217 232

254 292

397 382

137 146

158 “ 219 178 201

95 101

108 119

138 119

70 73

78 84

94 74

197 211

232 268

363 346

124' 132

144 162

197 179

85 90

97 106

122 102

62 65

69 74

82 62

74 78

83 91

103 83

FACT=

1 .0 .75

.50 .25

.0 0 BIN

1 .0 .7 5

***

212 213

214 218

226 352

124 125

126 128

133 186

*** ***

335 337

340 348

382 502

179 180

163 189

t n r ***

***

433 436

441 455

'523 633

220 223

0. 2

***

506 510

517

649 743

**•

553 559

570 598

" 753“

0 .3

*** ***

578 585

0 .3 5 0 .4

pcont =***

0 .0 5

ro

o

0 .1

H i

0 .4 5 ■***-

***

0 .5

0 .6 5 0 .7 0 .7 5 0 .8 0 .8 5

*** *** *** *** *** ***'

*** *** ***

.50 .25

.0 0 BIN

1 .0 .75

.00 BIN

REQUIRED NUMBER OF PATIENTS

545 560

~?57“ 489

- 374

538

'

160

401

443 523

645 833

329 355

395

758 '

471

743

174 187

207 239

320 302

109 116

126 142

171 151

92 98

106 118

"138 118

' 2 82' "3W ” 306

412

650 633

149 161

1V6 205

247 248

233 254

264 344

521 502

121 130

143 164

205 186

1B0 197

221 242

372 352

109

CRC Handbook of Sample Size Guidelines for Clinical Trials

378

TABLE 3: ALPHA= 0.01 P0WER= 0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 80

DEL=.10 FACT=

DEL=.15 1 .0 .7 5

.50 .25

DEL=.20

1 .0 .7 5

.50 .25

.0 0 BIN

*•*

2 i2 213

215 218

228 352

124 125

127 129

133 186

O .i

•* • *»»

336 338

341 350

382 502

iUO 181

184 190

0 .1 5

••• **»

434 437

443 458

$23 633

222 225

o .i

••• **•

507 512

521 543

649 743

0 .2 5

***

553“ 562

574 605

0 .3

*** **•

58 r 590

0 .3 5

DEL=.25 .0 0 BIN

1 .0 .7 5

.50 .25

.00 BIN

73 83

57 57

58 59

60 62

~^>s~ ■ 102

70 71

73 74

11 74

103“ 1 0 8 105 112

11& 119

80 82

83 86

90 84

113“ 116

119 125

135 131

87 89

91 95

101 92

2 l7 219

119 123

128 135

148 141

91 93

97 101

109 98

189 204

234 231

123 127

133 142

157 147

93 96

100 105

114 101

176 183

193 210

245 239

124 128

135 145

163 151

93 96

101 107

117 102

435 435

174 182

193 212

251 241

122“ 127

134 145

165 151

91 95

100 107

117 101

304 340

440 435

169 178

i9 o 210

251 239

118 124

132 143

163 147

88 92

97 104

115 98

259 273

294 332

435 426

162 171

184 204

246 231

113 119

127 138

158 141

84 88

93 100

110 92

953 954

243 257

280 318

421 409

152 162

174 194

235 219

106“ 112

119 131

150 131

78 82

87 93

103 84

501 584

910 904

2 2 7 " ' 261 239 299

397 ' 382

IT T " 150

162 181

219 201

98 103

110 121

138 119

72 75

79 85

94 74

457 539

845“ " 833

20 3 "'' 239 218 275

363 346

126 136

147 ' 165

197 179

88 93

99 108

122 102

63 66

70 75

82 62

409" 487

758 743

180 194

213 245

320 302

112 120

129 1 7 1 151 144

76 80

85 92

103 83

293 318

356 426

650 633

154 166

1*3 210

267 248

94 100

108 119

*** *#•

243 265

297 355

521 502

113” - 148 135 167

205 186

***

188 204

229 270

372 352

.50 .25

.0 0 BIN

1 .0 75

.5 0 .2 5

88 89

90 91

94 118

69 69

70 71

203 248

119 121

123 127

133 151

89 90

91 94

230 239

264 302

142 145

148 155

166 179

252 256

264 278

317 346

159 162

168 176

194 201

755“ 833

272 278

“288 ' 307

360 382

169 174

181 193

606 646

842 904

282 290

303 327

395 409

175 181

***

587“ ' 619 598 668

908 954

285 294

310 338

420 426

0 .4

•••

576 590

616 675

952 984

281 292

31o 343

0 .4 5

•••

532“ 569

600 667

974 994

272 285

0 .5

*** **»

ST8538

577 “ 975 649 984

0 .5 5

*** •**

47r 501

540 620

0 .6

*** ***

4 33" 459

0 .6 5

* '« ' ***

387 414

0 .7

*** ■ ■ -n o *** 367

0 .7 5

**'*

0 .8

PCONT=*** 0 .0 5

0 .6 5

DEL=.30

.0 0 BIN

1 .0 .75

REQUIRED NUMBER OF PATIENTS

138 118

"

'

379

TABLE 3: ALPHA= 0.01 POWER= 0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 90

DEL*. 10

DEL=. 15

DEL=.20

1 .0 .75

.50 .25

.00 BIN

'*** • **

213 214

215 219

228 352

125 126

127 129

133 186

0. 1

*** ***

336 339

343 352

382 502

180 182

185 191

0 .1 5

••• *•*

435 439

"475 461

523 633

223 226

0.2

••• **•

- 509 " £24 514 547

649 743

FACT=

1.0 .75

PCONT=*** 0 .0 5

0.25

***

.00 BIN

.00 BIN

1.0 .75

.50 .25

.00 BIN

70 71

73 83

57 57

58 59

60 62

89 90

92 94

97 102

71 72

73 74

"'"77

166 179

104 106

108” 112

TIB 119

81 " 82

84 87

90 84

160 164

169 ' 194 178 201

114 117

120 126

135 131

81 89

02 96

101 92

17l

148

92 94

98 102

109 98

.50 .25

.00 BIN

1.0 75

.5 0 .25

88 89

00 91

94 118

59 70

203 248

12o 121

124 127

133 151

231 241

264 302

113 146

“ 150 155

254 258

266 281

317 346

.50 .25

DEL*.25

1.0 .75

REQUIRED NUMBER OF PATIENTS

74

*•*

558 565

578 611

755 833

274 280

291 310

360 382

176

183 194

217 219

121 124

129 136

141

***

584 594

612 654

842 904

285 293

307 331

395 409

177 183

192 206

234 231

124 129

134 143

147

94 97

101 106

114 101

jr. 35 "*** ***

591 603

525

908 954

289 299

314 343

420 426

179 186

196 213

245

678

239

125 130

137 146

163 151

94 98

102 108

117 102

0 .4

581 597

624 686

952 984

285 297

315 348

435

1 7 8 " 197 215

129

136 147

165 151

93 96

T01

185

251 241

124

435

117 101

*** **•

558 577

510

974 994

277

440 435

173 181

194" 213

90 94

115

145

163 147

99

239

121 126

131""

290

310 346

251'

680

105

98

***

525 548

585 663

975 984

264 279

301 338

435 426

116

187 207

245

115

175

231

121

129 140

158 141

86 89

94 101

92

*** ***

486~

553 635

953 954

249 264

286 325

155 165

178 197

235 219

108 114

122 132

150 131

80 84

88

409

94

103 84

145

219

122

112

138 119

73 76

81 86

74

122 102

65 67

71 75

0 .3

0 .4 5 0 .5 0 .5 5

•••

0 .7 0 .7 5 0.8 0 . 8$

421

'

443 '

514

471

598

910 904

230 245

268 305

397 382

153

166 184

201

100 105

398 426

470 553

045 833

209 224

245 281

363 346

13l 139

150 167

198 179

00 94

" m ~ 109

'351

422 500

758 743

18*

320 302

115 122

132 146

78

199

219 250

' 171

379

151

82

87 93

••• • **

3d3 329

368

6$0

188 214

261 248

lid

633

150 171

97

438

103

121

138 118

••• ***

252

307

129 138

205

364

521 502

151

274

170

186

104

236

372

276

352

JT.6 “ ” *** *** 0 .6 5

511

'"

••• **• • **

*** ***

211

'

157

103 83

108

ilo

94 ""52 62

"

DEL*.30

CRC Handbook of Sample Size Guidelines for Clinical Trials

380

TABLE 3: ALPHA= 0.01 POWER= 0.8 EXPECTED ACCRUAL THRU MINIMUM F0LL0W-UP= 100

DEL=.10 FACT=

D E L :.15

1 .0 .7 5

.50 .25

.0 0 BIN

1 .0 .7 5

PCONT=***

.50 .25

DEL:. 20 .0 0 BIN

1 .0 .75

D EL:. 25

.5 0 .25

.0 0 BIN

1 .0 75

.50 .2 5

DEL=.30 .0 0 BIN

1 .0 .7 5

.50 .25

.00 BIN

REQUIRED NUMBER OF PATIENTS

0 .0 5

**• ***

213 214

214 220

228 352

125 126

127 129

133 186

89 89

90 92

94 118

69 70

70 71

73 83

57 58

58 59

6d 62

0 .1

*** ***

33V 340

344 353

382 502

181 183

186 192

203 248

120 122

124 128

133 151

90 91

92 94

98 102

7l 72

73 75

77 74

0 .1 5

••• ***

431 440

445 464

523 633

224 227

233 243

264 302

144 147

' 151 156

166 179

104 106

109 113

118 119

81 83

84 87

0 .2

••• *•*

s ir516

521 552

649 743

255 260

268 “ 317 283 346

161 165

171 ' 179

194 201

113 118

121 127

135 " " 131

88 90

93 96

101 92

0 .2 5

•** **•

360 568

583 617

755 833

2V6 283

294 313

360 382

173 178

183 196

217 219

122 126

130 137

148 141

93 95

98 103

109 98

0 .3

•••

588 598

JIT " 661

842 904

288 297

310 335

395 409

179 185

"174 208

234 231

126 130

136 144

157 147

95 98

102 “ T T 4 '' 107 101

0 .3 5

••• #**

595 608

633 687

908 954

292 303

319 348

420 426

182 189

199 215

245 239

127 132

138 148

163 151

95 99

lo 3 109

117 102

0 .4

•** ***

586 603

633 696

952 984

200 302

320 353

435 435

180 188

200 217

251 241

126 131

138 148

165 151

94 98

102 108

117 101

282 295

316 352

440 435

176 185

197 215

251 239

123 128

136 146

163 147

91 95

100 106

115 98

0 .4 5

563 585

' 620' 692

974 994

"

'

90 84

0 .5

♦** ***

533 557

596 675

975 984

270 284

306 344

435 426

169 178

190 210

246 231

u s123

131 141

158 141

87 91

95 102

110 92

0 .5 5

•** ***

495 522

565 648

953 954

234 269

292 330

421 409

159 169

181 200

235 219

ill” 116

123 134

15ff 131

81 85

89 95

103 84

0 .6

•** **•

453 481

526 612

910 904

236 251

274 311

397 382

148 157

169 187

219 201

l0 2 107

" 114 123

138 119

lA 78

81 87

94 74

0 .6 5

•**

408 437

483 566

845 833

214 229

251 286

363 346

134 142

133 169

197 179

91 96

102 110

122 102

66 68

72 76

82 62

0 .7

••• • **

361 390

433 512

758 743

191 204

224 255

320 302

118 125

133 148

171 151

79 83

88 94

103 83

0 .7 5

••• «•*

312 339

“ 378 448

650 633

164 176

192 218

267 248

99 105

ll2 122

138 118

*•*

260 282

316 373

321 502

133 142

154 173

205 186

•••

20i 218

242 282

372 352

0 .8 0 .8 5

'

'

381

TABLE 3: ALPHA=0.01 PQWER=0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 110

DE1=.05 FACT=

DEL=.10

1 .0 .75

.50 .25

.0 0 BIN

"50'0 601

503 608

571 1104

*■«

***

'

1100 1113

1237"

'

1747

338 340

m y - 1523

15 IT"

W

0.1

1096

0.15 0.2 0725

O ' 0 .3 5 01

*** ••• **• ***

fn *•# *«

*** "*■”

• **

0.75 '**»

***

0 .5 0 .5 5 0 .5

077"

.50 .2 5

.0 0 BIN

1 .0 .75

.50 .25

.00 BIN

133 186

89 90

91 92

94 118

59 70

7l 71

72 83

382 502

182 184

187 192

203 248

121

354

125 128

133 151

90 91

93 95

98 102

523

■225

633

229

234 244

264 302

145 148

157

155 179

105 107

109 113

118 119

270 285

317 346

153 166

172 180

194 " 201

115 119

122 127

135 131

295 316

361 382

174 179

186 197

2 l7 219

123 127

131 138

148 141

- ~ - 2 9 r “ 314

395

181'

300

338

409

188

195 209

234 231

127 132

13 1 145

157 147

29 5 306

323 351

420

184 191

201 217

245 239

129 133

140

426

149

163 151

183 191

202 219

' 251

128 133

140“ 149

165 151

345

m

r

1752

1841

1884

2339" 2791

512 518

7798“ ' 3192

- m v ~ 2082 2067

2129

■ 2 « 7 - 2219 "7 1 8 7 “

5 3 0 ' ■ 549 '

257“

556

743

262

553 " ' 587 571 622

755

' '278

833

285

' 591

' 522

2281

3513

602

668

m r

2259

' 539

908

2352

7784“ ' 3754

599

2242

614

695

954

2198

842 904

'

122

_

..'

'

7172“ 2245 “ 3703“

5 9 2 " ' "571“

952

“ 293“

325

435

2210

609

984

306

357

435

571 592

'"539“ ' 974

2B5 300

321 356

440 435

177“ 187

199 218

239

125 130

lS ’T 147

163 147

541 565

' 505

3l2 349

435 426

1 1*1 181

193 212

246 231

119 125

132 142

158 141

2

2352

3915

m - 2151 ■7534“ '

3995

2115

1753 1791

5577"

1903

3754

*■ ” " '1329“ 1491 *** 1387 1733

3788 3513

706 703 687

994

975 .......... 274“ 289 984

241

251

'5 0 4 '"' 575

953

“ 257“

297

531

660

954

275

335

421 409

153 172

184 202

235 219

112 118

125“ 135

150 131

■' 452

' 538

492

624

910 904

241 256

279 315

397 382

151 160

l7 l 189

219 201

104 109

115 124

138 119

“ 217“

1654 "3755“ ' 2059 3915

*** ■ ' I 574“ 1581 ' 3705

-

4 17 ’ ■ "777“ ' 845 ■"

448

578

833

234

256 290

363 346

157 145

156 171

197 179

93 98

103 111

122 102

370 400

444 523

758 743

195 209

22* 259

320 302

120 127

137 150

171 151

80 84

89 95

103 83

' 321 348

■"355 457

550 633

168 180

195 221

257 ” 248

101 107

114 124

138 118

“ 257 " 324

521

136 145

157 175

205

1303“ ' 7T8'5~ 1552 3192

***

770 1002

lll9 1361

2796 2791

755 826

935

' 2722

1157

2309

290

380

502

0 .T 5 " * " “ 593 *** 653

"748

1754 1747

305 224

' 248

372

931

287

352

"427

538

11'24 *

469

665

1104

*•*

1 .0 75

128 130

m r 1188

0T"

.00 BIN

126

478 " 449 467 442

*** ■ m r 2029 • ** 1970 2193

O.'ff"

.50 .25

125

*« " •**

0 .7 5 '

1 .0 .75

228

2309

1591 0755

.00 BIN

DEL=.2 5

352

215 220

1545

3995

•••

213 214

1516

2295

*•*

.50 .25

DEL=.20

REQUIRED NUMBER OF PATIENTS

PCONT=*** 0705

1 .0 .75

DEL=.15

186

CRC Handbook of Sample Size Guidelinesfor Clinical Trials

382

TABLE 3: ALPHA= 0.01 POWER= 0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 120

DEL=.05 FACT=

DEL=.10

1 .0 .7 5

.50 .25

.0 0 BIN

*•* • **

600 601

603 609

641 1104

214

217

228

126

215

220

352

0 .1

••• • ••

1094 1096

1101 1115

1237 1747

339 341

346 356

0 .1 5

••• *•*

T5T3'

1525 1549

1&13 2309

439 443

451 469

1855 1890

2339 2791

514 521

2798 3192

565 574

PCONT=*** 0 .0 5

0 .2

••• ***

1 .0 .75

.50 .25

DEL=.2 0

i 3L=.15 .00 BIN

.0 0 BIN

1 .0 .7 5

.50 .25

.00 BIN

92

118

70 70

71 71

73 83

121 123

125 128

133 151

90 91

93 95

97 102

264 302

146 148

157

166

106

158

179

108

110 113

119

272 286

317 346

164 168

173

194 201

117 119

123 128

135

181

299 318

360

188 198

211 219

124 128

132 138

148 141

.50 .2 5

.0 0 BIN

1 .0 75

.50 .2 5

128 130

133 186

89 90

~9T~

127

382 502

182 184

188 193

203 248

523 633

226 230

235 245

533 559

649 743

258 264

591

755

1 .0 .75

DEL=.2 5

REQUIRED NUMBER OF PATIENTS

1517

1837 1843

2o61

'

ITS

131

0 .2 5

••• ***

2070

2087 2137

627

833

280 288

382

176 181

0 .3

••• ***

2190 2202

2224 2292

3182 3513

394 606

627 674

842 904

293 303

317 341

395 409

183 189

198 211

234 231

129 133

138 146

157 147

0 .3 5

••• • **

2232 2247

2277 2366

3484 3754

603 619

646 703

908 954

299 310

326 355

420 426

186 193

203 218

245 239

130 135

141 150

163 151

2197 2216

2256 2370

3702 3915

"59T

648 715

952 984

297 310

329 361

“ 73T

616

435

185 193

205 221

231 241

129 134

141 150

165 151

••• *»•

2098 2123

21^74 2317

3834

577 600

637 713

974 994

290 304

325 360

440 435

181 190

202 220

251 239

126 132

r37 148

163 147

***" ***

1949

2075" ~3'5'79

548

616

975

279

316

2220

3995

574

697

984

294

353

435 426

175"

1981

184

196 214

246 231

121 127

134 143

158 141

"1763

1884

3836

511

264

302

3915

540

954

280

339

421 409

165 174

186 204

235

2090

586 671

953

1804

219

114 119

126 136

150 131

284 320

397 382

153 162

174 191

219 201

105 110

117 125

138 119

0 .4 0 .4 5 0 .5

0 . 55 0 .5 0 .6 5

***

1TD'4

3705

471

548

910

" n r

1937

3754

501

635

904

261

*** ' T775 «« * 1407

1517

3488 3513

425

504

260"'" 363

589

239

294

346

139 147

l5fc 173

197 179

94

457

845 833

224

1768

99

104 112

122 102

' m o " 1331

3185 3192

454 532

758 743

199 213

232 262

320 302

122 129

138

409

171 151

82 85

90 95

103 83

650 633

171 183

199

267 248

103 108

115

223

— 274" ' 331

521

139 148

160 177

205 186

•••

0 .8

0 .9

'

1557

1211

0781

"

1608

*** • **

077“ 0 .7 5

3995

***

1588

1146 "2775" ..... 379

397

1025

1395

2791

466

775"

962

2322

848

1187

2309

297

387

502

"' 510"

770

673

956

1764 1747

211 229

253 291

372 352

554

1124

681

1104

-9 5 1

***■ " T O " 484

356

151 124

138 118

383

TABLE 3: ALPHA=0.01 PQWER=0.6 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP^ 130

DEL=.0 5 FACT=

1 .0 .75

.50 .25

DEL=.10

0.1

0 77 0 .2 5 O'. 3' 0 .7 3 0 .4 01? 0 .3 ' 0 :3 3

0 .3 5

0 .5 5 0 .9 '

.50 .25

.0 0 BIN

1 .0 75

.50 .25

.0 0 BIN

1 .0 .7 5

.5 0 .25

.00 BIN

641 1104

214 215

217 221

228 352

126 127

128 130

133 186

89 90

91 92

94 118

70 70

7i 72

73 83

***

1095 '1132

382

183 185

188 193

£03 248

l£2 123

126 128

133 151

91 92

93 95

98 102

£27 231

236 246

264 302

1'47 149

153 158

163 179

103“ 108

110 114

118

153' ~ 174 169 182

194 201

118 120

124 128

135 131

217

125 129

133 139

148 141

1097

1117

173'7' 1747

339 342

347 357

*•*

1514 1519

1527 "T713

440 445

453 471

633

^

1839 1845

1858 '7 7 3 9 ' 1896 2791

516 523

535 563

649“ 743

265

288

317 346

••• • ••

£064 2073

2091 2145

567 577

594 632

755 833

£82 290

301 320

360 382

177 182

189 200

219

***' ***

IT73

2230 "3IB2

597

632

842

2205

2303

3513

610

680

904

£96 305

320 343

395 409

185 191

20b 212

231

130 134

139 146

157 147

m *•»

2235 2252

2285

3484 3754

"307 623

652 710

908

302 313

330 358

420

188

195

205 220

245

426

239

132 136

142 150

163 151

*** • **

2232

2266

3702

2223

2389

3915

621

723

984

301 —333— 435 365 435 314

188 196

201 223

241

131 136

142 151

165 151

*” ■ *•*

2104 2132

2186 2339

7734

' 583 " 607

646 722

994

18T 192

204 221

25l 239

128 133

143

3995

149

163 147

*»'*■ **•

1737“"7730

3'879 3995

555 582

625 707

***■

1773"' 1903 ”773 6

***

1992

*** **'* *•*

m

1552

2381

2246 2119

2309

2798 3192

'

601-” 655

502

523

954

952 ' 974

260 1 7 4 ”

294 309

330 364

440 435

283

321

435 426

177 186

196

246

357

216

231

123 128

135 144

158 141

519 ' 595

953

3915

549

954

268 284

307 343

421 409

168 177

189 206

235 219

116 121

128 137

150 131

250 266

288 323

397 382

156 165

176 192

219 201

107 112

116 126

138 119

' '228 243

265 297

363 346

141

16b 174

197 179

96 100

10'5

149

112

122 102

124

I« T " 152

171 151

83

131

86

90 96

103 83

ib 4 110

116 125

138 118



681

1727

3705

479

558

910

3754

510

645

904

1361 "1343 'T IB S ' 1426 1802 3513

435 ” 514

845 -

466

598

833

1159

1357

3185

203 “ 233“

1621

3192

7 8 7 — 463 418 541

758

1233

743

217

265

320 302

970

1173 1427

£796 2791

' 336 ’ 405 364 474

650 633

175 186

£02 226

248

52l 502

141 150

162 178

205 186

*** *•*

377 691

*«' »•*

497

4513

231 ’

298

1969

793 869

'

234

119

984

1625

'*” ■ ***

'

'

975

1370

1047 o:s~

1 .0 .75

■350 ' 604 602 610

O .T 0775

.00 BIN

DEL=.25

*** ***

1818 773"

.50 .25

DEL=.20

REQUIRED NUMBER OF PATIENTS

PCONT=*** 0 .0 5

1 .0 .75

.00 BIN

DEL=,15

973

23"22

280 ' 338

1215

2309

304

393

790

1734 '

2 I3 -

258

372

978

1747

234

295

352

' 33B 696

1124 1104

267

'

CRC Handbook of Sample Size Guidelines for Clinical Trials

384

TABLE 3: ALPHA= 0.01 POWER= 0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 140

DEL=.05 FACT=

DEL=.10

1 .0 .7 5

.5 0 .25

.0 0 BIN

PCONT=***

1 .0 .75

.50 .25

DEL=.15 .00 BIN

DEL=.20

.50 .25

.0 0 BIN

1 .0 75

.50 .2 5

126 127

128 130

133 186

90 90

91 92

1 .0 .75

DEL=.2 5 .0 0 BIN

••• ***

601 602

604 611

641 1104

214 216

218 221

228 352

0 .1

••• ***

1095 1098

il0 3 1119

1231 1747

340 343

348 358

382

183

502

186

189 194

203 248

122 124

126 129

133 151

••• ***

1315 1520

1529

431 446

455 473

523

1556

1813 2309

633

228 232

238 247

254 302

147 150

153 159

166 179

***

m o 1847

1861 1902

2339 2791

517 525

338

261 “ 275 267 289

317

566

649 743

346

165 170

'175" 182

194 201

***

2066 2075

2095 2153

2798 3192

570 580

TTT 636

755 833

284 292

303 322

361 382

179 184

i9 b 200

517

M ' 2209

2236 2314

3182 3513

600 613

637 686

842 904

298 308

322 346

395 409

186 193

2292 2395

1484 3754

6 ll 628

657 717

908 954

304 316

333 361

420 426

0 .2 0 .2 5 0 .3 0 .3 5

•••

.50 .25

.0 0 BIN

71 72

72 83

REQUIRED NUMBER OF PATIENTS

0 .0 5

0 .1 5

1 .0 .7 5

' 9T~ 118

' ' 7 0 '" 70 91 92

73" " ' 97“ 95

' 107" ' 111

102

118

109

114

11*“ 121

123'-- '1 3 3

119

128

131

219

T26"" -■133 139 130

141

201 213

533-----

T3T~ 140 "~r 3 T

231

135

147

147

190 197

207 221

245 239

133 137

143 151

163 151

"

148

***

2239 2257

0 .4

••• ***

2207 2230

2275 2406

"3702 3915

606 627

662 731

952 984

304 317

336 368

435 435

190 198

209 224

251 241

132 137

144 152

165 151

0 .4 F

*** **•

2111 2140

2199 2361

3834 3995

58$ 613

653 730

974 994

298 312

333 368

440 435

186 195

206 223

531 239

129 134

141 150

163 147

0 .5

••• • **

1*65 2002

2076 2271

3879 3995

561 589

633 716

975 984

287 302

325 361

fl'5 426

179 188

200 217

246 231

124 129

136 145

158 141

o . s r '*** •**

1784 1831

1922 2148

3836 3915

526 557

604 691

953 954

2 12 288

311 347

421 409

170 179

191 208

235 219

117 122

129 137

ISO 131

0 .6

•••

1583 1641

1?48 2000

3705 3754

467 518

567 654

910 904

254 270

292 327

391 382

158 167

178 194

219 201

108 113

119 127

138 119

0 .6 5

••• **•

13*76 1446

1567 1833

3486 3513

442 475

523 607

845 833

232 247

26B 301

363 346

144 151

162 176

1$7 179

97 101

106 113

122 102

0 .7

*** ***

ir 7 6 1254

1382 1652

318 5 3192

395 426

471 550

758 743

2d7 221

239 268

32b 302

126 133

142 153

171 151

83 87

91 96

103 83

0 .7 5

•** • **

989 1069

1197 1456

2796 2791

343 371

412 481

650 633

178 189

205 228

267 248

106 111

118 126

138 118

0 .8

••• ***

814 890

1009 1242

2322 2309

286 310

344 398

521 502

143 152

164 180

205 186

0 .8 5

•••

643 709

#09 999

1764 1747

251 ' ' 262 238 299

0 .9

•••

462 510

$81 710

1124 1104

372 352

"

"

385

TABLE3: ALPHA= 0.01 POWER= 0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 150

D ELs.05 FACT=

1 .0 .75

.50 .25

"555 612

DEL=.10 .00 BIN

70 70

71 72

73 83

1237 1747

341 344

34*“ 359

382 502

184 186

189 194

203 248

123 124

126 129

133 151

9i 92

94 95

'97 102

442 448

457 475

523 633

22* 233

239 248

254 302

' 148 151

154 159

166 179

"157 109

n r

118" 119

2339 2791

519 527

541 568

549 743

253 268

277 291

317 346

TT7 " 175 ' 174 ' 170 183 201

20*9 2161

27*8 3192

572 583

501 640

755 833

286 294

305 324

350 382

180 185

1*2 201

2245

3182 3513

603 617

541 691

842 904

301 ” 335” 348 310

3*5 409

188 194

202 214

' 234

2325

m *»*

2243 "2350 2262 2409

34*4 3754

615 633

553

908 " 954

'307

723

*** ***

2 2l2 2236

2285 2424

3752 '

611 633

668 738

984

*** *•*

"2117 2148

2211 2382

3834 ■'" 3995

555“ 738

***

1973 2013

20*1 "3879“ 2295 3995

541 725

975 ' "

***

17*4 1844

1*40 2175

3915

565

***

15*5 1657

1770 2029

3705 3754

494 526

1842 1849

1854 1908

***

2058 2078

••• *•*

21*9 2213

0765 ' ***

**•

0 .8

m *•*

1105 1121

3915

3835

"T372"" n ? o

348*8

1864

3513

1464

' 1194 "1407

620

— 55F 596

'

533

— 455" 483

157 147

134 138

144' 152

"153" 151 155 151

435 435

192 200

210 226

241

133 138

14T 153

974 ' '

351

994

316

357 371

440 435

18U 197

208 224

251 239

135 136

143"" 163 147 151

291 306

329 364

435 ' 426

182 190

202 219

245 231

17 3 " 137

984

131

146

158 141

512 699

953 954

275 292

3 l5 350

421 ' 409

172 181

193 209

235 219

118 123

130 138

150 131

575 663

910 904

257 274

2*6 330

3*7 382

150 169

180 195

21* 201

157 114

120 127

138 119

531

845 ' 833

353 346

145 153

' 153

197

98“ '

157" 122

177

179

102

113

102

143 154

170 151

84 88

92 97

103 83

119 127

138 118

615

' 452" " 479

758

"

'

235

272

251

303 243 270

320 302

128 134 157 112

180 192

208 230

267 248

103l 1266

2323 2309

292 316

34*“ 403

521 502

146 154

156 181

205 186

65& 725

827 1019

1754 1747

225 242

265 302

372 352

473 521

5*4 723

1124 1104

831 909

147

340 371

550 633

••• *•*

133 136

141

231

307 320

952

4 l* 487

2775"

148 141

245 239

350 378

1221 1484

134 140

208 222

2791

1007 1089

127 130

sn 219

192 199

743

*•*

125 ” 135" 129 131

420 426

557

1682

117 121

336 363

433

1274

m

"594T

114

319

210 224

318V 3192

0 .8 5 " 577"

.00 BIN

94 118

*•*

0775

.50 .25

9l 92

1516 "1531 "1813“ 1521 1560 2309

077

1 .0 .75

90 90

••• ***

0 .6

.0 0 BIN

133 ' 186

d .i5

0 .5 5

.50 .25

139 130

1(5*6 1099

575

1 .0 75

125 127

••• **»

0745

.00 BIN

228 352

b .i

0 .4

.50 .25

218 221

601 602

o r -

1 .0 .75

215 216

**• *•*

0 .3

.00 BIN

DEL=.2S

641 1104

0.O5

0 .2 5

.50 .25

DEL=.20

REQUIRED NUMBER OF PATIENTS

PCONT=***

0 .2

1 .0 .75

DEL=.15

251

'

CRC Handbook of Sample Size Guidelines for Clinical Trials

386

TABLE 3: ALPHA= 0.01 PQWER=0.8 EXPECTED ACCRUAL THRU MINIMUM F0LL0W-UP= 160

DEL=.05 FACT=

DEL=.1 0

1 .0 .75

.50 .25

.0 0 BIN

601 603

605 613

641 1104

215 216

218 222

1096 1100

1106 1123

1237 1747

34l 345

350

PCONT=*** 0.O5 0 .1

••• •••

1 .0 .75

.50 .25

DEL=.15 .00 BIN

1 .0 .75

DEL=.20

.50 .25

.0 0 BIN

1 .0 75

228 352

127 "T29 128 130

133 186

360

382 502

184

190 195

203

187

248

523 633

230 234

239

DEL=.25

.50 .2 5

.0 0 BIN

1 .0 .7 5

.50 .25

.00 BIN

9 t5 ~

91

94

90

92

118

70

71

71

72

73 83

123 125

127 129

133

9l 93

94

98"

95

102

264

148

248

302

151

155 ' 166' 159 179

108 109

112 "1 1 8 114 119

278 292

317

168

176’ - T 9 T "

171

183

201

122

129

360

181

193

217

128

135 "1 4 8 140 141

REQUIRED NUMBER OF PATIENTS

151

0 .1 5

*+•

1517 1523

1533 1564

1 8 l3 2309

443 449

436

o .2

••• • ••

1643 “1867 1851 1913

2339 2791

521 529

543 571

6*9 743

264 270

0 .2 5

* •• ***

53 637

845 833

245 260

281 311

353 346

150 158

157 180

198 179

lo l 104

ib 9 115

122 102

0 .7 '

> rr' *•*

1243 1331

1474 1763

422 454

5oo 576

758

219 232

250 276

320 302

132 138

145

743

156

171 151

87 90

93 98

103 83

••• *•*

1058

1285 “ Z793"

1146

1560

2791

368 397

438 504

550 633

188 199

214 235

267 248

lio 115

121 ' 138 128 118

***

'880' ' 1090

15T" 170 160

2b6 186

0 .7 5 0 .8

0.85 0 .9

3185 3192

962

1332

2322 2309

307 331

354 416

521 " 502

* « " 70d

236 253

276 310

5*72 352

***

770

876 1071

1764 1747

♦ **

504 554

527 756

1124 1104

184

389

TABLE 3: ALPHA= 0.01 PQWER=0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP=19Q

DE1=.15 FACT=

1. 0

.50 .25

.75

.00 BIN

PCONT=*** 07TC ' * * * •

0.1 0 .1 5 0 .2 0 . 25 ' 0 .3 0 .3 5 0 .4 0 .4 5 0 .5 ' 0 .5 5 O .T o. 65 0 .7 0 .7 5 O .T 0 7*5 0 .9 '

1.0 .75

1. 0 .75

.50 .25

.00 BIN

1.0 75

.50 .25

.0 0 BIN

.50 .25

1. 0 .7 5

.00 BIN

127

129

133

90

' 92

73

352

128

131

186

91

92

118

" 70 71

71

222

72

83

34'3

352 362

382 502

186 188

191 196

203 248

124 125

127 130

133 151

92 93

94

347

96

98 102

232

242 250

264 302

150 153

156 160

166 179

216 _ 219

■ 607 615

1104

217

* * * •

1098 1102

1109 1129

1237 1747

• •

1520 1526

1339 1574

1813 2309

446 453

• * • *

.00 BIN

REQUIRED NUMBER OF PATIENTS

m 604

• •

.50 .25

1**7

1857

" m S - 23'39 1930 2791

‘'

'*33 “ 123“ ' 481

236

633

■550

649

" 267

578

743

273

282 295

317 346

"292

312

301

329

'

94 "

" 109

112 115

118 119

123

126 130

135 131

110

.... m

..

T 70"' 174

178 185

194 201

360 382

184 189

195 ' 204

2 l7 219

130 133

136 141

148 141

135

• *

2076 2089

2798 3192

581

614

755 "

2192

593

653

833

• * * *

2210 “ 2264 2228 2367

3182 3513

614 ' 658

8*2

631

708

904

30* 319

333 355

395 409

T93 199

20? 218

234 231

139

143 149

147

* *

* *

2258 2282

2330 2462

3484 3754

629 650

683

908 954

317 329

345 372

420 426

198 205

214 226

245 239

138 142

147 154

163 151

• • • *

2231 2262

2324 2489

3702 3915

629 ' 691

952

.... 31*

151

137 '

332

435

198 206

213

984

351 380

435

653

230

241

142

14* 155

165 151

• * '"21*2 '2260 • • 2182 2460

3*34

615 '“ 3 * 3 " 974

' 313

435

195 203

214 229

1"35 ' 145“

643

349 381

251 "

3995

239

139

153

* * • *

*

* •

• • *

* *

2116

525 534

-T2*-

744 762 764

994

'

328

440

163 147

2005

2151

3*79' '

591 ~ 669

975

303

2055

2384

3995

622

753

984

319

341 374

435 426

189 197

208 223

246 231

130 135

148

156 141

1834 "2010” 3836 1896 2273 3915

550 592

642 728

953 954

289 305

327 361

421 409

179 188

199 213

235 219

122 127

133 140

150 131

271'

167

113 " 123

520 ' 605

910'

555

692

904

287

382

175

183 199

210

3754

308 340

397

2134

201

117

129

136 119

3488 3513

477“ 511

560 643

845 833

248 263

283 313

363 346

152 159

168 180

197 179

id l 105

l it) 115

122 102

3185 3192

428 460

506 1 7'5B 582 743

221 235

253 278

320 302

133 140

14? 157

17b 151

8? 90

94 98

103 83

111 116

122 129

138 118

1345 ~I8T9"' 3705 " 1719

""

* • • •

1450

1675

1534

1971

• • * ♦

1259 1348

1787

* * * *

1074 "TJB*” 2796

373

443

6 5 0 ''

T9D —213“

1164

1582

402

508

633

201

236

267 " 248

172 185

206 186

*

141

157

1494

2791

* •

895

1108

2322

312 ' ' 369

521”

153

978

1352

2309

335

420

502

161

* * •

713'

891 1087

239

279

784

1747

256

313

372 352

* * * •

5T3 563

637

1124

766

1104

'

"'

CRC Handbook of Sample Size Guidelines for Clinical Trials

390

TABLE 3: ALPHA= 0.01 POWER= 0.8 EXPECTED ACCRUAL THRU MINIMUM F0LL0W-UP= 200

DE1=.0 5 FACT=

DEL=.1 0

1 .0 .7 5

.5 0 .25

.0 0 BIN

PCONT=***

1 .0 .75

. 50 .25

DEL=.1 5 .0 0 BIN

1 .0 .75

DEL=.20

DEL=.2 5

.50 .25

.0 0 BIN

1 .0 75

.5 0 .2 5

.0 0 BIN

1 .0 .7 5

.50 .25

.0 0 BIN

REQUIRED NUMBER OF PATIENTS

0 .0 5

•**

602 604

607 615

641 1104

216 217

220 223

228 352

127 128

129 131

133 186

90 91

92 92

94 118

70 71

71 72

73 83

O .i

*** *•*

iO W 1103

1110 1131

1237 1747

344 347

353 363

382 502

186 189

192 196

203 248

124 126

126 130

133 151

92 93

94" 96

98 102

**•

1521“ 1 5 4 1 ” 1813 1528 1578 2309

448 454

464 483

$23 633

233 237

243 251

264 302

151 153

156 161

166 179

109 111

113 115

ll8 119

*•*

1849“ 1879 1859 1935

2339 2791

527 536

552' 580

649 743

268 274

283 296

317 346

171 174

"179 185

194 201

121 124

127 130

135 131

••• ***

2078 2092

2120 2200

27*8

583 596

617 656

755 833

294 302

313 331

360 382

185 190

196 204

217

3192

219

130 133

137 142

148 141

**•

2213 2232

2270 2376

3162 3513

617 634

661

842 904

310 320

353 356

395 409

194 200

206 218

234 231

136 139

147“

712

150

157 147

2337 2475

0 .1 $ 0 .2 0 .2 5 0 .3 0 .3 $

**• *•*

2262 2287

3484 3754

633 654

687 748

908 954

319 331

348 373

420 426

199 206

2 l5 227

24$ 239

138 143

148 154

163 151

0 .4

**• ***

2236 ' 23'33' 3702 2269 2504 3915

633 658

696 767

952 984

320 334

353 382

435 435

200 207

217 231

251 241

13T 143

148 155

165 151

0 .4 5

••• *•*

2148 2190

2271 2478

3834 3995

620 648

692 770

974 994

316 331

332 383

440 435

197 205

215 230

251 239

136 140

146 153

163 147

0 .5

m ** *

2013 2066

216$ 2405

3879 3995

596 628

67S 759

975 984

306 322

344 376

435' 426

190 199

210 224

246 231

131 135

141 149

156 141

0 .5 5

**• ***

1844 1909

2027 2296

3836 3915

565 598

648 735

953 954

292 308

330 363

421 409

161 189

2oo 214

235 219

123 128

134 140

1$0 131

0 .6

••• ***

1657

1868 2157

3705 3754

$26 561

612 698

910

311 342

397 382

187

177

200

219 201

IT T

904

274 289

16'9

1734

118

123 129

138 119

*** *•*

1464 1551

1695 1995

3488 3513

...... 763 517

566 649

84$ 833

251 266

266 314

363 346

102 106

lid 115

122 102

*** ***

1274 “ 1514 1366 1811

3185 3192

433 466

512 587

758 743

224 237

233 280

320 302

88 91

94 98

103 83

**•

1089“ 1325

6$0 633

218

267

407

448 513

192

1604

2796 2791

378

1181

203

237

248

*** *• •

909 994

1125 1371

2322 2309

316 340

373 423

521 502

154 163

173 186

20$ 186

725 797

905 1102

1764 1747

242 259

262

372

315

352

522

647 775

TT24

0 .6 5 0 .7 0 .7 5 O.fl 0 .6 5

0 .9

*** • **

572

1104

" "153 ~ T 59“ 160 181

197

'

179

135 ' 148 ‘ 171 141 "

112 117

158

151

12 2 ' n r 129

118

"

391

TABLE3: ALPHA= 0.01 POWER=Q.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 225

DEL=.0 5 FACT=

D E L :.10

D E L :.15

1 .0 .75

.50 .25

.00 BIN

••• ***

603 605

608 617

~~J41 1104

217 218

220 223

228 352

o .r

*** **•

1100 1105

1113 1136

1237 1747

345 349

355 364

0 .1 5

*•* **•

1524 1 5 4 6 1586

1 8 l3 2309

450 457

467

1531

*** ***

1833 1864

1886 1947

2339 2791

••• ***

20*4 2099

2131 2217

••• ***

2220 2242

•••

0 .0 5

0 .2 0 .2 5 0 .3 0 .3 5

.50 .25

.00 BIN

1 .0 .7 5

DEL*.25

.50 .25

.00 BIN

1 .0 75

.50 .2 5

.0 0 BIN

1 .0 .7 5

.50 .25

128 129

130 131

133 186

91 91

92 93

93

71" 71

71

73

118

72

83

382 502

187 189

192 “ 203 ' ' 197 248

12$ 126

128 130

133 151

93 94

95 96

97 102

523 633

234

244 " 264

152“ "157

166

239

252

154

161

179

110 111

1T3'

485

115

118 119

530 541

556 585

649 743

271 277

285 297

T80 186

"194" 201

122 125

127 131

"135 131

2798 3192

588 601

623 663

755 833

297 305

3 l7 333

360

187 192

198 206

217 219

131

382

134

138 142

148 141

3182 3513

624 641

670

2400

842 904

314 325

339 359

39$ 409

197

210

202

220

234 231

137 141

145

720

150

157 147

2271 2300

2356 2505

5484 3754

641 663

697 758

908 954

324 336

352 377

420 426

202" 209

217“ 228

245 239

140' 144

149 155

163 151

952 984

326 340

358 386

435 435

203 210

220 232

251 241

140 "' 150 144 156

165 151

357

138 142

148 154

163 147 158 141

PCONT=***

1 .0 .7 5

DEL=.20

.00 BIN

REQUIRED NUMBER OF PATIENTS

302

" 317" ' ' 1 7 2 ” 346 176

0 .4

••• ***

2248 2285

2357 2541

3702 3915

642 668

708 779

0 .4 5

••• • **

2134

2300 2521

3834 3995

631 660

705

974

2211

783

994

322 337

387

440 435

200 208

218 232

251 239

*•*

2033 2091

2199 2453

3879 3995

60$ 641

690 773

975 984

31* 329

350 381

435 426

194 202

212 226

246 231

133 137

143 149

0 .5 5

••• • **

1869 1940

2067 2349

3836 3915

578 612

663 748

953 954

299 315

336 367

421 409

185 193

203 216

235 219

125 130

135 ' 150 141 131

O .i

*•* **•

1687 1770

1912 2213

3705 3754

540 576

627

910 904

280 296

317 347

397 382

172 180

189 202

219 201

11'6

711

120

124 130

138 119

1498

1742 2051

34*8 3513

496 531

662

845 833

257 272

'291

1590

318

363 346

156 163

172 183

197 179

104 ' ' m 107 116

122 102

••• ***

1 3 l0 1407

1561 1865

3185 3192

446

525

758

479

599

743

23d 243

260 283

320 302

137 1 S D ” 159 143

171 151

89 92

103 83

*** ***

in s 1221

1370 1654

2795 2791

390 419

460 523

650 633

197 208

221 240

267 248

117” 119

138 118

••• *•*

943 1031

1165 1414

2322 2309

326 349

382 431

521 502

15ff 166

175 188

205 186

••• • **

754'

938 1135

1764 1747

24$

827

266

288 320

372 352

••• ***

594

669 796

1124 1104

O '.T~

0.75" *** 0 .7

0.75 0 .8 0 .8 5 0 .9

542“

581

124 130

'

95 99

CRC Handbook of Sample Size Guidelines for Clinical Trials

392

TABLE 3: ALPHA= 0.01 POWER= 0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 250

DEL=.0 5

DEL=.1 0

DE1=.1 5

1 .0 .75

.50 .25

.00 BIN

*** ***

604 606

610 618

ST1

217

221

228

1104

219

224

352

***

1102 1107

1116 1140

1237 1747

347 350

356 366

382

••• ***

1526

1550

1534

1594

1013 2309

452 459

470 488

b.2

••• ***

1856 1869

1893 1960

2339 2791

534 544

561 589

649

0 .2 5

***

***

2089 2106

2141

592 607

67T' 669

755

2235

2798 3192

*** *•*

2227 2251

2298 2423

3182 3513

630 649

677 727

842

••• ***

2281 2312

2374 2533

3484 3754

649 672

•••

2261 2301

2380 2576

3702 3915

* * * “ 2180 '2328 *** 2231 2561 *** " 2 0 5 3 “ 2233 *** 2116 2498

FACT=

PCONT=***

ITD5 0 .1 0 .1 5

b .3 0 .3 5 0 .4

0.45 ff75"

***

O'. 65 O'. 7" a i r 0 .8 '

.00 BIN

.50 .25

.0 0 BIN

1 .0 75

.50 .25

.0 0 BIN

1 .0 .7 5

.50 .25

.0 0 BIN

130 131

133 186

91 91

92

129

93

94 118

71 71

72 72

83

188 190

193 197

203 248

125 127

133 151

93 94

95

130

96

97 102

236 240

245 253

264 302

152

158

110 112

118

162

166 179

113

155

116

119

273 279

287 299

317"'

181 187

194 201

123 125

128 131

135 131

1 .0 .75

REQUIRED NUMBER OF PATIENTS

502

523 633

128

128

72

346

173 177

300 ~ 317' 308 335

360 382

189 193

199 207

217 219

133 135

139 143

148 141

904

318 328

342 362

395 409

199 204

212 221

234 231

139 142

146 151

157 147

707 767

908 954

328 340

357 380

420 426

204 211

219 230

245 239

142 145

150 156

163 151

652 679

719 789

952

331 345

363 390

43'5~

222 234

241

142 146

151

435

206 213

TST

984

157

165 151

3B34 "

642

717' ' 974

328 ' 362

3995

672

794

994

342

440 435

203 211

221 233

251 239

139 144

149 155

163 147

3879'

620

702

975 " "

317“ ' '355

435

3995

654

784

984

334

426

197 205

215 228

246 231

134 139

144“ 150

158 141

421 409

188 195

205 218

235 219

127 131

136 142

150 131

117 121

126 131

138 119

743 833

391 385

"

2105

3836 '

590

676'

953

305 m

1970

2397

3915

625

761

954

320

372

*** ***

1715 1804

1953

3705 "

64b 723

286 301

350

397 382

175

3754

553 589

910

2264

182

191 203

219 201

*** **«

1530 ""TO 3" 3488 ' 1627 2102 3513

509 544

593 673

843 833

26T 183

109 113

117 125

141 126

... 15I_._ 'T 5 T ~

192

411 449

196 200

2 o r " 252......

341

217

261

339

352

467

372

495

207 211

219 234

281 284

145

343

1072"-----348

365

512

211

226

391

530

217

244

151

158 171

204 191

' 110

354

303 300

ITT”

1172

114

120 129

148 131

347' 354

368 400

544 553

210 217

228 249

318 310

145 151

150 174

211 195

109 113

120 130

152 132

*** " 715 “ 7*5 ■ m r ~ - ■ *** 727 795 1276

337 ' 346

363

564

204 ' '2 2 r “ 325

214

565

212

249

313

142 148

'1 5 7 '"

400

173

195

104 111

118 129

152 131

*** ***

193 204

218 245

324 310

136 142

152 ' 170

212 191

1(32 107

114 125

149 126

184 193

209

319 300

128 135

146 163

203 183

96 101

108 120

143 119

305

119 "1 3 7 ” 126 154

194 170

89 94

101 112

134 109

241

108 116

124 142

178 154

81 86

92 102

121 96

113 127

158 133

71 76

82 90

106 80

98

13"4 '

110

108

649 ' 557 652 674

799

1237

678

713” " 1263“ '

320 '

351

570

690

773

1289

331

392

565

1

184“

148

'

•••

668 739

126T" 1276

298

333

564

640

311

379

553

*** ***

563

615

1233”

274

312

546

581

696

288

360

530

170 180

196 224

*** **•

497” “ T51T" 11813" 644 1172 519

247 263

288 336

515 495

" "T O 166

181 209

10 r e - ' " 2 2 0 " 261 307 236

139 149

164 190

256

97

449

232

103

■ m — 231 208 274

415

121

144“

391

131

167

221 196

e4 90

163

198

347

177

235

322

' " 102 110

121 139

179 153

'* « ' 425”

***

' «1

498'

1237

1081

***

7S T ~ 394

525

964

*** *«*

308 334

375 457

843 821

0 .8 ....." « * '

250

311

676

274

382

651

192

240 294

482

***

*»*

0 .8 5

.50 .25

178 180

*** “ 537” - _5 5 y »*• 559 574

588

0 .7 5

1 .0 75

391

442

456 0 .7

.00 BIN

159

0 .2 5 "« * ■

0 .4

.50 .25

152

0 .2 ' ***

0 .3 5

1 .0 .75

.00 BIN

' 159 160

0 .0 5

0 .3

.50 .25

REQUIRED NUMBER OF PATIENTS

PCONT=***

0 .1 5

1 .0 .75

DEL=.20 DEL=.25 DEL=.30

***

211

456

471

■ 132 " 161

266

190

241

144

237

284

284

CRC Handbook of Sample Size Guidelines for Clinical Trials

456

TABLE 4: ALPHA= 0.01 POWER= 0.9 EXPECTED ACCRUAL THRU MINIMUM FQLL0W-UP= 60

D E L = .10

D E L = .15

D E L = .20

D E L = .2 5

DEL=.30

.50 .25

.00 BIN

1 .0 75

.50 .2 5

.0 0 BIN

1 .0 .75

.50 .25

.0 0 BIN

113 113

115 117

l2 l 153

88 88

"3V " 91

94 108

73 73

74 75

77 80

263 322

151 153

335""' 160

172 196

112 113

116 119

"126 133

89 90

92 95

*9 96

28* 300

342 391

179 182

186 194

216 232

12* 131

135 “ 153 141 154

100 102

105 109

117 109

319 322

329 346

4TI 449

1*8 202

208 220

252 261

140 143

148 ' "175 ' 156 170

107 ' 114 110 119

131 119

980 1081

342 347

356 378

457 495

210 215

222 238

795

1092 1172

352 359

371 3*9

512 530

215 221

231 250

303 300

150 154

162 175

743 751

*768 814

1177 1237

352 360

375 409

544 553

2 i4 221

233 255

318 310

14* 155

0.4

*** ***

"773 734

"755 812

1235 1276

343 353

371 411

564 565

209 218

231 256

325 313

0 .4 5

***

685 699

126

794

1263 1289

327 339

' 361 404

570 565

201 210

225 252

**•

634 651

684 763

1264 1276

306 321

345 392

564 553

190 200

0. 55

*** ***

574 595

634 721

1236 1237

283 299

324 373

546 530

0 .6

"*T» «**

510 535

578 671

1180 1172

257 274

300 349

0 .6 5

*** 00 0

446 473

51'9 614

10*5 1081

230 247

0 .7

*TT» • *#

384 412

459 551

983 964

324 352

396 481

265 290 204 224

FACT=

1 .0 .75

.50 .25

.00 BIN

*** **«

274 274

216

29S~

279

456

160 160

162 165

172 241

O .i

4** **•

432 434

437 445

495 651

229 231

234 240

0 .1 5

TT*

538 560

565 578

6 19 821

282 284

***

650 654

661 680

841 964

000

7lO 715

*724 751

**»

740 746

Vs*

PCX)NT _ * • * 0. OS

0.2

0 .7 5 0.3 0 .3$

0 .5

0 .7 $ 0 .8 0. 85

4171

0*0

1 .0 .7 5

.50 .25

.00 BIN

1 .0 .75

REQUIRED NUMBER OF PATIENTS

' 7*1 "" " 284

1 T 7 " 157 151 168

ill 115

119 " 141 127 126

203 191

113 117

122 131

163 178

211 195

112 116

"122 132

152 132

145 152

16l 177

214 195

109 114

121 131

152 131

326 310

140 147

157 174

212 191

105 ""“ 117 128 110

14* 126

216 244

319 300

132 140

150 167

205 183

99 104

143 119

176 187

204 232

305 284

123 131

141 158

1*4 170

92 97

515 495

162 173

1&* 216

284 261

113 120

130 146

178 154

84 89

*5 105

273 320

471 449

145 156

171 196

101 108

117 131

158 133

74 78

84 *2

202 218

242 285

415 391

127 137

150 172

221 196

88 93

101 112

134 108

843 821

172 187

208 245

347 322

107 115

IT? ' 144

179 153

32* 401

676 651

140 151

169 197

266 241

“ 253' 308

482 456

"756 ''" 232

191 183

'

111 122

1"48~ 131

"~10'4""" 1 3 7 “ 109 115 ' 121" 96 106 ' 80

'

457

TABLE 4: ALPHA= 0.01 POWER= 0.9 EXPECTED ACCRUAL THRU MINIMUM F0LL0W-UP= 70

DEL=.10 FACT=

1.0 .75

DEL=.15

.00

.50 .25

BIN

275

' 277 280

296 456

0T

"*** ***

435

438 447

”49 r

0715 "*** • **

3 3 9 " 557 562 582

679 821

m

.50 .25

BIN

1 .0 75

.50 .25

BIN

1.0 .75

.50 .25

BIN

.00

.00

.00

113 114

ll'S 117

121 153

88 89

90 91

94 108

73 73

74 75

77 80

230 " 235 242 232

263 322

152 ' 157 154 161

172 196

113 114

116 120

133

126

90 91

92 95

99 96

291 303

342 391

181 183

IBS 196

216 232

130 132

136 142

153 154

101 103

106 110

117 109

321 " 333 350 325

411 449

200 - 210’ 204 222

232 261

142 145

150' 158

173 170

109 111

115 121

131 119

'344 350

360 384

467 495

212 217

226 241

281 284

149 153

159 170

19i 183

113 116

121 128

141 126

"1092 1172

"335 363

376 406

512 530

2l8 224

235 254

303 300

152 157

165 177

204 191

"115 119

124 133

148 131

776 ' '1177 827 1237

356 365

382 417

544 553

218 226

238 260

318 310

152 158

166 181

211 195

114 119

125 134

152 132

0.25

*** ' "717 •** 718

0 .3 '

*** ' ~ T f Z ~ 765 750 806

0.4

1.0 .75

172 241

*** ' ~532~~ '553 *«* 656 686

*«*

.00 BIN

DEL=.30

162 165

0 .2 '

0733

.50 .25

DEL=.2 5

REQUIRED NUMBER OF PATIENTS

PCONT=***

O.'OS'"” * *•*

1.0 .75

DEL=.20

747 757

• • • ' T79*•* 741

651

341” 964

729 “W 760 1081

T60 161

” 7B3 286

755 829

■”1233 1276

" ~ m — 380 420

564 565

214 223

237 261

325 313

149 155

155 181

214 195

112 116

123 133

132 131

360

o: 43 ” « * ***

572 ' 708

739 813

1753 1289

333 " 370 347 415

570 565

206 216

23'I 2 58

326 310

143 151

151 177

212 191

107 113

120 130

149 126

O .T

■575 663

577 784

1264 1276

'314 ' 354 329 403

564 553

"175 206

222 250

319 300

136 144

154 171

205 183

102 107

114 125

143 119

"771" 308

334 384

546 530

182 193

210 238

305 284

127 135

145” 162

194 170

95 100

107 117

134 109

756 283

311 360

515 495

167 ' 193” 179 221

284 261

117 124

134 149

" 178 154

86 91

77 106

121 96

239 " 283 256 330

471 449

151 ' 177“ 161 201

256 232

105 111

120 134

138 133

76 81

86 94

106 80

252 295

415 391

132 142

153 177

221 196

91 96

104 115

108

310 ' 216 195 253

347 322

119

ni

130 ” 177' 147 153

'« * ***

0 753 "*■**■ '' TB3~~ 651 ' '123'6 **• 609 743 1237 0.6

*** ***

573 ” 597 ”"TITO 550 694 1172

0.53 ' w **•

4'50 490

539 '“ Iff73 637 1081

0/7-----«■« ***

379 429

■ 478 "~753— 964 573

0.75

• **

339 368

500

*'** *•*

778 305

418

*'** *•*

2l5 235

0 .8 ' 0.85

414 ""843"

344

821

n

r

651

7 5 5 " "487" 320 456

210 227

146

158

175

203

266 241

134

CRC Handbook of Sample Size Guidelines for Clinical Trials

458

TABLE 4: ALPHA= 0.01 POWER= 0.9 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 80

D EL*.10

DEL=.1 5

DEL*.20

1.0 .7 5

.50 .25

.00 BIN

*•*

27 4 275

277 281

296^ 456

160 161

163 166

172 241

**• **•

434 436

434 449

495 651

231

236 244

263 322

**• **•

560 564

570

679 821

284 288

293

586

306

342 391

••• **•

654 658

667 692

841 964

322 327

336 354

••• ***

715 721

734 768

980 1081

347 353

0 .3

••• ***

746 755

771 816

1092 1172

0 .3 5

••• ***

751 762

784 840

0 .4

•••

"734“ 748

776 844

694 717

“ 73 r 830

651 674

FACT=

.00 BIN

1.0 75

.50 .2 5

.00 BIN

1.0 .7 5

.50 .25

.00 BIN

0.O5

113 114

116 118

121 153

88 89

90 92

94 108

73 74

74 75

80

0.1

153 155

158 162

il2 196

113 115

117 120

126 133

90 91

93 95

99 96

0.15

182

189 “ 198

216 232

T31

185

134

137 “ 133” " 143 154

"102 104

107 110

117 109

0.2

411 449

202 206

213 225

252 261

143 147

1 5 2 “ “ 175" " 160 170

110 113

116

l3 l 119

0 .2 5

365 389

437 495

215 220

224 244

281 284

151“ 155

162 172

359 367

382 412

512 530

221 228

238 257

303 300

T54~' 160

167 “ 304 179

191

121

1237

360 371

388 425

544 553

221 230

242 264

318 310

155" 161

169 183

211 195

117 121

1235 1276

353 366

”387 428

564 565

218 227

241 266

168 184

2 l4 195

0 .4 5 0 .5

*#* •••

1263 1289

339 354

3 78 424

570 565

210 221

•** ***

"713 803

123T" 1276

321 337

363 412

564 553

0 .5 5

595 621

667 764

125~6 ' 1237

299 316

344 394

614 715

1180 1172

274 292

1095 1081

241

.50 .25

.00 BIN

1 .0 .75

REQUIRED NUMBER OF PATIENTS

'T177'

233

'

"325

" ' 152

141 183

"" 1 1 5 " 118

"

"117

122

77

122 129

“ H I”

126 134

“ 148

121

'1 5 2 132

136

■n r T Z 5 "

126 131

119

135

152 131

212 191

110 115

122 132

“ r4 7 126

158 174

205 183

104 109

116 126

143 119

13l 138

149 164

144 170

47 102

109 118

134 109

284 261

120 127

13? 152

178 154

89 93

99 108

121 96

182 205

256 232

108 114

123 136

158 133

78 83

88 95

80

93 99

106 116

134 108

159

236 263

326 310

137 154

164 180

200 211

227 255

319 300

140 147

546 530

1T7 199

215 243

305 284

320 370

515 495

173 184

230 226

265

292 339

471 449

156 166

*** ***

535 565

0 .6 5

**• ***

474 " 5 5 5 “ 658 505

0 .7

••• ***

n r 445

"495' 592

983 964

218 235

2 60 303

415 391

137 146

160 180

221 196

0 .7 5

**•

^352 383

430 518

843“ 821

187 " 223 260 202

347 322

115 123

134 150

153

*»*

290 317

358 432

676 651

151 " l 6l 164 208

2*6 241

**• • ••

224 245

276 330

482“ 456

0 .8 5

'

313

0.6

0.8

DEL*.30

.50 .25

PCONT=***

1 .0 .75

DEL*.25

il9

ld6

459

TABLE 4: ALPHA= 0.01 P0WER= 0.9 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 90

DEL=.10

DEL=.15

DEL=.20 DEL=.2SDEL=.30 .50 .25

.00 BIN

1 .0 75

.50 .2 5

.0 0 BIN

1 .0 .7 5

.50 .25

.00 BIN

114 115

'116' 118

121 153

89 89

90 92

94 108

73 74

76

77 80

263 322

154 155

158 163

172 196

295 308

342 391

153 186

191 199

324 329

338 357

411 449

204 208

980 1081

349 356

368 393

467 495

777 825

1002 1172

362 371

386 417

755 768

792 852

1177 1237

364 375

*•*

739 755

785 857

1233 1276

***

706 726

762 846

*•*

660 684

***

FACT=

1 .0 .75

.50 .25

.00 BIN

1 .0 .75

.50 .25

.00 BIN

0.O5 ~ i r r ***

275 276

278 282

206 456

161 162

163 166

172 241

0.1

***

434 437

441 451

495 651

232 234

238 245

***

562 " 3 7 2 ” 565 590

670 821

286 289

535 ' 37 r 661 697

841 964

711 724

738 775

“ JJT **•

749 759

***

PCONT =***

O .lS 0 .2

0. 35 0 .4 0 .4 5 0 .5 0. 55 0 .6 0 .6 5 0 .7 0 .7 5 0 .8 0.8S

REQUIRED NUMBER OF PATIENTS

116

121

126 133

91 92

93 96

99 96

2 f3 232

132 135

138 144

153 154

103 105

107 111

117 109

2 l5 226

252 261

145 148

153 161

175 170

" 111 114

'1 1 7 122

131 119

217 222

231 247

281 284

153 157

163 173

191 183

T T5“ 119

124 130

512 530

223 231

241 260

303 300

156 162

169 181

204 191

118 122

127' 135

304 431

544 553

225 233

246 268

318 310

157" 163

172 185

2 ll 195

118 123

128 137

152 ' 132

35b 371

393 436

564 565

221 231

246 270

325 313

133 161

171 186

214 195

116 121

127 137

r3 2 ~ ' 131

1263 1289

345 361

383 432

570 565

2 l4 225

"2'4r ' 326 267 310

150 157

157 183

2 l2 191

112 117

124 133

149 126

727 820

1264 1276

32T 345

371 421

564 553

204 216

232 259

319 300

143 150

15T“ 176

205 183

106 111

113 128

143 119

605 634

682 782

1236 1237

3o6 324

352 402

346 530

192 204

220 247

305 284

134 141

131 167

194 170

99 104

11T" 120

154 109

***

547 578

630 734

1180 1172

281 300

328

515

378

495

177 189

205 230

284 261

123 130

'1 4 0 154

178 154

90 95

lo l 109

121 96

*** ***

486 519

'"573" 676

1005 1081

254 273

300 347

471 449

160 171

186 209

256 232

110 117

“ 123'

158 133

80 84

89

138

96

106 80

*■**' ***

425 459

' 511" 610

983 964

225 242

261 310

415 391

141 150

163 183

221 196

95 101

IBB 118

134 108

»•*

364 396

444 533

~BT3' 821

193 208

230 265

347 322

118 126

***

301 329

370 445

676 651

T 55"' " 186 169 212

266 241

ttt ' • **

233 254

286 339

482 456

"***

0 .25 0 .3

1 .0 .75

T 3 T “ 179 152 153

T F T " 118

'

'

141 ' 126 148 131

CRC Handbook of Sample Size Guidelinesfor Clinical Trials

460

TABLE 4: ALPHA= 0.01 PQWER=0.9 EXPECTED ACCRUAL THRU MINIMUM F0LL0W-UP= 100

DEL=.10 FACT=

DEL=.15

1 .0 .75

.5 0 .2 5

.00 BIN

*** ***

275 276

278 283

296 456

161 162

164 167

172 241

0 .1

••• ***

'435 438

442 453

495 651

232 235

239 246

0 .1 5

*** •**

563 567

574 593

679 821

287 291

0 .2

••• ***

657 663

674 702

841 964

0 .2 5

••• ***

720 727

743 782

0 .3

••• ***

752 763

0 .3 5

••• ***

0.4

•••

0 .4 5 0 .5 0 .5 5 0 .6 0 .6 5

0.7 0 .7 5 0 .8 0 .8 5

1 .0 .7 5

.50 .25

.00 BIN

1 .0 .75

DEL=.25

DEL=.30

.50 .25

.00 BIN

1 .0 75

.50 .25

.0 0 BIN

1 .0 .75

.50 .25

.00 BIN

114 115

116 118

121 153

89 90

91 92

94 108

74 74

75 76

77 80

263 322

154 156

159 164

172 196

115“ 116

118 121

126 133

91 92

94 96

99 96

297 310

342 391

184 187

192 200

216 232

133 136

139 144

153 154

103

TUB"'

117

105

111

109

326 332

341 360

411 449

252

154 162

175 170

112 115

ll8 123

131 119

980 1081

352 359

372 397

154 " 165

191 183

117 120

131

126

783 834

1092 1172

365

120 124

129 136

148 131

760 773

79$ 863

i3 o 138

152 132

• **

ITS " 129

132 131

PCONT=*** 0 .0 5

D EI=.20

REQUIRED NUMBER OF PATIENTS

' 205 " 217 210

228

261

146 149

'467 495

219 225

234 249

281 284

159

175

512 530

226 233

244 263

303 300

158"

171

375

391 422

164

183

204 191

1177 1237

368 380

400 437

544 553

228 236

249 271

318 310

159 165

174 187

211 195

120 124

745 762

7$5 —T235 1276 870

363 377

400 442

364 565

225 235

249 273

325 313

*** ***

713 734

773

1263 1289

' '351 367

392 439

370 565

218 229

245

860

271

***

668 694

739 836

1264 1276

333 351

379 428

564 553

209 220

737"

***

615 645

696 799

1236 1237

312 331

360 410

546 530

••• **•

558 " 644 591

751

1180 1172

288 307

336 385

••• ***

498 533

1095 1081

261 280

307

471

693

354

449

*** *»*

437 " 525

983 964

231 249

843 821

198 214 161 173

472

588

625

375 " 457

••• • ••

408

547

*** ***

311 339

456

676 651

***

240 262

294 347

482 456

382

157”

173

164

188

214 195

122

138

326 310

152 160

170 185

212 191

114 119

125 135

149 126

263

319 300

146 153

163 178

205 183

108 113

120 129

143 119

196 208

224 251

305 284

137 144

154 169

194 170

101 106

112 121

134 109

515

181

261

126 133

142 156

178 154

92 97

IZJ2'

193

209 234

2B4

495

110

121 96

164 175

190 212

236 232

113 119

127 139

158 133

82 86

98 103

110 119

134 108

274

415 391

144 154

—T77

316

186

221 196

235 270

347 322

121 129

13$ 154

153

190 216

266 241

179

'

125 ■ 141 ■■

90 97

106 80

461

TABLE 4: ALPHA= 0.01 P0WER=0.9 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 110

DEL=.05 FACT=

1.0 .75

.50 .25

DEL=.10

.00

1.0 .75

BIN

PCONT=*#•

.50 .25

DEL=.15

.00 BIN

1.0 .75

DEL=.20

DEL=.2 5

.50 .25

BIN

1.0 75

.50 .25

BIN

1.0 .75

.50 .25

BIN

.00

.00

.00

REQUIRED NUMBER OF PATIENTS

276 277

279 283

296 456

161 163

164 167

172 241

114 115

116 118

121 153

89 90

91 92

94 108

435 438

443 455

495 651

233 236

240 247

263 322

155 157

160 164

172 196

ll 5 117

119 122

126

rvsfl "1969 “ 2351 1962 1991 2994

55T~ 568

576 596

619

288 292

299 311

342 391

185 188

193 201

215 232

n r 136

140 145

153 154

*** **•

2376 “ 2392 ~ 3033 " 2381 2425 3619

657 665

677 707

964

328 334

344 362

411 449

207 211

218 230

252 261

147 151

155' 163

175 170

0.25

**• ***

2664 2672

727 731

747 788

m ' — 354 " 375 400 1081 362

467 495

221 227

236 251

281 284

156 160

166 176

191 183

0.3

*** *•*

2326 '7 8 5 9 2838 2922

4127 4556

756 767

789 842

1092 1172

368 378

395 427

512 530

228 236

247 265

303 300

160 166

173 184

203 191

7377 "7919 “ 4517 2891 3002 4869

7ST 779

807 873

IT77 1237

"372 384

405“ 442

544 553

230 239

253 " T I T 274 310

161 168

176 189

211 195

750 769

8d4 882

1235 1276

367 382

405 448

564 565

228 238

253 276

325 313

159 166

176 189

214 195

*** ***

5T1

*** ***

1416 '1423 1418 1435

or i s

*** ***

0.2

0735

77 7 778

“7S0- ~T32 786 1432

0.05

1604 2265

2687 1629 " 2733 4140

821 m

133

0.4

**• ***

2827 2845

0.45

*** ***

76'97""7762 T 9 7 7 2715 2899 5181

717' 743

784 874

1263 1289

356 373

390 445

570 565

222 233

249 274

326 310

155 162

172 186

212 191

075

*** ***

7490 2520

2579 2751

5031 ' 5181

677 704

751 850

1264 1276

339 3 58

385 435

564 553

212 224

240 266

319 300

148

155

165" 180

205 183

0.55

*** ***

'2240 2278

2353 “ 4975 " ' 2562 5077

625"" 709 656 814

1236 1237

318 338

367 417

546 530

200 212

228 254

305 284

139 146

156 170

194 170

175? 2008

2101 2347

55F 603

658 766

1180 1172

"294 314

343 392

515 ■ 495

185 197

212 237

284 261

128 135

144 157

17ff 154

267 286

314 360

471 449

l6 s 178

193 215

256 232

115 121

129 140

158 133

"237 255

280 321

415 391

147 157

170 188

221 196

99 105

111 120

ld4 108

124 "T4Z"~ 179 156 153 131

2881 2988

4802 5077

*806 4869

0.65

*** ***

1569 1730

TB43 “ 4524“ 2118 4556

507 545

601 708

IE75 1081

0.7

*'** • •*

T3B9 1462

1591 T17TT 1882 4140

44F 484

539 639

964

0775

'*'** • **

TT3T- 1 3 5 0

1626 3619

3ff5" 419

469 560

T O "' 821

203

219

240 275

347 322

0.8

«* ***

708" ' 1120

1011 2994

3 2 0 "~ 392 466

673” 651

155“

194 219

241

2*F

301

270

354

482 456

0.85

**•

1215

1640

989

1388

703

890

776

1115

079 ■■-«*■■■ "501 •** 556

640 799

2288 2265

1458 1432

'

349

m

177

266

462

CRC Handbook of Sample Size Guidelinesfor Clinical Trials

TABLE 4: ALPHA= 0.01 POWER= 0.9 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 120

DEL=.0 5 FACT=

DEL=.10

1 .0 .7 5

.5 0 .25

.00 BIN

PCONT=***

1 .0 .75

.50 .25

DEL=.15 .0 0 BIN

1 .0 .75

DEL=.20

DEL=.2 5

.50 .25

.0 0 BIN

1 .0 75

.50 .2 5

.0 0 BIN

1 .0 .7 5

.50 .25

.0 0 BIN

REQUIRED NUMBER OF PATIENTS

0 .0 5

••• ***

777 778

780 787

832 1432

276 277

0 .1

••• **»

1417 1419

1424 1438

1604 2265

***

1959 “ 1971 1963 1994

0 .2

••• • *»

2377 2383

0 .2 5

••• *♦*

279 284

296 456

162 163

165 167

172 241

115 115

117 118

121 153

89 90

91 92

94 108

437"

445

439

495 651

234 236

240 248

263 322

155

456

157

160 165

172 196

116 117

119 122

126 133

2351 2994

565 570

578 599

"779 821

289 293

300 313

342 391

"186 189

194 202

216 232

135 137

141 145

154

2395 2431

3033 3619

661 667

6*0 711

841 964

329 336

346 365

411 449

2o* 213

220 231

252 261

148 152

156 163

1 77' ’

2666 2674

2691 2742

3629 4140

724 734

T51 794

9*0 1081

356 364

378 403

467 495

222 229

238 253

281 284

157

168

162

177

191 183

••• ***

2830 2842

2865 2933

4127 4556

759 771

79$

1092 1172

371 382

399 430

512 530

231 238

250

850

268

303 300

162 167

175 185

203 191

••• **•

2881 2896

2926 3017

4519

768 784

814 882

1177 1237

377“

$44 553

233

388

409 447

242

255 276

318 310

163 169

17* 190

211

4869

0 .4

***

2*32 2851

2891 3008

4*02 5077

75$ 776

812 893

1234

371

'411

TS4

387

453

565

256 279

325 313

161 168

177

1276

231 241

214 195

0 .4 5

••• «•*

2698 2724

2774

4973

1263 1289

361 378

404 451

225

5181

794 886

' '570

2923

726 751

565

236

252 277

326 310

*•*

2498 2531

2595 2780

5031 5181

684 713

763 864

1264 1276

345 363

392 441

564 553

216 227

244 269

**•

2250 2291

2373 2596

4975 5077

634 667

721 828

1236 1237

324 344

373 423

$46 530

204 215

••• ***

1973 2025

2126 1 * 0 7

1180

780

1172

3o0 320

349 398

515

4869

57* 614

'771

2386

495

*** ***

1686 1751

1872 2160

4524 4556

519 556

614 722

1081

273 292

320 366

***

ira

1622 "7T31T 1925 4140

459 495

551

983

652

964

242 260

285 326

1383 1681

3626 3619

396 430

481 571

843 821

208 223

243T “ 337 279 322

329 358

'401

179

475

676 651

197 222

254 276

308 360

482 456

0 .1 5

0 .3 0 .3 5

0 .5 0 .5 5 0 .6 0 .6 5

0 .7

1487

o .7 r

***

1157

0 .8

•••

931 1015

1151 1425

3011 2994

0 .8 5

•** **•

725

916

2288

799

1146

2265

0 .9

**• • **

517 573

659 820

1458 1432

1242

1095

181

191

153

170

195

157”

174

164

188

319 300

150 158

167 182

232 257

305 284

re r149

158 172

170

189 200

216 240

284 261

130 137

146 158

178 154

47l 449

17l 181

“ 19S217

256 232

117 123

13l 142

158 133

415 391

150 160

172 190

221 196

101

llS

IT? " "

106

121

108

157

179 153

266 241

126

134

-

'

212 191

207 1*3

194

463

TABLE 4: ALPHA= 0.01 PQWER=0.9 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP* 130

DELs.0 5

DELs.1 0

1 .0 .7 5

.50 .25

.0 0 BIN

*** *•*

773"

781 788

’ 537 1432

*** ***

T718' "1775“ 1604 1420

1440

*** **•

m o 1964

1973 1998

FACT=

O .i 0 .1 5

.50 .25

.0 0 BIN

1 .0 .7 5

DEL=.20

DEL=.25

.5 0 .2 5

.0 0 BIN

1 .0 75

.5 0 .2 5

.0 0 BIN

1 .0 .7 5

.5 0 .25

.00 BIN

REQUIRED NUMBER OF PATIENTS

pcont =***

0 .0 5

1 .0 .7 5

D E1=.15

280 285

296 456

162 163

165 168

172 241

115 116

117 119

121 153

90 90

91 92

94 108

2265

437 ■ 446 440 458

495 651

235 237

241 248

263 322

156 158

161 165

172 196

116 118

120 122

126 133

2351 2994

566 571

580 602

679 821

290 295

302 314

342 391

187 190

195“ 203

216 232

135 138

14l 146

153 154

7379 “7398" "3033

331 338

348 367

411 449

209 214

221 232

252 261

149 153

157 164

175 170

779

276 278

2385

2437

3619

662 670

683 716

841' 964

*** *•*

"7558 2677

2696 2750

3629 4140

727" ' 756 737 800

980 1081

358 367

381 406

467 495

224 230

240 254

28l 284

158 163

16^ 178

19i 183

***

***

73 3 3 2846

2870 2944

4127

7Y2" ' 800

Tff*7

4556

775

858

1172

374 ' 402 385 434

512 530

233 240

252 269

303 300

163 169

176“ 187

204 191

***

***

78U5 2901

2934" 4519

772

' 821

3032

4869

789

891

1237

413 451

544 553

236 245

258 278

318 310

16 5 171

179 191

211 195

***

***

2837 2858

2900 3027

4802 5077

761 782

821 903

_ 17341276

376 - 415 391 458

564 565

234 244

259 282

325 313

163 170

179 192

214 195

***

2705

■7787 "7973

732

5181

759

1263' " 1289

410 456

570 565

228 239

255

2947

804 898

'355

2732

279

326 310

159 166

176 189

212 191

*** *•*

2507

2611 2809

5031

692 722

773

446

564 553

219 231

247 272

319 300

152 160

16*-

876

1264 1276

3 5 c r 397

2542

183

205 183

0 ." 5 5 - o t **♦

TOO

23*3“ 7*75

1236

2629

5077

642 677

732

2305

841

1237

'3 2 7 ‘ 379 349 428

546 530

207 219

235 259

305 284

143 151

160 173

194 170

0.6

V>U

7150

"305

515

264

2423

A m 4869

1180—

2042

0 .2 0 .2 5 0 .3 0 .3 5 0 74 0 .4 5 075

0.'65

*** *** *•*

1703

1900

1772

2200

5181

' 1177' ' ” 379“

326

355 403

495

192 203

219 242

261

132 139

148“ 160

178 154

4524 4556

57* 567

626 735

1095 1081

278 298

325 371

471 449

174 184

199 220

2 36 232

119 125

132“ 143

158 133

469 506

362 664

983 964

247 265

290 330

415 391

153 162

174 192

221 196

102 107

ll4 122

134 108

843-----821

212 228

' 27* 282

347 322

128 136

145 159

179 153

' 177" 184

200 224

266 241

1653

4130

1965

4140

0."75

**•

1179 1268

1414 1720

3626 3619

7S5

491

440

581

*** *♦*

*5T

T H O - 3UT1 1460 2994

337

410

676

366

483

651

*** **»

775"

941 " 2288

487

1174

2265

~75ff 283

314

821

366

456

*« **•

537

677 840

1458 1432

0^

589

369

1172

1511

0 .8 5

383

794

TOO

1041

392

625

TF7 — 683

077 ...." * " ■ ***

0 .8



CRC Handbook of Sample Size Guidelines for Clinical Trials

464

TABLE 4: ALPHA= 0.01 POWER= 0.9 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 140

DEL=.05 FACT=

DEL=.10

1 .0 .75

.50 .25

.0 0 BIN

778 779

782 789

832 1432

277 278

280 285

**«

1413 1421

1426

1604 2265

438 441

447

1442

*** •**

1966

1975 2002

2351 2994

2380 2387

2401 2443

3b33 3619

***

2670 2680

2700 2758

3629 4140

••• **•

2836 2849

2876 2956

4127 4556

•••

2838 2906

2941 3046

"4519

776

4869

2841 2864

2910 3045

*** ***

2711 2741

• **

0 .0 5 0 .1 0 .1 5 0 .2 0 .2 5 0 .3 0 .3 5 0 .4 0 .4 5 0 .5

"***

**•

•••

0 .5 5

.50 .25

.00 BIN

DEL= .2 0

.50 .25

.00 BIN

1 .0 75

296 456

162 “ 165 164 168

172 241

115“

495 651

235 238

242 249

263 322

157

459

567 573

582 604

679 "

291 296

303

821

316

657” 672

686 719

841 964

333 339

350 369

729 740

76b 805

980 1081

360 370

T87”

467

409

753

806 865

1092 1172

376 388

794

827 899

1177 1237

382 396

4802 5077

755 789

829 913

1235 1276

2799 2970

4973 5181

739 766

813 909

2515 2552

2627 2837

5o3i 5181

699 731

2271 2319

2412 2662

4975

PCONT=***

1 .0 .75

DEL=.15 1 .0 .75

.50 .25

.0 0 BIN

1 .0 .7 5

.50 .25

.0 0 BIN

117 119

121 153

90 90

91 92

94 108

159

161 166

172 196

116 118

120 123

126 133

342 391

188 191

1*6 203

216 232

136 138

142 146

153 154

411 449

150

158 " 1 7 5

215

233

261

154

165

226 232

241 255

281 284

159 164

170

T91

495

178

183

406 437

512 530

235“

254 271

303

165

177"

243

300

170

187

204 191

717“

544 553

238 247

260 280

318 310

167

455

181

173

192

211 195

379 396

42b 462

564 565

237 —2 6 l 247 284

325 313

T55 172

181 “ 214 193 195

1263 1289

370 388

415 461

570 565

231 242

258 282

326 310

161 168

177 191

212 191

784 888

1264 1276

354 374

403

564 553

222 234

250 274

319 300

154 162

171

451

184

205 183

651 686

743 853

1236 1237

335 355

384 433

546 530

210 222

238 262

305 284

145 152

162 174

170

1*5 206

221 244

284 261

134 141

149 161

178 154

177“

201 221

256 232

120 126

134 144

158 133

221 196

104 “ TI5 109 123

108

REQUIRED NUMBER OF PATIENTS

1961

5077

'

779

116

2

n r~ '222 "' 252

***

1799

2174 "7805“

2059

2459

4869

597 635

694 806

1180 1172

311 331

360 408

515 495

••• *«*

1717 1793

1927 2238

4524 4556

539 578

637 746

1095 1081

283 303

33b 375

471 449

••• ***

1449 1535

1683

413b 4140

478

573 675

983 964

252 270

295 334

155“

176

2003

391

165

194

*** ***

1201 1292

1443 1756

3626 3619



501

449

591

843 821

" 215 232

253 285

347 322

13d" 138

160

• ••

9*7 5 1065

1207

344 374

418 491

676 651

175

2b3

1492

3011 2994

187

226

266 241

0 .8 5

••• • **

764 842

964 1201

2288 2265

266 288

32b

482 456

0 .9

••• **»

545

694

“T458"

605

858

1432

0 .6 0 .6 5 0 .7 0 .7 5 0 .8

DEL=.2 5

516

371

415

'

187 '

147 ' 179 153

'



170

194

134





465

TABLE 4: ALPHA= 0.01 POWER* 0.9 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP* 150

D EL:.0 5 FACT=

DEL=.10

•••

.00 BIN

.00 BIN

1.0 .7 5

.50 .25

.00 BIN

172

1T5 " 117 116

119

121 153

90 91

91

241

92

94 108

157 159

162 166

172 196

118

120 123

126 133

164

166 168

236 239

243 250

263 322

— 2'9T“ 304

.00 BIN

~ ^IW 779

782

” 277 '

281

296

163

790

832 1432

278

286

456

1427 1444

1604 2265

439 442

448 460

495 651

1.0 .75

DEL=.25

.5 0 .2 5

.00 BIN

.50 .25

.50 .25

DEL=.20

.50 .25

1.0 .75

PCONT=*" 0 .0 5

1 .0 .75

DEL=.15 1.0 75

REQUIRED NUMBER OF PATIENTS

117“

0 .1

••• ***

i4 r? 1422

0 .1 5

•••

"1962

f977 “ 2351

297

317

158 192

197 204

215 232

153"

821

342 391

"172

2994

584 607

137“

2006

"578 574

"679

1967

139

147

154

• •• ***

2382 2389

2404 2448

3033 3619

666 674

689 723

841 964

334 341

3 52 370

411 449

212 217

223 234

252 261

151“ 154

159 165

175 170

• •• ***

2672

2704

362

386 411

467 495

227 234

243 257

281 284

160 165

171

2767

3629 4140

930

2683

179

191 183

***

2839 2853

2882 2967

0.35

• •• ***

2892 2911

2949 3061

0 .4

••• **•

0.2 0.25

**»

731

' 764

743

811

1081

4127 4556

76 8 783

811 871

“ TO9 2

379

1172

391

409 440

512 530

236 244

2 56 272

303 300

166 171

188

203 191

4519 4869

780 799

834 907

1177 1237

385 400

421 458

544 553

240 249

262 282

3 18 310

166 174

182 193

211 195

2846 2871

2920 ~4TO2 3064 5077

" 771

' 836

1234 "

383 ' 424

'167“

1276

400

249

264 286

325

922

"564" 565

239

795

313

173

182 194

214 195

*** “ 2717 • ** 2749

ZS12 ” 4773 2993 5181

***

2523 2563

2643 2864

••• ***

2281 2332

2432 2693

•** ***

2012 2076

2 l97 2493

0 .6 5 " * «

'1735 1813

0 .3

0 .4 5 0 .5 0 .5 5 0.6

•••

0.7 " *** *** 0 .75" m 0.8 0 .8 5 " 0 .9 '

*** **•

'

--

'

372

466

745

- 822

'T O T -

374

419

570

1289

392

465

565

260 284

326 310

179

919

234 245

153“

773

170

192

212 191

5031

706

' 793

T264"

“ 359

5181

739

899

1276

379

407 455

564 553

225 236

252 276

3 l9 300

156 163

172 185

205 183

4975 5077

"559 " 754 864

1236 1237

339 360

389 438

546 530

213 224

240 264

305 284

147 154

163

695

175

194 170

4806 4869

605 644

705 817

1180 1172

315 336

365 412

"515' 495

197 209

224 246

284 261

135 142

150 162

178 154

1751' 4 s n 2274 4556

" 548 587

' 648 757

1095 1081

288

335 379

'471' "

179

307

449

190

203 223

2 56 232

122 127

135 144

158 133

'

W

i5 e 167

178 195

221 196

105 110

116 123

134 108

132

148 161

179 153

"1455" 1710

4130

487

' 583

4140

525

685

964

253 274

299 338

415"

2039

1222

1771"""3623

" 422

' 509

1316

1791

457

599

843 821

220 235

256 288

347 322

178

205 228

2 66 241

1558

3619

351

“ 425

2994

382

498

676 651

862

956 " 2 m 1226 2265

~ 271 294

' 325 375

482 456

560 619

7E9 874

” 993“ 1087

“782""

178

m

r ” 3G il ' '

1523

1458 1432

190

391

'

139

CRC Handbook of Sample Size Guidelines for Clinical Trials

466

TABLE 4: ALPHA= 0.01 P0WER= 0.9 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 160

DEL=.0 5

DEL=.10

DEL=.15

1 .0 .7 5

.50 .25

.00 BIN

*•*

778 780

783 790

832 1432

277 279

281 286

296 456

**•

1419 1422

1429 1447

1604 2265

439 443

449 462

0 .1 5

*** ***

1963 1968

1979 2010

2351 2994

570 575

072

*** ***

2383 2391

2407 2454

3033 3619

0 .2 5

••• **•

2674 2686

270# 2775

0.3

•** ***

b .35

DEL=.20

D EI=.25

.50 .25

.00 BIN

1 .0 75

.50 .25

.0 0 BIN

1 .0 .7 5

.50 .25

.00 BIN

163 164

166 168

172 241

116 116

118 119

121 153

90 91

92 93

94 108

495 651

236 239

244 250

263 322

158 160

162 166

172 196

117 119

120 123

126 133

586 609

679 821

203 298

306 318

3H 391

189' 193

108 204

216 232

"■ 137 140

143 147

153 154

667 676

692 727

841 964

336 343

354 372

411 449

213 218

225 235

252 261

'

152 155

160 166

175 170

3629 4140

734 746

768 815

980 1081

365 374

380 414

467 495

229 235

244 258

281 284

162 166

172 180

191 183

2842 2857

28## 1 1 2 7 2978 4556

771 787

816 877

1092 1172

382 394

412 443

512 530

238 246

257 274

303 300

167 173

179 189

204 191

•••

2896 2916

2957 3076

4519 4869

784 804

840 915

1177 1237

388 403

425" 462

5 4*~~ 553

242 252

264 284

318 310

169 175

183 194

211 195

0.4

••• ** *

2851 2878

293d 3082

4802 5077

773" 801

#44 931

1235 1276

387 403

42# 470

564 565

241 252

26 6 287

325 313

168 175

184 195

214 195

0 .4 5

••• •**

2724 2757

282$ 3015

"4973 5181

751 781

830 928

1263 1289

378 397

424 469

570 565

236 247

263 286

326 310

164 171

180 193

212 191

0 .5

••• **•

2531 2574

2659 2890

5031 5181

713 747

803 909

1264 1276

363 383

412 460

55*

227 239

255 278

319 300

15'8" 165

m

553

186

20$ 183

**• ***

2291 2346

2451 2723

4975 5077

667 704

764 875

1236 1237

344 364

394 442

546 530

215 227

243 266

305 284

155

164 176

194 170

0 .4

•**

2025 2093

2220 2526

4806 4869

3X4 654

715— l l # 0 1172 828

320 341

370 416

51'5 " " 495

200 211

226 248

284 261

137 143

T52 162

178 154

0 .6 5

*** •**

1751

1970 2308

4524 4556

$56 597

"SOT""' 1095 768 1081

292 312

339 383

471

205 225

123"" 136

449

182 192

256

1833

232

129

145

158 133

1487 1580

1738 2074

4130 4140

592 694

983 964

260 278

303 341

415 391

160 169

1#0 ' 221" 196 196

106

534

' 116 124

134 108

1242 1339

1408 1823

3626 3619

430 466

518 608

843 821

223 239

260 291

347 322

134 141

i$ o 162

181 192

20# 230

266 241

FACT=

PCONT=• * • 0.O5 0 .1

0 .5 5

0 .7

***

0 .7 5

1 .0 .75

.50 .25

.00 BIN

REQUIRED NUMBER OF PATIENTS

495

*** ***

1015

125#

1109

1552

3011 2994

358 388

432 504

676 651

0 .6 5

*** •••

700 881

1008 1250

228# 2265

276 299

330 380

482 456

0 .9

••• ***

573 633

724 890

1458 1432

0 .8 '

1 .0 .75

179 153

“ _....

149

111

467

TABLE 4: ALPHA= 0.01 PQWER=0.9 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP=17Q

DEL=.05 FACT=

D E L = .10

DEL=.20 .00 BIN

1 .0 .7 5

.50 .25

.00 BIN

IT T ” 117

118 119

121 153

90 91

92 93

94 108

263 322

158 160

163 167

172 196

irr" 119

121 123

126 133

.00 BIN

1 .0 75

163 164

166 169

172 241

450 “ 793“ 463 651

237 240

244 251

.50 .25

.00 BIN

.50 .25

779 780

783 791

332” " 1432

277 279

282 286

1604 2265

440 444

.00 BIN

1 .0 .75

D E L = .25

.50 .25

.50 .25

1 .0 .75

REQUIRED NUMBER OF PATIENTS

PCONT=*** 0 .0 5 " ■*** ***

1 .0 .75

D E L = .15

296 456

'

O .i

*** ***

0 .1 5

••• **•

1964 1970

1*81 2014

2351 2994

571' 577

588 611

679 821

294 299

307 319

342 391

190 194

196 205

215 232

138 140

143 147

153 154

***

2383“ 2410 2393 2460

3033 3619

669 678

695 730

841 964

337 344

355 374

411 449

214 219

225 235

252 261

152 156

160 166

175 170

0 .2 5 "*** ***

2677“ 2712 2688 2783

3629 4140

736" 749

771 “ 78'0' 820 1081

553“ 376

391 416

467 495

230 237

246 259

281 284

162 167

172 180

191 183

0 .3

***

2843 2861

2893 " 7T27 2989 4556

777 791

821 883

” “ 587” 396

415 446

512 530

240 248

259 275

303 300

168 174

18d 190

203 191

O'. 35

***' ***

2907"' 2964 2921 3090

4519 4869

' 788 809

0 .4

••• **•

2856 2884

7*07” 5077

0 .4 5

*** '' 2 7 JO- 2837 "7773” ........757— *** 2766 3037 5181 787

0 .2 '......

0 .5 ” " « * **•

' 1420“ 1430 1423 1449

2940 3100

2559” 2674 2585 2916

1092 1172

846 “ 11'77 1237 922

391 406

428 465

544 553

244 254

266 285

318 310

171 177

184 195

211 195

851 939

1235 1276

39d 407

432 473

564 565

244 254

268 289

325 313

170 176

185 196

214 195

838 937

1263 1289

' 382“ 401

428 473

570 565

239 250

265 287

326 310

166 173

181 194

212 191

5031 '■" ' 720— 811 5181 755 918

1264 1276

368 388

416 463

564 553

230 242

257 280

319 300

139 166

175 187

205 183

218 229

'7 7 5 “ 267

305 284

150 157

165 177

194 170

781 807

•**

" 2'30T" 2470 2359 2753

4975 5077

674— 773 885 713

1236 1237

348 369

398 ' " 575" 446 530

0 .6

*** *•*

2058” 2242 2109 2558

4806 4869

622— 725 837 662

1180 1172

324 345

374 420

515" 495

'

202 214

228 249

284 261

138 145

153 163

178 154

0 .6 5

*** ***

1757 1853

2004 2341

4524 4556

565— 667 777 606

1095 1081

296 316

344 386

471' "” 449

184 194

207 226

256 232

l'Z7 130

137 146

156 133

0 .7 " '*** *•*

1503 1601

1764 2107

4130 4140

503” 543

601 ~ 9 JT ~ 703 964

264 282

307 344

415" 391

161 170

182' ' 221 197 196

107 112

117 124

134 108

0 .7 5 " '

***

125T" 1524 1361 1854

3626 3619

437 ' " 526 615 473

843 ' 821

TTT 242

263 ' "347" '" 293 322

135 142

151""" 179 163 153

0 .8

*** ***

1057"' 1282 1130 1580

5011 2994

364 "■ 439 510 395

676 651

183 195

2 l0 232

0. 65

*** ***

816 " 1028 899 1272

2288

281

335

482

304

384

456

*** **•

585— 738

I45B"

0755

0.9

646

905

2265 1432

'

266 241

CRC Handbook of Sample Size Guidelinesfor Clinical Trials

468

TABLE 4: ALPHA= 0.01 PQWER=0.9 EXPECTED ACCRUAL THRU MINIMUM F0LLQW-UP=180

DEL=.05 FACT=

1.0 .75

.50 .25

.00 BIN

•••

119 780

784 792

832 1432

1.0 .75

276 279

•••

1420 1424

1431 1451

1604 2265

441

0.15

***

1965 1971

1983 2018

2351 2994

0.2

«* ***

2386 2395

2413 2466

***

2679 2691

•••

.50 .25

.00 BIN

1.0 .75

D E L = .20

DEL:= .25

.00 BIN

1.0 75

.50 .25

.00 BIN

1.0 .75

1 3 6 ’ 172 169 241

116 117

118 119

121 153

160

158

163 167

172 196

- - 171 194

199 205

.50 .25

.50 .25

.00 BIN

90 91

2 3

94 108

119

118

21 23

126 133

216 232

138 141

44

153

REQUIRED NUMBER OF PATIENTS

PCONT=*** 0.05

D E L = .15

D E L = .10

**»

282 287

296 456

163 165

444

464

651

495

238 240

245 251

263 322

578

572

590 613

879" 821

293 300

308 320

342 391

3033 3619

671 680

697 " 841 733 964

338 346

357 " 4ll 375

449

220

215

226 236

252 261

153 156

61 66

175 ~

2717 2791

3629 4140

738 751

775 824

980 1081

368 378

393 417

467 495

231 238

247 260

281 284

163 168

73

81

101 183

2847 2865

2899 3000

4127 4556

777 795

825 888

1092 1172

386 399

417 448

512 530

242 249

260 276

303 300

169 175

81

204

• ••

***

2904 2926

2972 3104

4519 4869

792 814

852 928

1177 1237

394 409

431 467

544 553

246 255

268 287

318 310

172 178

96

85

211 195

**»

2861 2891

2949 3118

"755" ' 857 812

946

1235 1276

393 411

436 477

' 564

565

246 256

291

270

325 313

171 177

86 97

114

*•*

2736 2774

2830 3059

4973 5181

762

794

846 945

1263 1289

386 404

432 476

570 565

241 252

267 289

310

167 174

83

212 191

0.5

•••

• **

2547 2595

2690 2941

5d3l 5181

727 763

820 927

1264 1276

3 71 392

420

564 553

232 244

259"

319 300

161 168

76

205 183

0.55

••• • **

23l2 2373

2489 2781

"4975 5077

682 721

782 894

1236 1237

352 373

402 449

346 530

220 232

"547 269

305 284

158

151

67

194 170

0.6

•** **«

2051 2126

2264 2589

4806 4869

630 671

734 847

1172

1180

328 349

378 423

495

515“

205 216

230 251

284 261

140' ' 54 146

64

178 154

0.65

***

*# •

1783 1872

2028 2373

4524 4556

614

573

676 786

1081

1095

300 320

347 389

471 449

186 196

209 227

256 " 232

125 131

38 46

138 133

***

1622

1523

1789 2138

413d 4140

511

610 711

983 964

285

267— T U T 347

415

163 172

163 198

221 196

IbB 112

18 25

134 108

0.75

*** ***

1280 1383

1349 1884

3626 3619

444 481

622

533

843 821

23d 245

265

347

137 144

152 163

179 153

0.8

*** ***

1053 1151

1305 1606

3011 2994

370 401

445

676 651

186 197

2l2 233

266 241

1047

2288

283

339

482 456

752 918

1458 1432

0.1

0.25 0.3 0.35 0.4 0.45

0 .7

0.85 0.9

***

• **

• ** m

***

'

916

"597 659

1293

"4B02 ” 5077

2265

551

308

451

516

387

467

295

391

322

'

282

-3 2 3 ""'

47

90

94

78

154

170

191

195

"

469

TABLE 4: ALPHA= 0.01 PQWER=0.9 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 190

DEL=. 05 FACT=

D E L :.10

1 .0 .75

.50 .25

.00 BIN

PCONT=*** 0 .0 5

0.1 0 .1 5 O.Z

0.25

0 .3 5 0 .4 " 0 .4 5 0 .5

.50 .25

.00 BIN

1 .0 .7 5

.50 .25

.00 BIN

278

282

793

1432

280

287

294 456

144 165

167 169

172 241

116 117

118 119

l2 l 153

90 91

92 93

94 108

*•*

■n r r 1425

1432 1453

1404

441 445

452

495 651

252

263 322

159“

465

238 241

245

2265

163 167

172 196

118 119

121 123

133

**• ***

1946“ 1985

2351

573 ' 591

679 ....

295

2994

580

615

821

301

342 391

137

2021

309 321

19T" 199

1972

141

144 148

154

••• ***

2386 2397

2416 2472

3033 3619

672 682

700

841 964

340 347

""358

736

376

161

124 153

195

206

213 232

4 ir"

21"3 221

227 237

252 261

154

449

157

161 167

174 170

281 284

164 168

174 181

191 183

*•*

2481 ' 2721' 5J29

778 " 9 8 0

37 I T

2799

740

2694

4140

754

828

1081

380

395 419

467 495

233 239

248 260

••• ***

2850 2868

29o5

4127 4556

780 799

830 " 1092 893 1172

389 401

420 450

512 530

243 251

262 277

303

170

3011

300

176

182 191

203 191

**♦ ***

2907 2931

2979 3118

4519 4869

796 819

857 934

1177 1237

397 412

434

544 553

248 257

269 288

318 310

173 179

186

470

196

211 195

***

2866 ' 2959 2897 3136

4802 '

77D

397

818

864 954

T274""

5077

1276

414

439 479

564 565

248 258

272 292

325 313

1^2 179

198

214 195

••• ***

' '2743"" 2862 2783 3080

4973 5181

T48 ' 801

853 953

1253.....

389 ' 475 408

479

570 565

243 254

269 290

326

1289

310

168 175

184 195

212 191

2555" 2705

5031 5181

733 770

828 936

1264 1276

375 396

424 470

544 553

234 246

261 283

319 300

162 169

177 189

205 183

4975 5077

489 729

790 903

1236 1237

354 377

404 453

546 530

222 234

249 270

305

157

284

159

146 179

194 170

4304

" ■“737 679

743 856

1180

332“

232 252

284 261

155

495

207 218

141

353

382 426

515"

1172

147

165

176 154

*•*

1798 "2P32" 4524 ------ 533 1890 2404 4556 622

485 794

"1095 1081

3u r 324

392

471 449

188 198

ill 229

236 232

126 132

138 147

133

*** **•

r n r ~ ' 1813 1643 2168

'4T30

51 8 "" 618 559

719

983' 964

271“ 289

313 349

415 391

145

4140

174

185 199

221 196

109 113

118 125

134 108

*** *•»

1298 1404

1573 1912

3426 3619

451 488

540 629

843 821

233 248

268 297

347 322

138 145

153 164

179 153

*** •**

rc 7 0 " 1327 1170 1631

3m 2994

"tti 407

450

676 651

' 188 199

214 234

266 241

*** ***

847

1065

22*8

■■"270

343

933

1313

2265

312

391

*« ***

409 671

744 ' 931

1432

2808

0 .4

2043 "225* 2142 2618

0 .9

1 .0 75

781

2322 2386

0.85

.00 BIN

REQUIRED NUMBER OF PATIENTS

0 .5 5 .... m *•*

0.8

.50 .25

832

2966

0 .7 5

1 .0 .75

784

2606

0 .7

.00 BIN

D E L :.25

779

••• ***

0 .4 5

.50 .25

D E L :.20

*** ***

***

0 .3

1 .0 .75

D E L :.15

"t o • **

2308

4869

1458

'

521

482 456

"

351'

'

187

158

CRC Handbook of Sample Size Guidelines for Clinical Trials

470

TABLE 4: ALPHA= 0.01 POWER= 0.9 EXPECTED ACCRUAL THRU MINIMUM F0LL0W-UP= 200

DEL=.05 FACT=

DELs.lO

1 .0 .7 5

.50 .25

.00 BIN

PCONT=***

1 .0 .7 5

.50 .25

DEX=,15 .0 0 BIN

1 .0 .75

DEL=.20

.50 .25

.0 0 BIN

1 .0 75

.50 .2 5

DEL=.2S .0 0 BIN

1 .0 .7 5

.5 0 .25

.00 BIN

REQUIRED NUMBER OF PATIENTS

0 .0 5

•••

***

779 781

785 794

832 1432

278 280

283 287

296 456

164 165

167 169

172 241

116 117

118 ' 121“ " 119 153

91 91

92 93

94 108

0 .1

••• **♦

1422 1425

1433 1455

1604 2265

442 446

453 466

495 651

239 242

246 252

263 322

159 161

164 167

172 196

118 120

121 124

126 133

***

1967 1974

1987 2025

2351 2994

574 581

593 617

679 821

297 302

310 321

342 391

192 195

200 206

216 232

139 141

144 148

153 ” 154

000

2389 2399

241* 2477

3033 3619

'674

702 739

841 964

341 349

360 378

411 449

217 221

228 237

252

154

684

261

158

162 167

175 170

tT.25" *** **•

2683 2697

2725 2807

3629 4140

743 757

782 832

980 1081

372 382

397 421

467

234

165

175

495

240

261

284

169

182

191 183

0 .3

***

2853 2872

291b 3022

412 7

783 802

834 898

1092 1172

391 “ 322 404 452

512 530

244 252

263 278

303 300

171 176

183 191

204

4556

•••

*•*

2911 2936

2987 3132

4519 4869

799 823

863 940

1177

400 415

437 472

544 553

249 259

271 289

318 310

174 180

187 197

211 195

*** *•*

2871 2904

2969 3153

4802 5077

795 823

870 960

1235 1276

400 417

442 482

564 565

249

273

260

293

325 313

173 180

188 198

214 195

*** ***

2749 2791

2874 3100

4973 5181

773 807

860 961

1263 1289

392 412

439 482

' ~~2'43

• ••

2563 2617

2721 2990

5031 5181

739 777

836 944

1264 1276

379 399

428 473

*** ***

2332 2399

2526 2835

4975 5077

696 736

799 911

1236 1237

360 " “410" 456 381

••• ***

2076

2307 ' 4'806 2647 4869

644 687

751 864

n8b 1172

336

2158

357

385 430

495

0 .6 5

***

1813 1909

2074 2433

4524 4556

3*8 630

693 802

1095 1081

307 327

354 395

"'471' 449

0 .7

••• • **

1558 1663

1*37 2197

4130 4140

521' 566

625 726

963 964

274 292

316 352

415: 391

0 .7 5

*** 000

1316 1424

1596 1940

3626 3619

'457 494

547 635

843 821

235 250

270 299

347 322

••• ***

1087 1189

1348 1655

3011 2994

382 412

456 526

'676 "

190 201

216

266 241

***

862 949

1082 1332

2288 2265

294 316

347 394

482 456

••• • ••

619 683

0 .1 5 0 .2

0 .3 5 tT T -

0.45 0 .5 0 .5 5 0 .6

0 .8 0 .8 5 0 .9

*** •••

“ 777 " 1458 944

1432

1237

651

236

H570"

' 249'“' 2 8 1 "

191

"T70"" 1*3"" 212

565

256

271 292

326 310

176

196

191

5 tt " 553

237 248

263 284

319 300

163 170

178 189

2b5 183

546 530

224 236

251 272

305 284

' 154 160

169 179

194 170

513

209

220

234 253

284 261

142 148

156 165

178 154

190 200

212 230

256 232

127 133

139 147

158 133

167 175

186 200

221 196

110 114

119 125

134 108

“ TC9 146

154 165

179 153



471

TABLE 4: ALPHA= 0.01 PQWER=0.9 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP- 225

DEL*.0 5 FACT=

1.0 .75

.50 .25

DEL=.10 .00 BIN

0 .1

•••

***

*** »**

0 .2 0 .2 5 ' 0 .3

0.45 0 .5

1 .0 .75

.00 BIN

1 .0 75

.50 .25

.0 0 BIN

1 .0 .75

.50 .25

.00 BIN

147

172

149

241

117 117

118 120

121 153

91 91

92 93

94 108

160 162

164 168

172 196

119 120

122 124

126 133

342 391

' 193 197

201 207

2 l6 232

140 142

145 149

153 154

411" 449

219 223

230 239

252 '"

154

261

159

143 148

174 170

174

.50 .25

784

831

... 279

284

295

782

795

1432

281

288

454

fro 1427

1434

1604

444

455

"495 '

1440

2265

448

468

651

597 621

473

299 ” 312“

821

304

323

708 745

841 964

" " 3"44 352

380

1992 "235'1 ------577 '

_ _ 240 243

247

263"

253

322

2034

*** " 2393 *** 2404

2491

3619

689

2233

2735

790

980' ' “ 374

401

447"

2827

3"429 4140



2704

764

841

1081

384

424

495

236 243

251 263

281 284

147 171

183

191 183

2850

2925 "T127

"771

844

3048

4556

811

910

1097" 1172

428”

2882

512 530

248 255

264 281

303 300

174 178

185 192

203 191

253 262

275 291

318 310

174 182

189 198

211 195

325 313

174 182

190 200

214 195

*** *** ***

••• *** *** *** "*** ***

2994

144 165

1977

0 .3 5 " * * * *** 0 .4

.00 BIN

780

0.15 ■' *** ■ 1949 **#

.50 .25

REQUIRED NUMBER OF PATIENTS

PCONT=*** 0 .0 5

1 .0 .75

DEL=.15 DEL=.20

2424 ■ w

584

"578

2921

3004

"4519

309

875

1177

2949

3165

4869

834

954

1237

2883 2920

2973" "4302' " "30-4 ' 885

1233

3194

1276

5077

"2755 "2705"“ 4777 2812

3150

836

976

787

877 978

5181

822

'2533

2758 “5031

"754

2443

3047

5181

793

— 396

363”

409

457

404" 421

443 ' 54'4" 478 553

' 407 424

"1243 " ” 400 1289 419

254

277"

264

296

447 ' 570" ' 489 565

249 260

294

326 310

173 179

187 197

212 191

564 553

241 252

247 287

3 l9 300

144 173

181 191

205 183

544 530

229 240

255“

305 284

157 143

171

275

181

194 170

213 224

237 254

2d4 261

145 150

158 144

178 154

194

214 232

254 232

130 135

'111 148

158 133

139 202

"221 194

nr

178

120 124

134 108

142

155"

149

146

179 153

449” 488

854 962

I24T~

337”

434

1274

408

480

564 565

0 .5 5 " * * * **•

2758

2570 “ 4775

"712

818

1235"

35B-

418

2432

2898

5077

754

930

1237

389

442

0 .6

2107

2357 “ 4 305'

‘1180

344

393 “ 515"

2714

441 705

770

2197

883

1172

345

434

0 .4 5

"“ *** *** '*** **»

4869

1750 "2129“"752T 1953

505

712 ■ '1095 "

2502

4556

448

820

1081

495

315 ‘ 362“ ' 471" 449 401 335

*** *•*

1599

1893

■4130

323“

4140

443 743

282”

2265

' "5T2 583

933“

1710

944

299

357

415" 391

0.73" ***

1359

1450

7524

"772

242

2003

3619

509

543 449

843

1471

821

257

216 303

347 322

217”

264 241

0 .7 "

***

O.ff- ' *** •••

TT7B

1397 ""3011""

394

448 " 4 7 4 -

1233

1710

2994

425

534

451

0 .8 5

*** *•*

897'

1123 1374

2288

703

354

482—

2265

325

401

454

••• *•*

445 709

805

"T458"

972

1432

0 .9

986

—T9"4” 205

'

238

203

170

275"

114

DEL*.25

CRC Handbook of Sample Size Guidelines for Clinical Trials

472

TABLE 4: ALPHA= 0.01 PQWER= 0.9 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 250

1 .0 .7 5

.50 .25

.0 0 BIN

781

787

783

797

r a 1432

PCONT=*** c :o 5 - - * * • • O'.i C .15 0 .2 0 .2 5

F.3 O'. 35 0 .4 0 .4 5 0". 5 '

O'. 55 O'. 6 0 .6 5 0 .7

IT. 75

.50 .25

.0 0 BIN

1 .0 .75

.0 0 BIN

117 118

120

121 153

161

165 168

172 196

1 .0 .7 5

.5 0 .2 5

.00 BIN

91 "

92

94

92

93

108

119 121

122 124

133

141 143

146 149

154

164 168

170

175 166

168

172

170

241

445 450

457 470

495 651

241 244

248 254

263 322

679 821

301 306

3 l4 325

342

195

391

198

202 " 216 208 232

411 449

220 225

23l 240

252 261

467 495

239 245

253 264

281

168 172

177

284

183

191 183

1429

1465

2265

* * * *

1972 1 7 7 7 " "2351

579'

600

1980

2043

587

624

* * “ 7Z397 • * 2409

2434

3033

682 ' 7IT

841"

2504

3619

694

751

964

355

* *

"2693

2746

3629

754 ""~797

2711

2846

4140

770

* • •

2891

* * • • * * • •

2994

2867 “ 2719” ~*I27 3073

4556

2930

3024

4519 " "

2962

3198

4869

2896

3017

4802

2937

3234

2781 2833

2935 3197

* "2303 • • 2669

119

2 96' 456

1604

* * •

.5 0 .2 5

284

1439

* •

1 .0 75

289

1424

• *

.0 0 BIN

282

" "230"

* * • *

• •

.5 0 .25

REQUIRED NUMBER OF PATIENTS

” " 3 47“

366 382

163

" IT T 160

126 153 175

980

380 ' 405

849

1081

390

428

79* ' 854 819 919

1092 1172

401 414

432

512

461

530

251 258

269 282

303 300

175 180

186 193

204 191

1177 1237

411 427

449 482

544 553

257 266

277 293

318 310

177“ 184

191 199

211 195

564 565

257 267

280 298

325 313

178 184

192 201

214 195

278 297

326 310

175“ 181

189 199

212 191

887”

817 844

966

817 848

898

1234

413

437

5077

990

1276

431

494

4973 5181

799 835

892 993

1264

' '407

454

570 " " "254

1289

427

494

565

264

2794

5031”'

3100

5181

768 809

870 979

1264 1276

394 415

443 486

574" 553

256

271 290

319 300

168 175

182 192

205 183

426

546 530

233 244

2 58 277

305 284

159 165

172 182

194 170

2383

2613 "4775

727 ' 835

1236'

2464

2957

5077

770

947

1237

376 397

468

245

• *

2138

2405

4806"'" 4869

899

1180 1172

352 373

400 442

'"3r5

2776

677 722

787

2235

495

217 228

24l 258

284 261

147 152

159 167

178 154

* • * •

1886 1996

2180 2565

4324

620 664

728 836

1095 1081

323 342

368 406

471 449

197 207

219 234

2 56 232

132

4556

136

142 149

158 133

* * • •

T638

1945

4130

557 ' ■533“ 599

757

328 361

415 391

173 181

113

4140

288 305

221

2326

983 964

191

1755

204

196

117

122 127

134 108

486 “ 576' 523 661

843 821

247 262

280 306

' 377

144

322

151

158 167

179 153

479' ' 676

199 209

223 241

" 276"

* *

** * * •

1"399 'T 7 0 T 3426 1516

2060

3619

* * ' ~n65 1274

1443

TO11

1760

2994

0". 85

* • •

1160 1415

2288

0 .9

*■ * " -578 * • 734

JT.fl

1 .0 .7 5

DEL=.2 5

DEL=.20

DEL=.15

DEL=.05

• •

929 1021

2265

830

"TT58

997

1432

406 437

545

311' '" 363 333 406

651

482— 456

241

473

TABLE 4: ALPHA=0.01 PQWER=0.9 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 275

DEL=.05 FACT=

DEL=.10

1 .0 .75

.50 .25

.00 BIN

1 .0 .75

.50 .25

D EI=.15 DEL=.20 DEI=.2S .00 BIN

1 .0 .75

.50 .25

.0 0 BIN

1 .0 75

.50 .2 5

.0 0 BIN

1 .0 .75

.50 .25

.0 0 BIN

REQUIRED NUMBER OF PATIENTS

PCONT=*** 0 .0 5

**♦ ***

78 r 784

788 799

832 1432

280 282

285 289

295 456

155 166

168 170

172 241

11T 118

119 120

121 153

91 92

92 93

94 108

0 .1

••• *•*

1425 1431

1442 1470

1504 2265

447 451

459 471

495 651

242 245

249 255

263 322

16l 163

165 168

172 196

120 121

122 124

126 133

0 .1 5

• • • ~ T 9 7 4 - ■2001 *** 1983 2051

2351 2994

'582' 590

604 628

579' 821

303 308

315 326

342 391

196 199

203 208

215" " 232

142 144

146 149

153 154

0 .2

•••

” 2*00 2414

2441 2517

3033 3619

585 ' 698

718 756

841 964

349 357

358 384

411 449

222 227

233 241

252 261

158 161

165 169

175 170

***

2699 2718

2755 2864

3629 4140

759 776

804 855

980 1081

383 394

408 430

467 495

241 247

'2 5 5 ' 266

281 284

169 173

1*78 184

l9 l 183

403“ 418

435 464

512 530

253 261

271 284

303 300

177 182

187 194

204 191

260 268

280 295

318 310

180 186

192 200

2 il 195

261 271

283 300

325 313

180 186

193 202

213 195

0 .2 5

'

0 .3

• • • “ 2575 "2933 ■ T O T - " *** 2901 3097 4556

0 .3 5

••• ***

"2 9 3 9 2974

0 .4

•** ***

2708 2953

0 .4 5

**'*" **»

0 .5

~ rm

804 _ 853 928 827

' 1792“ -" 1172

'3043 " T 5 I7 3228 4869

825 ' 854

897 977

1177 ' 1237

TO” 432

454 486

544 553

3041 3271

827 860

91l 1002

1234 1276

419 437

451 498

554 565

1254 " 1289

414 433

450 499

577 565

251 268

281 299

325 310

177 183

190 199

212 191

" 4 5 0 " 564 491 553

249 260

274 292

319 300

l7 l 177

184 193

205 183

4802 5077

'"

' ■2954 “ 4773“ 3241 5181

'

811 848

905 1007

*** “ 2723'' 2830 “ 3737' *** 2695 3150 5181

'

781 823

885 993

~ nzr 1276

401 422 " 383“ 404

432 473

545 530

237 248

261 279

305 284

151” 167

174 183

194 170

2854

***' • **

2408 2495

2554 3011

T973 5077

741 785

850 961

1235 1237

07J— *****»

2158 2271

2450 2833

4805 4869

592 ' 737

803 914

"TTfi0~ 1172

337“ 379

407 446

513 ' 495

2z r 231

244 260

284" 261

149 154

160 168

178 154

0.T 3 ^

***

1920 2036

2227 2623

*5244556

535 679

744 850

1095 1081

"327“ 348

374 410

47l 449

200 210

22l 236

256 232

133 138

143 150

158 133

"***" **•

1575 1797

1994 2383

T137 " 4140

570' 612

6?2 769

983 964

294 311

333 365

415 391

175 184

193 205

221 196

T1'4” 118

122 127

134 108

**•

1435 1557

1747 2112

3625 3619

378 536

588 671

843 821

252 266

285 309

347 322

14T 153

160 168

179 153

”1270 ' 1484 1312 1806

30 IT 2994

415 447

489 553

575' 651

202” 213

225 243

265 241

7 2 8F 2265

719" 341

370 411

482 456

0 .5 5

o .r 0 .7 5

O'.T ” * « " »•* 0."K 0.9"

»*• ***■ •**

' "957" ' 1195 1053 1451 589" 756

853 1019

1458 1432



CRC Handbook of Sample Size Guidelines for Clinical Trials

474

TABLE 4: ALPHA= 0.01 PQWER=0.9 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 300

D E L = .0 5

FACT=

D E L = .10

D E L = .15

.5 0 .2 5

BIN

1 .0 .7 5

.50 .25

BIN

172 241

117 118

119 120

121 153

91 92

92 93

94 108

262 322

162 164

166 169

172 196

120 121

123 124

126 133

3b4 310

317'' ' 342 327 391

177'

204 209

215 232

142

147

200

144

149

153 154

841 964

352 360

3?b 386

411 449

223 228

23*" 241

252 261

159 162

165

175

169

170

811 862

98b 1081

386 397

"4 I T " 433

467 495

243 249

257 267

281 284

171 175

170 184

191 183

811 834

871 936

1092 1172

409 422

440 467

512 530

256 263

272 285

303 300

178 183

188 195

203 191

4519 4869

834 862

9b7 986

1177 1237

42l 437

458 490

544" ' 553

262 271

282 297

318 310

182 187

193 201

211 195

3064 3307

4802 5077

836 870

922 lb l 3

1234 1276

424 442

465"

564

502

565

264 273

286 302

325 313

182 188

104 203

214 195

2812 2874

2993 3283

4073 5181

822 860

919 1019

1263 1289

419 439

465 504

570

26b 271

284 301

326 310

179 185

“ 192“

565

212 191

2643 2721

2864 3197

5031 5181

793 836

800 1006

1264 1276

407 428

455 496

564 553

252 263

276 294

319 300

ll2 178

2432 2526

2693 3062

4075 5077

754 799

864 075

1236 1237

389 410

438 478

546 530

240 251

264 281

305 284

163 169

2197 2306

2493 2887

4806 4869

7b5 751

817 027

1180 1172

365 385

412 451

515 495

224 234

246 262

284 261

155

160

1953

22*74 2677

4$24 4556

648 693

757"'

1095 1081

335 354

379 414

471 449

203 212

223 237

256 232

135 139

144

862

151

158 133

2039 2435

4130 4140

583 625

685 780

"933“

338 368

415 391

178 186

206

221 196

11'5

964

299 316

195

1837

123 128

133 108

1471 1596

1791 2160

3626 3619

509 547

509 681

843 821

256 270

288 312

347 322

148 154

161 169

179 153

1233 1348

1523 1847

3 b ll 2994

425 456

4 7 3 "' 676 560

651

205 216

228 244

266 241

986 1082

1226 1483

2288 2265

325 347

375 416

482 456

709 777

874 1039

1458 1432

.0 0

1 .0 .75

. 50 .25

.5 0 .2 5

BIN

782 785

790 800

832 1432

28l 283

286 289

295 456

166 167

153" 170

1427

1444 1474

1404 2265

448 453

46b 473

493“ 651

243 246

250 255

1987

2006 2059

2551 2994

'584 593

607 630

679 821

2404 2419

2448 2530

3033 3619

689 702

723 760

2704 2725

2767 2882

3429 4140

764 782

0 .3

2882 2910

2967 3121

4127 4556

b . 35

2949 2987

3b6l 3258

2920 2969

PCONT

"*tt

1433

" 1977

0 . 15 0 .2

***

0 .4 0. 45 0 .3 0. 55

ttt ttt

0 .6 0 .6 5 0 .7

**•

2074

ttt

1710

b. 75 “i t 1*' *•* 0 .8 0. 85 0 .9

1 .0 .7 5

BIN

.0 0

BIN

.0 0

.0 0

REQUIRED NUMBER OF PATIENTS

0 .0 5

0 .2 5

DEL=.25

1 .0 75

.0 0

.50 .25

1 .0 .7 5

b. l

DEL=.20

ttt ttt **• T tt

200

185 104

205 183

"'175

194 170

183

150 " 162“

119

178 154

475

TABLE 4: ALPHA= 0.01 POWER= 0.9 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 325

DEL=.0 5

DEL=.10 DEL=.15 DEL=.20 DEL=.2 5 .50 .25

.00 BIN

1 .0 75

.50 .2 5

.0 0 BIN

1 .0 .7 5

.50 .25

.00 BIN

144 167

148 170

172 241

118 118

119 120

121 153

02 92

93 93

94 108

495 651

244 247

25b 255

273 322

162 164

166 169

172 196

121 122

123 125

124 133

' 410 633

679 821

306 311

316 328

342 391

198 2bl

"2T33

216'

209

232

"143 ""147“" 145 150

153 154

' 493 706

727 764

841 964

""334 362

372 388

411 449

225 229

235 242

232” ' 261

140 162

166 170

175 170

3629 4140

769 787

814 867

980 1081

389 400

4f4 435

447 495

245 251

258 268

281 284

17 2 175

180 185

191 183

298r 3143

4127 4556

'817 841

879 944

1095— 1172

413 426

444 470

5 l2 530

258 265

274 286

303 300

180 184

18$ 196

203 191 "211 195

1 .0 .75

.50 .25

.00 BIN

0.0'5' *** ***

783 785

791" 802

832 1432

281 283

284 290

296 456

O .i

*** **•

1429" 1435

1477 1478

1404 2265

449 454

462 474

*** ***

1979 1990

2011 2067

2331 2994

" 38 7 596

0 .2

•••

2408 2424

2456 2542

3033 3619

0 .2 5

••• • **

2709 2732

2777 2899

0 .3

•** ' 2879" *** 2920

FACT=

PCONT=***

0 .1 5

0735

1 .0 .75

.50 .25

.00 BIN

1 .0 .75

REQUIRED NUMBER OF PATIENTS

***

■ 2959 2999

31377 3286

4517 " "“ 842 4869 871

914 995

1177 1237

' 727 441

442 493

574 553

245 273

284 298

318 310

184 188

194 202

•**

2932 2985

3077 3342

4802 5077

845 880

933 "T273 1023 1276

429 447

471 506

564 565

266 276

288 303

325 313

184 189

197“" 2 l4 203 195

0 .4 5

*** ' 2828" "3021 •*» 2895 3322

4973 5181

"832 ' 872

930 1030

1243 1289

423 444

47b 508

57b 565

243 273

286 302

324 310

181 ' 193 186 201

212 191

o: 5

* « ” ' 2 665 *** 2746

2897 3242

507T" 5181

805 848

911

i'2'74 1276

413 433

44b 499

544 553

255 266

279 295

319 300

174 180

184

1018

195

205 183

2454 2556

2731 3110

4975 5077

766 811

877 987

1236 1237

395 416

443 482

546 530

243 253

266 282

305 284

164 170

177 184

194 170

2534

4807

2937

4869

718 764

830 938

1180 1172

371 391

417 454

'3T5 495

227 236

248 263

284 261

152 157

163 170

178 154

0 :5 S " » «“ ' 19*5' 2317 *** 2111 2727

440 706

770 873

1095 1081

340 359

384 418

471 449

206 215

225 238

256"

4556

232

136 140

145 151

158 133

' 174"4" 2082 1875 2484

4130 4140

595 637

497 790

983 964

304 ' T O 371 320

415 391

181 188

196 207

22l 194

117 120

124 128

134 108

' 1503' 1831 1633 2205

270

3619

291 314

347 322

150 156

162 170

179' ' 153

23b 246

244 241

0 .4

0 .5 5

*** ***

0 .4

*** ‘ 2257" *•* 2340

0 .7

•••

0.T5" *a

*•*

4524

3427

1559

30IT

1886

2994

0 .8 5 " *« ■ " ' 1013- 1255 lH O 1512

2265

0 .8

***

1244 1381

o.» - * « ■ - ' 72T" 894 *•*

796

1057

227*" 1437" 1432

“ 520" ■” 409

"843 ' '

689

821

274

' "434" ' 504 567 464

676 651

218

381

' '482 456

558

'331 353

420

20B '

'

"

CRC Handbook of Sample Size Guidelines for Clinical Trials

476

TABLE 4: ALPHA= 0.01 POWER= 0.9 EXPECTED ACCRUAL THRU MINIMUM F0LL0W-UP= 350

DEL=.05

DEL=.1 0

DEL=.15 .0 0 BIN

1 .0 75

.5 0 .2 5

.0 0 BIN

1 .0 .7 5

.50 .25

.0 0 BIN

16* 167

T*9

172 241

118 118

119 120

121 153

92

170

92

93 93

94 108

495 651

244 247

251 256

263 322

T 53 165

i* 7 169

172 196

121 122

123 125

12* 133

*12 635

678 821

307 313

319 329

342 391

199 202

205 210

216 232

""'143 145

150

154

696 710

73l 768

841 964

356 364

374 389

411 449

226 230

23* 243

252 261

160 163

1** 170

174 170

3629 4140

773 792

822 872

98b 1081

392 402

41*

467 495

24* 252

259 269

281

436

284

173 176

i8 b 185

191 183

4177

823 848

886 950

"1092 1172

4 i* "'"447 429 472

512 530

260 267

276 287

303 300

181 185

190 196

204

4556

3097 3314

4519 4869

849 879

925 1003

1i 77 1237

430 445

544 553

267 275

286 299

318 310

185 190

195 202

211 195

2945 3001

3109 3374

4802 5077

854 890

943 1032

1235 1276

434 ""475" 451 509

564 565

2*9 278

29b 305

325 313

185 190

197 204

214 195

w ***

2843

3048 3360

4973 5181

842 882

941 1040

17*3 1289

430 449

474 511

570 565

2*6 276

288

2915

304

32* 310

182 188

194 202

212 191

**«

2682 2770

2929 3284

5031 5181

8 l6

1028

12*4 1276

418 439

4*5 503

565 553

258 268

281 297

319 300

176 181

188

859

195

205 183

*«*

2480 2585

2767 3156

4975 5077

778 824

890 998

1236 1237

400 421

447 485

54* 530

246 256

2*8 284

305 284

166 171

17*7 185

194 170

••• **•

2253 2373

2574 2984

48b* 4869

729 776

T42 949

1180 1172

376 396

422 458

515 495

229 239

250 265

284 261

153 158

164 170

178 154

***

2016 2147

2357 2774

4524 4556

672 717

782 883

1095 1081

345 364

388

471 " 449

208 217

227

421

239

256 232

13T 141

146 152

158 133

*•*

1776 1911

2123 2529

4130 4140

606 648

707 799

983 964

308 325

415 391

183 190

198 208

221 19*

l l8

373

121

124 129

134 108

••• • ••

1537 1668

1869 2246

3626 3619

— 530 567

*19 696

843 821

264 277

294 316

347 322

152 157

T*"3

179 153

• ••

1294 1413

1593 1921

3 0 li 2994

442 472

513 572

676 651

2IT 221

232 247

266 241

••• • **

1037 1136

1282

2288

1539

2265

337 358

385 423

482 456

•••

7TC" 813

911 1073

1458 1432

.50 .25

.0 0 BIN

••• ***

783 786

792 803

832 1432

282 284

286 290

29* 456

*** ***

1430

1450 1482

1604 2265

451 456

4*3 475

2016 2074

23£>1 2994

589

1993

598

0 .2

*** —7411 *** 2429

2463 2554

3o33 3619

0 .2 5

••• **•

2714 2739

2787 2915

*« •*»

2896 2929

2995 3165

0 .3 5 ~~*** •**

2968 3012

0 .4

•••

0 .4 5

PCONT=***

0 .1 5

0 .3

0 .5 0 .5 5 0 .6 0 .4 5 " 0 .7 0 .7 5

0.8 0 .8 5 0 .9

**•

1 .0 .7 5

.0 0 BIN

1 .0 .7 5

O .i

DEL=.25

.50 .25

FACT=

0 .0 5

DEL=.20

.50 .25

1 .0 .75

REQUIRED NUMBER OF PATIENTS

1437

1982

'

”923

466 496

345

170

147 “ 153

191

477

TABLE 4: ALPHA= 0.01 POWER= 0.9 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 375

D E L = .10

D E L = .05

1.0 .75

1.0 .75

.50 .25

.00 BIN



784

793"

m

172

804

1432

2'8Z 284

149

787

290

456

167

170

241

11S 118

120

121 153

* *

1432" 1453

1404 2265

452 457

465 476

495 651

245 248

252 256

243 322

163 165

167 169

*

1984" 2020 ”2351 1997 2081 2994

591 600

615 637

"579 821

309 314

320 329

342 391

199 202

206 210

358 366

376 390

410 449

227 231

447

PCONT="* 0 .0 5 0 .1

07T5 0 .2 ' 0725 0 .3 0 .3 5 0 .4

0.45

*

.50 .25

D E L = .20

D E L = .15 .00 BIN

1.0 .75

.50 .25

.00 BIN

1.0 75

.50 .25

1439

1486

"2415"' 2470 2434

2565

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757“ ' 294

'3033' " 3619

599”

735"

714

771

8*1 964

"" 1 5 7

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93 93

94 108

172 196

121 122

123 125

124 133

215 232

144 146

148 150

153 154

"237

252

243

261

161 164

167 170

175 170

248 253

260 269

281 284

" 17* 177

181 186

191 183

2720 ' 2797

3429

778“

827

980

374

2746

2931

4140

797

877

1081

405

419 438

495

• •

2903 2939

3008 3185

4127 4556

829 854

892 956

1092 1172

4 l9 432

450 474

530

241 268

277 288

303 300

182 186

191 197

204 191

*' *

2977

3113 "T51'9"

1177

3340

4869

"85S 887

'933

3024

' "449 “ 544 498 553

240 277

287 300

318 310

184 191

194 203

211 195

* *

2957 3017

3131 3405

4802 5077

862 898

544

271 280

291 306

325 313

184 192

197 205

214 195

*

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51'2 ""

1010

1237

433 449

952 1041

1235 1276

438 455

479 512

■851“ "951 '

1243

570

1049

1289

"434 453

” 478

892

514

565

248 278

290 305

324 310

183 189

195 202

212 191

I T 3 " 449” 504 443

565 553

241 271

283 298

319 300

177 182

189 194

205 183

* 0 5 " 452

544 530

248 258

270 285

305 284

167 172

178 185

194 170

232 241

252 266

284 261

15* 159

164 171

178 154

210 219

228 240

2 56 232

138 142

147 152

158 133

22l 196

118

122

125 129

133 108

565

825“

93*" TT44

870

1038

1276

'2503

2801' 1975

738“

901

"1734

2613

3198

5077

835

1007

1237

425

488

2280 ' 2411

1804 4869

740 787

853"

3028

959

1T30 1172

3#1 400

426 ' 515 ' 495 461



"204< r ' 2394 2180 2818

4524

483 728

79'2 892

1095'

4556

1081

350 368

392 423

471 449

O'.T— --” •

T80T- 2141 1945 2571

4T30

” 513”

349 376

184

658

312 328

4r5

4140

391

191

199 209

153 158

164 171

” *



0 .5 “ "”

* *

0” T T ^ •

o .s r 0.9

'"

*

2940 "5 0 3 0 "'

0 .8 ''

.00 BIN

92

3323

0 . 65'

.50 .25

92

119

2702

0. 55"

1.0 .75

REQUIRED NUMBER OF PATIENTS

'

2794

O .T~

.00 BIN

2405

5181

'

"T547 " 1905' -J S 2 1 1701

2285

3619

*'

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1322 ■ IS2T" 3011 "' 1443



TOOT ' 1308 T W 1160 1564 2265



830

1954

928' 1088

2994

1158 1432

717"

983'

808

964

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527 " 843

267

297 “ 347

576

703

821

280

317

322

**9“

5 2 0 "' 474

213 223

234 248

264 241

"539“

479

"3*2“ 363

577

651

390"

482 456

426

- 179- 153

CRC Handbook of Sample Size Guidelinesfor Clinical Trials

478

TABLE 4: ALPHA= 0.01 POWER= 0.9 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 400

DEL=.05 FACT=

D E L = .10

1.0

.75

.50 .25

BIN

*** • **

"7ff3" 788

793 805

832 1432

285

• **

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1433 1441

143? 1489

1504 2265

458

0.15' '*** ***

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2023" "2531 2994

0.2 "■***

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2477" 3033 2575 3619

717

.00

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2000 2439

2725

2088

2807

3429

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2753

2946

0.3

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2910 2948

3206

4556

0.35

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313-2 3364

4519 4869

0.4

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2969 3033

3435

5077

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2874 2954

3100 3430

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.75

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1.0

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.75

DEL=.20

.50 .25

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75

1.0

.50 .25

119

.00

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.00

m

4140

r ' 4127"

5T53" 4802

94 108

170

147

172 196

121 122

124 125

126 133

206

210

216 232

144 146

148” 153 150 154

228 232

237 244

252 261

162 164

147 171

175 170

172” 241

118 119

477

444

495 651

246 249

257

252"

263 322

164 165

"593 603

617 639

679 821

315

510""- 32l

330

342 391

2dO 203

702

739 774

841" 964

36o 367

378 391

411 449

453

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832

407

w r

421 440

447" 495

249 255

270

261

281 284

178

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881

980 1081

175

802

186

191 183

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898 962

"TO 92

42-2 435

452 476

530

512"

263 270

278 289

303 300

183 187

191 197

2b4 191

*53"

940 "T177 1017 1237

437” 472" 501 452

544 553

271 279

289 301

318 310

187 192

197 203

211

442 459

482 514

564 565

273 282

293 307

325 313

188 193

198 205

214 195

439 458

482 517

570 565

271 280

292 306

326 310

185 190

196 203

212 205 183

" 7*2”

894

1172

" *70- ' 950"" " 1235

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195

907

1048

1276

4973 5181

860 901

95 T " 1058

1253 1289

2990" 5 0 3 T 3361 5181

836 880

944 1047

1254 1276

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428 448

473 509

564 553

243 273

284 299

319 300

178 183

189 196

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410 430

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260

2*1

275“ 305 286 284

169 173

1 7 7 “ 194 186 170

385 405

430 463

515 495

234 243

253 267

284 261

156 160

145 171

178 154

354 372

395 426

471 449

212 220

230 241

256 232

139 143

147 152

158 133

316 332

352 378

415' 391

186 193

200 210

221

119

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134 108

154 159

145 171

179 153

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4975 5077

799 845

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751 798

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2074 2213

2453 2860

4524 4556

693 739

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668

724 815

983 964

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1596 1732

1940" 2321

347 584

635 709

843 821

283

299 319

347 322

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454 484

524 582

676 651

216 225

234 249

266 241

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1184

347

394 429

482 456

3525" 3619

1082

1352 1588

2265

777

944"

1438 1432

846

93 93

149 171

2853 3239

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92 92

167 168

2524 2640

0.9

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121

296 456

***

0.85

1.0

153

287

'2721 2818

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.00

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120

291

283

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0.55

DEL=.25

REQUIRED NUMBER OF PATIENTS

PCONT=*** 0.05

1.0

DEL=.15

1102

22*3"

368

"

"

~

196

122

191

479

TABLE 4: ALPHA= 0.01 POWER= 0.9 EXPECTED ACCRUAL THRU MINIMUM F0LL0W-UP= 425

DEL=.05 FACT=

DEL=.10

1 .0 75

.50 .2 5

.0 0 BIN

1 .0 .7 5

.50 .25

.00 BIN

169 171

172" " 241

n r~ 119

120 120

121 153

92 93

93 93

94 108

263 322

164 '"T57“ 170 166

121

257

122

124 125

126 133

316

322 331

3 4 2 ' '" 391

201 203

207 211

232

145 146

148 150

153 154

36 i 369

379 392

410 449

229 233

238 244

252 261

162

165

167 171

175 170

399'

423 441

467 495

250 256

262 271

281 284

175 “ 182 178

186

191 183

512 530

265 271

280 290

303 300

134T

192 197

204 191

273 281

290 302

318 310

193

198 204

211 195

” 275“~ 295

765

795

832' '

253“

288

295

789

806

1432

285

291

456

454 459

467 478

"473 651

249

595

619 641

679 821

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742 777

841 964

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1493

2265

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2003

2994

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2586

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5579“

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885

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904 967

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425

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475

544"

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503

553

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485 516

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486 519

2960

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2958

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3149 3388

4519 4869

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1276

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869

970

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2974

3462

910

1065

1289

461

0.35' 0 .4

3463

5077 5181

293 307

326 310

186 191

197 203

212 191

477 511

564 553

265 274

286 300

319 300

179 184

190 197

205 183

546 530

253 262

273 287

305 284

170 174

180 186

194 170

236 244

255 268

284 261

156 161

166 171

178 154

214 222

231 242

256 232

140 144

148 153

158 133

187

2bl

194

210

221 196

12o 122

126 129

133 108

803'

414“

459

855

921 1025

1236 "

5077

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466

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2465

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2102" 2468 2244 2899

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4556

748

811 908

1095“ 1081

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734 822

933 964

642

843

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3ol

715

821

286

320

531

676 651

218 226

250

*•*

" 1855" 7 2 3 7 ' 4T30 " 2009 2648 4140

1624" 1972

3526

1762

2355

3619

555 592

' 1375“ 1684 w *** 1498 2013

301 r 2994

" 467 492

0 .7 5 ’ *■**

0.83"“ " * “ ***

0.9

273 282

4975

2867 3277

0 .8

570 565

43 2

2545

0 .7 “

214 195

452

2667

0.6 3

199 206

1754

0 .5 3 "™*“ **•

*'**

*•*

HOT" 1354

586

7733""

351 '" 397

2265

372

1206

1609

791 860

958

R 58“

1115

1432

431

482 456

‘ "

188

137 193

1276

5181

188

325 313

1055

3397

215 "

'

308

953

3017' 5031'"

172 196

284

845'

2739 2841

0 .6 "

1023

890

T < i_ ***

0 .5 "

D E L :.25

.50 .25

1 .0 .75

.50 .25

1 .0 .75

DEL=.20

REQUIRED NUMBER OF PATIENTS

0 .0 3

0 .2 '

.00 BIN

1 .0 .75

PCONT=***

O .i'

D E L :.15

358“ - 3 9 r

4 rr

376

449

428

3 1 9 " 354' 379 335

237

415 391 347 322 266 241

"

155 " 165 160

172

179 153

CRC Handbook of Sample Size Guidelines for Clinical Trials

480

TABLE 4: ALPHA= 0.01 PQWER=0.9 ___ EXPECTED ACCRUAL THRU MINIMUM F0LL0W-UP= 450

D E L =.05 FACT=

D E L = .10DEL=.15

1 .0 .7 5

.50 .25

.0 0 BIN

PCONT=***

1 .0 .7 5

.50 .25

.00 BIN

1 .0 .75

D E L =.20

D E L = .2 5

.5 0 .25

.0 0 BIN

1 .0 75

.50 .2 5

.0 0 BIN

1 .0 .7 5

.50 .25

.00 BIN

94 108

REQUIRED NUMBER OF PATIENTS

0 .0 5

••• *•*

786 789

793 807

831 1432

284 285

288 291

296 454

167 168

149 171

172 241

in 119

120 120

121 153

92 93

03 03

0 .1

•••

1434 1445

1440 1496

1504 2265

433 440

468 479

495 451

247 250

253 257

262 322

164 166

168 170

172 196

122 123

124 “ 124 125 133

0 .1 5

*** *•*

1992 2006

2034 2101

2351 2994

597 407

621 642

678 821

342 391

'201

207

214" '

204

211

232

145 147

***

**•

2426 2448

2491 2595

3033 3619

708 723

*745 779

841 964

363 370

380 393

411 449

230 234

239 244

252 241

***

2736 2767

2627 2975

3429 4140

790 811

84l 889

980 1081

401 411

424 442

468 495

25l 257

263 271

••• *•*

2925 2967

3o4fl 3243

4127 4556

844 871

910 972

1092 1172

428 440

45? 479

512 530

266 273

000

3006 3061

3165 3411

4519 4869

875 907

054 1029

1177 1237

443 458

478 504

544 553

"273

2093 3064

3194 3490

4802 5077

885 922

976 1062

1234 1276

449 " 488 466 518

564 565

285

2905 2993

3 i5 o 3493

4973 5181

877 919

978 1073

1263 1289

447 465

489“ "570 522 565

284

0 .2 0 .2 5 0 .3 0 .3 5 0 .4 0 .4 5

*** •••

....312 “ 32 5~ 317 331

“n r 150

153 154

143 145

168 171

174 170

281 284

174 179

183 186

' 191 ’ 183

260 290

303 300

185 188

192 108

203 191

291 303

318 310

189 193

198 204

211 195

296 309

325 313

190 194

200 206

213 195

275 ” '2 9 4 308

" 173 310

282

277

187 '" 1 9 7 192 204

— 212 191

0 .3

***

2758 2864

3047 3431

5031 5181

854 899

962 1063

1244 1274

436 455

480 514

544 553

247 274

'287 301

319 300

181 185

191 197

205 183

0 .5 5

••• **•

2570 2693

2806 3313

4975 5077

818 864

030 1033

1234 1237

418 438

442 496

546 530

255 264

275 288

305 284

171 175

18l 186

194 170

0 .4

*** ***

2357 2493

2714 3146

4806 4869

770 817

883 984

1180 1172

393 412

434 448

515 495

237 246

256 268

284 241

158 142

144 172

178 154

0 .4 5

*** ***

2129 2274

2302 2936

4524 4556

712 757

820 915

1095 1081

' " 342 379

4oF 430

471 449

214 223

232 243

256 232

141 144

146 153

158 133

0 .7

**•

1893 2039

2245 2683

4130 4140

643 685

743 828

983 964

323 338

d 57 381

415 391

180 195

202 211

221 196

120 123

124 “ TTT 108 130

0 .7 5

*** 000

1650 1791

2003 2387

3426 3419

543 599

649 720

843 821

276 288

303 322

347 322

154 161

172

••• *•*

1397 1523

1710 2040

3011 2994

468 498

536 590

676 651

219 228

23* 251

246 241

*•*

1123 1226

1374 1630

2288 2265

356 375

401 434

482 456

805 874

972 1127

0 .8 0 .8 5 0 .9

•**

1456 1432

166

179 153

"

481

TABLE 4: ALPHA= 0.01 P0WER= 0.9 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 475

DEL=.05 FACT=

1 .0 .7 5

.50 .25

785 790

795 808

*** • **

1438 1446

1453 1499

*** ***

1994 2009

••• *•*

2430 2453

2478 2605

•••

DEL=.10 .00 BIN

0 .1 0 .1 5 0 .2 0 .2 5 0 .3 ' 0 .3 5 0 .4 0 .4 5

.00 BIN

1 .0 .75

DEL=.25

.50 .25

.0 0 BIN

1 .0 75

.50 .2 5

.0 0 BIN

1 .0 .7 5

.50 .25

.00 BIN

TO

1432

286

291

296 456

167 168

159 171

172 241

lid 119

120 120

121 153

92 93

93 93

94 108

1604 2265

456 461

469 479

495 651

246 250

254 257

'26"2 322

165 166

168 170

17 2 196

122 123

124 125

125 133

2038 ■~ZTCT

599

313“

821

318

342 391

202 204

207 211

216 232

1'49

609

324 332

145

2994

623 644

679

2107

147

150

153 154

3033 3619

711 726

748 782

841 964

334“ 372

381 394

' 411

231

449

235

239 245

252 261

163 166

168 171

175 170

***

'2740' 2*33” 3529 2773 2988 4140

794 814

845

980 1081

403 413

426 443

4^7 495

252 257

264 271

281 284

173“ 179

183 187

191 183

***

2932 2976

3050

4127 4556

849 876

443

459 481

" 5T2

976

1092 1172

430“

3261

530

267 274

281 291

303 300

185 189

193 198

203 191

3015

3182 3433

4519 4869

881 913

950 1034

1177 1237

44* 461

480 506

544 553

273” 283

292 303

318 310

l9b

3073

194

199 204

195

••• **•

3005 3079

3214 3516

4802 5077

892 929

963 1068

1234 1276

••• ***

2920 3011

3173 3523

4973 5181

885 927

986 1079

2776 2886

3074 3463

5031 5181

862 907

2592

2928 3348

4975 5077

"T 23"' 873

2745 3182

4805 4869

- " 779"

•••

*•*

0 .5 0 .5 5

.50 .25

DEL=.20

REQUIRED NUMBER OF PATIENTS

PCONT=*** 0 .0 5

1 .0 .75

DEL=.1 5

***

2718

0 .5 ' "«*

7381

***

2521

284

826

288

892

915

520

565

279 287

297 309

325 313

191 195

200 206

213 195

1264 ....... 4 50“ 1289 469

492 523

570 565

276 285

293 309

326 310

188 192

"ITS204

212 191

971 1070

1264 1276

44b 459

483 516

564 553

259 278

289 302

3 l9 300

l6 1 186

191 198

205 183

939 1040

1236 1237

422 441

456 498

"5'4"5 530

257 265

276 289

305 284

172 176

181 187

194 170

891

1180 1172

397

439 ' “5T4 470 495

239 248

557“ 269

284 261

l£ 8 162

157 ' 178

416

172

154

'403~~ 471 431 449

217 224

233 243

256 232

141 145

149 153

158 133

121 124

127 130

134 108

990

' '45IT- ~~49T" 564 469

••• ***

2155 2303

2534 2971

4524 4556

720 766

828 922

1096 1081

365 382

0 .7

•••

1920 2068

2296 2716

4130 4140

55l 693

750 834

983 964

326 340

359 383

415 391

190 196

2b3 211

221 196

0 .7 5

*•* ***

1676 1818

2032 2417

3626 3619

569 606

655 725

843 821

276 290

305 323

347 322

157 162

167 172

179 153

' 1421 1548

1735 2065

3bn 2994

474 503

541 593

676 651

221 229

240 251

256 241

359 379

403 436

482 456

0 .6 5

0 .8 ' 0 .8 5

**'* ' ***

1142 1246

1396 1649

2288 2265

0 .9

*** **•

818 887

984 1138

1458 1432

211

CRC Handbook of Sample Size Guidelines for Clinical Trials

482

TABLE 4: ALPHA= 0.01 PQWER=0.9 EXPECTED ACCRUAL THRU MINIMUM F0LL0W-UP=5QQ

DEL=.0 5 FACT=

DEL=.10

1 .0 .7 5

.50 .25

.00 BIN

PCONT=***

1 .0 .75

.50 .25

DEL=.15 .00 BIN

1 .0 .75

DEL=.20

DEL=.2 5

.50 .25

.00 BIN

1 .0 75

.50 .2 5

.0 0 BIN

1 .0 .7 5

.50 .25

.0 0 BIN

REQUIRED NUMBER OF PATIENTS

0 .0 5

* •• ***

787 791

797 808

832 1432

284 286

288 292

296 456

168 168

170 171

172 241

118 119

120 120

121 153

92 93

93 93

94 108

0 .1

*** ***

1439 1448

1465 1502

1604 2265

457 463

470 480

495 651

248 251

254 258

263 322

165 167

168 170

172 196

122 123

124 125

126 133

0 .1 5

***

1997 2013

2043 2113

2351 2994

600 610

"524 645

678 821

3 l4 319

325 332

342 391

202 205

208 211

216 232

146 147

T4T~ 151

153 154

0 .2

***

2434 2458

2504 2614

3033 3619

713 729

7 SI 784

841 964

366 373

383 394

411 449

231 235

240 245

252 261

164 166

168 171

175 170

0 .2 5

*** *•*

2746 2780

2846 3001

3629 4140

797 818

848 895

980 1081

405 415

428 444

468 495

253 258

264 272

281 284

177 180

183 187

- 1W - 183

0 .3

••• ***

2939 2985

3073 3278

4127 4556

854 881

919 980

1092 1172

432 445

461 482

512 530

268 275

282 292

303 300

186 189

193 198

203 191

•** ***

3024 3085

3198 3454

887 919

966 1039

1177

449

'483 ' T43

1237

463

508

553

277 ~ 293 285 304

318 310

191

4869

195

199 205

211 195

G73

«* ***

3017 3094

3234 3541

4802 5077

898 936

990 1073

1234 1276

456 472

493 522

563 565

280 288

298 310

325 313

192 196

201“ 207

213 195

0 .4 5

••• ***

2935 3030

3197 3551

4973 5181

892 934

993 1086

1263 1289

453 472

494 525

570 565

278 287

291 310

326 310

189 193

198 204

21'2 191

0 .5

••• *•*

2*7^4 2908

3100 3494

5031 5181

870 915

978 1076

1264 " 1276

433' 462

486 518

564 553

'" 5 7 1 279

290 303

319 300

182 187

192 198

205 183

***

2613 2743

2957 3380

4975 5077

835 882

947 1047

1236 1237

426 444

468 500

546 530

258 267

277 289

305 284

173 177

182 187

194 170

**•

2405 2548

2776 3215

4806 4869

787 834

899 997

1180 1172

400 419

442 472

515 495

241 249

258 270

284 261

159 163

168 173

178 154

**• ***

2180 2330

2565 3004

■ ra n " 4556

728 774

836

1095 1081

368 385

406 433

471 449

2TT~ 234

928

••• ' W **• 2096

2326 2748

4130 4140

558 700

757 839

983 964

328 343

361 384

415

••• **•

1701 1844

2060 2445

3626 3619

576 613

661 729

843 821

280 292

306

••• *•*

1*43

1760 2089

3011 2994

479 508

545

676 651

223

597

231

••• *•»

1160 1265

TTI'5 ' 727HT 1666

2265

363 382

406 438

456

***

830 900

997 1148

1458 1432

0 .3 5

0 .5 5 0 .6 0 .6 5 0 .7 0 .7 5 0 .8 0 .8 5 0 .9

1571

432

'

'

'

226

244

256 232

391

19i 197

204 212

221 196

347 322

158 162

167

324

179 153

241 252

241

266

173

' "

'

142

149

158

145

153

133

122

127 130

133 108

124

483

TABLE 4: ALPHA= 0.01 POWER= 0.9 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 550

DEL=.02 FACT=

1.0 .75

.50 .25

DEL=.0 5

0 .7 5 078 0 .8 5

.00 BIN

172 241

110 110

120“ 121

121 153

'

im 1452

1470 1507

1604 2265

459 464

471 481

495 651

249 252

255 258

263 322

166 167

168 170

172 196

*** **•

11247 TT295 1 337T _ 11263 11390 17482

200T 2019

2051 2123

2351 2994

' 504“ 614

628 648

679 821

316 320

326 333

342 301

203 206

208 212

215 232

*** ***

14068 T * l* 2 T7703" 14093 14289 21583

2 flr 2468

2517 2631

3033 3619

'718 734

756 788

841 964

368 375

384 396

411 440

233 236

241 246

252 261

***

15080 15195 2155T '

2755

2864

2794

3025

3629 4140

804 825

855

16124 16406 25032

901

980 1081

408 418

430 446

467 405

255 260

266 272

281 284

*** **•

17321 T 7466 24877"

1092 1172

437 448

464 484

512 530

270 277

284

987

292

303 300

3736

7701 T 728 7782

392T” 7329 S61"S 12731

17369 17757 27831

***"■ - T7820 TFffI3’ 2757*" *** 17884 18400 29979

***

**•

m

17655 1 7 7 1 8 ' 7947*" " 17749 18422 31475

' 928

2953

3097

3004

3309

1T27 4556

863 890

3043 3109

3228 ”1519 3493 4869

930

976 1048

117? 1237

454 468

486 510

544 553

280 287

295 305

318 310

301T 3124

3271 3588

4802 5077

"911 949

1002 1084

1234 1276

461 477

498 525

564 565

283 201

300 311

325 313

906 948

1007 1097

175* 1289

459 477

499 529

570 565

281 280

290 311

326 310

"■885“

15952 "17278 30757"

2 951' 3241

4973

17061 17926 32322

3066

5181

3604

877“

15785" 15200 31310"'

2830T 3150

5030 '

15923 17023 32517

2950

3553

5181

930

993 1088

1264 1276

450 468

491 521

564 553

274 282

292“ 304

319 300

14272 14802 312E3" "

2551 2790

3011

4975 5077

850 897

96l 1058

1236 1237

432 450

473

3442

503

546 530

261 260

270 291

305 284

9

1180 1172

407 424

446 475

5T4 405

244 251

260 271

284 261

37*

410 436

471 440

22l 228

236 245

256 232

12530 1'3204 30357" " 2450-

2833

4805

“ 803“

12755 14457 30955

2599

3278

4869

850

1009

* * * ' ' TU579 11529 28807 10967 12996 29197

' 222T 2384

2523

4524 4556

“ 743“

850

3066

789

939

1095 1081

-m ***

-t o *#* *** •**

*•*

390

83*7 ' 9*85

199*"' 2383

4r30

”672

9210

2148

2807

4140

714

769 849

983 964

347

365 386

415 301

193 199

205 212

221 196

3-525 3619

—588“ 624

671 737

843 821

285 296

309 326

347 322

159 164

168 173

179 153

225 233

243 253

266 241

*** ' ■ 7T55 7586

07? 0 .9 5

.50 .25

170 171

"3713

14449 15831 32061

077

1 .0 .7 5

168 169

0755

0755

.0 0 BIN

296 456

074 ■■■**»

07S

.50 .2 5

289 292

0 .2

075'

1 .0 75

285 287

0 .1 5

0 .'45

.0 0 BIN

831 1432

7710

0.-35

.50 .25

810

*■« ***

0 .3

1 .0 .75

799

3702 3706

0725

.00 BIN

788 792

***' **•

071

.50 .25

REQUIRED NUMBER OF PATIENTS

PCONT=*** 0705

1 .0 .75

.00 BIN

DEL=.JODEL=,15 DEL=.20

26555 .... 11507 26789

"8T39

236D8"

17 *T" 2112

10017 23730

1894

2498

1484 1614

1805

3011

” 189“

553

2133

2994

517

602

676 651

1174" 1451 1699

2288 2265

360 388

411 441

482 456

853— 1019

1458

1167

1432

5576

■5701” 19973"

6137

8513

4392

"5528” 1 5 5 IT

4828

6947

15660

1300

3507

m o

3563

5209

10557“ 10648

923

1914

■2143 3022

'50 n ~ 4986

2125

20021

333

CRC Handbook of Sample Size Guidelines for Clinical Trials

484

TABLE 4: ALPHA= 0.01 POWER= 0.9 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 600

DEL=.02 FACT=

DEL= .0 5

1 .0 .7 5

.50 .2 5

.0 0 BIN

••• ***

3703 3707

3715 3740

3921 7329

790 794

800

832

811

1432

0 .1

•• * **•

7703 7713

7lZS

8615 12731

1444 1455

1474 1511

0 .1 5

••• ***

11251 11303 13324 11269 11408 17482

2006 2025

0 .2

••• • **

14075 14155 17703 14101 14316 21583

2448 2477

'2530 2647

0 .2 5

••• **♦

16098 16214 21586 16137 16445 25032

2767 2807

0 .3

••• **•

17334 17492 24877 17387 17809 27831

0 .3 5

**• ***

0 .4 0 .4 5

.0 0 BIN

1 .0 75

.50 .2 5

286 287

289 292

295 456

168 169

1604 2265

460 466

473 482

495 651

25d 252

2059 “ 2351 2133 2994

607 617

63d 649

679 821

3033 3619

723 739

760 791

841 964

2682 3047

3629 4140

811 832

862 905

2967 3022

3121 3339

4127 4556

87l 898

17837 18048 27524 17908 18470 29979

3061 3132

3258 3530

4519 4869

*** ***

17688 17963 29494 17780 18514 31475

3064 3152

3307 3631

4802 5077

**• ***

16982 17337 30769 17100 18043 32322

2993 3100

15823 16276 31340 15974 17169 32517 ••• ***

0.6

•••

0 .6 5

0.7

1 .0 .7 5

.00 BIN

1 .0 .75

DEL=.20 .0 0 BIN

1 .0 .7 5

.50 .25

170

172

171

241

119 119

120 “ 131 153 121

255 258

262 322

166 167

169 170

172 196

317

' '377

321

334

342 391

204 “ 209 206 212

232

370 377

386 397

410 449

234 237

241 246

252 261

980 1081

411 421

433 447

467 495

257 261

267 273

281 284

936 993

1092 1172

440 452

467 486

512 530

278

293

300

907 940

986 1055

1177 1237

436 472

490

544

513

553

282 289

297 306

318 310

922 960

1013 1093

TZT4

466 482

502 528

565

3263

"4973 - - 919 5181

961

1019 1106

1753 — _ 465

3653

2864 2990

3197 3606

5030 5181

899 944

1006 1098

14320 14898 31203 14513 16008 32061

2693 2835

3062 3498

4975 5077

***

12591 13324 30358 12837 14665 30955

2493 2647

••• ***

" T0758T 11676 28807 11071 13228 29197

2273 2433

0 .5 0 .5 5

.50 .25

DEL=.1 5

.50 .25

PCONT=*** 0 .0 5

DEL=.10

.00 BIN

REQUIRED NUMBER OF PATIENTS

7792

1276

563

215 '

272 ""285 " 303

286 " ""302 " 325 ” 293 312 313

"50'3

570

284"""“301

1289

482

532

565

292

1264 1276

435 473

494 524

564 553

276 “ 294 284 305

300

864 911

975 " 1236

546

1237

437 455

"478

1069

506

530

263 271

281 292

305 284

2887 “ 4804 3335 4869

817 864

926 1019

1180 1172

412 430

451 478

513 495

246 253

262 272

284 261

5777“ 4524

757 802

862 948

1095 1081

379 395

414 439

471 449

223 230

237 245

256 232

3122

4556

2435

312

326 ' 310

319

«* • •*

8947 9338

10056 26555 11752 26789

2039 2197

4130 4140

6U5 726

780 857

983 964

338 352

368 388

415 391

T93~“ 206

2860

200

213

221 196

••• **»

7277 7733

8522 23608 10261 23730

1*790 1939

2160 2545

3626 3619

599 635

68d 744

843 821

288 299

” 3TT 327

347 322

161 164

169 174

179 153

**•

5808 6289

7082 8741

19973 20021

1523 1655

1847 2173

3011 2994

498 526

560 607

676 651

228 235

244 254

266 241

d .8 5

**•

4519 4970

5&91 7143

13656 15660

1226 1332

1483 1728

2288 2265

375 394

416 444

482 456

O'. 9

«*

3311 3677

4248 5356

10666 " " 8 7 4 10648 944

1039 1183

1457 1432

0 .9 5

**• »*»

1976 2191

2513 3095

5 b ll 4986

0 .7 5 0 .8

-

"

485

TABLE 4: ALPHA= 0.01 PQWER=0.9 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 650

DEL=.02 FACT=

DEL=.05

1 .0 .75

.50 .25

.00 BIN

•••

3704 3708

3717 3744

3921 7329

***

7706 7717

7738 7802

8615 "" 1447 12731 1459

PCONT= • • • 0 .0 5

O .i

***

1 .0 .75

.50 .25

DEL=.10 .00 BIN

1 .0 .75

DEL=.15

.50 .25

.00 BIN

1 .0 75

.50 .25

DEL=.20 .00 BIN

1 .0 .75

.50 .25

.00 BIN

REQUIRED NUMBER OF PATIENTS

11256 11312 13324

790 795

802 812

831 1432

286 288

290 292

296 456

168 169

170“ 171

172 241

119 120

120 120

121 153

1478 1516

1604 2265

462 467

474 483

"495' '

250 253

'253“

263 322

166 168

159"

172

259

171

196

2351 2994

61b 619

633 652

679----821

318 322

328 334

342 391

205 207

210 212

216 232

727

841 964

372 379

387 ' 411 398 449

235“ 238

242 246

261

651

0 .1 5

*** • **

11274 11425 17482

2011 '20*7 2031 2142

0 .2

••• ***

14081 14169 17703 14111 14343 21583

2456 2486

2542 2662

3033 3619

743

764 794

0 .2 5

• ••

«**

16175 16233 21586 16149 16483 25032

2777 2820

2899 3069

3629 4140

816 838

867 910

980 1081

414 423

435 449

467 495

258 262

268 274

281 284

0 .3

••• ***

"17347 17519 24877 17404 17862 27831

2981 3039

3143 3366

4121 4556

879 906

944 999

1092 1172

444 455

470 488

512 530

274 280

286 294

303 300

***

178'53 18083 27524 17931 18540 29979

3079 3154

3286 3564

4519 4869

"9T6 950

995 1062

1177 1237

462 476

493 515

544 553

284 291

298 307

318 310

••• ***

m n

18010 29494 17811 18605 31475

3087 3180

3342 3671

4802 5077

933 971

lb23 1100

1234 1276

471 487

506 530

564 565

2B8 295

303 314

325 313

*•*

17012 17396 30769 17140 18158 32322

3b2l 3134

3322 3698

4973 5181

930 973

1030 "1263 1115 1289

503“ 534

570" 565

286 294

302 313

326 310

0.5

*** **»

"15860 16352 31340 16024 17313 32517

2891 3028

3242 3655

5b30 5181

912 957

lb l7 1108

461 478

5db 527

565 553

279 286

295 306

319 300

0 .5 5

*** **•

14368 14994 31203 14577 16181 32061

273i 2877

3110 3550

4975 5077

877 924

987 "1236“ 1078 1237

443 460

482 509

546 530

26 6 274

282 293

305 284

***

12653 13444 30358 12919 14866 30955

2534 2692

2937 3388

4806 4869

830 877

938 1028

1180 1172

“ 317 434

453 480

515" " 495

248 255

263 273

261

«* ***

10837 11821 28807 11175 13450 29197

2317 2480

2727 3174

4524 4556

77b 814

873 957

1095 1081

384 399

418 441

471 449

225 231

238 246

256 232

0 .7

••• ***

9047 9464

2082 2243

2484 2908

4130 4140

697 T 9 0 737 864

983 964

342 355

3 7 i ' 315" 390 391

197 201

207 214

221 196

0 .7 5

••• ***

7395“ 86"99 7875

23608 10491 23730

1831 1982

2205 2589

3626 3619

609 644

291 302

314 328

347 322

162 166

170 174

179 153

***

5935 6435

7255 8956

19973 20021

1359 1693

1886 2209

3011 2994

533

612

676 651

230 237

246 255

265 241

0 .8 5

••• ***

4639 5104

5845 7327

15656 15660

1255 1362

1512 1754

2288 2265

38b 398

419 446

482 456

0 .9

••• **•

3410 3785

4368 5493

10666 10648

894 963

1057 1198

1458 1432

0 .9 5

«*

■2033“ 25T9

0 .3 5 0 .4

0745

0.6 0765

0 .8

2253

10221 26555 11985 26789

3162

5011 4986

689 750

506 “ 567

1264 1276

'843 " 821

' “ 370“ 487

252 "'

233

CRC Handbook of Sample Size Guidelines for Clinical Trials

486

TABLE 4: ALPHA= 0.01 POWER= 0.9 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 700

DEL=.02 FACT=

DEL=.05

1 .0 .7 5

.50 .25

BIN

.0 0

•••

• **

3705 3710

371$ 3747

“572"! 7329

0 .1

••• ***

7708 7720

7743 7812

0 .1 5

PCONT=*** 0 .0 5

1 .0 .75

.50 .25

DEL=.10 .0 0

BIN

1 .0 .75

DEL=.15 .0 0

DEL=.20

.50 .25

BIN

1 .0 75

.50 .2 5

BIN

1 .0 .7 5

.50 .25

BIN

.0 0

.0 0

REQUIRED NUMBER OF PATIENTS 792 796

803 814

831 1432

286 288

290 292

296 456

169 170

170 171

172 241

119 120

120 121

12l 153

8615 12731

1450 1462

1482 1520

1604 2265

464 468

475 484

495 651

251 254

256 259

263 ' 322

TS6 168

169 170

172" 196

•••

1126b 11321 13323 11280 11443 17482

2016 2037

2074 2150

2351 2994

612 622

635 653

678 821

319 324

329 335

342 391

205" 207

210 212

215 232

0.2

••• *»*

14088 14182 17703 14120 14370 21583

2463 2495

2553 2675

3033 3619

731 747

768 797

841 964

374 381

389 398

411 449

236 ""2*3 239 247

252 261

0 .2 5

**♦ **•

16118 16252 21586 16162 16522 25032

2787 2833

2915 3088

3629 4140

822 843

872 914

980 1081

” *16" 425

436 450

467" 495

259 264

268 274

281 284

0.3

**♦ •••

17360 17545 24877 17422 17915 27831

2994 3056

3165 3392

4127 4556

886 913

950 1004

1092 1172

447 458

472 ' 512 489 530

" 273“ " 287 281 294

303 300

*•*

17872 18118 27524 17954 18610 29979

3097 3176

3313 3595

4519 4869

925 958

1003 1068

1177 1237

466 479

496 516

17734 id b 5 5 29494 17841 18695 31475

3109 3208

3374 3708

4802 5077

943 981

1032 1108

1234 1276

0.35 0 .4

'

544 553

286 292

299 308

475 ~5TJ9 490 532

564 ' 565

770" 297

305 ' "“325" 314 313

'5TB " 310

0 .4 5

••• **•

17041 17455 30769 17179 18273 32322

3048 3166

3360 3740

4973 5181

941 983

1040 1123

12*3 1289

474 491

511 536

570 565

288 296

304 314

0 .5

••• *•*

15898 16427 31341 16074 17455 32517

2929 3065

3284 3701

5031 5181

923 968

1028 1116

1264 1276

465 482

503 529

565 553

281 288

297 —319 ' 307 300

0 .5 5

••• ***

14417 15089 31203

2767 2918

3155 3597

4975 5077

89b 936

998 1087

1236 1237

447 464

485 511

546 530

268 275

284 293

305 284

••• ***

12714 13563 30357 13001 15061 30955

2574 2735

29*4 3436

4806 4869

842 888

949 1036

1180 1172

422 438

458 482

515

250 257

264

25*'

495

274

261

••• **•

10915 11963 28807 11277 13663 29197

2357 2523

2774

782 825

883 964

1095 1081

388 403

421

3222

4524 4556

471 449

227 233

240 247

256 232

*** **•

7T*5 9588

10382 26555 12206 26789

2123 2286

2529 2953

4130 4140

707 747

799 871

~7TT~ 964

358

392

415 391

198 203

208 214

221 196

***

7511 8013

8867 23608 10710 23730

1869" 2246

3626 3619

618 653

696

2022

843 821

294 304

316 330

347 322

163 166

170 174

179 153

*** •**

^0 5 7 6575

7419 9158

19973 20021

1593

1727

2242

3011 2994

5T3 ~ 572 615

676 651

232 239

247 256

266

539

•••

4755" 5991 7499

1283 1389

1539 1778

2288

5232

15656 15660

2265

385 402

423 449

482 456

•**

3503 3887

4481 5620

10666 10648

912 980

1073 1211

1458 1432

*•* • *»

2049 2311

2641 3225

5011 4986

0 .6 0 .6 5 0 .7

0.75 0 .8

0.85 0 .9 0 .9 5

•**

14642 16350 32061

2628 1921

755

443

34 5 " 373

241

326 310

'

487

TABLE 4: ALPHA= 0.01 POWER= 0.9 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 750

D E L :.02 FACT=

DEL:.OS

1 .0 .75

.50 .25

.00 BIN

6 .0 5 0 .1 0 .1 5 0 .2

0 .3 0 .3 5

1 .0 75

.50 .25

.0 0 BIN

1 .0 .7 5

.50 .25

.00 BIN

***

3706 3711

3722

3921

804 814

287

7329

793 797

831

3751

1432

289

290 293

295 456

169 169

170 171

172 241

119 120

126 121

153

••• ***

7711

7748 7822

8615

1452

12731

1465

1486 1523

1604 2265

465 470

476 484

495 651

251 254

256 259

263 322

167 168

169 171

172 196

••• ***

11265 11330 13324 11286 11460 17482

2020 2043

2081 2158

2351 2994

613 625

637 654

679 821

320 325

329 335

342 391

205 208

210 213

215 232

***

14095 14195 17704

2470 2504

2565 2688

3033 3619

735

77i 799

841 964

376 382

390

751

399

410 449

236 240

243 247

252 261

2797 2845

2931 3106

3629 4140

827 849

877 917

979 1081

419 428

436 451

468 495

260 265

269 274

281 284

17440 17967 27831

3008 3073

3185 3416

4127 4556

692 919

956 1009

1092 1172

450 460

474 490

512

277 282

288 295

303 300

17890 18154 27524 17978 18679 29979

3115 3198

3340 3625

4519 4869

933 966

1010 1074

1177 1237

469 483

499 518

544 553

286 293

300 308

318 310

0 .4

17757 18101 29494

3131 3234

3405 3743

4802 5077

952 990

1041 1114

1234 1276

479 493

512

17872 18785 31475

564 565

291 298

366 315

325 313

17071 1T514 30769 17219 18386 32322

3074 3197

3396 3779

4973 5181

951 994

1049 1130

1264 1289

478 494

514 ” 570' 538 565

290 297

305 314

325 310

15936 16503 31340 16125 17594 32517

2960 3100

3323 3743

5030 5181

934 979

1038 1123

1264 1276

469'

506 531

565 553

282 290

298 308

319 300

*** **•

14465 15184 31203

2861 2957

3198 3642

4975 5077

901 947

1008 1094

1236 1237

452 469

4TB

14706 16516 32061

513

546 530

270 277

265 294

305 284

••• **•

12776 13680 30356 13082 15249 30955

2611 2776

3028 3482

4806 4869

853 899

959 1043

1180 1172

426 442

460 484

514 495

252 259

265 274

284 261

••• ***

10993 12102 28807 11379 13868 29197

2396 2565

2818 “ r a r 3265 4556

792 835

892 971

1095 1081

392

406

423 444

471 449

226 234

240 248

256 232

•••

" ro ra - 10538 26555 9708 12419 26789

2161 2326

2571 2994

4130 4140

717

807 877

983

415

964

349' 361

376

757

393

391

199 204

209 214

22l 196

703

843 821

296 306

318

347 322

164 167

171

331

179 153

234 241

248 257

266 241

7723

0 .4 5 0 .5 0 .5 5 0 .6 0 .6 5 0 .7 0 .7 5

T6127 16271 21586

•••

17374 17572 24877

*** • ** •••

1 .0 .75

REQUIRED NUMBER OF PATIENTS

••• ***

••• **»

.00 BIN

16175 16560 25032

••• *•*

7624 8146

9030 23608 10917 23730

1905 2060

2285 2665

3625 3619

627 661

760

**•

6175 6709

7576 9349

19973 20021

1625 1760

1954 2271

3611 2994

520 545

619

676 651

***

4864 5354

6130 7662

15656 15660

1308 1415

1564 1799

2288 2265

390 406

426 450

482 456

0 .9

••• ***

3592 3984

4588 5740

10667 10648

928 997

1088 1222

1458 1432

0 .9 5

••• ***

2 i4 l 2366

2698 3282

4986

0 .8 0 .8 5

D E L :.20

.00 BIN

14128 14396 21583 0 .2 5

.50 .25

D E L :.15

.50 .25

PCONT=***

1 .0 .75

D E L :.10

5011

577

486

534

530

175

HI

CRC Handbook of Sample Size Guidelines for Clinical Trials

488

TABLE 4: ALPHA= 0.01 POWER= 0.9 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 800

DEL=.0 2 FACT=

1 .0 .75

.50 .25

DEL=.05 .0 0 BIN

0 .1 0 .1 5 0 .2 0 .2 5 0 .3 0 .3 5 0 .4 0 .4 5

0.5 0.55 O .i' 0 .6 5

0.7 0 .7 5 0 .8

0.85 0 .9 0 .9 5

***

.50 .25

.0 0 BIN

1 .0 .75

DEL=.15

DEL= .2 0

.50 .25

.0 0 BIN

1 .0 75

.5 0 .2 5

.0 0 BIN

1 .0 .7 5

.50 .25

.0 0 BIN

REQUIRED NUMBER OF PATIENTS

PCONT=***

0.05

1 .0 .75

DEL=.10

3707 "3724

794 798

805 815

832 1432

287 289

79T 293

294 454

149 170

171 171

172 241

119 120

120 121

121 153

1*55

444

***

3713

3755

3921 7329

• **

7713 7726

7753 7831

8415 12731

1448

1489 1527

1604 2265

471

477 485

495 451

252 254

257 259

243 322

147 148

170 171

172 196

••• **•

11269 1133r 13324 1 1 2 9 2 11477 17482

2025 2048

2088 2145

2351 2994

"417 427

539"

479

454

821

321 325

330 334

342 391

204 208

210 213

216 232

••• *«*

14102 ~ i r z w 17703 14137 14423 21583

2477 2513

'2575“ 3033 3619

739 754

774 801

841 944

378 " 391 384 400

4 ir 449

237

2700

240

244 247

252 261

•** ***

14137 I5 2 9 f 21584 16188 16598 25032

2807 2858

2944 3123

3629 4140

832 853

881 920

980 1081

421 429

440 452

495

241 245

216 275

281 284

*** ** •

17387 17598 24877 17457 18020 27831

3022 3089

3204 3438

4127 4556

898 924

952" 1013

1092 1172

452 443

474 492

530

278 283

289 295

303 300

*• *

17908 18189 27524 18001 18749 29979

3132 3218

3344 ■TOT3452 4869

' 940 973

1017 1079

1177 1237

472 ~ ~ so r~ 485 520

544 553

289 295

30l 309

318 310

••• **•

17780 'IBTT7" 29494 17903 18874 31475

3153 3259

3435 3775

4802 5077

940 998

1048 1120

1235' "

482 497

514 534

554“

1274

545

293 300

307 315

325 313

*** ***

17100 17573" 30749 17258 18499 32322

310o 3224

3430 3815

4973 5181

741 " 1058 1003 1134

1263 1289

482 498

517 540

545

292 298

306 315

326 310

*** ** *

15974 16578 31340 16175 17731 32517

2990 3134

3341 3782

5031 5181

944 988

1047 1130

1264 1276

473 489

509 533

544 553

284 291

299 308

319 300

*** *•*

14770 16677 32041

3239 3483

4975 5077

911 957

1017 1101

1236 1237

454 472

491 515

544 530

272 278

286 295

305 284

■*** **•

1'2'83T 13795' 30358

2447

3070

2815

3523

4804 4849

844 909

968 1050

1180 1172

430 445

463 486

'

13163 15432 30955

495

253 240

267 275

284 261

•** ***

11071 12238 28807 11479 14065 29197

2433 2404

2860 3306

T 52T

802 845

901 977

1095 1081

395 409

424 444

471“

"

4554

449

230 235

241 248

256 232

*** ***

9338 9827

2197 2345

2611 3032

4130 4140

726 745

815 882

983 964

352 344

378 394

415“ 391

200 205

210 215

22l 196

*** «**

1940 2095

2321 2699

3424 3619

435 448

709 764

821

299 308

” 319

8276

332

347“ 322

145 148

171 175

179 153

*»*

6838

9531

19973 20021

1455 1791

1985 2299

3011 2994

524 551

622

676 651

234 242

249 257

264 241

***

*'**

4970 5471

6262 7816

15656 15660

1332 1439

1588 1819

2288

2245

" 394 410

429 452

456

**•

3477" "4490 4076

5852

10447 10448

944 1012

1102 1233

1458 1432

*« »*•

2191 2418

2753 3336

5 0 ll 4984

r « n 15279 31203

10488 26555 12621 26789

7733 '9184'

23608 11115 23730

4'2ff9” '7724

2835 2993

'

582

843'

482

'

'

447“ 512“

'

570

515”

489

TABLE 4: ALPHA= 0.01 POWER= 0.9 EXPECTED ACCRUAL THRU MINIMUM F0LL0W-UP= 850

DEL=.0 2 FACT=

DEL=.05

1 .0 .75

.50 .25

.00 BIN

PCONT=***

1 .0 .75

.50 .25

D E L :.10 .00 BIN

1 .0 .75

D E L :.IS

D E L :.20

.50 .25

.0 0 BIN

1 .0 75

.50 .2 5

.0 0 BIN

1 .0 .7 5

.5 0 .25

.0 0 BIN

REQUIRED NUMBER OF PATIENTS

0 .0 5 '

*** ***

3708 3714

3726 3758

3921 7329

794 799

806 816

832 1432

288 289

291 293

295 456

169 170

171 171

172 241

120 120

120 121

121 153

0 .1

••• *•*

7716 7730

7751 7841

8615 12731

1458 1471

1493 1530

1604 2265

467 472

478 485

495 651

253 255

257 259

263 322

"158" 169

170 171

172 196

JT IT

*** ***

“ TTZ7J “T1T47 13323

2029 2054

2095 2171

2351 2994

619 629

641 657

379

11298 11494 17482

821

322 326

331 336

342 391

2o7 208

210 213

"213 232

**• ***

14108 14222 17703 14146 14450 21583

2484 2521

2586 2711

3033 3619

742 757

777 803

841 964

379 385

392 400

4 l0 449

238 241

244 248

252 261

***

T6TT7 16310 21585 16201 16637 25032

2817 2870

2960 3139

3629 4140

836 858

885 923

980 1081

423 431

441 453

467 495

262 266

271 275

2 81 284

0 .3

*** *•*

17400 17624 24877 17475 18072 27831

3035 3105

3224 3459

4127 4556

904 931

967 1017

1092 1172

454 465

478 493

5 l2 530

280 284

290 295

303 300

0 .3 5

*** ***

17925 18224 27524 18025 18818 29979

3149 3239

3388 3678

4519 4869

947 980

1023 1083

1177 1237

475 " 503 488 521

544" 553

"29TT 295

302 309

318 310

0 .4

••• ***

17803 18193 29494 17933 18963 31475

3174 3284

3463 3805

4802 5077

969 1006

1055 1125

1234 1276

485 ' 499

516 537

563 565

294 301

308 316

323 313

0 .4 5

**• ***

"171 JO 17632 30769 17298 18609 32322

3126 3255

3462 3849

4973 5181

970 1011

1065 1142

1263 1289

486 501

519 542

370 565

293 300

307 316

326 310

0 .5

*** *•*

i'6012 16653 31340 16226 17866 32517

3019 3166

3397 3819

5031 5181

953 997

1055 1136

1264 1276

477 493

5T1 535

564 553

286 292

300 309

319 300

0 .5 5

••• ***

14561 15372 31203 14834 16835 32061

2867 3029

3277 3722

4975 5077

921 966

1025 1107

1236 1237

459 475

494 516

546 530

273 280

287 295

305 284

***

12899 13910 30357 13244 15608 30955

2681 2852

3109 3562

4806 4869

873 918

976 1056

1179 1172

433 448

465 487

514' 495

255" 261

267 275

284 261

••• *•*

1114* 12371 28807 11578 14255 29197

2468 2641

2899 3344

4524 4556

" sn 854

908 983

17596" 1081

398 412

428 447

449

231 236

242 248

2 56 232

**• *•*

9433 9943

10835 26555 12816 26789

2232 2401

2648 3067

4130 4140

7T4 773

821 887

983 964

354 366

379 395

415 391

2ol 205

210 215

221 196

0.75"" « *

7840 8401

9336 23608 11305 23730

1972 2129

2355 2730

3625 3619

642 674

715 768

843 821

301 310

321 332

346 322

165 169

172 175

179 153

0 .8

*•*

6399 6962

7870 9705

19973 20021

1684 1820

2013 2324

3011 2994

531 556

586 624

676 651

237 243

250 257

266 241

0 .6 5 " ***

307T 5583

6388 7962

15656 15660

1354 1462

1609 1837

2288 2265

397 413

431 454

481 456

*•*

***

3758 4164

4786 5959

10667

958 1025

1115

10648

1243

1458 1432

**• • **

2238 2467

■ZBTO 5012

0 .2 0 .2 5

0 .6 0 .6 5 0 .7

**•

• ••

0 .9 0 .9 5

3386

4986

'

"

47r '

'



CRC Handbook of Sample Size Guidelines for Clinical Trials

490

TABLE 4: ALPHA= 0.01 P0WER= 0.9 EXPECTED ACCRUAL THRU MINIMUM F0LL0W-UP= 900

DEL=.02 FACT=

DELs.05

1 .0 .7 5

.5 0 .2 5

.0 0 BIN

3709 3716

372# 3762

3921 7329

795 800

*7718 7733

7763 7850

8615 12731

PCONT 0 .0 5

1 .0 .7 5

.50 .25

DEL=.10 .0 0 BIN

1 .0 .7 5

DE1=.15

.50 .25

.0 0 BIN

1 .0 75

DEL=.20

.5 0 .2 5

.0 0 BIN

1 .0 .7 5

.5 0 .25

120

121

120

153 172 196

REQUIRED NUMBER OF PATIENTS 807 816

831 1432

288 289

291 293

296 456

170'

171

172 "

170

171

119

241

120

1460

1 49F 1604 1532

2265

468 473

479

1474

486

495 651

253 255

257 260

262 322

168

170

169

171

11278 11356 13323 11304 11511 17482

2034 2060

2101 2178

2351 2994

621

642

678

658

821

323 327

332 336

342 391

' "207

630

0. 2

14115 14236 17703 14156 14476 21583

2491 2530

2595 2721

3033 3619

745 760

? 79

84l 964

380 386

393 401

“ 411

0 . 25

16156 16329 21585 16214 16675 25032

2#27 ~ 7 v r r 3629 2882 3154 4140

840 861

424 " T O "

926

980 1081

0 .3

17413 17451 24#77 17492 18124 27831

3048 3121

3243 3479

4127 4556

9 l0 936

972 1019

1092 1172

17943 18260 27524 18048 18887 29979

3165 3258

3411 3702

4519 4869

954 986

1028 1088

m e

T7826 18239 29494 " 17964 19051 31475

3194'

3491 3834

4#02 """ 5077

976

3307

1013

0. 45

17159 1 7691 3o?70 17337 18719 32322

3150 3282

3493 3881

4973 5181

0 .5

T5049 16727 31340 16276 17997 32517

3047 3197

3431 3854

14609 15465 31203 14898 16989 32061

2898 3062

12960 H 0 2 3 30358 13325 15780 30955

0 .1 0 .1 5

.0 0 BIN

805

889

'211 " '216

209

213

-239

"244 " 252~~

449

242

248

261

-263

271

281'

267

276

284

"" TOO

290

305" 300

-

232

433

453

468 495

457 467

479 494

512

478 490

504

1237

522

"5 4 4 553

1062 1130

1234 1276

458 ' 502

518

"564 ■"

539

565

302

978 1019

1073 1147

1263 1289

489 504

527”

570 "'' "

294 ' “ TOB'"“ 326

543

565

301

316

310

5031 5181

962 1006

1063 1142

T264

480

514

564

"287

1276

496

536

553

294

301 309

300

3313 3758

4975 5077

930 975

1033 1113

1236 1237

462" 478

496 518

546 530

275 281

288 296

305 284

2714 2887

3146 3599

4806 4869

883 927

983 1061

1180

436 451

468 488

"515

256 262

269 276

28'4"

1172

11226 12502 28807 11676 14438 29197

2502 2677

2936 3379

4524

401

4556

820 862

9524 10977 26555 10056 13002 26789

2265 2435

2683 3100

4130 4140

7945 8523

9432 23608 11485 23730

2oo3 2160

23#? 2759

5506

#008 9870

19973 20021

1710

7082

1847

5169 5691

6509

15656

8101

15660

0 .9

3836 4248

4879 6059

10666 10648

0 .9 $

2282 2513

2452 3432

5012 4986

0 .3 5 0 .4

0. 55 0 .6 0 .6 5 0 .7 0. 75 0. 8

0.85

w 987

'743“ " #2#

1095 1081

414

470 448

963 964

357 368

396

381

780

891

3626 3619

649 681

720 771

#43 821

303 312

322 333

2o40 2348

3011 2994

536 560

590 627

676 651

238 244

251 258

1376 1483

1630 1854

2288 " " " 2265

401 416

434 455

482 456

972 1038

ll2 7 1252

1458 1432

530

495

285

''

"291 297

-■303'- 318 309 310

296

" 308 " 325

" 232“ 449

237

415 391

166 169

"JT T 322

266 241

296

316

313

319—

261

243 " 256 249

232

202

2io

206

216

221 196

172 176

179 153

'

491

TABLE 4: ALPHA= 0.01 POWER= 0.9 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 950

DEL=.02 FACT=

DEL=.05

D E L :.10 .00 BIN

1 .0 75

.50 .25

.00 BIN

1 .0 .75

.50 .25

.00 BIN

2*8 290

291 293

295 456

169 170

171 172

172 241

120 120

120 121

121 153

1504 ' 2265

"4 5 7 473

479 486

495

254

257

651

255

260

262 322

158 169

170 171

172 196

2107 2183

2351 2994

622 632

644

577 821

324 327

331 336

342

659

391

207 209

211 ” 7T5 213 232

2497 2538

2605 2731

3033 3619

74* 762

781 806

841 964

' '7 * 1 387

394 401

239 242

245 248

261

15165 16348 215*5 16227 16712 25032

2837 2893

29*8 3168

3629 4140

844" 865

892 928

980 1081

425 434

443 454

495

264 267

272 276

2*1 284

17426 17677 24*77 17510 18175 27831

3060 3136

3250 3497

4127 4556

914 941

976 1022

1092 1172

45*

481 495

512 530

281 286

291

469

296

303 300

17961 18294 27524 18071 18954 29979

3181 3277

3433 3725

4519 4869

950 992

1034 1091

1177 1237

4*0 492

506 523

544 553

292 298

304 " O T" 310 310

17849 182*5 29494 17994 19138 31475

3214 3331

3516 3860

4802 5077

983 1020

106* 1134

1235 1276

491 504

520 539

565

297 303

310 ' 373 317 313

171*9 17750 30769 17376 18827 32322

3173 3309

3523 3911

4973 5181

986 1027

1079 1152

1264 1289

492 506

523 544

570 565

295 302

309 317

325 310

150*7 16*02 31340 16327 18127 32517

3073 3227

3454

5030 5181

971 1014

TB7ff" 1254

3886

1147

1276

4*3 498

516 538

564 553

289 295

302 310

319 300

14657 1555* 31203 14962 17138 32061

292* 3095

3348 3792

4974 5077

939 983

1040 1117

1236 1237

466 481

49* 519

546 530

276 281

289 296

284

13021 14134 30357 13404 15947 30955

2745 2921

31*1 3633

4806 4869

89l 935

990 1066

11*0 1172

439 453

470 490

514 '

257

495

262

269 276

284 261

11303 12530 28*06 11773 14615 29197

2534 2711

2971 3412

4524 4556

82* 869

922 992

1096 1081

471 449

233 238

249

243

256 232

9618 " n i'1 3 25555 10167 13182 26789

2296 2468

2717 3131

4130 4140

749

834 895

203

787

211 216

22l 196

8047 8640

9622 23508 11658 23730

2032 2191

2417 "752T 2786 3619

655 686

172

179 153

5509 7198

8141 19973 10027 20021

1736 1873

2055 2370

3011 2994

'541

5253 5795

6625 8234

15656 15660

1396 1502

1548 1870

22*6

403

2265

418

3911 4328

4967 6154

10566 10648

9*4 1051

1138 1260

1432

2325 2558

2*9*

5011 4986

.50 .25

.00 BIN

0 .0 5

3710 3717

3730 3765

3921 7329

796 801

808 817

831 1432

0 .1

7721 7736

7757

8515 12731

1453

7860

1477

1499 1535

112B2 11354 13323 11309 11528 17482

2039 2065

14122 14249 17703 14164 14503 21583

PCONT =*•*

0 .2 0 .2 5 0 .3 0. 35 0 .4 0 .4 5 0 .5 0 .5 5 0 .6 0 .6 5

m "" *93 _— 473 ' ' 503 ' 513

1037

1073

1172

497

507

530

3747 3863

4017 4217

4517 4869

1093 1113

1133 1153

1177 1237

523 527

533 537

543 553

19223 20723 29493 19773 22683 31475

3887 4023

4203

4803 5077

1137 1157

1183 1207

1233 1276

543 547

553

4443

557

563 565

122657 129102

18933 20727 30767 19597 22993 32322

3937 4093

4293 4563

4973 5181

1157 1177

1203 1233

1263 1289

543 553

557 563

565

64953 67887 65937 73303

125223 130144

18253 20327 31337 19037 22843 32517

3917 4083

4297 4593

5d33 5181

1153 1173

1203 1227

1263 1276

537 543

553 557

563 553

59387 63083 60637 69527

124957 128582

17283 19593 31203 18173 22297 32061

3tfZ3

4217 4523

4973 5077

1123 1147

1173

1237

""12J

533

547

3997

1203

1237

527

537

530

52953 57513 54527 64893

121657 124416

16107 18583 30357 17073 21387 30955

3663 3837

4063 4363

4807 4869

1073 1093

1117 1147

1177 1172

493 497

503

513 495

46153 51577 48077 59657

115933 117648

14787 17343 "ZSS07 ' 15797 20153 29197

3443 3613

3823

4523 4556

997 1017

1043 1067

1093 1081

447 453

457 463

~ 473“

4107

0 .7

39443 45563 41687 53977

107203 108275

13353 15887 26553 14367 18593 26789

~ ^ S Y T T 3507 3313 3763

4 l2 7 4140

697 917

937 957

983 964

397 403

407 407

413 391

0 . 75

33153 39593 35583 47903

95693 96300

11823 14217 23607 12787 16707 23730

2 6 l3 2947

3113 3327

3627 3619

777 793

807 823

843 821

333 337

337 343

347 322

27363 33647 29783 41373

81427 81721

10177 12313 19973 11047 14463 20021

2367 2497

2627 2793

3013 2994

633 643

653 663

677 651

257 263

263 263

267 241

21927 27547

64433 64538

8357 9077

10107 15657 11783 15660

1883 1957

2047 2153

2267

24123 34183

457 463

467 473

483 456

0 .9

16483 20903 18227 25877

44743 44753

6243 6753

7453 8533

10667 10648

1267 1307

1347 1397

1457 1432

0 .9 5

10193 12733 11223 15323

22367

3517 3743

4027 4417

5013 4986

4633 5203

7707 7680

0 .2 0. 25

***

0 .3 0 .3 5 0 .4

**•

***

0 .4 5 0 .5 0 . 55 0 .6 0. 65

***

0 .6 0 .8 5

0 .9 8

**•

$703 6427

22364

2265

” T67 ■" 677' " "

263 263

“ 87-----167

507

567

449

DEL=.15

511

TABLE 4: ALPHA= 0.01 POWER= 0.9 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 4250 DEL=.01 FACT=

DEL=.02

DEL=.10

DEL=.05

1 .0 .75

.50 .25

.0 0 BIN

0. 01

1990 1994

1$94 2001

2005 7480

730 730

736 736

736 2539

0.0 2

4395 4406

4417 4438

4480 12479

1414 1414

1420 1427

0.OS

13310 13384 13338 13518

13994 27050

375B " 3818 3790 3860

0 .1

29353 29551 29424 29934

32573 48918

7880 7940

43842 44193 43959 44887

"55512 54045

DEL=.15

.50 .25

.0 0 BIN

1 .0 75

.50 .25

.0 0 BIN

1 .0 .7 5

.50 .25

.00 BIN

241 241

241 241

241 691

120 120

120 120

120 281

88 88

88 88

88 147

1431 3775

386 386

364 384

384 883

147 147

“ 147 147

I"47' 324

109 109

109 109

109 184

3924 7329

815 821

825 825

832 1432

294 294

294 294

294 454

T73" 173

173 173

173 241

8413 12731

1537 1554

1545

1401 2245

'455 " 492

1584

485

492

496 651

258 258

'242' "757“ 242 322

51453 48183

11547 11882 13320 11480 12286 17482

2196 2224

2298

2351 2994

442 444

473

“ 477 821

55699 57155

69129 84845

14559 15043 17704 14740 15739 21583

2748 2798

2934

3031 3419

811 815

825 832

843 964

*4029 44820 64295 44392

84869 98903

16795 17517 21587 17056 18501 25032

3195 3265

3354 3471

3430 4140

49404 70493 69767 72450

98278 110358

18289 19240 24876 18639 20577 27831

71853 73309 72338 74143

109126 119210

19107 20354 27522 19557 22012 29979

3748 3885

71694 73594 72328 77279

117275 125458

19330 20881 29492 19897 22868 31475

3913

49314 71744 70132 74390

122658 129102

0 .5

45138 48252 66180 73915

0. $5

POONT

0 .1 5 0 .2 0. 25 0 .3 0 .3 5 0 .4 0. 45

0 .6 0 .6 5 0 .7 o .7 s 0 .8

0.85 " 0. $ 0 .9 5 0 .9 8

1 .0 .75

.50 .25

.0 0 BIN

1 .0 .75

REQUIRED NUMBER OF PATIENTS

***

8040 8227

2254

2855

444

— 977 “ 9 S T '"951—

"'

337 '"337" '"343 " 343 391

337

400 400

453

440" "444 444

495

1091

494

1172

503

503 507

5 l3 530

534 538

545 553

549 554

545

943

3535 “ 3717" 4126 3630 3907 4556

1027 1044

lo55 1074

4034 4232

4519 4869

IW 1112

1133 1155

1174"

'5 7 T

1237

528

4051

4225 4459

4799 5077

1140 1141

1183 1208

1234 1274

545

19044 20913 30767 19755 23198 32322

3970 4124

4321 4583

4969 5181

"1141 1183

1208 1234

1261 1289

125223 130144

18410 20535 31340 19217 23074 32517

3949 4115

4328 4408

5029 5181

1155 1174

1204 1229

1261 1276

59620 43530 60948 70228

124957 128582

17440 19819 31202 18374 22539 32061

3860 T 2 T T 4030 4544

4976 5077

1129 ~TI7S~ 1236 1151 1204 1237

53249 58041 54913 45470

121855 124416

16302 18820 30359 17290 21640 30955

3701 3875

4094 4381

4804 4849

1074 1098

1123 1151

44519 52183

115933 117648

14988 17581 28808 16019 20397 29197

3482 3648

3853 4130

4523

48542 40474

4554

1002 1023

39883 44211 42214 54807

107203 108275

13541 16121 24555 14585 18824 24789

3195 3343

3779

4130 4140

33435 40251 34139 48702

95692 96300

12024 14434 23405 12998 14918 23730

2840 2972

3138 3343

3419

3424

27851 34249 30327 42099

81427 81721

10356 12509 17972 11234 14438 20021

2415 2521

2649

3010

2802

22373 28094 24411 34793

64433 44538

8507 9230

10254 15454 11918 15440

1898

2058

1973

2160

14837 21321 18412 24325

4473# 44753

10405 12959 11444 15541

22383

3547

4044

5012

22344

3784

4444

4984

4912 5277

5773

7?04

4484

7480

“ 5350' 7558 6860

8420

10644 10448

1278

1353

1314

1399

411 449

440

942

3535

407 407

1081

538

540

” 545 ' 554" " 570 549

544

545

535

'549"

544

545

554

553

524

534

545 ''

528

538

530

ll 7 6 1172

492 494

503 507

495

1044 1044

1098 1081

449

440

453

444

471 449

900 921

938 959

981 964

400

400

407 411

418 391

779 793

8 ll 825

#43 821

333 337

343

343

347 322

634 641

451 442

677 451

258

2994

242

242 242

249 ' 241

2288 2245

460

“ 471

464

475

481 454

1459 1432

513

"

CRC Handbook of Sample Size Guidelines for Clinical Trials

512

TABLE 4: ALPHA= 0.01 POWER= 0.9 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 4500 DEL=.0 1 FACT=

DEL=.02

DEL=.05

1 .0 .75

.5 0 .2 5

.0 0 BIN

0 .0 1

1995 1995

1999 1999

2006 7680

735 735

735 735

735 2539

0 .0 2

44o2 4406

4418 4440

4481 12679

1414 1421

1421 1425

0 .0 5

13312 13395 13339 13530

13991 27050

"'3776 ' 3821 3795 3862

0 .1

29366 29573 29438 29973

32572 48918

7890 7957

43860 44231 43984 44970

0 .2

55549 56130 55740 57277

.50 .25

.0 0 BIN

1 .0 .75

DEL=.10

DEL=.15

.5 0 .25

.0 0 BIN

1 .0 75

.5 0 .2 5

.0 0 BIN

240 240

240 240

244 691

120 120

120 120

""r z o 281

1432 3775

386 386

386 386

386 883

165 165

165 165

3923 7329

818 825

825 829

829 1432

296 296

8614 12731

1545 1556

1567 1583

1605 2265

51454 68183

11584 11910 13323 11708 12315 17482

2201 2231

2258 2303

69128 84845

14595 15112 17704 14779 15798 21583

2760 2809

0 .2 5

64076 64916 T 4 T C 6 64353 66570 98903

16845 17591 "21585 17115 18588 25032

0 .3

69465 70624 69855 72896

98276 110358

0 .3 5

71936 73477 72453 76485

0 .4

1 .0 .7 5

.50 .25

.00 BIN

86 86

86 86

86 167

165 326

109 109

109 109

109 186

296 296

296 456

" " 172' 172

487 487

491 491

491 651

262 262

262 262

252 322

2348 2994

660 667

667 671

678 821

334 341

341 341

341 391

2865 2940

3034 3619

8 l3 818

825 829

840 964

401 401

408 408

408 449

3 2 l0 3281

3367 3480

3630 4140

937 941

953 964

982 1081

'4'53'" "458 " 469 458 465 495

18352 19365 24877 18716 20692 27831

'"'3 5 5 1 3648

3761 3911

4125 4556

1031 i w r 1043 1072

1095 1172

498 498

503 510

510 530

109121 119210

19189 20483 27525 19661 22159 29979

3795 3911

4053 4245

4519 4869

1099 1117

1133 1155

1178 1237

525 532

532 536

543 553

7T505' 73819 72480 77689

117278 125458

19436 21030 29494 20028 23036 31475

3941 4076

4249 4474

4800 5077

1144 1166

1185 1207

1234 1276

543 548

555 559

566 565

0. 45

69461 72048 70327 76897

122655 129102

19189 21086 30772 19905 23396 32322

4001 4155

4346 4605

4969 5181

1166 1185

1207 1234

1263 1289

548 555

559 566

570 565

0 .5

65321 68610 66428 74512

125220 130144

18559 20730 31339 19391 23291 32517

3986 4148

4357 4631

5032 5181

1162 1185

1207 1234

1263 1276

543 548

555 559

566 553

0 .5 5

59858 63971 61260 70912

121957 128582

17632 20033 31204 18566 22766 32061

3896 4065

4278 4564

4976 5077

1133 1155

1178 1207

1234 1237

521 525

532 536

543 530

0 .6

53546 58564 55297 66416

121856 124416

16489 19050 30356 17497 21873 30955

3738 3907

4121 4402

4807 4869

1083 1099

1121 1151

1178 1172

491 498

503 510

"TIT'

0 .6 5

46886 52770 49001 61264

115935 117648

15191 17812 28808 16230 20629 29197

3513 3675

3878 4148

4526 4556

1005 1027

1043 1072

1095 1081

453 458

458 465

469 449

40312 46841 42731 55601

107205 108275

13762 16343 26553 14797 19043 26789

3225 3371

3558 3799

4132 4140

901' 926

941 960

982 964

401 401

408 408

413 391

0. 75

34102 40886 36678 49470

95696 96300

12214 14644 23606 13200 17115 23730

2865 2996

3153 3356

3626 3619

784 795

813 825

840 821

334 341

341 345

345 322

0 .8

28320 34867 30851 42798

81424 81721

10526 12686 19972 11411 14808 20021

2433 2539

2663 2816

3011 2994

633 645

656 667

678 651

TOT 262

262 262

266 241

0. 85

22000 28616 25080 35378

6 4432' 64538

8655 9379

10403 15656 12045 15660

1916 1988

2066 2168

2287 2265

450 465

469 476

480 456

1718 2 21720 18982 26749

44738 44753

6454 6960

7653 8693

10668 10648

1286 1320

1358 1403

1459 1432

0 .9 5

10605 13177 11651 15746

22384 22364

3608 3828

4103 4470

5010 4986

0 .9 8

4987 5351

7703 7680

PCONT =***

0 .1 5

0 .7

0 .9

i"JT"

*** • **

**•

1 .0 .7 5

REQUIRED NUMBER OF PATIENTS

5835 6533

8058 8238

172 —m 172 241

495

■ -

513

TABLE 4: ALPHA= 0.01 POWER= 0.9 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 4750 DEL=.01 FACT=

DEL=.02

D E L :.05

1 .0 .75

.50 .25

.00 BIN

0 .01

1991 1991

1998 2003

2010 7680

732 732

732 732

732 2539

0.O2

4402 4409

4421 4445

4480 12679

1417 1417

1421 1428

13315 13403 13344 13541

13992 27050

3780 3796

2937$ 296tiO 29453 30016

32569 48918

7900 7964

43882 44273 44012 45045

.50 .25

1 .0 75

.50 .25

.0 0 BIN

1 .0 .7 5

.50 .25

.00 BIN

241 241

241 241

2 4 1 ...... 691

122 122

122 122

122 281

87 87

87 87

87 167

1433 3775

383 383

383 383

383 883

170 170

r7 0 " 170 170 326

110 110

li b 110

-n o 186

3827 3863

3922 7329

615 823

823 827

827 1432

293 293

293 293

293 456

170

170 170

241

8071 8249

6613 12731

"T547

2265

495 651

2*5

1587

490 " "490 490 490

-257~ 257

1559

51450 68183

11605 11942 13320 11729 12346 17482

2205 2236

2264 2300

2347 2994

661 668

668 673

680 “

55578 56196 55785 57400

69128 84845

14626 15160 1)702 14823 15849 21583

2770 2818

28)0 2941

3032 3619

811 815

623 835

839 " 964

0 .2 $

64121 65007 64418 66753

84867 98903

16890 17662 2158$ 17167 18671 25032

3222 3293

3376 3483

3630 4140

934 946

953 965

977 1081

G. 3

69532 7b747 69940 73142

98274 110358

18414 19455 24874 18794 20801 27831

3570 3661

3780 3922

4124 4556

1048

1077

72025 73652 72564 76804

109123 119210

19239 20607 2)522 19763 22293 29979

3815 3927

4d69 4259

4520 4869

lld 8 1120

1136 1155

7 l9 l6 74044 72631 78093

f 172 74

19538 21177 29494 20148 23200 31475

3970 4100

4267 4492

4801 5077

1148 1167

1191

125458

I2 3 T

1207

1276

69603 72334 70517 77393

122653 129102

19317 21260 30772 20053 23580 32322

4034 4183

4366 4615

4972 5181

1172 1191

1215 1238

1262 1289

65506 "SB966 66674 75094

125225 130144

18707 20927 31342 19562 23492 32517

4017 4176

437B 4647

5031 5181

1167 1184

1207 1231

fl.55

60091 64402 61563 71574

124957 128582

17804 20243 7T204 18754 22982 32061

3927 4093

43 o2 4580

4972 5077

1136 1160

0 .6

53845 "59074 55673 67137

121857 124416

16676 1926$ 30356 17697 22091 30955

3768 3939

4148 4421

480$ 4869

4724) $3346 49451 62027

115932 117648

15382 18030 26805 16438 20844 29197

3547 3708

3903 4164

4073"5 47449

13949 16557 26556 15002 19253 26789

"3257

43228 56362

107204 108275

3400

3582 3815

34560 41495 37200 50199

95692 96300

12394 14840 23611 13387 17298 23730

2894 3020

28777 35443 31353 43459

81423 81721

ib69$ T z r e r 19970 11582 14966 20021

23212 "27111 25527 35937

64430 64538

8784 9515

175d7 22095 19336 27150

44741 44753

IT iT 7050

7739 8767

0.95

10802 133)9 11855 15940

22368 22364

3654 3867

4136 4492

0. 98

5d5$ 5418

7)03

REQUIRED NUMBER OF PATIENTS

0.0$ 0 .1 0.15 0 .2

0 .3 5

**•

• ••

0 .4 0 .4 $ 0 .5

***

ff.65 0 .7

0.75 0 .8 0 .8 5

0.9

1 .0 .75

DEL=.15

.0 0 BIN

PCONT

.00 BIN

D E L :.10

.50 .25

1 .0 .75

• **

***

5698 6575

7680

157F 1607

170“ '

l7o

257

265

m r 336

340

391

400'

407

'412

407

407

449

455 459

459 467

467 495

1089 1172

495 502

502 507

530

1179 1237

526 530

538 538

553

542

554

“572

550

554

565

550 554

562 566

566 565

1262 1276

542 550

554 554

553

1179 1207

1238 1237

526 530

530 538

542 530

1064 1108

1124 1155

1179 1172

495 495

502 507

495

4520

1005

4556

1029

ld 4 8 1072

1096 1081

455

467

449

4129 4140

91b 922

942 965

982 964

400 400

4d) 412

412 391

31)4 3369

3625 3619

787 799

81l 827

839 821

336

336

340 340

348 322

2454 2557

267$ 2822

3012 2994

637 645

657 661

673 651

257

26$ 265

265 241

10537 15655 12163 15660

1927 1998

2074 2169

2288 2265

459 467

"471

483 456

1066)

1290 1326

1362 1409

1457 1432

10648

"5007 4986

1037 ' 1060

478

821

322

340 ' ' 3'40

514 542

562

514

455 ■ 459 ' 471

257

'

CRC Handbook of Sample Size Guidelinesfor Clinical Trials

514

TABLE 4: ALPHA= 0.01 PQWER=0.9 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP=5QOO DEL= .0 1 FACT=

DEL=.02

DEL=.05

1 .0 .7 5

.5 0 .2 5

.0 0 BIN

0 .0 1

1991 1996

1996 2004

2008 7680

733 733

733 733

733 2539

0 .0 2

4404 4408

4421 4446

4479 12679

1416 1421

1421 1429

POONT =*•*

1 .0 .7 5

.50 .25

DEL=.1 0

DEL=.15

.50 .25

.0 0 BIN

1 .0 75

.5 0 .2 5

.0 0 BIN

1 .0 .7 5

.5 0 .25

.0 0 BIN

241 241

241 241

241 691

121 121

121 121

121 281

83 83

83 83

83 167

1429 3775

383 383

383 383

383 883

166 166

166

166 326

108 108

id s 108

108 186

.0 0 BIN

1 .0 .75

REQUIRED NUMBER OF PATIENTS

0 .0 5

13321 13408 13354 13554

13991 27050

3783 T ffT T " 3921 3804 3866 7329

821 821

821 829

829 1432

291 296

296 296

295 456

171“ ' 171 171 171

171 241

0. i

29391 29621 29466 30054

32571 48918

7916 7979

8616 12731

1546 1558

1571 1583

1504 2265

491 491

491 491

496 651

258 258

258 258

258 322

• »*

43904 44316 44041 45121

51454 68183

11529 11971 13321 11754 12379 17482

2208 2233

2265 2304

2354 2994

558 666

671 671

679 821

333 341

341 341

341 391

*** • **

55608 55258 55829 57521

69129 84845

14658 15208 17704 14858 15904 21583

2779 2821

2879 2946

3033 3619

816 821

829 833

841 964

404 404

408 408

408 449

64166 55104 64479 66929

84855 98903

16933 17733 21583 17229 18746 25032

3233 3304

3383 3491

3629 4140

941 946

958

979 1081

458 458

458

966

466

466 495

59596 70879

98279 110358

18479 "T9545 24879 18871 20904 27831

3591 3679

3791 3933

412$ 4556

1033 1046

1058 " W l " 1079 1172

496 504

504 508

"'5CT8

70021 73379 0. 35

72108 73821 72679 77121

109121 119210

19354 20721 27521 19858 22421 29979

3841 3946

4091 4271

4516 4869

1108 1 1 4 1 “ 1179 1121 1158 1237

529 529

533 541

541 553

0 .4

72029 74266 72779 78491

111219 125458

19641 21316 29491 20271 23354 31475

3991 4121

4291 4504

4804 5077

1154 1171

1191 1208

1233 1276

545 546

554 558

566 565

0 .4 5

69746 72616 70708 77871

122658 129102

19441 21421 30771 20196 23754 32322

4058 4208

4391 4633

4971 5181

1171 1191

1215 1233

1255 1289

558' 566

571' " 565

55691 59321 66916 75658

125221 130144

16854 21108 31341 19721 23683 32517

4046 4204

4404 4666

5029 5181

1171 1191

12o8~ 1233

1266 1276

541 546

554

555

558

553

60321 64833 61871 72216

124954 128582

17966 20441 31204 18933 23183 32061

3958 4121

4329 4596

4971 5077

1141 1158

1183" 1233 1237

533 541

545

1208

521 529

0. 5

54133 '39579 56054 67841

121854 124416

16846 19471 30358 17883 22296 30955

3804 3966

4171 4433

4804 4869

1091 1108

1129 1154

1179 1172

496 496

504 508

“ SIS"

0 .6 5

4 i7608 53904 49891 62754

115933 117648

15558 18233 28808 16633 21046 29197

3571 3733

3929 4179

4521 4556

1016 1029

1057 1071

1096 1081

454 458

458 466

471 449

0 .7

41146 48041 43721 57096

107204 108275

14133 16754 26554 15191 19446 26789

3279 3429

3504 3829

4129 4140

916 929

945 966

983 964

404 404

408 408

416 391

0 .7 5

35004 42079 37708 50896

95696 96300

12571 15021 23508 13571 17479 23730

2916 3041

3191 3379

3629 3619

791 804

816 829

841 821

333 341

341 341

345 322

0.8

29216 35991 31846 44091

81429 81721

10846 13016 19971 11741 15108 20021

2471 2571

2691 2829

3008 2994

541 646

554 666

579 651

258 258

265 266

266 241

0.85

23508 29591 25958 36466

64433 64538

8 9 l5 9646

10666 15654 12271 15660

1941 2008

2083 2179

2291 2265

458 466

"471 479

463 456

0.9

17829 22458 19671 27529

44741 44753

6641 7141

7821 8833

10666 10648

1295 1329

1366 1408

1458 1432

10983 13571 12046 16121

22383 22364

3904

4155 4516

4986

5121 5483

7704 7680

0 .1 5 0 .2 0. 25 0 .3

0 .5 O'. 55

0 .9 5 0 . 98

***

Mr **•

***

•••

5954 6621

8083 8266

5008

’ ” 547 " 554

530

530 495

515

TABLE 4: ALPHA= 0.01 POWER= 0.9 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 5500 DEL=.01 FACT=

1 .0 .75

.50 .25

DEL=.05

DEL=.02 .00 BIN

PCONT=***

1 .0 .75

.50 .25

.00 BIN

1 .0 .75

DEL=.15

DEL=.10

.50 .25

.00 BIN

1 .0 75

.50 .2 5

.0 0 BIN

1 .0 .75

.50 .25

.00 BIN

REQUIRED NUMBER OF PATIENTS

***

***

1739"' 1998 1998 2003

2003 7680

733 733

733 733

733 2539

243 243

243 243

243 691

119 119

' 119 119

119 281

86 86

86 86

86

••• ***

4404 4418

4478 12679

1420 1420

1420 1425

1434 3775

380 380

380 380

389 883

169 169

169 169

169 326

T IT 114

114 114

114 186

0 .0 5

••• ***

13333 13429 13369 13575

13993 27050

3790 3804

3832 3868

3923 7329

820 820

829 829

829 1432

293 293

293 293

293 456

169 169

169 169

169 241

0 .1

••• **♦

29415 29668 29498 30135

32569 48918

7938 8006

8108 8287

8617 12731

1549 1563

1571 1585

1604 2265

4 9 0 ' ' 490 490 490

490 651

0 .1 5

*•* *•*

43940 44403 44092 45274

51456 68183

11669 12027 13319 11801 12434 17482

2218 2245

2273 2305

2347 2994

664 669

669 678

0 .2

••• ** •

55678 56384 55911 57768

69130 84845

14722 15299 17700 14936 15995 21583

2795 2836

2891 2952

3034 3619

8 l5 820

0 .2 5

••• *•*

64263 65289 64601 67274

84869 98903

17026 17865 21583' 17334 18888 25032

3263 3323

3405 3502

3625 4140

939 953

0 .3

••• ***

69722 71133 70198 73855

98275 110358

18599 19727 24878 19020 21096 27831

3620 3708

3813 3950

4129 4556

0 .3 5

•••

72279 74163 72906 77738

109124 119210

19507 20945 27523 20043 22664 29979

3873 3983

4115 4285

***

72252 74708 73077 79264

117278 125458

19837 21583 29489 20497 23640 31475

4038 4162

***

70038 73181 71091 78810

122654 129102

19680 “21729" 30768 20469 24080 32322

*** ' *•»

66059 7dOl9 67406 76756

125225 130144

•••

60793 65674 62484 73443

O.Ol 0.O2

4423 4445

237"

257

257

265

265 322

678 821

339 339

339 339

339 391

829 834

843 964

403 403

408 408

408 449

958 966

980 1081

458 458

463 463

463 495

1040 ' 106'3" 1049 1076

1090 1172

499 504

504 504

513 530

4519 4869

1109 1123

1145 1159

1178

526 532

532 540

545

1237

4321 4528

4803 5077

1159“ 1192 1178 1214

1233 1276

545 ' 545

554 559

559 565

4107 4253

4431 4657

4973 5181

1178 1200

1219 1241

1260 1289

554

559 568

568 565

19130 21454 31340 20038 24039 32517

4101 4253

'' 5 0 2 r 5181

1178 1192

1214 1241

l2 6 o 1276

545"'

534 ” 568

4693

545

559

553

124955 128582

18269 20808 31203 19273 23558 32061

4010 4175

4368 4624

4973 5077

1145 1164

1186 1214

1233 1237

523" 532

532 540

345'

**♦

54720 60550 56791 69166

121856 124416

17183 19859 30355 18250 22683 30955

3854 4019

4211 4464

480T 4869

1095 1118

I l3 l 1159

1178 1172

499 499

504 513

513 495

••• • «*

48313 54976 50747 64139

115935 117648

15904 18621 28810 16999 21426 29197

3625 3785

3969 4203

4519 4556

'' 1021” ' 1G3T 1035 1076

1095 1081

458 458

463 463

449

*** ***

41955 49165 44664 58474

107204 108275

14474 17128 26555 15555 19795 26789

3331 3469

3639 3854

4129 4140

' 944 966

980 964

403

930

403

400 408

*16 391

**«

35864 43198 38674 52218

95695 96300

12893 15368 23604 13910 17796 23730

2960 3075

3221 3400

3625 3619

793 801

815 829

843 821

339 339

339 348

348 322

'3 0 0 5 3 37038 32775 45283

81423 81721

11141 13314 19974 12040 15376 20021

2506 2603

2713 2842

3007 2994

642 650

655 664

678 651

265 265

265 241

'*** ' 24369 30493 ••• 26780 37450

64538

9153 9882

10899 15657 12475 15660

1962 2030

2099 2190

2286 2265

463 463

47l 477

485 456

0 .9

••• ***

18420 23145 20313 28233

44738 44753

6810 7305

7970 8955

10665 10648

1 3 id 1338

1379 1412

1453 1432

0".95

*** " 11334 13933 **« 12406 16449

22389 22364

3763 3969

4225 4555

5009 4986

0 .4 0 .4 5 O'. 5 0 .5 5 0 .6 0 .6 5 0 .7 0 .7 $

•••

0 .8 0 .8 5

0 .9 8

5243 5600

6059 6700

7704 7680

917

"

167

554'

"" 257" 265

553

530

471

CRC Handbook of Sample Size Guidelines for Clinical Trials

516

TABLE 4: ALPHA= 0.01 PQWER=0.9 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 6000 DEL=.0 1

1. 0

DEL=.02

.00

1. 0

.75

.5 0 .25

BIN

.75

***

1990 1999

1999” 1999

2005 7680

0 .0 2

44 4 • **

4405 4414

4429 4450

4480 12679

0 .0 5

44 4 ** *

13339 13444 13375 13594

13990 27050

3790 3814

*•*

29434 29710 29530 30205

32569 48918

7954 8029

0 .1 5

44 4 • **

43964 44479 44149 45424

0 .2

444' • ••

0. 25

FACT=

PCONT=*** 0 .0 1

.50 .25

DEL=.1 0

DEL=.05 .0 0 BIN

1. 0 .75

.5 0 .25

.0 0 BIN

244 244

“ 244 _ 691

1. 0 75

.5 0 .2 5

DEL=.15 1.0 .75

.0 0 BIN

.5 0 .25

.0 0 BIN

REQUIRED NUMBER OF PATIENTS 730 730

'730 730

' _n z c r ~ 1420 1420 1429

"7T9------ "244 2539 244

T 7 4 ' 124 124 124

124 — 281

"8'5 85

““ r e 85

85 ' 167

1429 3775

385 385

385 385

385 883

169 169

139 " 169 169 326

109 109

109 109

109 186

3835 3874

3919 7329

820 820

829 829

829 1432

295 295

295 295

295 456

169 169

169 169

169 241

8134 8305

8614 12731

1555 1564

1579 "1 6 0 0 1585 2265

490 490

490 490

490 651

259 259

259 259

259 322

51454 68183

11704 12079 13324 11845 12484 17482

2230 2254

2275 2314

2350 2994

664 670

670 670

679 821

STO340

340 340

340 391

55744 56515 55999 58000

69130 84845

14779 15385 17704 15010 16084 21583

2809 2845

2899 2959

3034 3619

814 820

829 835

844 964

400 409

409 409

409 449

44 4 ** *

64354 ' 53470' 64729 67615

64665 98903

17110 17989 21589 17440 19015 25032

3280 3340

3415 3514

3625 4140

940 949

964 970

979 1081

460 460

460 460

469 495

0 .3

4 44 '

69650 71389 70369 74320

96275 T B 7 3 T 19894 24874 110358 19159 21274 27831

3649 3730

3835 3964

4129 4556

1045 1054

1069 1075

1090 1172

499 505

505 505

514' 530

0 .3 5

444 “

72454 74500 73135 78340

109120 119210

19660 21154 27520 20224 22879 29979

3910 4015

4144 4309

4519 4869

1120 1129

1144 1159

1174 " 1237

529 535

535 535

544 553

0 .4

44?

72475 75145 73375 80014

117274 125458

20029 21835 29494 20719 23899 31475

4075 4204

4354 4540

4804 5077

1165 1180

1195 1210

1234 1276

544 550

550 559

565 565

0 .4 5

444'

70324 73735 71479 79705

122659 129102

19909 '2 Z B rr 30769 20725 24370 32322

4150 4294

4433 4684

4969 5181

1189 1204

1219 1240

1264 1289

550 559

759 565

565 565

44'4

***

66430 70705 67885 77794

125224 130144

19390 21'759 31339 20329 24355 32517

4150 4300

4480 4714

5029 5181

1180 1204

1219 1240

1264 ' 1276

544 550

550 559

565 553

0 .5 5 " T T T • ••

61255 66490 63085 74605

124954 128582

16565 21154 31204 19594 23899 32061

4060 4219

4405 4645

4975 5077

1150 1174

1169 1210

1234 1237

529 529

535 544

544 530

55294 61489 57514 70420

121855 124416

17494 20209 30355 18580 23029 30955

3904 4060

4249 4489

4804 4869

1099 1120

1135 1159

1180 1172

499 499

505 505

514 495

0 .1

0. 5

*•* ***

'

'

0 .6

4 14

0. 65

449

49000 55999 51580 65434

115930 117648

16234 18979 28804 17344 21760 29197

3679 3820

4o00 4225

4525 4556

1024 1039

1054 1075

1090'" 1081

454 460

460 469

469 449

0.7

4 44 • ••

42730 50230 45565 59764

1072OO 108275

14794 17470 26654 15889 20119 26789

3370 3505

3670 3874

4129 4140

925 934

949 964

985 964

400 409

409 409

415 391

0. 75

44 4

36679 44254 39595 53434

95695 96300

13195 15685 23605 14215 18079 23730

2995 3109

3250 3415

3625 3619

799 805

820 829

844 821

340 340

340 340

349 322

o n r - 44 4 " 30850 38014 33649 46375

81424 81721

11410 13585 19969 12310 15610 20021

2539 2629

2734 2860

3 o io 2994

640 649

655 664

679 651

259 259

265 265

265 241

25075 31330 27550 38350

64429 64538

9379 11110 15655 10105 12649 15660

19 b 4 2044

2119 2194

2290 2265

460 469

475 475

484 456

18985 23770 20905 28870

44740 44753

6955 7450

8110 9055

10669 10648

1 3 l5 1345

1384 1414

1459 1432

4’4'4

11450 14260 12730 16744

22364 22364

3829 4024

4270 4585

5014 4986

44 4

5350 5704

7705 7680

***

♦ **

44 4

*♦* 0 .9 0 .9 5 0 .9 6

44'4

**•

***

6145 6760

517

TABLE 4: ALPHA= 0.01 P0WER= 0.9 EXPECTED ACCRUAL THRU MINIMUM POLLOW-UP= 6500 D E L = .01 FACT=

D E L = .02

DEL=.05 1.0 75

.50 .25

.00 BIN

1.0 .75

.50 .25

.00 BIN

238 238

238 238

238 691

118 118

ll8 118

281

118

86 86

86 86

86 167

1435 3775

384 384

384 384

384 883

'167 167

167 167

167 326

iu r 108

108 108

1'08 186

3843 3878

3921 7329

823 823

823 823

833 1432

29? 297

297 297

797 456

173

173 173

173 241

8152 8325

8317 12731

1554 1565

1581 1587

1603 2265

492

492

492 492

492 651

51452 68183

11743 1212? 13319 11889 12523 17482

2237 2253

2285 2312

2351 2994

661 671

'371" 677

677 821

.00 BIN

000

1993 1993

2003 2003

2009 7680

736 736

733 736

736 2539

0.02

*«' ***

440# 4414

4431 4447

4479 12679

1418 1418

1424 1424

0.O5

**c • **

13352 13460 13384 13612

13996 27050

3797 3813

4 4 'f

***

29456 29758 29563 30278

48918

32570

7973 8048

000

— 44T5T6 44532 44205 45559

PCONT _ * • t

0.1 0715

4 4T

***

D E L = .15

.00 BIN

.50 .25

0. 01

D E L = .10

.50 .25

1.0 .75

1.0 .75

.50 .25

.00 BIN

1.0 .75

REQUIRED NUMBER OF PATIENTS

173

'

265

265

235"

265 322

336

336

336 336

346 391

275

***

55807 56642 56083 58228

79132 ' 84845

14841 15464 17701 15074 16157 21583

2816 2865

2962

2903

3033 3619

'817 823

833 833

839 964

401

TCI

411"

** 4

"34432 35655 64848 67946

84838 98903

17197 18097 21585 17544 19131 25032

3293 3358

3433 3521

3628 4140

947 953

963 969

1081

960

460 460

"460" 466

Mi • **

69983 71341 70536 74771

110358

96274

16838 20047 24873 19293 21428 27831

3657 3748

3846 3970

4556

4122

1075 1061

1077

1067

1093 1172

498 498

508

508 530

***

72626 74836 73363 78921

109123 119210

19813 21347 27522 20398 23080 29979

4041

3937

4165 4317

4522 4869

1132

1175"

531 531

541 541

553

***

72697 75583 73672 80735

117281 125458

20209 22072 29486 20924 24136 31475

4113 4230

4375 4561

4798 5077

1181

" ' 547

557 557

563 565

***

70611 74283 71862 80572

129102

122330

20122 22263 30766 20967 24640 32322

4327

4493

075

4fT *•*

36772 71375 68368 78785

125217 130144

19641 22062 31341 20599 24656 32517

0. 55

***

61722 67286 63672 75703

124957 128582

18844 21471 31205 19895 24207 32061

0.2 0.25

0.3 0.35 0.4 0.45

000

~4ST

4197

4701

" 4187" 4512

1176 “ 1143

411

508"

4 ll

449 763“ 495

541 '

1158

1237

1174 “ 1197 1213

1229 1276

4937 5181

1191 1207

1223 1240

T26T

557 ' 563 557

563

5032 " '

1171

1223 1240

1262"

547

'557" ' 563

1289

547

573 "' 565

4333

4733

5181

1207

1276

547

557

553

4103

4262

4441 4668

4977 5077

i r s s “ 1377" 1240

1175

1213

1237

£31 531

541" 541

547 530

0.6

*** ***

55862 32386 58218 71592

121853 124416

17788 20534 30360 18893 23340 30955

3953 4100

4284 4506

4604 4869

1110 1125

1142 1158

1181 1172

498 498

508 508

'3 1 4

0.65

4 44

49371 53977 52378 66646

115932 117648

13537 19299 28806 17658 22072 29197

3713 3862

4035 4246

4522 4556

"102"8 1045

lo61 1077

1093 1081

460 460

466 466

466 449

107206 108275

15091 17782 23557 16196 20404 26789

3417 3547

3699 3888

4132 4140

931 937

953 969

980 964

401 411

411

391

3271

839

821

336 336

346 346

346 322

677 651

265 265

265 265

265 241

000

0.7

'4 T T

000

43473 51241 46421 60958

o.ls

■**T *•*

"37451 45234 40467 54572

95391 96300

13482 15938 23303 14506 18335 23730

3033 3141

3433

3628 3619

80l 807

817 833

0. 6

~4*T

31601 38929 34471 47390

81423 81721

11662 13633 19976 12566 15822 20021

2552 2653

2751" 3011 2871 2994

54T 655

“ 331

25745 3 2 IT3 28269 39183

64433 64538

9582

1129# 15653 10307 12810 15660

2058

2003

2123 2198

2283 2265

466

466

“ 473“ " 482

19505 24353

4"47'4I " "7093

10648

1327 1353

1385 1418

1457 1432

5ffI0 4986

• 00

0.65 ■ « T

***

0. 9 0.95 0.98

000

21455 29456

44753

7583

8233 9153

m4 4 T

11954 14554

22387

388# 4073

4311 4609

4 44

000 44T-

000

13037 17008

344T 5796

22364

3228 " 77o?

6819

7680

177335""

671

476

456

'

495

41T"' 417

CRC Handbook of Sample Size Guidelinesfor Clinical Trials

518

TABLE 4: ALPHA= 0.01 PQWER=0.9 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 7000 DEL=.01 FACT=

DEL=.02

0.O2

.50 .25

DEL=.15

DEL=.1 0

.50 .25

.0 0 BIN

1 .0 75

.50 .25

.0 0 BIN

1 .0 .7 5

.50 .25

.00 BIN

239 239

239 239

239 691

116 116

116 116

116 281

81 81

81 81

81 167

1429 3775

379 379

379 379

390 883

169 169

169 326

110 110

110 110

110 186

.50 .25

.00 BIN

1989' 2000

2000 2000

2006 7680

.0 0 BIN

729 729

729 729

740 2539

4415 4421

4432 4450

4485 12679

1422 1422

1422 1429

1 .0 .75

REQUIRED NUMBER OF PATIENTS

POONT

0.01

1 .0 .7 5

DEL=.05

1 .0 .75

' ' 169" 169

0 .0 5

13357 13480 13399 13626

13994 27050

3802 3820

3844 3879

3925 7329

827 827

827 827

827 1432

291 291

291 291

291 456

169 169

169 169

169 241

0.1

29481 29807 29586 30350

32572 48918

7991 8061

8177 8341

8615 12731

1562 1569

1580 1586

1604 2265

484 495

495 495

495 651

256 256

256 256

256 322

0 .1 5

44070 44647 44262 45697

51355"' 68183

11782 12167 13322 11929 12559 17482

2245 2262

22 86 2315

2350 2994

670 670

670 676

676 821

337 337

337 337

344 391

55871 56775 56169 58455

69130 84845

14897 15545 17704 15149 16227 21583

2829 2864

2916 2969

3032 3619

816 827

827 834

835 964

407 407

407 407

407 449

64545 65840

84769 98903

17284 18211 21582 17634 19237 25032

3312 3371

3441 3529

3627 4140

950 956

967

64971 68272

974 1081

460 460

460 466

466 495

0.3

70110 71895 70705 75202

98274 110358

18946 20189 24879 19430 21571 27831

3697 3774

3861 3984

4124 4556

1055 “ 1X572“ 1090 1061 1079 1172

501 501

501 512

512 530

0 .3 5

72794 75174 73592 79479

109154 119210

19955 21530 27521 20567 23262 29979

3966 4065

4187 4334

4520 4869

1125 1131

1149 1160

1237

530 536

536 536

547 553

75927 76014 73966 81421

117279

20381 22289 29492 21127 24347 31475

4141' 4264

4404 4579

4800 5077

1177

125458

1184

12ol 1219

1236 1276

547 554

554 554

565 565

70897 74824 72234 81397

122651 129102

20329 22534 30770 21204 24890 32322

4229 4362

4520

4975 5181

1195 1212

1230 1247

554

4719

1289

554

565 565

565

67159 72035 68850 79724

125224 130144

19885 22341 31336 20865 24914 32517

4229 4369

4544 4754

5027 5181

1195 1212

1230 T 2 5 5 1247 1276

547 554

554 554

565 553

62182 68051 64254 76749

124955 128582

19104 '2T76'4 31207 20171 24487 32061

4 l 52 4292

4474 4684

4975 5077

1166 1177

1195 1212

530 536

536 536

530

56425 63256 58910 72706

121857 124416

18071 20836 30356 19191 23619 30955

3995 4135

4310 4526

4806 4869

1107 1125

1142 ' r i7 7 " 1160 1172

501 501

5CJI

"512"'

512

495

50324 '57912 53152 67782

115931 117648

16822 19605 28810 17960 22352 29197

3756 3896

4065

4264

4520 4556

1037 1044

1061 “ 1 0 W 1079 1081

460 460

466 466

449

44199 52196 47244 62084

107199

15376 18071 26552 16490 20672 26789

3452 3575

3721 3907

4124 4140

932

956

108275

939

967

985 964

407 407

407 414

414 391

95695 96300

13742 16234 23612 14775 18572 23730

3056 3172

3295

799 810

816 834

337

3441

3627 3619

'7 4 5 -

41294 55626

821

337

344 344

""333"' 322

32316 39789 35250 48329

81421 81721

11894 14057 19972 12797 16017 20021

' 25B4

2770 2875

3015 2994

652 652

'659'

2671

670

676 651

256 267

267 267

267 241

26377 "32731 28950 39957

64429 64538

9770 11474 15556"" 10494 12944 15660

2017 2076

2140 2210

2286 2265

" "466" ' 477 477 466

484 456

19996 24896 21974 30000

44741

7221 7711

8341

44753

9227

10648

1335 1359

1394 1422

1457 1432

12226 14834 13311 17242

22387 22364

3931 4124

4351 4631

5010 4986

5531

6305

5874

6871

7705 7680

0.2 0 .2 5

0 .4 0 .4 5 0 .5

CT350.6 0 .6 5

0.7 0 .7 5

0.8 0 .8 5 0 .9 0 . 95 0. 98

"'37176 46170

10662

'

967

1177

1265

1236 1237

'

571' "

547

455

"

519

TABLE 4: ALPHA= 0.01 P0WER=0.9 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 7500 D E L :.01 FACT=

DEL=.02

DEL=.OS

1 .0 .75

.50 .25

.00 BIN

0.01

1993 2000

2ood 2000

2011 7680

736 736

736 2539

C.tfT"

4411 “4437 4418 4456

4475 12679

13362 13486 13411 13643

DEL=.10

D E L :.15

.50 .25

.0 0 BIN

1 .0 75

.50 .25

.0 0 BIN

1 .0 .75

.50 .25

.00 BIN

237 237

237 237

237 691

118 118

118 118

118 281

87 87

87 87

67 167

1418 ' r c r r T 4 3 0 1418 1430 3775

380 380

387 387

387 883

152

162

162

162

162 326

105"" 106

105 106

106 186

13993 27050

3811 3830

3849 3886

3924 7329

818 818

830 830

830 1432

293 293

293 293

293 456

174 174

174 174

174 241

29506 29843 29618 30406

32574 48918

8011 8086

8187 8356

8611 12731

1561 1568

1580 1587

1606 2265

493 493

493 493

493 651

256 256

256 256

2 56 322

44105 44724 44318 45830

51455 68183

11818 12211 T3325 11968 12593 17482

2243 2262

2293 2318

2349 2994

668 668

666 680

680 821

343 343

343 343

391

55936 56900 56255 58662

69125 84845

14956 15612 17705 15211 16299 21583

2836 2881

2916 2975

3031 3619

816 830

630 837

837 964

406 ' 406' 406 406

406 449

64636 66024 65105 68581

84868 98903

17368 18 312 "71385" 17731 19336 25032

3331 ' 3455' 3631“

950

3387

961

'9 3 1 968

' ”980' 1081

462 462

495

76243 72155 70880 75624

98274 110358

19055 20330 T4875 19550 21706 27831

3793

3987

4556

1062

1081

72961 75511 73824 80030

109118 119210

20093 21699 27518 20724 23431 29979

3987 4093

4205 4343

4512 4869

1136 1137

1149 "IT73" 1168 1237

73149 "76437 74262 82093

1172 7 5 125458

20555 22493 29487 21312 24549 31475

4175 4287

4418 4587

4805 5077

1186

71187 75361 72612 82186

122656 129102

20536 22768 7 0 774 ... '" 4261 21418 25111 32322 4393

4543 4730

4974 5181

""57574 72660 69324 80630

125225 130144

20105 22599 31336 21106 25168 32517

4261 4400

4568 4768

5030 5181

m y 1212

62630 68799 64831 77743

124955 128582

19355 22036 31205 20443 24743 32061

4186 4325

4493 4711

4974 5077

1168 1186

56975 64093 59574 73756

121850 124416

18331 21125 30361 19468 23881 30955

4025 4168

4336 4543

50956 50865 53900 68855

115936 117648

17086 19887 28805 18237 22606 29197

3793 3924

4081 4280

0 .7

44893 53105 48043 63143

107206 108275

15643 18343 26555 16756 20911 26789

0. 75

38911 47656 42080 56618

95693 96300

0 .8

32993 46599 35993 49212

PCONT

***

0 .1 5

0.2

*0 0

0. 25 0 .3

0. 35

**'* '

• **

0.4 0.45 0 .5

***

0 .5 5 0 .6

0.65

***

0 .8 5

0.9

***

0 .9 5 0. 98

.50 .25

.00 BIN

1 .0 .75

REQUIRED NUMBER OF PATIENTS

0. 05

0.1

1 .0 .75

• ••

736 736

3530

4140

3718 "7873" 4130

' "7335" T O T " 1093"

1175" 1205

462 462

500 '' 51r "

343

452

500

511

511 530

530 537

537 537

537 553

1731"

549 556

556 556

568 565

1261

1172

1212

1276

' " 1193 "T231 1212 1243

1289

556 556

568 568

568 565

1224 1243

1261 1276

549 549

556 556

568 553

1193 1212

1231 1237

530'' 537

537 537

549 530

4805 4869

T f r r ll4 9 1130 1156

1175' 1172

506 500

511' 511

"3T1 495

4524

1036 1055

1062 1081

1093 1081

455 ' 462

462 462

'474 449

3481 "77T3~ 4130 3605 3912 4140

931 943

96l 968

980 964

466 406

406 406

418 391

13993 16475 "73611 15024 18781 23730

3087 3193

3312 3455

3624 3619

8oo 811

8 l8 830

837 821

343 343

343 343

343 322

81425 81721

12lb6 14262 "19974 13018 16193 20021

' 7511 2686

2780 2881

3012 2994

650 650

661 668

680 651

256 268

268 268

268 241

26975 3353d 29593 40674

64430 64538

9943 11637 15650 10662 13074 15660

2630 2086

2143 2206

2293 2265

462 474

474 474

461 456

20461 2546d 22456 30493

44743 44753

7343 7824

1343 1362

1393 1418

1456 1432

12493 1 5 087 ' 22361 13568 17461 22364

4168

5618 5956

6368 6912

7700 7680

3980

8443 9305

10662 10648

4381 4655

4986

5011

4556

CRC Handbook of Sample Size Guidelines for Clinical Trials

520

TABLE 4: ALPHA= 0.01 PQWER=0.9 EXPECTED ACCRUAL THRU MINIMUM F0LL0W-UP= 8000 D E L :.01 FACT=

DEL*.02

.5 0 .25

.0 0 BIN

.0 0 BIN

125 ' 125

125 125

385 803

165 165

825 825

833 1432

1565 1573

1585 1593

11845 12245 13325 12005 12633 17402

2253 2273

2293 2325

69125 84845

15005 15673 17705 15273 16353 21503

2045 2805

65225 68885

04865 98903

17445 18405 21585 17825 19425 25032

70363 72405 71045 76033

98273 110358

73133 75033 74045 80553 *** **•

0 .0 2

0\0'5 0 .1 0 .1 5 0 .2

***

0 .2 5 0 .3 0"T35” 0 .4 0 .4 5 O'. 5 "

0.55 0 .6 0 .6 5 0 .7

.0 0 BIN

1 .0 75

1 .0 .7 5

.50 .2 5

.0 0 BIN

1*93 1993

2005 2005

2005 7680

733 733

733 733

733 2539

T4'H 4425

4433 4453

4485 12679

1425 1425

1425 1425

13373 13505 13425 13653

13993 27050

3813 3833

3853

29525 29893 29653 30473

32573 48918

8105

44153 44805 44373 45965

1 .0 .75

245 245

245 245

245 691

201

85 85

85 85

85 167

1433 3775

385 385

385 385

165 165

165 326

113 113

113 113

113 186

3885

3925 7329

825 825

293 293

293 293

293 456

173 173

173 173

173 241

0205 8365

0613 12731

1605 2265

493 493

493 493

493 651

265 265

265 265

265 322

51453 68183

2353

665 673

673 673

673

2994

021

333 333

345 345

345 391

55993 57025 56345 58873

2925 2973

3033 3619

025 025

033 033

045 964

405 405

405 405

413 449

' 64725 66205

3345 3393

3465 3533

3625 4140

953 953

965 973

973 1001

465 465

465 465

465 495

19165 20453 24873 19665 21825 27831

3733 3005

3893 3993

4125 4556

1053 1065

1073 1005

1093 1172

505 505

'505

513

505

530

109125 119210

20225 21865 27525 20865 23585 29979

4013 4105

4213 4353

4513 4869

1133 1145

1153

1173 1237

533

1165

533

533 545

553

73373 76865 74553 82733

117273 125458

20725 22685 29493 21493 24733 31475

4205 4313

4445 4605

4805 5077

1105 1193

1205 1213

1233 1276

553 553

553 553

565 565

71473 75085 72993 82945

122653 129102

20725 22993 30765 21633 25313 32322

4293 4413

4565 4745

4973 5181

1205 " 1 2 3 3 ' 'T2S5 1213 1245 1209

553 553

565 565

565 565

67885 73305 69785 81493

125225 130144

20325 22845 31333 21333 25393 32517

4293 4433

4593 4785

5033 5181

1205 1213

1225 1245

1265 1276

553 553

' 553

565 553

63045 69525 65393 78685

124953 128582

19593 22293 31205 20685 24985 32061

4213 4353

4525 4725

4973 5077

1173 1105

1205 1213

1233 1237

57513 64093 60233 74753

1218 53 124416

18585 21385 30353 19733 24125 30955

4065 4193

4365 4553

4005 4869

lll3 1133

1145 1165

51573 59653 54625 69873

115933 117648

17345 20153 28805 18493 22833 29197

3825 "TO5 3953 4293

4525 4556

1045 1053

S377'3

107205 100275

15885 18593 26553 17005 21125 26789

3505 3625

3765 3925

4125 4140

REQUIRED NUMBER OF PATIENTS

***

48793 64133

b.vs

.00 BIN

D E L :.15

.5 0 .2 5

O.Ol

.50 .25

D EL:.1 0

.50 .25

PCONT =*•*

1 .0 .75

DEL*.OS

1 .0 .7 5

125

■"

565

545

"" 533"

533

533

545

545 530

1173 1172

505 505

505

513

513

495

1065 1073

1093 1001

453 465

465 465

473 449

933 945

953 973

985 964

- - 405 405

"405 " 413

4 l3 391

39593 47905

95693 96300

14213 16705 23605 15253 18973 23730

3113 3213

3325 3465

3625 3619

005 013

025 033

845 821

333

42833 57553

345

345 ""33 F " 345 322

0 .8

3364 5 41373 36693 50045

81425 01721

12313 14465 19973 13213 16353 20021

2625 2705

2793 2893

3013 2994

653 653

665 665

673 651

265 265

265 265

0” 55"~

27545 34185 30193 41345

64433 64538

"IU1TT5' 11705 15653 10825 13193 15660

2b45 2093

2153 2213

2285 2265

465 473

473 473

485 456

20905 25873 22925 30953

44745 44753

7453 7925

0533 9373

10665 10648

1345 1373

1393 1425

1453 1432

12733 15325 13813 17665

22385 22364

4025 4205

4413 4673

5013 4906

*705

7705 7680

0 .9 0 .9 5 0 .9 8

ttt

6025

6425 6953

265 241

521

TABLE 4: ALPHA= 0.01 POWER= 0.9 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 8500 D E L = .01 FACT=

DEL=.02

0. 01 0. 02

***

.50 .25

DEL=.05

D E L = .10

.0 0 BIN

1 .0 75

.50 .25

.0 0 BIN

240 240

24d 240

240 691

120 120

120 120

120 281

1430 3775

386 388

388 388

388 883

163 163

163 163

" 153 326

290 290

.50 .25

.0 0 BIN

1990 2003

2003 2003

2003 7680

736 736

736 736

736 2539

4413 4426

4434 4455

4476 12679

1416 1416

1430 1430

PCONT =♦**

1 .0 .75

.50 .25

1 .0 .75

.00 BIN

1 .0 .75

D E L = .15 1 .0 .7 5

.50 .25

.00 BIN

91 91

91 91

91 167

REQUIRED NUMBER OF PATIENTS '

n 2~~' " n s 112 112

112 186

290 456

176 ' T76 176 176

176 ' 241

495 651

261

261

261

261

261

322

673 " 821

333 333

346 346

346 391

O.05

13380 13521 13436 13670

13996 27050

3 8l8 3831

3860 3881

T9 27 7329

821 821

821 835

835 1432

290 290

0 .1

29551 29934 29679 30529

32569 48918

8038 8123

6230 8378

8612

1565 1578

1566 1586

1600 2265

493

473

495

495

44193 448B6 44426 46084

31432 68183

11885 12288 13316 12041 12658 17482

2258 2280

2301 2322

2351 2994

665 673

"673 673

56063 57155 56433 59081

69132 84845

15059 15739 17707 15327 16411 21583

2853 2896

2938 2981

303'1 ' 3619

821 821

635 835

843 964

'4T0“ 410

4 l0 410

41o 449

64818 66391 65350 69183

84865 98903

17516 18501 21583 17906 19513 25032

3350 3406

3470 3541

3626 4140

949 962

962 970

983 1081

430 460

460 460

460 495

70492 72646 71223 76429

98274

19258 20576 24876 19776 21936 27831

3746 3818

3903 4001

4128 4556

1055 1068

1076

110358

1076

1090 1172

503 503

503 503

5 l6 530

73305 76166 74275 81061

109125 119210

20350 22008 27525 21009 23721 29979

4030 4128

4235 4362

4519 4869

1132 1140

1153 1161

1175 1237

537

537

537

537

545 553

73595 77279 74856 83356

117271 125458

20861 22871 29488 21668 24898 31475

4221 4328

4455

4795 5077

"1133

1204 1217

1238 1276

" 545

558

4617

558

558

558 565

71767 76386

122661 129102

20916 23198 30763 21830 25514 32322

4320 4447

4583

4965 '

1246

1260 1289

558

5181

1204 1217

1236

4753

566 566

566 565

125219 130144

20533 23o70 31336 21561 25599 32517

4328 4455

4604 4795

5029 5181

1204 1217

1225 1246

1260 1276

" 545 ' 538

566 553

124956 128582

19819 22539 31201 20924 25208 32061

4243 4383

4540 4731

4976 5077

' 1T75

121853 124416

18820 21638 30359 19981 24345 30955

4094 4221

4383

60866 75698

4575

4806 4869

52183 60470 55320 70832

115933 117648

17580 20393 28808 18748 23062 29197

3652

4128 4306

4519 4556

' 1047"

1068

3980

1055

1076

46211 54610 49526 65081

107199 108275

16121

18620 26555 17248 21328 26789

3533 3648

3775 3937

4126 4140

941 949

40253 46698 43555 58443

95695

14435 16921 23601 15476 19152 23730

3 l36 3236

3342

96300

3470

3626 3619

34269 42102 37371 50823

81423 81721

12509 14634 19968 13401 16496 20021

2649 2726

2798 2896

28098 34792 30776 41975

64436 64538

10256 11914 T3S34 10971 13295 15660

2054 2110

0 .1 5

'***

0 .2 0 .2 5 0 .3

***■ Mf

***

0 .3 5 0 .4 0 .4 5 0.5" " 0. 55

-**T *** *•* ***

0'."5T“ 0 .7

077S0 .8 MT

0.9

70245 82315

'63530 70224 65945 79574

21320 26321

44737 " 7558" 8620 TB670 ■

1353

23360 31379

44753

1374

8017

9428

■ n s s s " I3340— "4063“ ' 4447 4235 4689 14039 17843 22364

0.95 0.98

£3248" 73913

58040 65668

0 .6

0. 85

73361 83667

• **

12731

5773 6091

6487 6997

7706 7680

10648

5008' "■ 4986

1196

558 558

558

537 ' 537

1204 " m s 1217 1237

537

545

545 530

1TT9 " ri3 3 “ 1175 1132 1161 1172

503 503

5 03 516

516 495

1098 1081

460 460

460

473'

473

449

962 970

963 964

410 410

4 l0 410

418

613

82l

813

835

843 821

346 346

346 346

3010 2994

65l 651

665 673

673 651

261 261

261

2 l6 0 2216

2288

473 473

473

481 456

1395 1430

1459 1432

2265

1183

481

261

391

346 " 322 269 241

CRC Handbook of Sample Size Guidelines for Clinical Trials

522

TABLE 4: ALPHA= 0.01 POWER= 0.9 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 9000 DEL=.0 1 FACT=

DEL=.02

DEL=.05

1 .0 .7 5

.50 .25

.0 0 BIN

*

1995 1995

1995 2009

2009 7680

735 735

735 735

735 2539

*

4416 4425

4439 4461

4484 12679

1424 1424

1424 1424

*

13394 13529 13447 13686

13987 27050

3817 3840

0 .1

* •

29571 29976 29715 30584

32572 48918

8061 8137

0 .1 5

4 •

44227 44970 44475 46199

0 .2

* *

0 .2 5

*

1 .0 .75

.50 .25

DEL=.15

.0 0 BIN

1 .0 75

.50 .2 5

.0 0 BIN

1 .0 .7 5

.50 .25

240 240

240 240

240 691

119 119

119 119

119 281

82 82

82 82

T432 3775

389 389

389 389

”389 ' 883

164 164

164 164

164” 326

3862 3885

5721 7329

825 825

B25 825

825 1432

299 299

299 299

299 456

8241 8385

8610 12731

1567 1581

1581 1590

1604 2265

487 487

487 487

51450 68183

11909 12314 13326 12075 12682 17482

2256 2279

23bl 2324

2346 2994

667 667

"337" 681

56130 57277 56512 59280

69126 84845

15112 15801 17700 15382 16454 21583

2864 2895

2940 2985

3030 3619

825 825

825 839

839 964

64919 66570 65467 69472

84862 98903

"T 75F T 18591 21584 17984 19581 25032

3367 3412

3480 3547

3629 4140

951 960

960 974

982 1081

TT"

7GS2TT 72892

*

71385 76821

98272 110358

19365 20692 24877 19896 22042 27831

3764 3831

4011

4556

1064 1064

1172

501

510

530



73477 7 3 4 8 4 74504 81546

1W 17 119210

20481 22155 27524 21156 23856 29979

4056 4146

4245 4371

4515 4869

1131 H 3 4 ~ 1176 1140 1162 1237

532 532

532 546

546 553

0 .4

* •

73615 77685 75142 83954

117276 125458

2 ib 3 b 23032 29490 21831 25057 31475

4245 4349

447b 4619

4799 5077

m 3 1199

1207 1221

1230 1276

555 555

555 555

569 565

0745

4



72051 76897 73739 84367

122654 129102

21089 23392 50772 22020 25687 32322

" 4549 4461

4'605 " 4 9 6 5 ' 4762 5181

1207 1221

1230 1244

126* 1289

*

68609 74512 70701 83099

125219 130144

20729 23294 31335 21772 25791 32517

4357 4484

4627 4807

5032 5181

1207 1221

1230 1244

1266 1276

“ 555 555

5'55 555

569 553

*

63974 7 b 9 l2 66494 80444

1249S7 128582

2O031 22762 31200 21156 25409 32061

4281 4402

4560 4740

4979 5077

1176 1185

1207 1221

1230 1237

532 532

532 546

546 530

0 .6

* •

5856b 66412 61485 76596

121852 124416

19050 21876 30359 20211 24554 30955

4124 4245

4402 "4TO7 4582 4869

1117 1140

1154 1162

1176 1172

- “ 5TJ1" 510 510 501

510 495

0 .6 5

* *

52769 61260 55995 71745

115935 117648

17(112 20625 28806 18974 23257 29197

3876 3997

4146 4312

4529 4556

1041 1050

lb 7 2 1086

1095 1081

456 465

465 465

465 449

077"

4

46837 55604 50226 65976

107205 108275

16341 19041 26556 17466 21516 26789

3561 3674

3795 3952

4132 4140

937 951

960 974

982 964

4 ll 411

4 ll 411

4 ll 391

0 .7 5

T V

40889 4947b 44250 59271

95699 96300

1464b 17115 23609 15689 19320 23730

3156 3246

3359 3480

^629 3619

816 816

825 839

839 821

344 344

344 344

344 322

262 262

262 262

262 241

0 .0 1 0 .0 2



0.O5

*

0 .3 b. 35

b. 5 0 .5 5

*

• •

1 .0 .75

DEL=.10

.50 .25

PCONT=

.0 0 BIN

REQUIRED NUMBER OF PATIENTS

5907 "4124

"

'

105 186

172 172

172 172

172 241

487 651

262 262

262 262

" 26T 322

681 ' 821

344 344

344 344

3'4T 391

411 411

411 449

465 465

465 495

1072""1095 1086

4



34867 42801 38009 51554

81420 81721

12682 14811 19972 13582 16634 20021

2661 2729

2819 "5 E 0 7 " 2909 2994

659 659

667 667

681 651

0 .8 5

* •

28612 35376 31326 42562

64432 64538

io 4 o i 12044 15652 11107 13394 15660

2062 2121

2166 2220

2287 2265

465 479

479 479

479 456

0 .9

4

21719 26745 23766 31785

44736 44753

7656 8106

1356 1379

1401 1432

1455 1432

0795

4

13177 15732 14257 18015

22380 22364

4151" "447B 4267 4709

0 .9 6

TJ~ *

5834 6149

7l7bl 7680



6531 7026

8691 9487

10671 10648 5010 4986

"

" ~TU3' 105

'8 2 “ 167

Id s 105

0 .8



.0 0 BIN

“ 411 411 456 465 ■■ '

"

“ 501- " 510 “ 3TC

■ “ 535 " 569 555 569

'

'



569" ' 565

523

TABLE 4: ALPHA= 0.01 POWER= 0.9 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 9500 DEL*.01 FACT=

DEL*.02 1 .0 .75

DEL*.OS

1 .0 .75

.50 .25

.00 BIN

2001 2001

2001 2001

2010 7680

728 728

728 728

728 2539

4424 4433

4448 4457

4480 12679

1417 1417

1431 1431

I3401 13544 13458 13695

13995 27050

3830 3839

29599 30012 29741 30629

32 568 48918

8067 8153

""4*773 45045 44538 46319

51449 68183

56199 57395 56603 59462

69128 84845

65010 667 53 65589 69745

DEL*.15

.00 BIN

1 .0 75

.50 .25

.0 0 BIN

1 .0 .7 5

.50 .25

.00 BIN

244 244

244 244

244 691

125" ~T75 125 125

175 281

87 87

87 87

87 167

1431 3775

386 386

386 386

386 883

117

173

173

326

110

110 110

110 186

3863 3887

3925 7329

823 823

823 823

823 1432

291 291

291 291

291 456

173

173 173

173 241

8248 8399

8613 12731

I 3 7 T 1583 1574 1598

1607 2265

490 490

490 490

490 651

253 268

268 268

268 322

11938 12342 13315 12104 12713 17482

2263 2286

2295 2319

2343 2994

6 7 1 " '671

670

379

339 ■' "339

671

671

821

339

339

15159 15844 17700 15444 16498 21583

2865 2904

2937 2984

3032 3619

823

838

"738

410

410

410

823

838

964

410

410

449

84865 98903

17662 18674 "2T58U ' 18065 19657 25032

3379 3426

3483 3554

3625 4140

70743 73142 71565 77194

98269 110358

19458 20797 24873 19989 22141 27831

3783 3839

3925 4020

4 l2 4 4556

1060 1060

1075 1084

1064 1172

73655 76799 74724 82024

lo 9 l2 3 119210

20607 22293 27516 21286 23979 29979

4o68 4163

4258 4376

4519 4869

1132 1146

1155 1170

74044 78096 75436 84533

117269 125458

21177 23195 29489 21984 25205 31475

4267 4376

4495 4623

4804

1194

5077

1194

1203 1218

1227 1276

72334 77393 74106 85040

122651 129102

21263 23575 30772 22198 25855 32322

4362 4480

4614 4780

4970 5181

1218 1227

1241 1250

1265 1289

562 562

66962 75089 71147 83853

125225 130144

20930 23495 31342 21975 25974 32517

4376 4504

4647 4813

5027 5181

1203 1218

1227 1250

1265 1276

0. 55

64402 71574 67029 81255

124955 128582

20241 22982 31199 21367 25594 32061

4305 4433

4575 4756

4970 5077

1179 T 2 7 7 " l2 4 l 1194 1218 1237

0 .6

59073 67133 62089 77464

121853

19268 22094 30359 20431 24754 30955

4148 4267

4424 4590

4804 4869

1123 1132

1155 1170

«**

53349 62027 56659 72619

T15930

18033 20844 '78707"'" 19196 23448 29197

3901 4020

4163 4329

4519 4556

1051 1060

1075 1084

1099

117648

• **

47444 56365 50903 66815

107199 108275

16560 19253 26559 17676 21690 26789

3578 3688

3815 3958

4124 4140

942 956

41498 50199 44918 60055

95695 96300

14835 17296 23614 15880 19467 23730

3174 3260

3364 3483

3625 3619

814 823

35441 43454 38633 52242

81421 81721

17855 14969 19965 13758 16759 20021

2675 2747

2818 2913

3006 2994

657 657

29109 35940 31855 43122

64425 64538

10537 12166 15658

481 481

481 456

22094 27153 24160 32164

44737 44753

13378 15943 14455 18175

22388 22364

5896 6205

7*701 7680

PCONT

***

0 .0 5 0.1

o. 15 0 .2 0. 25

***

0 .3 0. 35 0 .4 0 .4 5

***

0 .5

0 .6 5 0 .7 0 .7 5 0. 8 0 .8 5 0 .9 0 .9 5 0 .9 8

1 .0 .75

REQUIRED NUMBER OF PATIENTS

O.Ol 0 .0 2

.00 BIN

DEL*.10

.50 .25

.50 .25

4T* **•

6570 7060

124416

'7077" 2168

173

" 956 ' "965 " 980 956 965 1081

2286 " — 477

11240 13482 15660

2120

2224

2265

7734 8185

8770 9530

10670 10648

1360 1384

1408 1431

l '4 S r " 1432

4139 4305

4495 4718

5003 4986

' 173 " ' 173 '

467

173

" '458

391

467 ' 467

458

467

505

505“

495

514

505

505

530

1179

536

1237

538

538 538

538 553

553

553

553

562

562 565

562 562

562 565

553

553

553

562

562 553

529 538

538 538

538 530

1179

505

1172

505

505 514

514 495

1081

458 467

467 467

467 449

965 965

980 964

410 410

410 410

410 391

838

823

838 821

339 339

339 348

348 322

657

'671

671

651

268 268

268 268

268 241

CRC Handbook of Sample Size Guidelinesfor Clinical Trials

524

TABLE 4: ALPHA= 0.01 PQWER=0.9 EXPECTED ACCRUAL THRU MINIMUM F0LL0W-UP= 10000 DEL=.0 1 FACT=

DEL=.02

DEL=.05 DEL=.10

1 .0 .75

.5 0 .2 5

.0 0 BIN

1991 1991

2007 2007

2007 7680

732 732

732 732

732 2539

4416 4432

4441 4457

4482 12679

1416 1416

1432 1432

13466 13707

13991 27050

3632 3841

3866 3891

29616 30057 29766 30682

32566 48918

6082 8157

8266 "8515 8407 12731

0 .1 5

44316 45116 44591 46432

51457 68183

11966 12362 13316 12141 12732 17482

0.2

56257 57516 56682 59641

69132 84845

65107 65932 65716 70016

0 .3 0 .3 5

0. 02

0 .1

0. 25

0.4 0 .45

***

0 .5

.0 0 BIN

1 .0 .75

.5 0 .2 5

DEL=.15

.0 0 BIN

1 .0 75

.0 0 BIN

1 .0 .7 5

241 241

241 241

241

115

691

116

115

115

116

281

82 82

1432 3775

382 382

362 382

382 883

166 166

166 166

155 326

"

3916 7329

816 832

832 832

832 1432

291

291

291

"'

291

291

456

1555

1582

491

491 491

491

1591

1607 2265

491

1582

651

2266 2282

2307 2332

2357 2994

666 666

666 682

15207 15907 17707 15491 16541 21583

2882 2907

2941 2982

3619

3032

832 832

84665 98903

17732 18741 21582 18141 19716 25032

3382 "3471 3432 3557

3632 4140

70882 73382 71732 77557

98282 110358

19541 2o9o7 24682 20091 22232 27831

3791 3857

3932 4016

73816 77116 74957 82482

109115" 20716 22416 27516

4091

119210

21407 24091 29979

4166

74266 78491 75732 85091

117282 125458

21316 23357 29491 22141 25341 31475

72616 "77855 74466 85682

122557 129102

69316 75657 71591 84582

130144

.50

.25

.0 0 BIN

REQUIRED NUMBER OF PATIENTS

13407 13557

0 .0 5

.50 .25

.5 0 .25

PCONT = • • • 0 .0 1

1 .0 .75

“ 82 82

82 167

107 ~~T07

107 "

107

107

186

153

155

166

166

156 241

257 257

257 257

257 322

582 821

341 341

341 341

341 391

832 832

841 964

407 407

' 407 407

407 449

957 957

955 966

982 1081

457 466

466 466

466 495

4132 4556

1057 1066

1082 1082

1091 1172

507 507

507 507

507 530

4266 4382

4517 ” 4869

1141 1141

1157 1166

1162 1237

532 532

541

4291 4382

4507 4641

4807 5077

1191 1207

1207 1216

1232 1276

557

"557

557

557

"553" 565

89

"72 80 62 69

' '

81 65

58

81

535

TABLE 5: ALPHA= 0.025 POWER= 0.8 EXPECTED ACCRUAL THRU MINIMUM F0LL0W-UP= 50

DEL=.1 0 FACT=

1 .0 .75

.50 .25

D EI=.1S .00 BIN

POONT=***

1 .0 .75

.50 .25

DEL=.2 0 .00 BIN

1 .0 .75

DEL=.25

B E U .3 0

.50 .25

.0 0 BIN

1 .0 75

.50 .25

.0 0 BIN

1 .0 .7 5

.50 .25

.00 BIN

REQUIRED NUMBER OF PATIENTS

0 .0 5

«* #*•

166 166

167 ' "178 170 275

97 98

99 100

104 145

69 69

70 71

73 93

54 54

55 55

57 65

44 45

45 " 46

47 48

0. 1

••• ***

262 263

265 271

299 393

140 141

143 147

159 194

93 94

95 98

104 118

69 70

71 73

76 80

55 55

56 58

50 58

0 .1 5

••• ***

338 340

33 3 354

409 495

172 174

177 185

207 236

110 112

115 120

130 140

80 81

83 86

92 93

~S2 63

65 67

71 66

0 .2

••• • **

395 398

403 418

507 581

195 198

203 214

248 271

122 125

129 136

152 157

87 89

92 97

105 103

67 68

70 74

79 72

0 .2 5

*** ***

432 436

443 464

591 652

210 214

221 235

282 299

130 133

139 ~ m r 171 148

92 94

98 104

116 110

70 72

74 78

'"'85 76

0 .3

••• ***

451 456

466 494

659 707

217 222

231 250

309 320

134 138

144 156

183 181

94 97

101 109

123 115

71 73

81

••• • **

454 461

474 509

710 746

218 225

235 257

328 334

134 139

147 160

192 187

94 98

103 111

127 118

11 73

82

92 80

0 .4

•••

444 453

470 511

745 770

214 222

235 260

340 341

132 138

147 161

196 189

92 96

102 111

129 118

69 72

76 82

92 79

0 .4 5

••• ***

423 434

455 ” 75 2 504 778

206 215

230 257

344 341

128 134

144 159

197 187

89 94

100 109

128 115

67 70

74 80

90 76

••• ***

395 408

433 487

762 770

195 205

221 250

341 334

122 128

138 155

193 181

“ HR 90

96 105

124 110

63 67

71 77

86 72

**•

361 377

405 464

736 746

182 192

209 239

329 320

121

131 147

184 171

80 84

90 100

117 103

59 62

65 72

81 66

0 .6

•••

325 343

373 435

7 l2 707

"167 178

195 225

311 299

105 112

122 137

1 71'...." 157

73 77

83 92

108 93

54 57

60 65

73 58

0 .6 5

••• ***

288 307

339 400

551 652

150 161

178 206

284 271

95 101

110 125

66 70

75 82

96 80

48 50

53

140

64 48

•••

251 271

302 361

593 581

133 143

158 184

250 236

83 89

”97 109

133 118

57 60

65 71

8l 65

21'5 ' 233

262 315

509 495

114 123

136 158

209 194

70 75

81 91

108 93

177 194

218

408 393

92

263

110 126

161 145

137 150

201

0 .3 5

0 .5 0 . j>5

0 .7 0 .7 5 0 .8 0 .8 5

*** •••

•**

r c 9 “ " 291 275

"

100

....

1M

155



75" 77

58

89 79

'

CRC Handbook of Sample Size Guidelines for Clinical Trials

536

TABLE 5: ALPHA= 0.025 P0WER= 0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 60

DEL=.1 0 FACT=

DEL=.15

1 .0 .7 5

.50 .25

.0 0 BIN

166 167

168 171

178 275

97 98

99 101

104 145

**• • **

263 264

267 273

299 393

140 142

T44 148

•••

340 342

346 358

409 495

173 175

1 .0 .7 5

PCONT=*** 0 .0 5 0 .1

o .is

DEL=.20

•••

.50 .25

.00 BIN

DEL=.2S

DEL*.30

.50 .25

.0 0 BIN

1 .0 75

.5 0 .2 5

69 70

70 71

73 93

54 54

55

57 '

44

45

47

56

65

45

46

48

159 194

93 94

96 99

104 118

69 70

71

“ 76

S'S

73

80

56

57 58

20” 58

"179187

206 236

111 113

116 121

130 140

80 82

84 87

92 93

63" 64

65

-71

67

66

“TO 5 103

68" 69

71 74

79 72

1 .0 .7 5

.0 0 BIN

1 .0 .7 5

.50 .25

.0 0 BIN

REQUIRED NUMBER OF PATIENTS

0 .2

••• ***

306 400

406 423

$07 581

197 200

206 217

248 271

124 127

131" 138

152 157

88 90

93 98

0 .2 5

•••

**•

434 439

448 471

591 652

212 217

224 239

282 299

132 136

141 150

170 171

93 96

TOO 105

116

71 73

75 79

'85

110

••• • **

454 460

472 503

659 707

220 226

236 255

309 320

136 141

148 159

183" 181

96 99

103 110

123 115

72 75

78 82

89 79

• ••

458 466

482 520

7 l0 746

222 229

241 263

328 334

n r

151

143

164

192 187

'■ 96

1W "T 27

72

" 79

118

75

84

••• *•*

449 460

136

150 165

■ 71—

0 .4 5

••• **•

0 .5

0 .3 0 .3 5 0 .4

"479 “ 775 '

113

196

95

T05 “ 129

99

113

118

74

78 83

92

189

92

102

128 115

69

76

"90" 76

770

219 227

24l 267

340 341

430 443

466 519

762 778

211 221

237 265

344 341

1T2 ' 148 138

163

197 187

96

112

••• ***

403 418

446 504

762 770

201 212

226 258

341 334

126 133

143 159

193 181

88 92

99 “ T 27- ' 108 110

••• ***

371 389

4 i9 481

"77?

188 200

217

"lTff 125

13$ 151

184 171

"82

T17

247

329 320

93

746

87

102

•**

336 356

388 452

?12 707

174 185

202 232

311

109 116

126

299

141

171 157

76 80

•••

300 321

354 418

66l 652

157 169

185 214

284 271

90 105

114 128

155 140

0 .7

•••

263 284

317 377

593 581

13? 150

16$ 191

250 236

87 93

ru r 112

133 118

0 .7 5

•••

226 246

276 330

509 495

120 129

142 163

209 194

73 78

84 93

10B 93

0 .8

**•

187 205

230 275

408 393

97 104

11$ 130

161 145

145 158

177 209

291 275

0 .5 5 0 .6 0 .6 5

0 .8 5

• **

**•

""

92 80

100

525

142

76

79

72

81

65 68

72 78

86 72

103

61 64

68 73

"ffl 66

86 94

108 93

56

62 66

73

58

72

77 84

06 80

79“ 52

55 58

64 48

59 62

66 72

81 65

58

-

-

537

TABLE 5: ALPHA= 0.025 POWER= 0.8 EXPECTED ACCRUAL THRU MINIMUM F0LL0W-UP=7Q

D E L :.10 FACT=

D E L :.15

1 .0 .75

.50 .25

.00 BIN

••• ***

166 167

16* 171

178 275

98 98

99 101

104 145

0 .1

•••

263 265

248 275

299 393

IT1 143

145 149

159 194

0 .1 5

•••

34l 343

348 361

409 495

rrc 177

181 189

206 236

d .z

**•

•••

398 "T O T 402 428

507 581

198 202

208 220

0 .2 5

••• ***

436 442

*32" 478

591 652

214 219

0 .3

***

457 464

478 511

659 707

0 .3 5

••• *•*

442 472

489 530

0.4 0 .4 5

*** ***

0 .6 0 .6 5 0 .7 0 .7 5 0 .8 0 .8 5

.50 .25

.00 BIN

1 .0 .75

D EL:.30 .00 BIN

.00 BIN

1 .0 75

.50 .2 5

.0 0 BIN

1 .0 .75

.50 .25

69 70

71 72

73 93

54 54

'5 5 ” 56

57 65

45 45

45 46

" 47 48

94 95

97 99

104 118

70 71

72 74

76 80

'5S 56

37 58

60 58

112 114

117 122

130 140

81 83

85 88

92 93

63 64

66 68

71 66

246 271

123

132 139

152 157

89 91

94 99

105

128

103

68 70

72 75

79 72

227 243

282 299

134 138

143 152

170 171

75 97

101 106

116 110

72 74

74 80

" 85 76

223 229

240 259

309 320

139 143

150 161

183 181

97 101

105 ' 123 115 112

74 76

79 83

89 79

710 746

226 233

246 268

328 334

140 146

153 166

192 187

98 102

107 115

127 118

74 76

80 84

92 80

223 232

247 272

340 341

139 145

' 1ST168

196 189

97 101

107 ' 129 118 115

73 75

79 84

92 79

717

'"HTC5" " IT T 142 166

94 99

ld5 113

128 115

70 73

77 '

187

82

90 76

REQUIRED NUMBER OF PATIENTS

'

T ** ***

"*34 466

488 536

745 770

••• ***

436 451

477 532

7 6 2 ' .... 778

227

243 271

344 341

411 428

457 518

742 770

207 218

235 264

3 41 334

130 137

146 162

193 181

90 95

101 109

124 110

67 70

74"" 79

86 72

••• • **

380 400

432 496

745 ' 744

m 206

224 254

32* 320

122 129

13* 154

184 171

85 89

95 " 103

117 103

63 65

49 74

81 66

»»•

346 368

402 468

712 707

180 192

209 239

311 299

113 120

13d 144

171 157

78 82

88 95

108 93

57"" 60

63 47

" 73 ' 58

311 333

368 432

641 652

163 175

1*2 219

284 271

102' 109

118 131

155' 140

7d 74

79 85

96 80

51"'" 53

56 59

64 48

**•

274 296

33d 391

593 581

145 156

171 196

250 236

90 96

103 114

133 118

6l 64

68 73

81 65

***

237 257

THT7" 342

509 495

125 134

147 167

209 194

76 80

86 95

108 93

**•

1*7 214

240 285

406 393

101 108

118 133

161 145

*** • **

152 165

184 216

2*1 275

d.5 0 .5 5

1 .0 .75

D E L :.25

.50 .25

PCONT=*** 0 .0 5

D EL:.2 0

•••

'

197 "

CRC Handbook of Sample Size Guidelines for Clinical Trials

538

TABLE 5: ALPHA= 0.025 POWER= 0.8 EXPECTED ACCRUAL THRU MINIMUM F0LL0W-UP= 80

DEL=.10 FACT=

DEL=.15

1 .0 .7 5

.50 .2 5

.0 0 BIN

PCONT=***

1 .0 .75

.50 .25

DEL=.20 .0 0 BIN

1 .0 .75

DEL=.25

.50 .25

.0 0 BIN

1 .0 75

DEL=.30

. 50 .2 5

.0 0 BIN

1 .0 .7 5

.50 .25

.00 BIN

"55 56

57 65

45 45

44 46

47" 48

56 57

57 59

60 58

~bT 65

66 68

7l 66

REQUIRED NUMBER OF PATIENTS

0 .0 5

•••

167 168

169 172

T7F 275

98 99

100 101

104 145

70 70

71 72

73 93

" 54 55

0 .1

••• ***

264 266

269 276

299 393

142 143

146 150

159 194

94 96

97 100

104 118

70 71

T 2 "" ""76" 74 80

o .i5

••• •**

342 345

350 364

409 495

175 178

182 190

207 236

113 115

118 122

130 140

82 83

85 88

“ 72" 93

0 .2

••• ***

4oo 404

413 432

507 581

200 204

210 222

248 271

127 129

134 140

152 157

90 92

'9 5 99

105 103

69 71

0 .2 5

*** ***

439 445

457 484

591 652

217 222

230 246

282 299

1T6 139

145 154

170 171

96 99

102 107

116 110

73 75

0 .3

••• ***

460 468

484 518

659 707

226 233

243 262

309 320

141 146

ITS163

103 181

99 102

TO 7 113

T2 '3 ' ” 115

75' ' 77

0 .3 5

••• ••*

466 477

4*6 539

710 746

229 237

250 273

328 334

143 148

156 168

192 187

100 104

109 ' 127 116 118

' 75 78

0 .4

•••

460 473

496 547

'77TT 770

727 237

251 277

340 341

142 148

157 170

196 189

99 103

'TO 9 " 1 2 9 116 118

74 77

“ 80 ” T f 79 85

443 459

486 543

762 778

221 232

248 276

344 341

138 145

154 169

197 187

96 101

106 115

72 75

~ 78 83

92 97

103 ' ' 124 111 110

68 71

75 80

87 91

97' 105

117 103

64 67

70 75

0 .4 5

*•*

'

T2'8...... 115

73 ' 75 - ?7 - -■ 80

79 72 85’ ‘ 76

80 84

89 79

81' 85

'' T T 80

' 90 ' 76

0 .5

•••

418 437

738 530

762 770

212 223

241 270

341 334

133 140

150 164

193 181

0 .5 5

••• ••*

389 410

444 509

7'46 746

200 212

“230 259

329 320

125 133

142 157

183 171

O .i

••• **•

356 378

414 481

712 707

185 197

215 244

311 299

IK 123

133 146

171 157

80 84

89 ' “ 108 97 93

58 61

54 " ’ 73 68 58

0 .6 5

*** ***

321 344

380 445

661 652

169 180

197 224

264 271

105 112

12o 133

155" 140

72 76

80 86

96 80

52 54

56 60

62 65

69 74

81 65

0 .7 0 .7 5

*•#

264 307

341 402

593 581

150 161

176 200

250 236

93 98

*•*

246 267

298 ” '509 352 495

129 138

151 171

209 194

78 82

104 112

121 136

141 145

0 .8

***

205 222

249 293

408 393

0 .8 5

*** • **

118' 172

191 222

291 275

... 1 W -

116

153 118

88 96

108 93

'"

"

86 72 ■ S I66

64 48

' " "

539

TABLE 5: ALPHA= 0.025 POWER= 0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 90

DEL=.10 FACT=

DEL=.15 1 .0 .75

.50 .25

DEL=.20 DEL=.25 DEL=.30 .00 BIN

1 .0 .75

.50 .25

.00 BIN

170 172

17'8"~ " ' 76" 99 275

100 102

104 145

PCONT=***

.0 0 BIN

1 .0 .75

.50 .25

.00 BIN

55 56

57 65

45 45

46 46

47 48

.50 .25

.00 BIN

1 .0 75

.5 0 .25

70 70

71 72

73 93

54 55

1 .0 .75

REQUIRED NUMBER OF PATIENTS

0 .0 5

*** ***

137 ' 168

0 .1

*** ***

225 " 270 267 278

Z7?~ 393

142 144

147 151

159 194

95" 96

98 100

104 118

71 72

73 74

76 80

56 57

58 59

60 58

0 .1 5

*** **•

'343 " 352 346 366

"409“ 495

176 179

134" 191

207 236

114 116

119 123

130 140

83 84

86 89

92 93

64 65

37 68

71 66

0 .2

*** ' "401 ' *** 406

413' 436

507 581

202 206

217" 224

248 271

128 131

135 141

152 157

91 93

96 100

105 103

70 71

73 76

79 72

0 .2 5

** * ***

441 448

461 489

591" 652

219 224

233" 248

282 ' 299

137” 141

147 155

170 171

07 100

103 108

116 110

74 75

78 81

85 76

***

463 472

467 525

359 707

229 236

247 266

309 320

143 147

154 164

183 181

100 103

106 114

123 115

76 78

81 84

89 79

***

470 ' ■” 503 547 482

710 746

232 241

254 276

328 334

145 150

156 170

192 187

101 105

110 117

127 118

76 79

82 86

92 80

*♦*

***

465 479

"504 556

745" 770

231 241

’ 233" ' 340 341 281

147 150

159 172

196 189

105

110 117

129 118

75 78

81 86

92 79

"***■ •**

449 466

473 554

762 778

226 237

~733~ 280

197 187

96 102

106 116

128 115

73 76

79 84

90 76

***

***

426 446

478

732”

m

770

228

246" 275

341 ' 334

133" 143

152 167

192 181

94 99

io 4 112

124 110

70 72

76

542

80

86 72

***

777 ’ 454

745

419

521

746

205 217

235 264

329 320

128 135

145 159

184 171

89 93

98 106

117 103

65 68

71 75

81 66

*** ' ' 335 ' 425 *** 388 492

712

' 170 202

220' 249

310 " 299

110' 126

135 ' 148

171 157

62 86

91 98

108 93

59

707

62

65 68

73 58

"T IO ' 390' 354 456

661 652

...... T73 185

207 229

284 271

108 114

T 23” 135

155 ' 140

73 77

81 87

96 80

53 55

57 60

64 48

273 ' 351

593 581

154 165

95“ 101

108“ 118

133 118

63 66

70 74

81 65

8084

9T3 97

108 93

0 .3 0 .3 5 0 .4 0 .4 3

0.5 0.55 0 .4

0.65 0 .7 0 .7 5 0 .8

0.85

***

*** *»* "*** •** ••• *•*

317

413

254 ' 307 276 361

« * "” 2T2 ‘ 256 *** 230 300 ■«* «**

307~ 495

180 " 250 ■ 236 204 155 174

209 161 145

406

107

124

393

115

138

134 ' 196

29T"

177

275

226

" r33 142

344 341

194

"T 4T ~ " 1 5 7 " 171 148

' 'TOT

CRC Handbook of Sample Size Guidelines for Clinical Trials

540

TABLE 5: ALPHA= 0.025 P0WER= 0.8 EXPECTED ACCRUAL THRU MINIMUM FQLLQW-UP= 100

DEL=.10

DEL=.15

0 .2 0 .2 5 0 .3 0 .3 5 0 .4 0 .4 5 0 .5

0 .6 5

0 .7 0 .7 5 0 .8 0 .8 5

45 45

46 46

47"

76 80

56 57

58 59

6o 58

86 89

92 93

65 66

67

69

71 66

92 94

97 100

105

“70 72

74

103

76

79 72

170 171

98 101

104 109

115 110

77 76

78 81

85 76

166

183 181

101 105

109 114

123 115

76 79

8l 85

79

147 153

160 172

192 187

103 106

11T" 118

127 118

77 79

82 86

92 80

147' 153

161 174

196 189

" 102 106

11T~ 118

129 118

76 79

82 86

92 79

144

159 - -177 187 173

100 104

109 117

128 115

74 77

80

9d

84

76

96 100

105 113

124 110

71 73

77 81

66 72

90 94

100 107

117 103

66 69

72 76

8l 66

65

1l 72

73 93

55 55

55 56

95 97

98 101

104 118

71 72

73 74

115

120 124

130 140

83 85

136 142

152 157

139 143

148

309 320

144 149

T56

280

328 334

260 285

340 " ' 341

275

99 99

100 102

104

173

145

**♦

265 268

27l 279

299 393

143 145

147

159 194

••• ***

344 348

354 368

409 495

177 180

207 236

117

**»

4o3 409

418 440

507 581

203 207

248 271

132

••• ***

443"

464 493

59J-

221 226

235

652

250

282 299

***

466 476

497“

S59

231

531

707

238

250 268

••• ***

474 487

509 554

710 746

235 244

257

*** ***

470

511

73 5 ~

235

485

564

770

245

•••

***

0.55 "***“ 0 .6

' 57 65

70 70

1 7 0 " 178

0 .0 5

0 .1 5

.0 0 BIN

.50 .25

167 168

.00 BIN

1 .0 .75

.0 0 BIN

REQUIRED NUMBER OF PATIENTS

PCONT=***

0 .1

.50 .25

1 .0 75

.50 .25

DEL=.30 1 .0 .75

.0 0 BIN

.50 .25

.0 0 BIN

DEL=.25

.50 .25

1 .0 .7 5

FACT=

1 .0 .75

DEL=.20

451

455

151

185 192

214 225

257

156

473

504 563

762 778

230 241

433 454

487 552

162

221 233

250 279

341 334

138 1 5 3

770

145

169

193 181

284

344 341

129

150

48

89"

405

464 531

746 746

209 222

239 268

329 ' 320

131”

428

138

147 161

184 171

••• ***

373 397

435 503

712 707

195 207

225 253

311 299

122 128

137 150

171 157

83 87

92 98

108 93

60 63

69

73 58

•••

339 363

400

661 652

178 190

206 232

284 ’ 271

110 T 2 5 '

155

466

117

136

140

75 78

82 88

96 80

53 55

58 60

64 48

302

109 119

133 118

65 67

71 75

81 65

• **

325

361 422

593 581

158 169

164 207

250 236

97 103

***

262 284

315 369

509 495

136 145

158 176

209

81 86

***

218 237

263 306

408“ 393

l'lO 117

126 139

161 145

**•

1*9 182

201 231

291 275

194

“ 91 98

108 93

'

541

TABLE 5: ALPHA= 0.025 POWER= 0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 110

DEL=.05 FACT=

1 .0 .75

DEL=.10

1639 1 1 8 6 " 1684 2496

—1715" 1749 "T457"' 1728 1811 2748

'1726 1744

***■' ***

1537 1567

***

0.7 0 .7 5 0 .8 0 .8 5

0.9

71 72

73 75

76 80

186 193

207 236

117

124

130 140

84 85

87 89

92 93

204 209

214 226

248 271

130 133

137 143

152 157

93 95

97 101

105 103

223 229

237 252

282 299

147“ 144

149 157

170 171

99 101

105 109

116 110

"252 ‘ 309 320 271

146 151

157 167

183 181

102 106

110 115

123 115



'

11T" 120

'

446 454

468 498

591 652

469 480

498 537

659 707

478— 515 561 492

710 746

238 247

261 282

328 334

149 154

162 173

192 187

104 108

112 118

127 118

474 491

518 572

745 770

238 248

263 288

347 341

149 155

163 176

196 189

104 107

112 119

129 118

m 480

511 571

762 778

"233 245

261 288

344 341

146 152

161 175

197 187

101 105

m 118

128 115

254

341 334

141 148

157 170

193

91

181

101

107 114

124 110

lOl

"

"

234 241

4 3 9 "' 496

762

3124

461

561

770

225 237

1397

1504" 3000

' 473 541

746 746

733

226

272

329 320

133 140

149'

1681

412 436

213

1433

163

184 171

92 96

108

117 103

381 406

444 512

712

199 211

229 256

311 299

124 131

139 152

171 157

85 88

93 99

93

182 194

210 235

284 271

113 119

127 137

155

76 79

83 88

94 80

65 68

71 75

8l 65

3062

1735""1357"” 2595" 2936

***" "1077 *** 1132

1227

7728"

1436

2748

***"

1083

239r 2496

***

'921" 982

*** ***

"775" “ 738

1294 1140

837

***" "53 r *** 697

***

104 118

1 .0 75

1777

1565

***"

99 101

1 .0 .75

.00 BIN

1624 "3033"

1284

*** **•

"

1780" 2896 1883 3062

0 .5

0 .4 5

96 97

507 581

345 349

* **' " 1 5 3 1 " 1 7 2 7 " 2999 *** 1674 1848 3124

*” “

159 194

' 405— 421 443 411

1418 1806

■*” ” 1 7 5 2 ' 1 7 9 3 “ 2725 *** 1765 1874 2936

**•

57 65

181

272 280

0 .4 5

0 .6 '

56 56

178

266 268

1456 1 8 2 7 " 1488 2182

“ 1*39 1445

* « ~ '"1617 *** 1623

***

55 55

409 495

"767 ' 1366

1183' 1196 1189 1217

0 .5 5

73 93

356 370

863 875

•** ***

***

71 72

148 152

178 275

0 .1 5

0 .4

'70 71

144 145

170 173

857 859

0 .3 5

.00 BIN

299 393

168 169

***“ **«

***

.50 .25

173' 145

.50 .25

REQUIRED NUMBER OF PATIENTS

0 .1

0 73"

1 .0 .75

100 102

“ 502 864

* « “ “ 470" *** 471

0 .2 5

.00 BIN

99 100

473 478

1 .0 .75

DEL=.2S

.50 .25

.0 0 BIN

.00 BIN

0 .0 5

**•

DEL=.20

.50 .25

.50 .25

PCONT=***

0 .2

DEL=.15

■ 790

972

"504" "533 555783

362

"335

399556864

"2155" 2182

1517" " 1806

1387" 1366 879

'

707

282

'

"337

409

641

372

475

652

309— 349 430 333

593 581

162 173

188 210

250 236

99 104

111 120

118

269 291

323 376

509 495

139 148

"161 178

209 194

83 87

92 99

lo d 93

724 243

269 312

408 393

112 119

128 141

161 145

173

205 234

291

187

275

140

133

id s

CRC Handbook of Sample Size Guidelines for Clinical Trials

542

TABLE 5: ALPHA= 0.025 POWER= 0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 120

D E L = .05 FACT=

DEL=.10

1.0 .75

.50 .25

.00 BIN

1.0 .75

.50 .25

DEL=.15 .00 BIN

1.0 .75

DEL=.20

.50 .25

.00 BIN

1.0 75

.50 .25

D E L = .2 5 .00 BIN

1.0 .75

.50 .25

.00 BIN

REQUIRED NUMBER OF PATIENTS

PCONT=***

178 275

99 100

101 102

104 145

70 71

71 72

73 93

55 55

56 56

57 65

393

2??

14T4 146

148 152

15? 194

96 97

99 101

104 118

72

71

73 75

76 80

358 372

409 495

179 182

167 194

206 236

116 118

121 124

130 140

84 85

87 89

93

406 413

423 445

507 581

206 210

■21'7 ' 248 271 228

131 134

138 143

152 157

93 95

98 101

105 103

2188" 2496

448 457

471 502

591 652

224 230

239 254

282 299

141 145

150 158

170 171

100 102

105 110

116 110

1755 1821

248? 2748

472 484

503 542

659 707

236 243

255 273

30? 320

148 152

159 168

183 181

103 106

110 116

123 115

1755 1770

1801 1888

2725 2936

482 496

520 567

710 746

T41 250

263 285

328 334

151 156

164 174

192 187

105 109

1T3 119

127 118

•••

• »*

1731 1751

1790 1900

2896" 3062

479 496

525 579

745 770

241 251

267 291

340 341

150 157

165 177

189

"103 ' 113 120 109

12? 118

0.45

• ••

1657 1683

1733 1868

299? 3124

466 486

519 579

762 778

237 " 7 5 3 ' 344 248 291 341

148 154

163 " 197 187 176

102

112 118

128 115

0.5

• •• • **

1545 1577

1640 1801

3034 3124

446 468

504 569

762 770

228 241

258 285

340 334

143 150

159 172

193 181

99

106 114

124 110

0.55

• •• • **

1406 1446

1522 1708

3000“ 3062

419 444

481 549

746

745

217 229

247 275

'359" 320

135 142

151 164

184 171

97

93

102 108

117 103

0.6

• •• • **

1251 1300

1390 15°4

2896 2936

388 414

452

712 707

202 215

232 259

3l0 299

126 133

153

141

171 157

86 89

94 100

108 93

0.65

*** ***

1093 1150

1250 1465

354

380

4l8 483

661 652

185 197

214 ' 284

238

271

114 120

128 139

155

77

84 89

96

2748

*** • **

938 1002

1107 1323

2491 2496

317 341

"377 " 593

191 212

250 236

101 106

112 121

133 118

66 69

72

81 65

••• • **

793 857

961 1168

2185 2182

84

93 99

93

•••

555“ "815 997 716 519 571

***"" 373

0.05

*« ***

470 471

473 479

502 864

168 169

171 173

O.i

**■*“ fl57 *** 860

*54 878

967 1366

267

273 281

0.15 ' * « “ 1186 *** 1190

1198 1221

1418" 1806

346 350

**■*“ 1441 1447

1459 1493

182? 2182

***

1618 1626

1543 1692

**♦

»*•

1720 1732

0.35

*** *•*

0.4

0.2 0.25 0.3

0.7 0.75 0.8

• *•

y; 85~ « * -

*• »

0.9

*» *

411

2VS8-

269

521

438

581

165 176

276 298

330 383

495

509

142 151

153 180

209 194

1815"" 1806

230 249

275

406 393

' 115

130 142

161

652 802

1380 1366

177 191

20? 237

291

468

879 864

568

317

275

121

145

''

88

196

140

108

"

106

103

80

76

92

60

543

TABLE 5: ALPHA= 0.025 POWER= 0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 130

DEL=.05 FACT=

1.0

.75

.50 .25

D E L = .10

«*■

0 :1

♦**

0.2

470 472

■***

**«

0.25

*** ***

1.0

.75

.50 .25

BIN

75

1.0

.50 .25

BIN

.00

1.0

.75

.50 .25

BIN

.00

.00

856

860

“143“ 169

174

275

178

99

101 102

104

145

70 71

72

100

72

73 93

55 55

56 56

57 65

665

977

"247“

274

299

145"

149 153

159 194

96 98

99

104 118

72 73

74 75

76 80

1418” ---- 347“ 1806 352

409

495

"180"

188 195

206

236

116 119

121 125

130 140

84

374

86

67 90

92 93

426 448

507

207 ' 218

248 271

132 135

138 144

152 157

94 96

98

105 103

142 146

106

116

158

171

103

110

110

169

160

133 181

104 107

116

111

123 115

880

864 1366

1 4 4 2 “ _I461 ~TJ2T- ' 1449 1499 2182

270

1620 1629

1447 ' 2188' 1700 2496

408 415

— 450" 459

1723“ 1740 " 2489“ 1736 1832 2748

0.35

***"" ***

1776

074

"*" ***

1736 1 3 0 0 ' 2895“ 1757 1917 3062

184

T654~ 1745 ' Z797"

"472 '

0.45" ***

.00

BIN

'3 0 2

***

0.3""***

.50 .25

DEL=.25

474

479

1 1 ' 8 7 “ 1200 1192 1225

0715

.75

DEL=.20

REQUIRED NUMBER OF PATIENTS

PCONT=***

0.05 "*** ***

1.0

.00

BIN

DEL=.15

1759" T308

** •

1691

*** • ••

1588

1901

1888

272?

2936

3124

"475 487

~ 485“ 501

502

492

171

282

359

475 505

507

546

525

572

531

585

525

586

393

146

183

101

101

581

212

229

591

'226"

241 ' 232 299 255

659

— 23F 246

257 275

309 320

149 154

710

243 253

266 287

328 334

"155" 158

165 175

192 187

106 109

114 119

127 118

244" “ 270“ ' 340

114"

12? 118

652 707

746

745

232

770

254

762

"240"

778

'

151 " 170

10

O

293

341

"157" 158

167 178

196 189

106 109

120

251

294

2"68

344 341

150 156

165 177

197 187

104 108

119

128 115

112

577

770

244

232

261 288

341 334

145 151

160 173

193 181

100

475

104

109 115

110

0.55' '*** "14TS~ 1540 '"3000“ • ** 1459 1734 3062

■"425"

489 557

746 746

233

220"

251 278

329 320

137 144

153 165

184 171

94 98

103 109

117 103

0.4

2898" 2936

— 395 '

460 528

712

707

206 218

236 262

310 299

128 134

143 154

171 157

87 90

95

421

100

108 93

***■' T 1 0 7 ~ 1272 -'272 8" *•* 1168 1493 2748

"361 ' 387

425 491

661 652

" 1 8 9 “ '217

264 271

116

122

"129“

155 140

78 81

"85

241

89

96 80

323 348

384 444

593 581

1 6 8 ' 173 179 214

250 236

107

113

133 118

67

122

1 3 76

81 65

2185“ — 282 " 336 388 2182 304

165 182

209 194

85 89

94

495

100

108 93

1 1 5 “ 132 123 143

161 145

0.5

***" • **

0.45' 0.7

"'*** *• *

0.75

i s s r 1455 ' 3034" 1825

1254“ 1410 1316 1622

7 5 3 ~ 1129 ~ 2 4 * r ' 1021 1351 2496

***" T10' *♦* 877

983

471

' 632

1194

254

649

"1330“' 1366

181"

734

0.65

***' ***

587

820

T8'3

479 580

422

451

“1815“" 1806

■***" ***

533

452

1019

O.fl

0.9 "■

3124

879

864

235

194

511

260

321

213

240

762

509

406 393

291

275

200

145 154

102

140

70

124

CRC Handbook of Sample Size Guidelines for Clinical Trials

544

TABLE 5: ALPHA= 0.025 POWER= 0.8 EXPECTED ACCRUAL THRU MINIMUM FQLLOW-UP= 140

DEL=.0 5

FACT=

1 .0 .7 5

.5 0 .25

471

474

472

DEL=.10 .0 0

BIN

PCONT=*** 0 .0 5 0 .1 0 .1 5

0.2 0 .2 5 0 .3

0.75 0 .4 0 .4 5

0 .5 0.75" 0 .4 0 .6 5

0."7 0 ."75 0 .8 0 .8 5 0 .9

•••

1 .0 .7 5

.50 .25

DEL=.15 .0 0

BIN

1 .0 .7 5

DEL=.2 0 DEL=.25

.50 .2 5

BIN

.0 0

1 .0 75

.5 0 .2 5

BIN

1 .0 .7 5

.5 0 .2 5

BIN

71

72 72

73 93

55 55

56 56

57 65

99 101

104 118

72 73

n 75

76 80

1"3B

85 86

88 90

92 93

.0 0

.0 0

REQUIRED NUMBER OF PATIENTS 149 170

171

480

502 864

174

178 275

99 100

101 102

104 145

71

967 1366

248 271

275 283

fc99 393

145 147

149 153

159 194

98

*•* **•

856

847

861

882

••• ***

1188 1193

1202 1228

1TO '

346 353

361 375

409 495

181 184

189 195

207 236

117

1806

122 125

140

***

1444 1451

1444 1504

1829 2182

410 417

428 ""507 450 581

208 213

220

248 271

rr2 — 1 3 9 135 144

157

94 96

99 102

105

230

••• **•

1422 ~ T 45i 1632 1708

2188 2496

452 462

476 509

591 652

228 234

257

282 299

143 147

152 159

170 171

101 103

104 110

114 110

••• ***

1726 1740

1744 1842

2489 2748

478

511

459

491

550

707

240 248

259 276

309 320

150 155

141 170

183 181

105 108

112 116

115

*** ***

1763 1781

1816 1915

2725 2936

489 505

530 578

7 ld 746

246 255

268 289

328 334

ITT 159

166 176

192 187

107 110

120

••• ***

1741 1764

1809 1933

2896 3062

486 507

536 591

745 770

247 257

272

340 341

154

296

148 179

189

110

121

118

1757

477- - 532 498 593

T42 778

243 254

271 296

344 341

131”

197

1908

2999 3124

158

113 119

128 115

457

243

97

119

160

152"

1'96

'

115

103

123 127 118

107 ’'"113" ' 129

***

1670 1699

*** ***

1571 1598

1670 1847

3033 3124

481

518 583

742 770

235 247

244 291

341 334

153

162 174

193 181

101 105

109 116

124 110

***

1426 1472

1556 1758

3000 3062

432 458

496 564

746 746

224 236

254 280

329 320

1T9

154

146

166

184 171

95 99

103 109

117 103

1276 1332

1430 1648

2898 2936

402 428

446

712 707

209 222

239 264

311 299

130 136

144 155

171

535

88 91

95 101

108 93

••• ***

llfc2 1165

1293 1520

2726 2748

368 394

432 498

64l 652

192 204

519

284 271

116 123

131 140

155" 140

79 82

85"

243

90

94 80

*»*

97i 1039

n sr

2491 2496

330 355

391 450

593

' 171 182

194 216

250 236

103 1 1 4 ' " 108 122

133

68

118

70

73 76

81 65

***“ **»

827 895

2184' 2182

287 310

342 393

509 495

" ' 147

1218

156

167 183

209 194

90

• **

687 751

651 1040

1812 1806

240 259

285 325

408

118 125

133 144

141 145

***

547

'484

601

837

1360 1366

184 198

216 243

291 275

• **

393 432

490 591

879 864

•••

1377

ioo4

581

393

ITS"

86

166 178

187

105 ' 109

95 101

157

108

93

545

TABLE 5: ALPHA= 0.025 POWER= 0.8 EXPECTED ACCRUAL THRU MINIMUM F0LL0W-UP= 150

DEL=.05 FACT=

1 .0 .75

.50 .25

DEL=.10 .00 BIN

PCONT=*** o ro r o~ r r

0.15" 0 .2 o .2 r 0 .3 ' 0 .3 5 0 .4 0 .4 5 '

0 .6 '

.00 BIN

1 .0 75

.50 . 25

.0 0 BIN

1 .0 .75

.50 .25

.0 0 BIN

54

57 65

172

178

100

101

174

275

100

102

104 145

71 71

72 72

73 93

55 55

56

T 49 '" 274

*** **•

1159“ I2U4

1418

1194

*** *** *** ***

1624 1635

*** **•

1729 ' 1772 “ 2 4 8 9 '

4"8I

515

1743

1852

2748

494

*** ***

1767 1786

1823 1927

2725 2936

*** ***

1746” ' 18i'9 1770

2896 3062

***

1675 ■ 1759 “ 2999“

T02"~

472

481

864

859

868 883

"7 5 7 ' 1366

74

299

145

271

283

393

147

150 153

158 194

97 98

100 102

104 118

72 73

75

76 80

349 354

362 377

409

182 185

189 196

206 236

118 119

122 125

130 140

85

1806

84

86 90

92 93

1443“ 1467

1829

411

430

507

1453

1510

2182

418

453

581

209 214

221 231

248 271

133 136

140 145

15^ 157

97

99 102

105 103

1656 1715

2188 2496

454

481 512

244 258

282 299

153

652

229 235

144

464

148

160

170 171

102 104

107 111

114 110

459 707

242 250

241 278

309 320

151

554

156

162 170

183 181

106 109

112 117

123 115

493 509

535 582

710 746

248 257

271 291

328 334

ISS 160

167 177

192 187

108 111

115 120

127 118

492 511

542

745 770

249 260

275

597

298

340 341

' 153 161

" 149 180

189

io d 111

114 121

129 118

538

742

245

273

599

778

257

298

344 341

153 159

168 179

19V 187

106 109

114 120

115

238 250

267 293

341 334

143 155

163 175

' 193" 181

102 105

110 116

124 110

~27T

257

239

282

329 320

141 147

156 147

184 171

96 100

104 110

117 103

310 299

131 137

14$ 154

171 157

89

264

92

96 101

108 93

--J75 - 222 245 206

284 271

119 125

132 141

79 82

84

140

90

95 80

174 184

198 218

105

236

109

lib 123

133 118

71

169 185

209

87 91

95 101

108 93

1232

1949

495

591

1708

1926

3124

482 504

** *

1549 1609

1484 1848

3034 3124

453 ” 524

742

487

770

*■«

***

1435 ' 1574 “ 30TOT 1485 1781 3062

*** • **

1347

1288

503

745 "

464

571

746

"408

' 474 542

712

2728

374 "" 439

2748

400

441 452

1449 "2398"~ 1672 2936

1135""■13T3 1202 1545

590

■“ 438

435

504

987' _' 1172

2491'

335

397

593

2496

361

456

581

842

1401

" 1074 '” 7185“ 1241 2182

913

*«*

702— 849

l8 l4

767

1060

1806

*** **•

559 -

499

1380

615

852

1366

0 .9 " **« ***

402" ' 500"

"579

442

864

400

■”

707

1057

««*

0.85

.50 .25

149

862

• **

1 .0 .75

170

***

0.75 ' **» 0 .8

.00 BIN

REQUIRED NUMBER OF PATIENTS

471 ■ 475

0.53" m *** 0 .7

.50 .25

*« *»*

075o .s r

1 .0 .75

DEL=.2 5

DEI-= .20

DEL=.15

2T2 " 241 225



293

347

509

149

315

398

495

158

"744

289

263

329

408 393

120 126

188 201

219

291

245

275

250

194

134

161

145

145

"

'

193“

■155" '

95

68

73

77

128

81 45

CRC Handbook of Sample Size Guidelines for Clinical Trials

546

TABLE 5: ALPHA= 0.025 POWER= 0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 160

DEL=.05 FACT=

DEL=.1 0

DEL=.15

D E I* .20

DEL*.25 .0 0 BIN

1 .0 .7 5

.5 0 .25

.0 0 BIN

72 72

73 93

55 56

56 56

57 65

97 98

lo o 102

104 118

72 73

74 75

76 80

2b7 236

118 120

122 126

13b 140

85 87

88 90

92 93

222 232

248 271

134 137

140 145

152 157

95 97

1 9 102

""105" 103

230 237

246 259

282 299

" 145 149

154 160

170 171

102 ' 107 105 111

116 110

659 707

243 251

262 279

309 320

152 157

163 171

183 181

107 109

123" 115

539 587

7 IB 746

250 260

273 293

328 334

168 178

192 187

10T~ 116

161

112

121

127 118

' 496 516

547 602

745“ 770

271 262

277 ~ 340 341 300

' IT7 163

17b 181

196 189

109" 112

116 122

129 118

2999 3124

486 509

543 604

7 62 778

248 260

276 300

344 341

154 161

"169 180

197 187

106 ""115 ' 110 120

128 115

1698 1888

3034 3124

468 493

530 596

762 770

241 253

270 295

341 334

150 156

164 176

193 181

103 106

'T I T 116

124 110

1446 1498

1591 1803

3000 3062

444 470

509

746 746

230 242

259 285

329 320

142 149

157 168

1 64" 171

'

577

97 100

105 110

117 103

••• **•

i3 b o 1361

1467 1696

2698 2936

414 441

481 548

712” 707

215 227

244 268

3 ll 299

133 139

146 157

171 157

'

89 93

97'" 101

108 93

0 .6 5

*** **•

1150 1219

1333 1569

2728 2748

380 406

445 ""1 S T 509 652

197 209

224 247

284 271

120 126

133 142

T55' 140

'

80 83

86 90

96 80

0 .7

**• • **

1002 1074

1191 1424

2491 2496

341 366

402" 461

593 581

176 186

200 219

250 236

lt)6 110

116 124

133 118

69 71

74 77

81 65

858 930

1043 1262

2186 2182

298 320

352 403

$09 495

'151 ' 160

171 186

209 194

88 92

?6 101

108 93

**• ***

713 783

866

1816

1079

1806

249 267

293 332

406 393

121 128

136 146

161 145

• **

713 867

1380 1366

191 204

222 247

291

628

509 610

879 864

1 .0 75

.5 0 .2 5

101 1 0 ' 4 145 103

71 71

150 154

159 194

162 186

190 196

507 581

210 215

464 514

591 652

484 497

516 558

496 513

1 .0 .7 5

.5 0 .2 5

.0 0 BIN

** *

471 473

'4 7 5 482

502 864

169 170

172 174

178 275

100 100

0 .1

**•

860 863

869 885

"967 1366

269 272

276 284

299 393

146 148

0 .1 5

*** ***

1190 1195

1206 1235

1418 1806

350 355

364 378

409 495

0 .2

*** ***

'111? 1455

1470 1515

1829 2182

413 420

432 455

*** **•

1626 1637

1660 1723

2188 2496

4 $ l7 467

*•*

1732 1747

"1777 1862

2489 2748

••• ***

1770 1791

1631 1940

2725 2936

0 .4

••• ***

1751 1777

1828 1964

2896 ' 3062

0745

” * •* •

1^83 1716

1781 1944

1577 1619 ••• ***

0 .6

0 .2 5 0 .3 0 .3 5

0 .5 0 .5 5

0.75 0 .8 0 .8 5 0 .9

.50 .25

.0 0 BIN

1 .0 .75

.5 0 .25

.0 0 BIN

REQUIRED NUMBER OF PATIENTS

PCONT=*** 0 .0 5

1 .0 .7 5

571 411 451

275

"

113 117

547

TABLE 5: ALPHA= 0.025 P0WER= 0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 170

DEL=.05

DEL=.10

.0 0 BIN

1 .0 .75

.50 .25

.00 BIN

2 2

73 93

55 56

56 56

57 65

9'ff" 99

00 02

10T 118

72 73

74 75

76 80

111 120

23 26

130 140

86 87

88 90

92 93

248 271

134 137

41 45

152" 157

96" 97

99 102

103" 103

247 260

282 299

146 150

54 61

170 171

103 105

108 111

116 110

245 253

264 280

309 320

153 158

64 72

18T 181

107 110

113 117

123 115

232 262

275 294

328 334

157 163

69 78

192 187

100

746

112

ll6 121

127 118

551 606

745 770

254 264

279 301

343 341

" 178" 164

71 81

196 189

109 113

117 122

129"

- T91 - 549 514 609

762 778

251 262

278 302

344 341

1T6 162

70 81

197 187

107 111

" rn > 121

" 128 115

233

341 334

151 157

66 77

103 181

nn 107

ill 117

124 110

1T4 150

58 69

184 171

98 101

105 110

117 103

171

90 93

97 102

108 93

81 84

87 91

96 80

69 72

74 77

65

.50 .25

.00 BIN

1 .0 75

.50 . 25

100 101

101 103

104 145

71 71

299 393

146 148

150 154

159 194

'

365 379

409 495

183 186

191 197

206 236

'

414 422

434 457

507 581

21l 216

223 232

7188 2496

459 469

486 517

591 652

232 238

1783 1872

2489 2748

486 500

522 561

659 707

1774 1796

1838 1952

2725 2936

500 516

543 591

710 "

••• ***

"I75I5 1783

1838 1979

2896 3062

500 520

••• ** *

1689 1724

1792 1962

2999 3124

1585

1712 1908

3033 3124

473 498

536 601

762

1607 1825

30oo 3062

449 476

515 582

2898 2936

419 447

FACT=

1 .0 .75

.50 .25

.00 BIN

0 .0 5

• • • “ "471 • ** 473

V fl 482

502 864

169 170

172 175

178 275

0 .1

*♦* ***

860 864

870 887

967 1366

270 273

277 285

0 .1 5

••• »*•

1191 1197

1208 1238

1418 1806

351 357

0 .2

*** ***

"1448 1457

1473 1520

1829 2182

***

1628 1640

1664 1730

• • • “ 1735 *** 1751 ••• ***

0 .4 0 .4 5

PCONT=***

0 .2 5 0 .3 0 .3 $

0 .5 0 .5 5 0 .6 0 .6 5 0 .7 0 .7 5 0 .8 0 .8 5 0 .9

1 .0 .75

.50 .25

.00 BIN

1 .0 .75

REQUIRED NUMBER OF PATIENTS

•**

1630

••• ***

1456

••• • **

DEL=.2 5

DEL,= .20

DEL=.15

1510

"1312” 1485

'

770

256

272 297

745 746

232 245

262 286

329 320

487 553

712 707

218 230

246 270

3 l0 299

134 140

47 57

157

227

140

"

1376

1718

••• ***

1164 1234

2728 2748

T85

1591

412

451 515

661 652

200 ' 211

248

284 271

122 127

34 43

••• ***

1016 1091

1210 1446

2491 2496

346 372

408 466

593 581

178 189

202 221

250 236

107 111

17 24

••• ***

872 946

1061

2184 2182

303 325

153 161

172 187

209 194

89 92

108

407

509 495

7

1282

02

93

••• *«*

730 798

902 1096

1816 1806

252 271

297

408

123

335

393

137 147

ill ' 145

••• ***

583 640

724 880

1380 1366

194 207

224 249

275

••• ***

419 460

518 618

864

1351

870

357

29l

"

129

1ST " 133 118 '

118

81

CRC Handbook of Sample Size Guidelines for Clinical Trials

548

TABLE 5: ALPHA= 0.025 POWER=O.B EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP* 180

DEL*.05 FACT=

DEL=.10

1 .0 .75

.50 .25

.00 BIN

1 .0 .75

.50 .25

DEL=.1S .00 BIN

1 .0 .75

DEL=.20

DEL*. 25

.50 .25

.0 0 BIN

1 .0 75

.50 .2 5

.0 0 BIN

1 .0 .7 5

.50 .25

.00 BIN

102 103

104 145

71 71

72 73

73 93

55 56

56 56

57 65

REQUIRED NUMBER OF PATIENTS

PCONT=*** 0 .0 5

*■” ***

472473

476 483

502 864

170 171

172 175

178 275

100 101

0 .1

***'' ***

651 864

871 889

967 " 1366

270 273

278 285

299 393

147 " T 3 T " 154 148

159 194

98 99

ld d 102

104 118

73 73

74 75

76 80

0 .1 5

«■*“ ***

IT92"" 1TR T 14 IB"" 1198 1242 1806

352" 358

366 380

409 495

184 “T 9 T 197 187

207 236

119 121

123 126

130 140

86 87

89 90

92 93

• **

1430'"'T 4 7 5 - 1829 1459 1525 2182

416 423

436 458

507 581

212 217

224 233

248 271

133” 138

141' 146

152 157

96 98

100 102

105 103

0 .2 5

*** • **

1630 1643

1668 1737

2188 2496

461 471

489 519

591 652

233 239

248 261

262 299

147 150

133“ 161

170 171

103 105

108 111

116 110

0 .3

**'* ***

n w 1755

1789 1881

2489 2748

489" 503

525 564

659 707

247 255

266 282

309 320

134 ' 159

164 172

183 181

106 110

114 118

123 115

• **

"1778 1801

1845 1964

2725 2936

503" ' 547 520 595

710 746

254 263

276 296

328 334

138 " 164

170 179

192 187

110 113

117 121

121 118

***

1761 1790

1847 “ 2*95 1993 3062

504 525

556 611

745 770

256 267

28l 303

340 341

159 165

172 182

196 189

110 113

117 122

129 118

0 .4 5

••• ***

1695 1733

1604 1978

2999 3124

493 519

554 614

762 778

253 265

280 304

344 341

157 163

171 182

197 187

108 112

116 121

128 115

0 .5

*** • **

"1593 1640

1726 1926

3034 3124

478 504

542 606

762 770

246 “ 273“ 299 258

341 334

152 159

167 177

192 181

TOT 108

112 117

124 110

0 .5 5

•** **•

1466 1522

1623 1845

3000 3062

454 481

521 588

746 746

235 247

264 288

329 320

1"43 151

159 169

184 171

98 102

106 111

117 103

0 .6

*** ***

1324 1390

1502 1739

2898 2936

425 452

492 559

712 707

220 232

249 272

3lO 299

135 141

148 158

171 157

91 94

98" 102

108 93

0 .6 5

*** »**

1177 1250

1370 1613

2728 2748

390 418

456 519

661 652

202 213

229 250

284 271

123 128

135 143

155" 140

81 84

87 91

96 80

0 .7

•** • **

1030 1107

1228 1467

2491 2496

351 377

413 470

593 581

■ 1 8 0 ' 204 191 222

250 236

ib 6 112

116 125

134 " 118

70 72

74 77

81 65

0 .7 5

*** *• *

686 961

1078 1301

2186 2182

307 "" 361 330 410

509 495

174 188

209 194

90 93

97 102

108 93

0 .6

*'**

743 812

917 1113

1816 1806

256 275

300 338

408 ...........124 ' 393 130

138 147

161 145

0 .8 5

* " *•*

594 652

736 893

1380 1366

196 209

226 251

291 275

0 .9

••• *•*

427 468

527 626

879 864

0 .2

0 .3 5 0 .4

155 163

549

TABLE 5: ALPHA= 0.025 POWER= 0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 190

D E L = .05 FACT=

D E L = .10

**•

.50 .25

.00 BIN

“ 477

477

502"

170

173

178

474

483

864

171

175

275

100 101

’ 271“ ~27F

1 .0 .75

0 .1 5 O.'Z 0 .2 5 0 .5

*'” r"

*** ' *" ***

• #*

0 .4

'

1193 "1717" 14I"8 " 1199 1245 1806 1451 "1479" 1829 1461 1530 2182 1633 1646

1672 1744

7181 " 2496

1782 1806

***

" I 7 '55 '" lr e r "78 9 5 ' 1796 2007 3062

2936

1702 " 1815 "2999 "" 1741 1994 3124

*«“ **•

0 .5

*** ' 1601 *** 1650 ** *

1853 1975

7725 "

***

0 .7 5

0 .5 5

967" 1366

■ * « “ “ 1740“ 1794" T459 • ## 1759 1890 2748

0 .3 5 " * «

.00 BIN

D E L = .20

D E L = .2 5 1 .0 .7 5

.50 .25

.0 0 BIN

55 56

56

93

56

57 65

.50 .25

.00 BIN

1 .0 75

.50 .2 5

.00 BIN

"102 103

104 145

7l 71

72 73

REQUIRED NUMBER OF PATIENTS

" 8 6 T '" 872 865 891

0 .1

1 .0 .75

1 .0 .75

PCONT=*** 0 .0 5 "

.50 .25

D E L = .15

1739 "31574" ' 1944 3124

T 4 7 5 ' 1638 1534 1864

299 393

147 149

f3T“

286

154

158 194

98 99

lo o 102

104 118

73 73

74 75

16 80

'3 5 3 359

367 381

409 495

184 187

192 198

206 236

119 121

123 126

130 140

86 87

89 90

92 93

417 425

438 460

507 581

2 l3 218

224 234

248 271

135“ 138

142 146

152 157

96 98

lOo 102

105 103

452” ""49T " 474 522

591 652

234 241

249 262

282 299

147 151

"157" 161

170 171

104 106

108 112

116 110

491 506

659 707

248 256

267 283

309 320

157“ 160

165 173

183 181

108 111

114 118

123 115

506 — 551 598 523

710 ......... 256' 265 746

278

328 334

159 165

171 180

192 187

" l l 'I

297

117 122

127 118

508— 560" 615 529

744 ' 770

2 5 8 " "2 7 3 269 304

340 341

160 166

173 183

196 189

111 “” n r 114 123

129 118

500 523

762 778

255 267

282 305

344 341

153 164

172 182

197 187

109 112

116 121

128 115

"547' ■762 ' " '2 4 7 " 277 301 611 770 260

341 334

154 160

168 178

193 181

105 108

112 117

124 110

146 152

160 170

184 171

99 102

106 111

117 103

473 509

"557" 567

558 619

745 ' 746

266 290

'3"29"“ 320

222 235

251 273

310 299

" 1"56 142

149 159

171 157

91 94

98 102

108 93

284 271

124 129

135' 144

"175 140

82 84

88 91

96 80

70 72

75 78

65

'470 458

"498"' 563

0 .5 5

* « ' ' T190 *** 1265

1387“ “ 7778 ' " 1633 2748

376 423

4 6 7 " 661 ■' 524 652

2 0 4 ' 230“ 216 251

0 .7

**'*■ ' T044 *** 1122

1746“ ■749T" 1486 2496

356' 382

"417 474

182 192

207""" 250 236 223

109 113

117 125

133 118

”155" 165

TJT~ 209

90 94

98 102

108 93

0 .8 0 .8 5 0.9"

1 0 9 5 " 715 5 1319 2182

* * '* ' ” 755" • ** 825

932

**'*"■ 505" *»* 663

905

* r r ~ ■ 435" *** 476

535

879“

633

864

1128

1316 1806

750

"

593 581

3 n “ ""355" 414 334

509 ' 495

250“ ""303"

408 393

278

341

1350 '

1'79

229"

291

1366

212

252

275

114

' 237 249

1519 "7873” " 1759 2936

0 .7 5 - * « “ “ 900" *** 976

712 707

"

"*«"■ ' 1335 •** 1403

0 .5

'

274

"459“ “ "525" 592 486

"3000 ' 3062

73

175 131

189

194

139 148

l6 l 145

8l

CRC Handbook of Sample Size Guidelines for Clinical Trials

550

TABLE 5: ALPHA= 0.025 P0WER= 0.8 EXPECTED ACCRUAL THRU MINIMUM F0LL0W-UP= 200

DEL=.05 FACT=

DEL=.10

1 .0 .75

.50 .25

.0 0 BIN

472

477

474

484

502 864

••• **•

862 866

873 892

0 .1 $

••• • **

1194 1201

b .2

••• •**

1453 1463

*** • ** ***

PCONT=***

0.05

***

1 .0 .75

.50 .25

DEL=.15 DEL=.20 DEL=.25 .00 BIN

1 .0 .75

.50 .25

.00 BIN

1 .0 75

.50 .25

.0 0 BIN

1 .0 .75

.50 .25

55 56

56 56

.00 BIN

REQUIRED NUMBER OF PATIENTS

' 170

173 175

100 101

102 103

104 145

71

275

12

72

73

73 93

967 1366

271 274

279 286

209 393

147 149

131

159 194

98 99

101 102

104

73

74

154

118

74

75

80

1214

n ra

354

1806

360

409 495

185 188

192 198

207 236

HTJ ' 124

“n o

86

1248

368 382

89

“ 92

121

126

88

90

93

1482 1535

1829 2182

418 427

44b

507

462

581

214 219

225 234

248 271

136 139

142 146

"152 ' "

97

100 103

103

1635 1649

1676 1751

2188 2496

464

493 524

591 652

235

250 263

282 299

148

156

T7CT

104

109 ' 116

242

152

162

171

106

112

110

1743 1762

1800 1899

2489 2748

494 508

531

S59

268

707

309 320

156 160

166

570

250 258

109 111

114

173

183 181

118

123 115

••• »**

1786 1811

i8 6 0 1986

2725 2936

509 527

£54 601

710 746

267

170 165

172"

192 187

118 122

127

180

***

1770 1803

1965

'511

564 619

745 770

b

285

174“

196

2020

2896 3062

270

•••

1708 1749

1826 2010

2999 3124

504 527

563

762 778

257 269

**•

1609 1660

1752

3034

487 513

250 262

279'-

3124

552 616

762

1962

341

302

334

0 .5 5

***

1485 1546

1653 1883

3000 3062

464

531

491

597

746

268 291

329 320

T47

746

239 252

0 .4

*** ***

1347 1417

1535 1779

2898 2936

435 463

503 568

712 707

225 237

253 275

311 299

143

159

••• ***

1202 1279

1404 1652

2728

100

466

661

2748

428

528

652

206 218

232 252

284 271

125 130

•••

1057 1137

1262 1505

2491 2496

361 386

503 581

184 194

207 224

250

478

236

9 l3 991

1111

2186 2182

315 338

369 417

509 495

166

- 176 190

209 194

111 838

94'6

1916

177

343

408 393

126

1806

263 282

306

1143

132

149

615

674

762 917

1380 1366

201 214

231 254

201 275

442 483

$42 640

879 864

0 .1

0 .2 5 0 .3 0 .5 5 0 .4 0 .4 5 0 .5

0 .6 5 b .7 0 .7 5

*•*

**• ***

•••

• **

0 .8 b .8 $

0 .0

•••

#•* *** ***

1337

476

532

623

178

- 5 7

171

770

257 26

284

280 " 328“ 298 334

'

140 157

ITT 114

118

179“ 113

IT T "

128

122

115

~I9 3'

ID 5

113“

181

109

118

110

161 171

184 171

lOb 103

107 111

117 103

IT T " 150

171 157

92 95

98 103

108 93

136 144

'155 140

82 85

88 91

96 80

lb 9 114

119 125

133 118

71

75

73

78

81 65

01 94

98 103

108 93

306 284 307

344 341

" 159

173

165

183

187

155

169

161

179

i6 r 145

'

175'

n r " " "129' 123 118

1'61 167

153

"

98

“ 7Z ~ ~ '

111 114

340 341

"

'

65

183

189

" 19T "■



551

TABLE5: ALPHA= 0.025 POWER= 0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 225

DEL=.05 FACT=

0 .2 0 .2 5 0 .3 0 .3 5 0 .4 0. 45 0 .5 0. 55 0 .6 0 .6 5 0 .7 0 .7 5

.50 .25

101 101

102 103

104 145

71 72

72 73

299 393

148 150

"132“ 155

158 194

99 100

101 102

371 384

409 495

186 189

193 199

206 236

120 122

124 ' 130' 127 140

422 430

443 465

507 581

216 221

227 235

248 271

137 140

143 147

2188 2496

469 481

499 529

59 1

238 244

253 264

282 299

*

475

502 864

170 172

173 175

178 275

f" *

863 868

87 6 896

967 1366

273 276

280 287

4

1197 1204

1218 1255

1418 1806

3 56 362

1456

1489 1546

1829 2182

1656

1686 1767

1751

• “ » 4“

* 4'

*

1 .0 .75

.50 .25

.0 0 BIN

1 .0 .75

.0 0 BIN

1 .0 .75

.50 .25

.0 0 BIN

93

56 56

56 56

65

104 118

73 74

75 75

76 80

87 88

89 91

92 93

9? 99

101 103

105”

149 "T57~" 170 163 171 153

105 107

109

116

112

110

REQUIRED NUMBER OF PATIENTS

1467

1640

652

' 73

152 157

57

103

*

1772

1813 1920

2489 2748

500 515

538 577

659 ..........253“ 241

27i 286

309 320

158 162

167 174

18 3 181

110 112

"TI5

707

119

123 115

4

1795 1823

1877 2013

2725 2936

516 534

542 409

710 746

261 271

283 300

328 334

162 167

173 181

192 187

112 115

118 122

118

1783 1819

1887 2052

2896 ........ 5 W 3062 542

574 427

745 770

264 '" 2 8 7 ” 309 275

340 341

164 169

176 185

196 189

113 116

119 124

129 118

1723 1769

1853 2046

2999 3124

513 538

573

762 778

252~~ 289

162 168

197

273

344 341

'175

433

184

187

111 114

118 122

128 115

1628 1684

1784 2002

3034 3124

498 524

543 424

762 770

305

341 334

157 163

171 180

192 181

107 110

114

267

118

124 110

1508 1574

1688 1927

3000 3062

475 503

543 407

745 746

244 257

272 294

329 320

150 156

163 172

18'4 171

ib i 104

108 112

117 103



1449

1573 1824

2898 2936

446 474

514 578

712 707

23b 241

257 278

311 299

140 145

152 160

171 157

93 96

99 103

108 93

4

1232 1313

1443 1698

2728 2748

411 439

477 538

661 652

211 222

234 255

284 271

127 132

138 145

155 140

84 86

89 92

95 80

1089 1172

1301 1549

2491 2496

371 397

432 487

593 581

188 198

21b 227

250 236

111 115

120 126

133 118

72 73

75 78

81 65

944 1024

1148 1376

2186 2182

325 347

378 424

509 495

141 169

179 192

209 194

92 95

99 103

lo 8 93

794 869

979 1177

1816 1806

271 289

313 348

4b6 393

129 134

i 4 r ... 161

639 699

788 942

"HETT 1366

206 219

235

291 275

459 500

559 656

879

* 4

• 4

* 4

* 4

• 4 “

* 4

• 4



0 .8

4

0 .8 5

4

0 .9

1 .0 75

478 485

4 “

DEL=.25

.00 BIN

.00 BIN

0 .0 5

DEL=.20

.50 .25

.50 .25

*

0 .1 5

DEL=.15

1 .0 .7 5

PCONT=

0.1

DEL=.10

• * 4



864

257

310

255"' 283

150

145

127

CRC Handbook of Sample Size Guidelines for Clinical Trials

552

TABLE 5: ALPHA= 0.025 POWER= 0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 250

DEL=.0 5 FACT=

DEL=.10

1 .0 .7 5

.50 .25

.00 BIN

'474 476

479 486

502 864

171 172

174 176

178 275

865 870

879 899

967 1366

274 277

282 288

PCONT=*** 0 .0 5 0 .1

•••

• **

***

DEL=.1 5

1 .0 .7 5

.50 .25

.00 BIN

1 .0 .75

DEL=.20 DEL=.25

.50 .25

.0 0 BIN

1 .0 75

.5 0 .2 5

.0 0 BIN

1 .0 .7 5

.50 .25

.00 BIN

101 101

102 103

104 145

72 72

72 73

73 93

56 56

56 57

57 65

299 393

149 150

152 155

159 194

99 100

101 102

104 118

74 74

75

75.....

76

80

REQUIRED NUMBER OF PATIENTS

0.15

*** ***

1199 1207

1223 1262

1418 1806

359 364

373 386

409 495

187 190

194 199

207 236

121 '"175 ' i3b 127 123 140

87 88

89 91

92 93

0 .2

•••

** *

1460 1472

1496 1557

1829 2182

425 434

447 468

507

218 222

228 236

248 271

138 141

T52

581

98 99

101 103

103

*** *•*

1645 1662

1696 1782

T189 2496

473 485

503 533

591 652

240 247

255 266

282 299

151 154

T5'S~" 170 163

171

106 108

110 112

116 110

•••

1758 1781

1827 1940

2489 2748

505 521

544 582

459 707

256 264

274 288

309 320

159 163

168 175

183 181

111 113

116 .. 123 119 115

1804 1836

1895

2725

2037

2936

523 542

616

71b 746

265 274

284 303

328 334

144

175

192

113

119

127

169

182

187

116

123

118

1795 1834

1909 2081

2846 3062

528 550

582 635

745 770

268 279

292 311

340 341

166 171

'177 ' 194

114

186

189

117

120 124

129 118

***

1739 1788

1878 2080

2999 3124

522 547

583 641

762 778

266 278

' 292 ' 344 313 341

164 170

177 185

197 187

112 115

119 123

128 115

••• *• *

1447 1708

1813

3034 3124

507 534

634

762 770

260 272

287 308

341 334

159 165

172 181

193 181

lb 8 111

115

2040

119

124 110

•••

1531 1602

1721 1967

3000 3062

485 513

553 616

746 746

249 261

274 297

329 320

152

144 173

184

158

171

102 105

109 112

103

1400 1479

1608 1865

2898 2936

456 485

524 587

712 707

234 246

260 280

311 299

142 147

154 161

172 157

94 97

100 104

93

••• ***

1261 1345

1460 1739

2728 2748

422 449

487 546

661 652

215 226

239 258

284 271

129 134

139 146

155 140

84 87

89 92

94 80

***

1118

1337 ""2'491 1588 2496

380 406

441

192 201

213 229

250 236

113 117

121 127

134 118

74

494

593 581

72

1204

74

78

81 65

972 1055

1181

2186 2182

333

1412

355

386 430

509 495

94 97

100 104

108 93

••• ***

822 897

lo b s 1207

1816 1806

277 295

319 353

4b8 393

*** ***

440 722

8 ll 965

1380 1366

211 223

239 260

275

••• • **

474

57'4

879

515

669

864

0 .2 5 0 .3 0 .3 5 0 .4 0 .4 5 0 .5 0 .5 5 0 .6 0 .6 5

0.7 b .7 5 0 .8

0.85 0 .9

*** ••• ••• •••

*»* •••

*•* *•*

570

573

291

....

T « 172

131 136

" 181" ' 209 193 194 143 151

161 145

'

147

157

"'

105



1 1 7 "" 108

553

TABLE5: ALPHA= 0.025 POWER= 0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 275

DEL=.05 FACT=

DEL=.10

0 .1 0 . 15

***'

***

***

072 "" « * '

0.25 0 .3

0735 0 .4 0 /4 5

0 75 0735

***

***

.0 0 BIN

1 .0 .75

.50

.25

.00 BIN

101 102

102 103

104 145

72 72

72 73

73 93

56 56

56 56

57 65

299 393

149 151

153 155

158 194

99 100

lO f 103

104 118

74 74

75 76

76 80

400 495

188 191

195'

206 236

122 123

125

130

200

127

140

88 89

90 91

92 93

450

507

470

581

219 224

2d0 237

248 271

139 141

144 148

152 157

98 100

101 103

105 103

282 299

152 155

15? 164

169 171

io4 108

110 113

116 110

309 320

T41

157“

145

175

183 181

112 114

116 119

123 115

502

171

174

178

476

480 487

864

172

176

275

646 871

881 903

947 1366

275 278

262 289

360 366

375 388

428 437

1 .0 .75

REQUIRED NUMBER OF PATIENTS

T2U1

1227

1418

1210

1248

1806

1444

1503

1829

1477

1567

2182

TOO

1704

508

591

'242“

254

1794

21'S9 2496

477

1669

490

537

652

249

247

549 587

459 '

258 ' 274

707

266

289

1745

1840

2489

" "'"510

1790

1958

2748

526

1*14

1911

2725

529

574

710

1848

2060

2936

548

621

746

248 277

305

328 334

166 171

183

192 187

114 " 120 123 117

127 118

*•*

1607 1850

1929 2109

2896 3062

535 557

590 641

745 770

272 282

295 313

340 341

168 173

170 186

196 189

115 118

121 124

129 118

*** ** «

1754

1903 2111

2999 3124

530 555

591 648

742

1807

778

270 281

295 315

344 341

166 171

176 186

187

113 116

119 123

128 115

*** *•*

1841 2074

7033

244

290"

770

275

310

341 334

161 167

182

193 181

109 112

115

3124

514 ” 582 543 642

742 " "

1730

119

124 110

***

1333

1752

1428

2003

3000 3062

495 523

166 174

164 171

103 106

109 113

117 103

1541

2*78

95"

1903

2936

***

• ** ***

***

***

1444



GO

o

***

174

745 '

253

279"

746

265

300

329 320

154 159

444 ' 534

712

594

707

238 249

244 283

310 299

T44

494

149

162

43r 458

494 553

441

284 271

131 135

'3 87” 414

449 500

250" "

2496

779

1217" ■21*4

"340”

392

509

1084

1444

2182

343

435

*44

1035 1234

1*14 1804

283 301

1380 1344

215 227

TIB'S ' 1513 ” 2728

•**

175“

542

*** ** * ***

2*9”

424

0745

0 /9

.50 .2 5

47~4

TT25 1508

0 .8 5

1 .0 75

.00 BIN

*** ***

0775

D EI=.25

.0 0 BIN

.00 BIN

.50 .25

0:5

0.7

DEL=.20

.50 .25

.50 .25

1 .0 .75

PCONT=***

07"O5

1 .0 .75

DEL=.1S

1375

1776

2748

1144 "lO T T 2491 1234

922

1623

*** ' •#*

550 742

' 833 986

*** ***

487 529

588 681

*7? 844

"

■'

219 ""242”

177

157

98

101 104

108 93

140“

155

147

140

85 87

90 92

80

73 74

76 78

81 45

133“ ” 171

652

229

260

593

195 204

” 215” 230

236

114 118

122 127

li}3 118

167 174

183 194

209 194

95 97

_'1 W ”

495

108 93

324 356

408 393

133 138

144 151

161 145

242 262

291 275

581

"

104

94

CRC Handbook of Sample Size Guidelines for Clinical Trials

554

TABLE 5: ALPHA= 0.025 POWER= 0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP^ 300

DEL=.0 5 FACT=

DEL=.1 0

0.1

*•* ***

.50 .25

DEL= .2 0

DEL=.25

.50 .25

.0 0 BIN

1.0 75

.5 0 .2 5

.0 0 BIN

1.0 .7 5

.50 .25

.00 BIN

101

102 103

io4

72 72

72 73

73

102

93

56 56

56 56

57 65

299 393

15b 151

153

158

156

194

100 100

lb 2 103

104 118

74 74

75 76

76 80

189 192

196 200

206 236

122 124

125 127

"~no" 140

88 89

90 91

92 93

221"'" 231 225 238

248 271

140 142

145 148

152 157

99 100

lb 2 103

105 103

153

160

109

ill 113

115

164

169 171

10F

156

162

112“

117 120

123 115

.00 BIN

1.0 .7 5

.50 .25

.00 BIN

475

461

502

172

174

178

477

488

864

173

176

275

8gy

967~

905

1366

276 279

283 289

1.0 .7 5

REQUIRED NUMBER OF PATIENTS

PCONT=***

0.05

1.0 .75

DEL=.15

ffSff"

873

*** *** “i*•* l‘

mn

•** *** ••• *•*

145

"

409

1274

1806

362 368

377

1213

389

495

1467 1482

15X0 1576

1829” 2182

43b 439

453“ 473

507 581

1656 1676

1715 1809

~zmn

461 493

511 540

591 652

244 250

258 268

262 299

1772

1652 1975

2486

515

554

1800

2748

531

591

659 707

261 268

" "278 ' 291

309 320

166

170 176

183 181

••• *»• ••• ***

1823 1860

1927 2081

2725 2936

535 554

582 626

710 746

271 280

291 306

328 334

167 172

177 184

192 187

' UT" 118

120 124

127 118

1T O 1865

1949 2134

ra w 3062

57T 564

597 647

745 770

275 285

298 315

340 341

169 174

18b 187

196 189

116 118

121 125

129 118

0 .4 5

••• *•«

1769 1826

1926 2140

2999 3124

538 563

599 654

762 778

273 284

298 317

344 341

166 173

179 187

197 187

114 117

12b 124

126 115

0 .5

*»» •••• **

1684 1752

3054T' 3124

524 552

590 649

762

293 312

340 334

163 169

11TT" l l 6

770

267 279

T7T " 193

2105

183

181

113

120

124 110

1574 1653

1781 2037

3oo0

5b3 531

571

745 746

282 301

329 320

'T57"

631

256 268

15?

3062

161

175

184 171

104 107

110 113

117 103

241' 253

266 285

310 299

145 150

156 ""171 157 163

96 98

101 104

108 93

245 261

284 ’ 271

132 136

T41 147

154 140

86 88

90 93

95 80

216 232

250 236

115 " 123 119 128

133 118

73 75

77 79

61 65

is r

95"'

101

98

104

108 93

0.15 0.2 0 .2 5 0 .3 0 .3 5 0 .4

0 .5 5

nv>

1232' 14IB-

2496

"

....

'

0.6

••• «*«

1535

1672 1937

2898 2936

474" 503

542 601

712

0 .6 5

***

1313 1404

1$45 1810

2728 2748

439 466

504 559

661 652

222 232

0 .7

*** *•» ••• ***

1171

1401 1655

2 ATT' 2496

397

456 506

593

1262

581

198 207

1024 1111

1241 1473

2186 2182

369

398 440

5b9 495

169 176

195

209 194

869 946

1060 "TfflT" 1259 1806

289 306

329 360

408 393

134 139

1"45 152

145

699 762

852 1004

219 230

245 264

29l 275

0 .7 5 0. 8 0 .8 5 0 .9

*** *** «»* ***

***

500 542

1380 1366

~imr~ ' 879 692

864

422

347

707

'

"

114

110

"

555

TABLE 5: ALPHA= 0.025 POWER= 0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 325

DEL=.05 FACT=

DEL=.10 1 .0 .75

.50 .25

DEL=.15

DEL=.20

.50 .25

.0 0 BIN

1 .0 75

.50 .2 5

.00 BIN

1 .0 .75

.50 .25

.00 BIN

101 102

103 103

104 145

72 72

73 73

73 93

56 56

56 56

57 65

299 ' 393

IS O 152

154 156

159 194

1TJ0 " 102 103 101

104 118

74 75

75 76

76 80

19 0~ 193

197 201

207 236

122 124

126 128

130 140

88 89

90 91

92 93

2'22~ 232 239 226

248 271

140 143

145 148

152 157

99 101

102 104

105 103

259 269

282 299

134 157

140 164

170 171

107 109

111 113

110

163

171 176

183 181

113 115

11? 120

123 115

178 184

192 187

116

173

118

121 124

127 118

171 175

181 188

196 189

T16

122 125

129 118

167 " 180

.00 BIN

1 .0 .75

.50 .25

.00 BIN

"476 478

482 489

502 " 864

172 173

174 176

178 275

1 .0 .75

REQUIRED NUMBER OF PATIENTS

PCONT=*** 0 .0 5

*** *♦*

0 .1

*** ' ***

ff79 875

886 908

947" 1366

'2 7 7 280

284 290

***



1206 1217

1234 1279

M IT 1806

' "3 6 4 370

_ 378 390

409 495

***"

1471 1487

1516 ' 1527" 1585 2182

433 442

455 475

507 581

***

1261 1683

1725

2188' 2496

484 497

515 543

591

246

1821

652

252

*** '

1779 1 8 6 5

519 536

559 595

659

" 263

707

270

280 292

309 320

710

0'.T5 0 .2

*«•

0727 ' ™ 0 .3 0755 0 .4 " 0.T 5 O'. 5

0.55 0 .6

0.65

1992

2489 2748

***" *•*

1632

1943 2101

2936

560

631

746

273“ 282

293 307

328 334

***

***”

1831 “ 1948 1880 2158

2897' 3062

” 548 571

603 652

745 770

278 287

300 316

340 341

**< ***

1784 1 9 4 9

2777"

762

" 277

3124

545 570

606

1844

660

778

287

301 318

344 341

*** ***

1702

1893

3033

532

597

762

' 2 7 f~

297

341

1773

2135

3124

559

655

770

282

314

* * * ‘ "T395 *•* 1676

1809

3000

745

" 260“

2068

3062

539

746

271

”1372

1701

2879"

482

549

712

1561

1969

2936

511

607

707

- 447 ' 474

511

661

22 5

565

652

235

***

**»

1872

0 .7 3 O.fi 0 .8 3 0 .9 “

'*■" ***

2166

2723”

1338 1 5 7 4 " 2728 1430

0 .7

'

1809

***

1841

2748

""340 ■■ 588

— 511— 578 637

177 '

197 187

"T15 117

120 124

128 115

334

165 170

176 183

193 181

T IT " 114

117 120

124 110

285 303

329 320

f37 162

168 175

184 171

105 107

110 113

117 103

245“

269

147 151

171

286

311 299

157

255

164

157

97 99

102 104

108 93

247 263

284 271

133 137

142 148

155 140

86 88

91 93

95 80

74 75

77 79

81 65

TI96 ' 1430

249r

404

463

593

2o r~

1289

2496

429

511

581

209

220 233

250 236

116 120

124 128

133 118

353 375

' 404 444

509 495

171 178

186 196

209 194

96 99

102 105

108 93

146 153

161 145

1685

* " • **

8*0

1083

1816

294

333

408

137“

968

1281

1806

311

363

393

141

714

870

1380

779

1020

1366

5T2 554

412

879“

701

864

—222— 248 234

266

291 275

119

187

1048 1 2 7 7 " 2157" 1136 1500 2182

***

167

116

174

***

***”

DEL=.25

CRC Handbook of Sample Size Guidelinesfor Clinical Trials

556

TABLE 5: ALPHA= 0.025 POWER= 0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 350

DEL=.05

DEL=.10

1 .0 .7 5

.50 .25

.00 BIN

* ***

502

479

482 489

864

172 173

*** **•

877

688 911

967 "" 1366

281

*** **•

1209 1220

1240 1284

1418 1806

365 371

•••

1475 1492

1523 1593

1829 2182

435

••• ***

1665 1690

1734 1833

2189 2496

••• ** •

1786 1818

1876 2007

2469

*** • ••

164^ 1883

1958 2120

••• ** *

1842 1895

FACT=

0 .1 0 .1 5 0 .2 0 .2 5 0 .3 C~. 35 0 .4 0 .4 5

o .r 0 .5 5 0 .6 0 .6 5 0 .7

0 .8 5

0.9

.00 BIN

1 .0 .75

DEL=.25

.50 .25

.00 BIN

1 .0 75

.50 .2 5

.0 0 BIN

1 .0 .7 5

.50 .25

.00 BIN

175

57 65

176

275

101 102

103 103

104 145

72 72

73 73

73 93

56 56

56 57

285

299 393

151

154 156

159 194

100 101

102 103

104 118

74

75

152

75

76

80

380 391

409 495

l9 i 194

197 201

206 236

123 124

T23 128

130 140

89 89

90 91

92 93

458 476

507

444

581

223 227

232 239

248 271

141 143

146 148

152 157

100 101

102 104

105 103

488 500

518

591 652

248 253

260 270

282 299

155

545

157

1'61 165

170 171

108 110

111 " T K 113 110

523 540

563 598

'659

265 272

281 293

309 320

164 168

172 177

183 181

113 115

116

707

120

115

2725 2936

545 565

593

710 746

295 309

328 334

"170“

T77

635

276 284

174

185

192 187

117 119

121 124

127 118

1986 2180

2896 3062

554 577

608 657

745

280 290

302 318

340 341

172 176

162 188

'196" '

117

189

120

122 125

129 118

• • • ' 1798" 1970 • »* 1861 2192

2999 3124

551

612

303 320

344 341

171 176

161 188

197 187

115

121

665

762 778

279"

577

118

124

128 115

1719“ 1917

871

2748

278

291

178

770

290

273

'

il7

“ 7'6 ' "

123

*** *•*

1793

2162

3034 3124

539 566

604 660

762 770

284

298 316

341 334

166 171

177 184

192 181

112 114

120

124 110

••• **•

1615 1699

1835 2096

3000 3062

518 546

585 642

745 746

263 274

267 305

329 320

159 163

169 176

184 171

106 108

111 114

il7 103

*** **•

1494"" 1729 1585

1998

2896 2936

489 518

612

712 707

248 258

27l 288

311 299

148 152

158 164

171 157

97 99

102 105

93

1361 1456

1602 1870

2728 2748

454 481

517

661 652

228

249 264

284 271

134 ~~T47 138 148

155

237

140

87 89

91 93

96 80

1219 1314

1457

2491 2496

410 435

468 515

593 581

203 211

221 234

250 236

117"'

1712

120

124 129

133 118

74 76

77 79

8l 65

1070 1159

1292 1524

2186 2182

359 381

408 447

509 495

173 160

188 197

209 194

99

102 105

93

••• **•

910 989

1104 1301

1816 1806

298 315

337 365

408 393

137 142

147 ' 161 153 145

**•

732 796

687 1035

1380 1366

225 236

250 267

275

*** **•

523 " 622

879""

564

864

••• ••• •**

0 .7 5 0 .8

.50 .25

DEL=.20

REQUIRED NUMBER OF PATIENTS

PCONT="* 0. 0'5—

1 .0 .75

DEL=.15

710

556

570

291

97""

106

108

557

TABLE 5: ALPHA= 0.025 POWER= 0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP* 375

DEL=.05 FACT=

DE1=.10

1 .0 .75

.50 .25

.00 BIN

*»*

477 479

483 490

'502' 864

---- 172 174

01

' *«" ***

875

"890“ 913

967'

879

1366

***

*** " n r r 1223

0715

***

0.2

• ••

1478 1496

•**

0 725

***

0 .3

0735““

.00 BIN

DEL=.25

.50 .25

.00 BIN

1 .0 75

.50 .25

.0 0 BIN

1 .0 .75

.50 .25

.00 BIN

102 102

103 103

104 145

72 72

73 73

73 93

56 56

56 57

57 65

107

"74

75

118

75

76

80

130 '

89 89

90 91

92 93

1 .0 .75

1671

178 275

' ” 278

286 291

299 ' 393

151'

281

152

154 " 1'59 ' 156 194

100 101

102 103

“ 367“

381 392

4(39 495

192 194

197 201

206 236

123

373

125

126 128

437 447

460 478

507 581

224 228

233 240

248 271

144

521 547

591 652

249 255

2 6l 270

282 299

567 601

659 707

267 274

283 294

309 320

597 638

710 746

286

310

1806

152? 1 5 2 7 “ 1600

2182

1696

1742 1843

2188 2496

••• ***

1793 1827

1888 2021

2488 2748

'

175 176

1244 1 4 1 5 1289

•**

***

.50 .25

DEL=.20

REQUIRED NUMBER OF PATIENTS

PCONT=***

0705'

1 .0 .75

D E U .1S

1'571 "1972” “ 272? 1895 2138 2936

' ' 790 ' 503 527 544 ' — 550“ 570

278 ''' 293“

141

140

152

16

146 149

157

100 101

102 104

105 103

'"1 ?? ' ""161 165 158

170 171

108 110

111 113

116 110

165 168

172 177

181

ll4 116

118 120

123 115

328 334

171 175

179 185

192 187

117 119

122 124

127 118

123“

1ST

••• •**

1854 1909

2o04 2200

2896 3062

559 582

614 661

745 770

283 292

304 319

340 341

173 178

183 189

196 189

118 120

125

129 118

• **

•••

1812 1878

1990 2215

2999 3124

557 583

6 l8 670

762 778

282 292

305 "" 344 341 321

172 177

182 189

197 187

116 118

1 2l 124

128 115

*** •**

17T6 ”1 9 4 0 ' 30 3"3

545

610

762

2 7 6 ' ' 300”

"175

573

665

770

287

317

340 334

"167

1813

172

184

193 181

112 115

11? 120

124 110

0:35 '*** •**

1634

1860

3000

525 '

3062

553

746

265 276

289 306

329 320

160 164

170 176

157

2123

591 647

745

1721

171

106 108

111” 114

ll7 103

ITT?' 1754

2898 2936

'" 4 9 6 “ 524

562 617

711 707

" 250 260

273 289

3 id 299

149 153

15f 164

171 157

” 98 100

102 105

108 93

"460 " 523 487 574

661 652

230 239

251 265

264 271

135 139

144 "153" 148 140

88 89

91 93

95 80

250 236

115'

12F

121

129

133 118

75 76

77 79

81 65

91 100

102 105

108 93

0 .4 0 .4 5 0 /5

075 0755 0 .7 0775' 0 .8 0755 0 .9

***

'

2188

3124

1608

2026

" T ‘ '1383 1480

1897

2748

” *** ■■ 1271

"1452

"2491

1337

1738

2496

***

w

*•*

'

1625 “ 2725

'1091 1 3 n - “ 2156 ' 1181

1547

••• i z r *** 1008

1320

1124 1 5 1 6

iT T ' "747" 811

902

*** ■~ 1 5 T *** 574

'"631

***

2182

1049 718

'

1806

1550 1366

879" 864

'

416 441

473 519

364 385

593

"205 " 225“

581

213

235

413

509

450

495

175 181

198

209 194

138 143

146 154

145

502"

340

408

319

368

393

728

252

291

239

268

275

189

161

CRC Handbook of Sample Size Guidelinesfor Clinical Trials

558

TABLE 5: ALPHA= 0.025 POWER= 0.6 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 400

DEL=.05

DEL=.10

1 .0 .75

.50 .25

.00 BIN

0 .0 5 ' *** • **

477" 480

484 490

502

0 .1

673

FACT=

0 .1 5 0 .2

0.27 0.3 0 .3 5 0 .4

0.45 0 .5

••• *** ••• ***

0 .6 5 0 .7 0 .7 $ 0 .8 0 .6 5 0 .9

.00 BIN

1 .0 .75

DEL=.25

.50 .25

.0 0 BIN

1 .0 75

.50 .25

.0 0 BIN

1 .0 .75

.50 .25

.00 BIN

173 174

175

864

177

178 275

892 915

947

279

1366

282

286 292

299 393

1248 1293

1418 1806

368 374

382 393

1452 ' 1535

1829 2182

440 449

880

120 1226 1501

1607

102 102

103

104 145

72 72

73 73

73 93

56 56

56 57

57 65

103

151

15T"

153

156

159 194

101 101

102 103

104 118

74 75

75 76

76 80

409 495

192 195

198 202

207 236

ITT” 125

126 128

130 140

89 90

90 91

92 93

462

507 581

225 229

234 240

248 271

142 144

146 149

152

479

157

100 ~T03 " 101 104

105 103

"

*** *•*

1674

1751

2169“

493

524

591

1703

1854

2496

506

550

652

250 256

263 271

282 299

156 159

162 165

171

109 110

112 114

116 110

*** ***

1800 1835

1899 2034

2469 2748

531

570 603

659 707

268 275

284 295

309 320

166 169

173

548

177

163 181

114 116

118 120

123 115

••• ***

i8 6 0 1906

1986 2154

2725 2936

554 574

401 642

710

260 288

299

746

311

328 334

172 176

180 185

192 187

118 120

122 124

127 118

••• ***

1865 1922

2020 2220

2894 3062

564 587

619 665

285 294

304 " 340

174

118

320

341

178

183 189

196

770

189

121

123 126

129 118

*** • ••

1526“ TUID

2999 '

543 588

778

284 294

307 " 344

3124

623 674

762

1895

323

341

173 178

183 189

197 187

117 119

122 125

126 115

3034 — 3124

' 616 669

762 770

279 289

302 318

341 334

169 173

179 185

193

113

116

12T

579

181

115

121

110

107 109

111 114

117 103

•••

0 .5 5 0 .4

.50 .25

DEI=.20

REQUIRED NUMBER OF PATIENTS

PCONT=***

*** ***

1 .0 .75

DEL=.15

2237

1752” 1962

552

745

170

1832

2212

1453 1742

3000 3062

531 559

597 652

746 746

268 278

291 “ 379 ...... 307 320

161 165

171 177

164

2148

1683

171

••• • ••

1779 2051

2896 2936

503 531

568 621

712 707

253 263

275 290

311 299

i5 o 154

159 165

171

1631

157

98 100

103 105

108 93

•••

1404

1652

2729

661 652

232 241

266

284 271

136 140

149

155 ' 140

88 90

91

2748

526 578

144

1922

466 493

252

1503

93

96 80

*** ***

1262 1360

1505 1761

2491 2496

422 446

476 523

593

207 215

224 236

250 236

119 122

125 129

133 118

7 5 '"

581

78 79

81 65

••• • »*

lirr

1337

369 390

190 '

209

453

509 495

174

1568

2144 2182

417

1202

183

199

194

98 100

103 105

108 93

*** **»

946'

1143

1813" ...... 304

343

1027

1337

1806

323

370

408 393

139 144

149 154

145

*** **•

762 826

917 1062

1380 1366

231 241

254

291

270

275

•••

542 584

640 725

879 864

*•*

153?

141

76

559

TABLE 5: ALPHA= 0.025 POWER= 0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 425

DEL=.05 FACT=

DEL=.10

93

56 56

56 57

65

101 102

102 103

104 118

206 236

' ” 124

127 128

235 240

248 271

142 144

T47

152

155

153

156

159 194

198 202

178

174

177

275

'"875

894

967 ■■'

260

917

1366

283

287 292

299

882

393

193 195

REQUIRED NUMBER OF PATIENTS 102 102

5?

74"

75

?6

75

76

80

140

89 90

91 91

93 93

149

152 157

ld l 102

'103 104

105 103

130

'

1216" '"125T~ 1418

370

363

4tJ9

1297

375

394

495

442 451

' 463 481

507 581

497 509

527 552

591 652

251 257

263 272

282 299

156 159

162 166

170 171

109 110

112 114

116 110

1807 ' 1910" 2463” 1844 2047 2748

53"5 551

574 606

659 707

270" 277

265 295

3o9 320

167 170

173 178

183 181

115 116

116 120

123 115

***

1869 1917

2O0O 2170

2725 2936

556 578

605 645

710 746

281 289

299 312

328 334

173 176

181 186

192 187

118 120

122 125

127 118

***

1876 1936

2037 2238

2896 ' 3062

569 592

' 623 668

745 770

287 296

30? 321

340 341

175 179

184 190

196 189

119 121

123 126

129 118

56*8 594

628 678

762 778

286 297

308 324

344 341

178

183 189

1 97 187

ll7 119

122 ' 128 115 125

281" 291

304 319

341 334

170 174

179 185

192 181

113 116

118 121

124 110

0.15 "*** ***

0 .4 5

73

73

72 72

175

864

0 .4

73

104 145

173

491

0 .3 5

.00 BIN

103 103

502—

0 .3

.50 .25

.50 . 25

484

0 .2 5

1 .0 .75

1 .0 75

0.05 "»**"' "” 478 *** 480

PCONT=***

0 .2

.00 BIN

.0 0 BIN

.0 0 BIN

.0 0 BIN

***

.50 .25

.50 .25

.50 .25

0. i

1 .0 .75

1 .0 .75

1 .0 .7 5

DEL=.2 5

DEL=.20

DEL=.15

- w ***

1229

1806

14ff" v r t m 1593 1634 2417

0.2

*** *•*

1929 1936

1952 ' 2448 1999 2922

544 " 557"' 679 596 778 552

0.25

*** ***

2165 2177

2199' 2930 2265 3342

$99 611

531"' "791 671 873

300 308

320 340

377 400

189 194

201 211

227 229

133 137

141 147

15S 148

0.3

••• ***

2303 2318

2349 ' 3331" 2438 3678

637 647

673 725

882 946

315 326

341 365

413 428

197 204

212 225

245 242

138 142

148 155

164 154

0.35

m ' 2347” 2410' 3648 • ** 2370 2526 3930

645 664

695' 758

950 999

322 335

352 381

439 446

2bl 209

219 233

257 250

140 145

151 159

170 158

***

2317- 2375' 7 8 7 r 2343 2543 4098

641 664

■ 322 7 0 2 " 997 ■ 336 774 1030

201 209

221 237

263 253

140 145

152 160

173 158

0.45

*** **•

2218 2252

2318 ' 4014 2500 4182

316 " '3S3“ 461 389 456 332

198 206

218 235

263 250

137 142

149 158

171 154

0.5

*** ***

2068 2111

2194 2410

345 382

456 446

19i 200

212 229

258 242

132 137

144 153

166 148

0.55

«'*" ' "M‘ *** 1935

2035" "4015 2285 4098

561 593

270 307

331 367

441 428

181 190

202 219

246 229

124 129

136 145

157 138

0.4

*** • **

1674 1740

1859 ' 3879 2133 3930

51"9" " 505" " 952' 946 553 696

271 287

311 346

416 400

168 177

189 204

229 211

115 119

126 133

144 124

0.65

*** **♦

1461 1538

1671 ‘3557" 1960 3678

T73— 508

558 647

884" 873

241““255“ 380 319 362 264

153 161

171 185

207 187

103 107

112 119

128 107

0.7

♦ **

1255 1339

1480 ‘33 ST1770 3342

423 456

504 585

794 ' ' 778

2Zl 235

255 284

335 316

134 141

150 162

179 158

89 92

96 101

108 87

0.75

*** «*"'

1060 1147

1285 1562

'

2927 2922

368 398

441 512

681 662

1*0 202

218 241

280 260

112 118

124 133

145 124

875 957

1085 1333

'

2431 2417

30 T 332

367 424

546 526

153“ 162

' 174

215 194

1847 1829

237 255

280 " 1 389 317 368

0.4

0.8 0.65 0.9

*** *** *** ***

57* 764 499 549

'

4061 4182

871 1073 625 760

'

1T77" 1156

' 573— 651

694 775

596 " H i 761 626 544 735

"

1020 1041

1020" " 303“ 1030 322 ' 998'"" 999

"

357 ' 455" " 389 456

190

627

TABLE 6: ALPHA= 0.025 POWER= 0.9 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 170

DEL*.OS FACT=

1 .0 .75

.50 .25

D E L = .10 1 .0 .75

.00 BIN

1 .0 .75

DEL=.2S

.50 .25

.0 0 BIN

1 .0 75

.50 .25

.0 0 BIN

1 .0 .75

.50 .25

.00 BIN

67T 1156

225 226

229 232

239 368

133 134

135 137

139 194

94 95

96 97

98 124

73 74

74 75

76 87

1158 1177

1575 1829

“757 361

332 377

400 526

193 195

199 204

212 260

129 130

133 135

139 158

96 97

98 100

102 107

*** —1589“ 1605 *** 1594 1638

1898 2417

464 470

480 500

548 662

"231 245

251 260

276 316

156 158

162 167

174 187

113 115

117 120

124 124

”545 554

529 599

679 778

276 283

fc92 306

331 362

176 180

185 192

203 211

155 128

131“ 135

141 138

' ' 302 310

322 341

377 400

190 195

202 212

22 1 229

134 137

i4r 147

155 148

317 328

343 367

413 428

199 205

213 226

245 242

139 143

148 155

164 154

325 337

355 383

439 446

203 210

220 234

257 250

141 146

152 " 170 160 158

203 211

222 238

263 253

141 146

152 161

173 158

”329 ' "23 4 *** 631 641

0.15

.00 BIN

DEL*.20

REQUIRED NUMBER OF PATIENTS

PCONT=***

071—

.50 .25

DEL=.15

»»*

i n r 1151

0.2 ”*** —1930' 'T755 *** 1938 2004

2778 ' 2922

0.25

*** '“ 2167 *** 2179

2930 3342

602 613

634 675

791 873

0.3

••• 1 JOS- 2354 *** 2322 2448

3331 ' 3678

635 651

677 729

682” 946

'2718 2540

3648 3930

649 668

'701 764

2705 2559

3876 4098

535 669

'708 781

997 1030

325 339

359 392

355“ 456

629 657

700 782

1020 1041

320 335

357 392

460 456

199 208

220 237

263 250

138 143

150 159

171 154

4061 4182

' “ 502 633

681 769

1020 1030

'309 325

348 385

452“ 446

19"3 202

214 231

258 " 242

133 138

145 154

166 148

0.35 '*** '—2353 *** 2375 0.4 07750.5

2203 2273

*** ***

~~7Tn~

***

—2224 “ 2331 2260 2520

2350

*** “ 2076 ' 2'209 *** 2121 2433

'401'4 ' 4182



' 950 999

'

o.sr- *** ***

—I89T 1948

2054 2311

4016 4098

567 601

651 742

998 999

293 " '5 3 7 310 370

441 428

133 192

" 204 220

246 229

125 130

137 145

157 138

0.6 ' ***

1687 1756

1879 2160

3'8T9 3930

"726 561

613 704

952 946

274 291

314 349

416 400

170 179

l9d 206

229 211

116 120

l2 6 134

144 124

*** —1372" *** 1556 *** —T 2 7 2 ' ***

1694 1988

3755 3678

4&0 515

566 654

884 873

251 267

289 321

38d 362

T55 " 173"" 207 187 163 186

104 108

113 119

128 107

1359

1503 1797

33T4 3342

430 463

511 592

794 778

224 238

258 286

335 316

136 143

151 ' 162

17b 158

89' 93

97 102

108 87

0.75

••• T 0 7 7 • •• 1166

no 8 1588

2957 2922

375 404

447 517

681 662

192 204

220 243

280 260

113 119

125 134

145 124

0.8

••• • **

*92 976

1106 1356

2431 2417

313 338

373 428

546 526

' "155 164

116 191

215 194

0.S5— *■»*" **•

708' 779

888 1091

T577 1829

' T41 259

233 320

389 368

0.9

509 560

637 772

1177 1156

0 .6 5 0.7

***

CRC Handbook of Sample Size Guidelinesfor Clinical Trials

628

TABLE 6: ALPHA* 0.025 POWER* 0.9 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP* 180

DEL=.05

D E L = .10

D E L = . 15

D E L = .20

DEL=.25

.50 .25

.00 BIN

1.0 75

.50 .25

.00 BIN

1.0 .75

.50 .25

.00 BIN

133 134

135 137

139 194

94 95

96 97

98 124

73 74

74 75

76 87

4o0 526

194 196

199 204

212 260

l2* 131

133 135

139 158

96 97

98 100

102 107

4b2 501

548 662

242 246

"252“ 261

276 316

1ST 159

142 167

174 187

113 115

117 120

123 124

1933" 1958 "233B“ ' 1940 2010 2922

547 " 571 601 556

479 778

278 284

293 307

332 362

174 180

184 193

2d3 211

126 128

132 136

141 138

0.25- ***

"2170“ 2707 "7730"" " 2182 2281 3342

40 4 "' 637 678 414

791 873

303' 312

324 343

377 400

191“ 196

203 212

227 229

135 138

142 147

155 148

0.3 ~

T 3 0 9 " 23'40 "333T 2326 2459 3678

438 ' 481 654 734

882 946

319 330

345 369

413 428

200 206

21? 226

245 242

140 144

14* 155

164 154

0. 35— 5*** *•*

1 T T T 2425 2380 2553

452 472

704 749

950 999

327 340

357 386

437 "" 446

204 212

221 235

2?T 250

142 147

153 160

170 158

0.4 " *** **•

■ 23 ST-' 23T5" '387?“ " ' 450"'' 713 2356 2576 4098 787 474

997 1030

328 342

362 394

455 456

205 213

224 239

263 253

142 147

153 161

173 158

0.45

T Z T T 2533 2269 2539

.00 BIN

***

"STO631

434 642

471 1156

225 227

229 233

239 368

'« « ***

W 1152

li'5 9 1179

Y29T" 1829

358'"" 367 378 362

0 .1 5 " *** ***

T 5 9 C " 1407 1596 1641

189T" 2417

445 471

0.2

*** ***

REQUIRED NUMBER O F PATIENTS

PCONT=***

O .i

1.0 .75

.00 BIN

.50 .25

0.05—

1.0 .75

.50 .25

1.0 .75

FACT=

344'8~ 3930

"

4013“ 4182

434 663

707 789

1020 1041

323 338

340 394

461 456

201 210

222 238

263 250

139 144

151 159

171 154

0.5 ~ *** •**

2083”■"2OT "404T"" 2132 2456 4182

408 639

488 776

1020 1030

312 329

352 387

456 446

195 " 215 204 232

258 242

134 139

146 154

166 148

0.55

*** ***

W 1961

2072 ” 3017" 2335 4098

574 607

459 750

" T 9 8" 999

297 314

337 373

441 428

185 194

205 222

246 229

126 132

138 146

157 138

0.4 '

*** ***

1499 1771

1879 2187

952 946

278 294

317 352

414 400

172 181

1*2 207

22* 211

117 121

127 134

144 124

0 .4 5

*** ***

149T" 1715 'T 4 3 2 1574 2015 3678

**♦

TT8T" 1573 1378 1824

0.7

*** ***

3877“— - 533— 420 711 3930 568

33331 3342

" 3*7 522

573 661

884 873

254 270

2*2 323

380 342

156 164

174 187

207 187

105 109

114 120

128 107

436 470

518 598

794 778

227 241

260 288

335 316

137 144

152 163

179 158

90 93

*7 102

108 87

ire- ' 126 120 134

14? 124

0.75— 1 »•*

tu ^ t

1185

13-Z7' 2927"" ' "380— 453 523 1613 2922 410

681 662

195 207

222 244

2d0 260

0.8

*** **•

9CT8 993

11T5 1377

2431“ 2417

317 343

377 432

526

544

157 166

17 7 192

215 194

0.65 ' *** *»*

722 794

903"

1847“ 1829

244— 262

287 323

389 368

0.9 ' '*'** •**

z r r ~ 448 571

1108

783

1177 1156

629

TABLE 6: ALPHA= 0.025 POWER= 0.9 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 190

D£L=.05 FACT=

D E L s .10

1.0 .75

.50 .25

.00 BIN

630

632

635

643

671 1156

227

226

229 233

239 368

1149 1153

1160

1295 1829

359 362

368 378

1591

1609

1*33 1942

PCONT = •** 0.05 0.1

***

0.15

1.0 .75

.50 .25

DEL=.15 .00 BIN

1.0 .75

DEL=.20

.50 .25

.00 BIN

1.0 75

133 134

135 137

139 194

400 526

194 196

200 205

DEL=.25

.50 .25

.00 BIN

1.0 .75

.50 .25

.00 BIN

94 95

96 97

96 124

73 74

75 75

87

212 260

130 131

133 136

139 158

97

96""

98 100

102 107

REQUIRED NUMBER OF PATIENTS

1181

76

1645

2417

1696

AST

403 502

546 662

242 246

253 261

276 316

157~~ 163 159

168

174 187

113' 115

120

117

124 124

2015

1961

2446 2922

349' ' 573 558

603

679 778

279 285

294 308

331 362

177 181

186 193

70 r 211

126 129

132 136

141 138

2172 2185

2212 2288

2929 3342

"606 619

640 681

791 873

305 313

325 344

377 400

192 197

204 213

227 229

135 138

142 148

133 " 148

ff.3

2311 2329

2366 2469

3331 3678

641 657

685 738

882 946

321 332

34? 370

413 428

201 207

216 227

245 242

141 145

150 156

164 154

0.35

2361 2385

2432 2566

3648 3930

656 677

710 774

950 999

329 342

360 387

439 446

206 213

223 236

257 250

143 148

153 160

170 158

2332 2363

2424 2592

3876 4098

'654 679

719 793

997 1030

331 345

365 "' 455 ' 396 456

206 214

225 240

263 253

143 148

154 162

173 158

0.45

2237 2277

2355 2559

4014 4182

639 668

713 795

1020 1041

325 341

363 397

460 456

203 212

223 239

263 250

140 145

152 160

171 154

0.5

2092 2142

2239 2478

4061 4182

114 646

695 782

1020 1030

332

315

355 390

456 446

196 205

2l7 233

258 242

140

135

146 155

166 148

'1712' 2b89 1974 2359

4016 4098

580 614

666 757

996 999

300

340 375

44l 428

167 195

207

317

222

246 229

127 132

139 146

1'57 138

19l9

626 718

952 946

261 297

32b

416 400

174 182

193 208

229

354

211

ll7 122

126 135

144 124

560

864 873

'257

207

" 'Io r

T IT 120

1ZF

98

106 87

1597 0.2

***

0.25 "VJI

0.4

• **

0.55 0.6

2212

3879 3930

539

' reo6 1591

1736 2041

3652 3678

493 529

667

rx * ' 1104 'T543" 3334

524 604

0. 75

' "1712

F it

0. 85 0.9

273

29'4 ' 380 325 362

778

230 244

263 290

335 316

139 145

' 11i5

1396

1849

3342

' 1110

1350 1636

2927 2922

386 416

459 528

68l 662

197 209

224 246

280 260

923 T O T 1010 1398

2431 2417

322 347

382 436

546 526

156 167

176 193

215 194

248 266

290 325

389 368

' 735 • **

575

443 476

1203

0.8

"

1786

***

0.65 0 .1

473

808

920 T 6 3 7 " 1124 1829

529 581

£58 793

ll7? 1156

"

n e - 175 165 188

121

187

TO164

179 158

127 135

1'45 " 124

109

91 94

102

107

CRC Handbook of Sample Size Guidelinesfor Clinical Trials

630

TABLE 6: ALPHA= 0.025 P0WER= 0.9 EXPECTED ACCRUAL THRU MINIMUM F0LL0W-UP= 200

DEL=.05 FACT=

1.0 .75

.50 .25

D E L = .10 .00 BIN

PCONT=*** 0 5 ’^

1.0 .75

.50 .25

D E L = .15 .00 BIN

1.0 .75

.50 .25

DEL=.20 DEL=.25 .00 BIN

1.0 75

.50 .25

.00 BIN

2W 227

635 644

* * •

1150 1154

llil 1182

1295 1829

3*9 " *49 363 379

0 .1 5

• • *

1592 1598

1611 1648

1898 2417

44* 474

0 .2

* • • *

1934 1944

1944 2021

2448 2922

0 .2 5

* • • ♦

2174 2188

2216 2296

0 .3

* * • •

2314 2333

0 .3 5

* • • *

0 .4

-* 7 1 1156

230 233

239“ 368

133 134

135 1 3 9 137 194

195 197

200

205

485 1 4 * “ 504 662

243 247

5*0 560

574 606

479 778

2930 3342

608 621

743 684

2371 2479

3331 3678

643 661

2365 2390

2440 2579

3648 3930

• * • •

2337 2369

2434 2608

0 .4 5

• • • •

2243 2285

2347 2577

0 .5

-

94

95

94 97

"512 240

130 131

133 ” T*9 136 158

253' 262

276 316

157 160

T53 168

280 286

295 309

332 362

178 182

791 873

306 315

327 345

377 400

489 742

882 946

323 334

349 372

413 428

659 681

715" 779

950 999

332 344

362 389

"439 446

3876 4098

45* 684

724 798

997 1030

333 347

347 398

455 456

■ ' 1 0 8 1 '2'6 1 4 3 216 241 253

4014 4182

644 674

719 801

1020 1041

328 344

344 399

44l 456

' 105 213

* • * •

2100 “2253 ~"405I 2153 2499 4182

419 652

?01 789

1020 1030

316 335

357 392

456 446

0 .5 5

* • * •

1922 1987

2106 “ 4 015 2383 4098

564 621

573 763

998 999

303 320

343 378

441 428

0 .6

* * • *

1724 1801

1938 2237

3879 3930

544 581

534 725

952 946

284 300

323 356

416 400

0 . 65

* * • •

1520 1608

17*6 2066

36*2 3678

500 535

*87 674

884 873

260 276

297 327

380 362

0 .7

• • • •

1319 1414

1567 1874

3334 3342

448 482

530 1 9 4 610 778

232 246

245 291

0 .7 5

* • * •

1126 1221

1349 1659

2927 2922

391 422

444 533

481 662

199 211

274 247

0 .8

* • • •

938 1026

ll4 l 1418

2431 2417

327" 352

366 440

546 526

160 169

180 1 1 5 194 194

0 .8 5

* • • •

748 822

934 1140

1847 1829

2*1 269

293 328

389 368

0 .9

* * • •

536 591

668 803

3". 1

.50 .25

.00 BIN

REQUIRED NUMBER OF PATIENTS 430 632



1.0 .75

"1177 1156

400 526

'

'

"

7* 124

'1 4 74 '

'1

94 97

'174 " 187

ST ' 75

75 87

99 ' f02 107 100

"114 ' 115

11* 1 2 4 120 124

'

187 ■' ’203 194 211

127 129

132 H I ' 136 138

'

' 193 198

204 214

227 229

136 139

143 1 5 5 148 148

"

202 208

217 228

245 242

207 214

224 1 5 7 237 250

1 9 ff“ 207

"

224“ ' 243 240 250

142 '"'150 145 156 -

~m 149

144 154

154 ■ 170 161 158

'

T 4 4 1 5 5 - ' 173 149 162 158 141 146

152 1 7 1 160 154

218 234

258 242

134 ' 141

' ” 188 197

208 223

246 229

128 ' 133

139 " 157 147 138

175 184

194 208

229 211

118 123

128 135

159 1 7 5 " 167 189

7C7187

104 110

115 ■ n r 107 120

335 316

140 146

154 164

179 158

9l 94

98 102

280 260

117 122

128 135

145 ' 124

147 155

'

144 148 "

144 124

108 87

"

631

TABLE 6: ALPHA= 0.025 POWER* 0.9 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 225

DEL=.05 FACT=

.7 5

.50 .25

***

63T 633

'1 3 7 " 645

*•*

1 1 5 1 '"T I6 7 1156 1187

1.0

D E L = .10

0.1

0 .1 5 '« * «»*

0 .5 5 0.6

.00

.7 5

.50 .25

BIN

1.0

74 74

?5 75

76 87

1295“ 1829

361 365

371 381

400 526

'1 9 5 ' 198

20l 206

212

i3 o 132

' 134 136

139 158

97 98

99

260

id 2 107

~ 470' 477

488' 507

548 ' " 662

276 316

156 161

164 168

174 187

114 116

T IT 120

124 124

298— 332 311 362

179 183

168

203

194

211

128 130

133 137

171 138

206 215

227 229

137" 140

144 149

155 " 148

2 f 7 ' 245 229 242

173“ 147

'151 157

164 154

" 1594" “T 6 TS“ 189fi 1602 1657 2417 17 3 8 “ T 771 1949 2034

790

4014 4182

686

•••

21 20

22 88

4061 4182

666

656 632

1776""2177 ' 4016“ 2018

2437

4098

***

1754“" I ? 8 3 1838 2294

3930

733 815 716 803



1041 TO TIT “ 1030 999

211

33T 349

367 393

439 446

217

339 353

373 403

455 456

3>2 404 364 397

325 341

752 946

514 550

602 687

T 84 873

" ' 267' 282

462 496

545' 622

"774 778

"- - 2 3 8 " 252 204 216

307

***

1164 1262

1416 1711

29 21 2922

404 434

476 543

681 662

0 .8

**'* • **

973"" 1203 1064 1463

2431 2417

337 362

396 448

'546' 526

'

0 .8 5

*■«

777“ “” 7*8” ' 1847"

258 276

299 333

"389' 368

'

164 172

205

100

226 239

257 250

146 150

"155"" 170 162

158

211 ' 229

219

243

263 253

14 T 151

T5S' 163

173 158

46l 456

208 217

377"' 263 250 242

143 148

134 161

171 154

456 446

202 210

221

258 242

138 143

149 156

166 148

T41 148

157 138

210



236

192

211

428

200

226

246 229

13d 135

416 400

179

197"

229

120

361

187

210

211

125

13d 136

144 124

303 332

380 362

162

179 191

201

170

187

1W 111

116 121

107

' 270“ " 3 T 5 295 316

142 149

156 166

179 158

93 96

49 103

108 87

119 123

12V 136

T45 '

383

27T ■'"379“

65U 739

0 .7 5

1829

413 428

5'60 597

1356" 1115 ' 3334“ 1456 1930 3342

1175

3 53 375

327 ' ''

195 200

327 338

"798 ” " "310 ' ” 377” -

*** ***

557"" 1 7 1 " '' 1177" 825 1156 613

3flT "33 CT"“ 3'77 ' 348 318 400

" 335" 350

1020

0 .7

854

'

999

737" ""797 810 1030

'1 3 0 - 688 635 778

3879

882 946

771 _"750' "' "

2396 2621

*'** ***

' ■791 - 873

690

2259 2306

2549

650" 691

245 '""T55249 263 282' 289

118

"2349 “ 7757" 3876".......6*9 695 2386 2645 4098

2179

” 5TTT ■""17 9' " 611 778

'1 5 0 '" 698 750 668

**• • **

***

BIN

98 124

1554 "~TB r e - ' 3652“ 1648 2124 3678

0 .9

.50 .2 5

96 97

*** ” 2374““ 2458” 3 6"4S *** 2402 2610 3930

***

.00

75

91 95

• **

0 .6 5

1.0

.0 0

139 194

2571"~ 238 5 “ 3331“ 2343 2503 3678

0.5

BIN

136 137

*'*'* ***

0 .4 5

.50 .25

133 134

'613 627

***

.75

239 368

2179“ ” 2326 "7730“ 2195 2314 3342

0 .4 '

1.0

230 233

0 .2 5 " '« * ***

0 .3 5

.00

BIN

226 228

554 564

0 .3

.50 .25

671 1156

7778“ 2922

0.2

*"** • **

.75

REQUIRED NUMBER OF PATIENTS

PCONT=*** 0 .0 5

1.0

.00

BIN

D E L = .15DEL=.20 DEL=.25

235 250

200 260

“T IT " 196

194

124

128



CRC Handbook of Sample Size Guidelines for Clinical Trials

632

TABLE 6: ALPHA= 0.025 POWER= 0.9 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 250

D E L = .05 FACT=

D E L = .10

1 .0 .7 5

.50 .25

.0 0 BIN

PCONT=***

1 .0 .7 5

.50 .25

DEL=.15 DEL=.20 DEL=.25 .00 BIN

1 .0 .75

.50 .25

.0 0 BIN

1 .0 75

.50 .25

.0 0 BIN

1 .0 .7 5

.50 .25

.0 0 BIN

REQUIRED NUMBER OF PATIENTS

0 .0 5

••• *•*

632 634

638 647

671 1156

227 229

231 234

239 368

134 135

136 137

139 194

95 95

96 97

98 124

74 74

75 75

76 87

0.1

••• »•*

1153 1158

1167 1191

1295 1829

362 366

372 382

4o0 526

196 199

202 206

212 260

131 132

134 136

139 158

97 98

99 101

102 ' 107

0 .1 5

••• **•

1597 1605

1621 1665

1898 2417

472 480

491 510

548' 662

246 251

2 56 264

276 316

159 162

165 169

174 187

113' 117

119 ' 124 121 124

0 .2 " *** ***

TR2

r r r r 2449 2046 2922

'557 568

585 615

679 778

285 291

3d0 312

332 362

181 185

189 195

203 211

129 131

134 "'141 137 138

O'. 25— »** ***

'21 8 4 2202

2237 2332

2930" " 3342

5-18 633

656 697

791 873

313 321

333 350

377 400

197 202

208

216

227 229

138 141

"145' 149

155 148

0 .3

™* ***

'2329 2352

2 397 2526

3331 3678

537 676

706 758

946

33! 342

357 378

413 428

207 213

221 231

245 242

144 148

152 158

164 154

*** ***

2384 2415

2477 2639

3648 3930

676 699

735 " 950“ ' 999 799

439 446

213 220

228

240

257 250

143“ ' 152

157 163

170 158

0 .4

*** ***

2361 2402

z m r 3875 2681 4098

578" 706

748 821

157 164

172 158

0 .4 5

*** *•*

"2275 2327

2473“ 4014 2663 4182

'667 698

745 —l'ozir 1041 826

0 .5

*** **•

71740 2204

2322 2595

4051 4182

544 679

730 816

0 .5 5

«*

"1771 2049

2186 2487

4015"' 4098

612 649

0 .6 " *** **•

1783 1873

2026 2347

3879 3930

0 .6 5

*** •**

1587 1686

" *** ***

T392 1495

0 . 75

*'**' ***

1199 1300

O.fl

*** ***

1006 1099

0 .3 5

0 .7

0 .8 5 0 .9

*** •**

1954

342 " 3 7 F “ 397 354

'

3*4“ 359

37B 407

455 456

2I"4 222

231 244

263 253

1*8"' 152

340 356

377“ 408

461 456

2 ii 219

230 244

263 250

1*3“ " 1'5 5 ~ 162 150

171 154

331'" 347

369 401

456 446

205 213

224 238

258 242

140 144

150 157

166 148

702 ""998"" 999 791

316 333

355 387

441 428

195 203

214 227

246 229

132 137

142 148

157 138

573 610

664 752

952 946

297 313

334 365

416 400

162 190

199 212

229 211

122 126

131 137

144 124

18*7" 3532 2177 3678

527 564

615 699

884 873

272 288

3dd 336

380 362

153 172

is r “ 192

207 187

109 113

117 122

12& 107

1650' 3334 1981 3342

474 509

557 633

794 778

243 257

274 298

335 "" 316

145 151

158 167

179 158

94 97

100 104

id s 87

1458 1758

2927 2922

41$ 445

487 552

681 662

208 219

234 252

280 260

l2U 125

130 137

145 124

1241 1504

2431 2417

346 371

404 455

546 526

167 175

185 198

215 194

"503 883

999 1207

1847 1829

753 ' 305 282 337

389 368

T 79" 633

712 844

1177 1156

997~ 1030

1050'' 1030

' "

'

633

TABLES: ALPHA= 0.025 POWER- 0.9 EXPECTED ACCRUAL THRU MINIMUM FQLLOW-UP=: 275

D E L = .05 FACT=

D E L = .10

C.I IT.'IT 0.2'

""»** •** "*** *** -**'* *•* ***

1.0 75

.50 .25

.00 BIN

1.0 .75

.50 .25

.00 BIN

134 135

134 138

139 194

96

95

96 97

98 124

74 74

75 75

74 87

400 526

197 200

207

203

212 260

132 133

135 136

139 158

98 98

99 101

id2 107

494 512

548 662

248 252

257 265

274 316

160 162

164 169

174 187

Tl'i" 1 1 9 117

121

123 124

561 572

589 619

479 778

'

287 293

302 314

332 362

182 186

190 196

203 211

129 132

134 137

141 138

423 638

442 703

- 79! -

316 324

334 352

37 1 400

198 203

209 217

227 229

T 37"

147

873

155 148

2413 "33 3T 2548 3678

663 682

713 765

632 946

335 345

360 380

413 428

209 215

222 232

245 242

144 1 5 3 “ 158 149

164 154

3'448 3930

683 707

744 807

950 999

344 358

375 399

439 446

215 222

230 241

'277

149 153

157 163

170 158

349 363

382 410

455 456

217 224

233 246

263 253

149 153

158" 165

172 158

757 ~T02TT ----3 4 7 " ' 382“ 441 837 456 1041 361 411

2l4 222

232 245

263 250

147 151

154 163

171 154

446

208 216

224 239

257 242

142 146

151 158

144 148

3*0“" 7 7 1 428 391

198 206

214 229

246 229

134 138

143 149

157 138

71 5 “ 400

184 192

20l 213

229 211

123 127

132 137

144 124

'432

439

471

1154

227 229

231 234

239 368

fT54" 1170 1159 1195

1295 1829

363 367

374 383

1 5 9 9 " " 142 r 1608 1672

1898 2417

475 482

648

635

1944 1959

1984 2058

2247

2348

2375” 2495

***

2427

074“ ""**» »**

2418

O'. 45

1.0 .75

REQUIRED NUMBER OF PATIENTS

2 IW " •** 2209 **• ~mz~ *** • ••

.00 BIN

.00 BIN

2362

0.35

DEL=.25

.00 BIN

.50 .25

.50 .25

£T.2T ”"»** 0.3

DEL=.20

.50 .25

1.0 .75

1.0 .75

PCONT=*** O'. OS

DEL=.15

2667

'

2448 2922

2727

3342

"

2373 '"2703" "3777' " '*87 2714

715

4098

*'** ""2270 "2452“ 4014" *** 2347 2701 4182



577 709

' 758 " w r 831

1030

'

150

077“ '"***“ 7T59" 2355 7 0 4 T *00 2229 2638 4182

“ 557 ' 690

827

0T57"

'127 661

715 802

' 998

'

585 623

474 763

952 946

'

537 576

428 " 884 " 710 873

' 277' 292

312 339

380 362

167 174

183 193

207 187

lit) 114

118 122

128 107

1424 ' 1 7 0 T 7337 1532 2028 3342

' 484' 520

548 " 7 9 4 T 643 778

248 261

278 301

335 316

147 153

168

15$

178 158

95 97

loO 104

108 87

1 2 7 1 "l'flr 79 27 1336 1801 2922

' 425 455

497 " 7 8 1 560 662

" '212' 223

237“ 254

280 260

122 126

137

isr

145 124

170 177

"187“ 199

2T5' 194

« * '- 1 9 7 5

2223” 701*

**•

2078

0.4

•••

1811 '2047" m v 1906 2395 3930

0T4S

'«*"1 7 1 8 *** 1722

0.7'"

«*'' ***

0.75"

*** *•*

0.8

000

o :fl5" *** ***

ff79“ - » t

2534

4098

18 ? r 3752 2226 3478

1037' 1274 1131 1540

273r 2417

“B"50 ” 1027 " 1847 909 1235 1829 1*5 651

' 731' 862

1177

1156

157 379

742

1020 1030

250

142

999

412 " 534" 461 526

1 7 T - 310 ' 3 8 9 " 288 341 368

" '" 3 3 7 ' 374 353

' "322" 338

405

— 302" ' '339' 369 318

774-----

"

CRC Handbook of Sample Size Guidelinesfor Clinical Trials

634

TABLE 6: ALPHA= 0.025 POWER* 0.9 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP* 300

DEL-.05 FACT=

D E L = .10

1.0 .75

.50 .25

.00 BIN

• **

633 635

"CTO" 649

671 1156

228 229

232 235

239 368

134 135

***

IT55- 1172 1161 1199

1295 1829

365 369

375 384

400 526

193 ' 203 207 200

0.15

*»* ***

1601 1611

1630 1680

1898 2417

477 484

496 514

544 662

24* 253

0.2

*** ***

1949" 1964

1993 2069

2448 2922

564 576

593 622

0.25

*** ““2T9 T *** 2216

2257 2364

7727 3342

2343 2371

2427 2569

3331 3678

668 689

PCONT=*** 0.05 O.i

0.3

1.0 .75

.50 .25

D E L * . 15 .00 BIN

1.0 .75

DEL*.20

DEL=.25

.50 .25

.00 BIN

1.0 75

.50 .25

.00 BIN

1.0 .75

.50 .25

.00 BIN

136 138

139 194

95 96

96 97

98 124

74 75

~~n' 75

75 87

260

132 133

135 137

139 158

98 99

loo 101

102 107

259 266

276 316

161 163

156 170

174 187

ll6 118

119 121

174 124

679 778

287“ 303 315 295

331 362

183 187

191 196

2d3 211

l3o 132

135 137

141 138

791" 873

318 327

338 353

371 400

200 204

210 217

227 229

140 143

146 150

154 148

720 771

882 946

336 349

363 382

4l3 428

211 217

224 232

245 242

147 150

154 159

164 154

150 154

138 ' 170 164 158

REQUIRED NUMBER OF PATIENTS

‘ 527 " 667 707 643

— 712

0.35

*** *•*

’2402“ 2512 2440 2693

3648 3930

690 715

752 815

750 999

349 362

379 402

439 446

217 224

232 242

2K 250

0.4

**• ***

2386 2434

2525 2746

3876 4098

6*5 724

767 839

997 1030

353 367

386 413

455 456

21* 226

235 247

263 253

151 155

159 165

172 158

0 .4 5

* « — 2305“ 2479 «•* 2367 2737

4014 4182

6&6 719

767 846

1020 1041

350 366

386 415

460 456

217 ' 234 224 246

263 250

148 152

157 163

171 154

0.5

••• • **

"2179“ "7386 2253 2679

m r 4182

666 701

753 837

1020 1030

341 357

379 408

456 446

210 218

226 241

258 242

143 147

152 158

166 148

0 .5 5

*** ■' 2 D i r "2758 *•* 2106 2577

4016 4098

635 673

726 812

998 999

364 394

4"4I 428

200 208

218 230

246 229

1 J5 '~ 139

144 150

157 138

0.6

r« " i 6 3 r 2104 •** 1938 2440

3879 3930

$96 634

688 773

952 946

307 323

343 372

415 400

187 194

203 214

229 211

125 128

133 138

144 124

0 .6 5

*** ***

1648 ‘ TWO 1756 2270

3652 3678

550 587

638 719

864 873

282 297

316 341

380 362

170 176

184 194

207 187

112 115

ll8 123

128 107

0.7

*** " 14 5 6 “ 1740 «•* 1567 2071

m r 3342

496 530

578 651

794' 778

2 57 265

281 303

33$ 316

149 154

161 169

178 158

96 98

101 104

108 87

0 .7 5

*** ■ ■1262" 1534 *** 1369 1840

7927 2922

434 464

505 567

681 662

2 15"' 226

239 256

280 260

123 ' 132 127 138

145 124

0.8

«* *•*

1064“ 1309 1161 1574

2431 2417

362 386

419 466

546 526

172 180

189 200

2 l$ 194

0 .8 5

*** **•

854 934

T55 3 1260

1847 1829

276 293

314 344

389 368

■613 668

748 877

1177 1156

0.9

' ' 327“ 343

'

635

TABLE 6: ALPHA= 0.025 P0WER= 0.9 EXPECTED ACCRUAL THRU MINIMUM F0LL0W-UP= 325

DEI*.05 FACT=

DEL=.10

1.0 .75

.50 .25

.00 BIN

PCONT=***

1.0 .75

.50 .25

DEI*.IS .00 BIN

1.0 .75

DEI*.20

.50 .25

.00 BIN

1.0 75

.50 .25

DEI*.25 .00 BIN

1.0 .75

.50 .25

.00 BIN

48 124

74 75

75 75

76 87

160 101

162 107

REQUIRED NUMBER OF PATIENTS

0.05

**♦ ***

£34 636

£41 650

£71 1156

224 230

232 235

239 368

135 135

136 138

139 144

0.1

•••

1157 1163

1175 1202

1245 1824

366 370

374 385

400 526

144 201

204 207

212 260

132 134

135 137

134 158

98 99

0" 15

*** **«

T£04" 1635 1615 1686

1848 2417

474 487

498 516

548 662

250 254

2£d 267

276 316

1£1 164

l£7 170

T74" 187

117 118

0.2

••• ***

1453 196?

2O0O 2080

2448 2422

'3£7 " 597 574 625

£79 778

291 247

305 316

331 362

104 188

142 147

203 211

131 133

n r 138

n r 138

0.25

•••

3200 2223

2267 2379

2430 3342

£32 648

£72 712

"77r 873

321 324

3-40 355

377 400

201 206

2TC“ 227 218 224

l4l 144

147 150

13 r " 148

0.3

*** **•

2350 2381

2440 2589

3331 3678

£74 645

726 777

882 946

341 352

3£5 385

413 428

213 218

225 233

245 242

0.35

••• *•*

2 4l2 2452

2530 2718

3£48 3430

£97 722

7£0 821

450 999

353 365

382 404

439 446

214 225

233 243

'257" " 250

"151" 155

154 164

170 158

0.4

••• *«*

2348 2450

254? 2775

387£ 4048

703 733

776 847

496 ' ' 357 " 390 371 1030 415

2'£3 253

"

152" 156

1£0 166

172 158

***

2322 2387

2505 2772

4014 4182

£95 728

777 855

1020 1041

"355 370

39d 417

4£d 456

213" 250

'

149 153

158 164

171 154

£7£ 711

7 £3 846

1025 1030

346 362

“352 411

45£ 446

235“ 258 242 242

144 148

153“ 1££ 154 148

0.4S

' 95' " 4£ 47 46

" "221" 237 228 248

"455' 456

214 226

236 247

' 125"' 123 121 124

" ' 178 ' '135" 154 151

11T 154

O T T "***

2148 “271T' 45"£T' 2277 2716 4182

0.55

*** *»*

2o4l 2134

2241 2618

4016 4048

£4£ 683

73£ 821

998 999

331 348

3£8 347

n r 428

203 210

220 231

24£ 224

136 140

145" 150

157 138

0.£

*** •**

T8S4 1968

2140 2481

3879 3930

*67' 645

£98 782

952 946

312 327

347 374

416 400

18? ~ 265 146 216

229 211

126 129

133 138

177" 124

0.65

••• *•*

1677 1784

1?£7 2312

3652 3678

5£0 597

£48 728

684 873

28£ 301

319 344

380 362

172 178

186 145

207 187

112 116

119 123

120 107

•**

1485 1544

1777 2111

3334 3342

5o£ 540

587 658

"774"" 778

' '253 268

284 305

"315 316

"T55” 162 164 156

"179" 158

9£ 94

161 104

108 87

***

1241 1401

15£8 1877

2427 " 2922

442 472

513 573

£8l 662

2l4 224

242 258

280 260

T 2 5 “ 133 124 138

" n r 124

**•

1040 1140

1339 1604

2431 2417

364 343

425 470

"573" 526

174 182

*«*

87£ 457

1077 1284

1847 1829

281 247

318 346

389 368

**• • **

£28 684

7£3 841

1177' 1156

0.7 0.75 0.8 0.85 0.9

'"195“ 2l5 201 144

'

”7 1 3 “ 220

CRC Handbook of Sample Size Guidelinesfor Clinical Trials

636

TABLE 6: ALPHA* 0.025 POWER= 0.9 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 350

DE L =.05 FACT=

D E L = .10DEL=.15 DEL=.20 D E L = .2 5

1.0 .75

.50 .25

.00 BIN

437 637

642 651

471 1156

0.1 ~



***

lis r 1165

1177 1206

1295"" 1829

.50 .25

.00 BIN

1.0 .75

.50 .25

.00 BIN

1.0 .75

.50 .25

.00 BIN

96 96

97 97

98 124

74 75

75 75

76 87

' 133 134

135 137

139 158

98 99

100 101

102 107

ll7 118

120 122

124 124

.50 .25

.00 BIN

1.0 75

135 136

137 138

139 194

199 201

204 208

212 260

251 " 260 255 267

T74 316

' ' 1 * 2 “ 147 164 170

REQUIRED NUMBER OF PATIENTS

POONT=*** 0.05

1.0 .75

229 230

232 235

239 368

'347 " "577" "400" 371 386 526

174~ " 187

0.15""*** " 1 * 04“ 1*70 "1798“ " *•* 1618 1693 2417

481 489

5oo 518

"5'7B" 662

**’ " T 7 5 7 " “ 20U7 "2448“ 1974 2090 2922

570 582

600 628

479 778

292 298

3d4 317

332 362

185“ 188

192 197

203 211

131 133

135 138

141 138

554 652

477 716

791 873

323 331

342 356

377 400

202 207

212 218

227 229

172 144

147 150

155 148

731 782

882" 946

344 354

368 386

413 428

214 219

226 234

245 242

149 152

155 159

164 154

950 999

356 369

384 406

439 446

221 227

235 244

257 250

152 156

140 165

170 158

0.2

0.25 "***■ ***

2205“ "2 2 7 7 "2930 2230 2394 3342

0.3

TTi_

2 3 5 7 “ 2*53 “33337" 2390 2608 3678

’ "577 700

0.35

***

2421 " 257* “5448“ 2465 2741 3930

’ 707"" "747 827 729

0.4

* " “ 2410" “ 25*8“ '"3775“ ••• 2465 2803 4098

711 741

784 854

997 1030

341 375

393“ 418

455 456

223 230

238 249

263 253

153 157

16l 166

173 158

0.45

m * “ '***“ 2337“ 2530 “ **• 2406 2804 4182

70"4 737

'"735 862

1020' 1041

359 374

393“' 460 456 420

221 228

237 248

263 250

150 154

159 164

17l 154

4T54I " 4182

485 721

772 854

1020 1030

350"’ 384 414 366

456 446

2 l5 222

231 243

258 242

T45 149

154 159

166 148

205 212

232

221

244 229

137 141

151

145

157 138

0.5

*** " 2 2 1 7 “ "2475 *** 2300 2752

0.55' ***

20*3 ' 2723 ~70f5“ 2160 2655 4098

455 693

744 830

"998 999

'5 7 5 351

372 399

741 428

0.4 '" *** **»

1789 ” 2173 "5779“ 1998 2520 3930

417"

708 790

952

316 331

35d 377

416 400

191 198

206 216

229 211

127 130

134 139

144

18 7 "

196

207 187

ll3 116

120 123

128 107

157

143 170

178

97 99

102 105

108 87

124"

134

145 124

655

946

"

0.45

***" **•

1704"“2002 "5*52“ 1820 2351 3678

570 607

457 735

"8W 873

290 304

322 346

380 362

173 180

0.7

***

'73347 is r r i m 1630 2148 3342

514 549

665

595

794 778

259 271

287 307

335 316

"152

T318""1 * 0 T ' "2927" 1430

1910

" 450

520 579

662

481

22l 231

244 259

280 260

129

***" **»

mr

"15*7 "2431" 1633 2417

' 375

'430 474

545"

1216

526

176 183

192 202

215 194

*»*

894 979

1305

322

' 387"

*»•

443 699

0.75 0.8 0.85 0.9

•* •

2922

1099 T847“ 1829

'777 " 1177 903

1156

480

399

285“

301

349

368

139

158

'

124

637

TABLE 6: ALPHA* 0.025 POWER* 0.9 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP* 375

DEL=.05 FACT=

DEL*.10 1.0 .75

.50 .25

DEL*.15 .00 BIN

1.0 .75

.50 .25

.00 BIN

0.05

*** " 65? **• 638

643 652

671 1156

229 231

233 235

239 368

O.i"

*** ' IT60 "1ITT0 *** 1167 1209

127? 1829

368 372

376 387

'"400' 526

0 . IS

*** *•*

1609 1621

1698 2417

483 491

502 519

“548" ' 662

-?73 585

603 630

"679" 778

DEL*.20

.50 .25

.00 BIN

1.0 75

135 136

137 138

139 194

96 96

200 202

2T53 208

212 260

252 256

261 268

' 294 300

1.0 .75

.50 .25

DEL*.25 .00 BIN

1.0 .75

.50 .25

.00 BIN

98 124

74 75

7$ 75

76 87

REQUIRED NUMBER OF PATIENTS

PCONT=***

1644 1699

' 77 97

133 134

136 137

139 158

99 99

100 101

102 107

276 316

163 165

167 170

174 187

117 118

120 122

124 124

' 307 317

332 362

166 ' 193 189 198

203 211

132 133

136 138

HI" 138

" 32?“ 343 358 333

377 400

203 208

213 219

227 229

142 145

148 " 153 151 148

"

072--- w * ' 1760 "2014 *** 1979 2100

244TT' 2922

0.25

*'** ■m o -"2286 *** 2237 2407

2930 ' " 640 " 680 ~ 1 7 T ' 719 3342 656 873

0.3

••• *•*

2364 2399

2466 2626

3331 3678

684 706

737 786

682 946

346 " 3 7 0 357 388

413" 428

21$ 221

227 235

245 242

149 152

156 160

164 154

0.35

••• " 2431 **• 2477

2563 2764

3648 3930

709 735

773 833

9$0 999

359 " 387 408 371

457" 446

222 228

236 245

257 250

153 156

160 165

170 158

" m v ~258"8 2480 2830

3876 4098

"718" 748

791 860

997 1030

364 378

395 419

45$ 456

239 250

263 253

154 157

162 167

172 158

0 . 4 ” '«* *** 0.4? 0.5' D7-5T

" 225" 231

2352 2425

2?T4 2834

401T 4182

712 745

793 869

1020 1041

362 377

396 422

460" 456

223 230

236 249

263 250

152 155

160 165

171 154

*** ' 2235 *•* 2322

2472 2785

4061 4182

693 730

781 861

lo20 1030

' 354 369

389 416

456 446

216 224

233 243

2 5 7 '' 242

146 150

154 160

166 148

40TT 4098

JZA 702

755 837

798" 999

" 340 355

37$ 401

44l 428

207 214

222 233

246 229

138 142

146 151

157 138

128 131

135 139

144 124

Tl'4"~ l2d 117 124

128 107

102 105

108 87

***

***

"■"203?""2373 2186 2691

0.6'

*** “1714 "22C6 '3877 2026 2557 3930

626 664

717 797

952 946

319 334

354 379

415 400

193 199

207 217

229 211

0.65

••• ***

1731 1849

2035 2387

36?2 3678

579 615

666 742

684 873

' 294 308

325 348

360 362

17$ 181

188 196

207 187

0.7"

«* **•

1541 1660

1643 2182

3334 3342

523 557

603 671

794 778

262 274

289 309

335 316

i$3 158

164 170

178 158

134? 1458

IS31 1941

2727 ' 2922

4?7 '- 527 487 584

681 662

224 234

24$ 260

260 260

127 130

134 139

145' 124

■ _ 1139 1241

1393 1659

243T 2417

331 404

" 193"

215 194

** ** * -■71*" "1120 * 999 1325 * * * _ TO” 79T **»

1 847 1829

289 305

o:7?" O.flT 0.85 0.9

'

-* »*-' *•*

712

915

1 177 1156

■ ' 435 478

32? 351

"54r 526 389 368

178 185

203

"

*8 100

CRC Handbook of Sample Size Guidelinesfor Clinical Trials

638

TABLE 6: ALPHA= 0.025 POWER= 0.9 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 400

DEL=.05 FACT=

D E L = .10

1.0 .75

.50 .25

.00 BIN

1.0 .75

.50 .25

D E L = .15 .00 BIN

1.0 .75

DEL=.20

.50 .25

.00 BIN

1.0 75

DEI=.25

.50 .25

.00 BIN

1.0 .75

.50 .25

.00 BIN

REQUIRED NUMBER OF PATIENTS

PCONT=*** 0 .0 5

*'** **»

635 638

6?r 653

*71 1156

230" 231

233 235

239 368

135 136

137 138

139 194

96 96

97 97

98 124

75 75

?5 76

76 87

0.1

*'** **•

1161 1169

11*2" 1295 1212 1829

"369 373

379 387

400 526

200 202

205 208

212 260

133 134

136 137

139 158

99 99

1O0 101

102 107

*»*

1611 1624

1648" 1705

1898 2417

485 493

504 521

54B 662

253 257

262 268

276 316

163 165

168 171

1^4 187

118 119

120 122

124 124

576— 588

6o6 633

679 778

295 301

309 318

332 362

187 190

194 198

203 211

132 134

136 138

141 138

' 684 “ 791” 722 873

327 335

345 359

3?7 400

204 209

214 219

227 229

143 145

140 151

155 148

0 .1 5 0.2 0 .2 5 0 .3 0 .3 5 " ' 0 .4 " " 0 .4 5 0.5" o .s r

' m r 1984

0.7 0.75 0.8 0 .8 5 0 .9

'

2 21 * “ 2296

2243

2421

2930 3342

643 660

***“ **»

2371 2409

2779 2643

3331 3678

689 711

742 790

882" 946

349 359

372 389

413 428

2l7 222

228 235

245 242

15b 153

156 160

164 154

***

2740 2489

2579 2785

3'64B~~ 3930

715— 779 838 741

*50“ 999

362 374

38 9 _ 439 446 410

224 230

237 246

257 250

154 157

16l 165

170 158

•**

" 2734 2496

2608 2855

3076 4098

724 755

798 866

997“ " 1030

367 381

398 421

455 456

226 233

241 250

263 253

155 158

162 167

173 158

*'** ***

2367 2443

257T 2863

4014 4182

719 753

’ 801 876

1020 1041

366 380

3^9 424

461 456

224 231

240 250

263 250

152 156

160 165

171 154

• ••

2253' 2344

2799~ 7 W 2817 4182

701 738

789 ”1023" 1030 868

“357” 373

392 418

456 446

218 225

234 244

258 242

141 151

155 160

166 148

« * -" ***

2 ro s 2211

2333 2724

701* 4098

673 711

763 844

998 999

' 343" 358

378 403

44l 428

208 215

223 234

246 229

139 143

147 151

157 138

m r~ 2053

2237 2591

3879 3930

634 672

725 804

952 946

323 338

356 381

416 400

194 201

208 218

229 211

128 132

13$ 139

144 124

***

***'

1756 1877

2066 2420

3652 3678

587 624

' 674 748

884 " 873

297 311

“3 2 7 “ 380 362 350

176 182

189 197

207 187

115 117

120 124

128 107

*** •**

1567 1688

1074 2214

3334 3342

"" 530— 610 677 564

794 778

265 277

291 310

335 316

154' 159

164 171

17^ 158

98 100

102 105

108 87

•••

1369 1485

1 5 5 7 ' 2927 1970 2922

464 494

533 588

681 662

226 236

247 261

200 260

128 131

135 140

14$ 124

*«"" **•

1161 1265

1418 1683

'2431 2417

'

386— 410

440 481

37* 526

180 186

194 204

215 '" 194

«*•

934 '1170' 1018 1343

1847 1829

-

*** *»•

668 725

1177“ 1156

*• •

0.6 0 .6 5

2021 ' 2448 2109 2922

803 925

2 9 3 " " 328 ' “389 368 308 353

639

TABLE 6: ALPHA= 0.025 POWER= 0.9 EXPECTED ACCRUAL THRU MINIMUM F0LL0W-UP= 425

D E L = .05 FACT=

D E L = .10

1.0 .75

.50 .25

.00 BIN

1.0 .75

.50 .25

DEL=.15 .00 BIN

1.0 .75

D E L = .20

.50 .25

.00 BIN

1.0 75

DEL=.2S

.50 .25

.00 BIN

1.0 .75

.50 .25

.00 BIN

REQUIRED NUMBER OF PATIENTS

PCONT=*# * 0 .0 5

*«" ***

53'5 639

544“ 654

57i 1156

230 231

233 236

239 368

135 136

137 138

139 194

96 96

97 97

98 124

75 75

75 76

76 87

b.i

*** ***

1153 1171

1185 1215

1295 1829

370 374

380 388

400 526

201 203

205 208

2l2 260

133 135

135 137

139 158

99 99

100 101

lo2 107

0.15' m *•*

1514 1627

1552“ 1898 1710 2417

485 494

505 522

548 662

254 258

263 ' 275 " 316 269

154 166

158 171

174 187

118 119

120 122

124 124

0.2

*•* *#*

1958 1988

2027" 2448 2118 2922

578' 591

6b8 635

679 778

297 302

309 319

332 362

187 190

"174 198

203 211

133 134

135 138

141 138

0 .2 5

*** **»

2250

2305 2433

588 ' 791 725 873

328 336

345 359

377 400

205 209

21 4 "' '227 220 229

' 144 146

14* 151

155 " 148

0 . 1 .. 0.35 073 0.45 0/5 '

***

~ 2 T ? r 2491 2418 2660

*** ***

2449 2501

000

' i n r 2511

2594 2805

"' 2271 2365

164 154

161 166

170 158

253 253

153 " 153 159 167

172 158

241 251

253 250

153 157

171 154

220 227

235 245

257 242

148 152

3'80 ’ 441 428 405

210 217

224 234

246 229

140 143

147 152

155 138

415 400

195 202

209 218

229 211

129 132

135 139

144 124

118

121 124

128 107

99 101

io3 105

108 87

593“ 745 715 794

882 946

3 T T ""374" 361 390

4l3 428

218 223

229 236

3648 3930

720" ' 784 747 842

731 999

365 376

439 446

225 231

238 '"2 * 7 246 250

977" 1030

370 '' 400 ' 455 456 384 423

228 234

242 251

TO20" 1041

"359 ' "40T 383 426

460 456

226 233

' 455 " 446

"2524“ 4051 2846 4182

m ' 1 9 * 1 '' 2255 *•* 2079 2623

151 " 155 154 160

3331" " 3678

* * * '“ 2 382“ 2500“ 1 0 1 4 “ *** 2461 2890 4182 *00

'547“ 664

2527“ "3875" " " 7 3 r 2879 4098 761

0. 55" m *T* ""2127" 2410 000 2235 2756 0.5

2930 3342

804 871

725" " 808 760 881 709" " 795 745 874

"'1020 ■ 1030

351 376

"4015" " '5 8 1 " 4098 719

771 850

998 999

' ' 345 361

■3879" " 3930

732 810

952 946

"" 325 341

54r 680

391 411

394 420

359 382

0.65

■1781 "209*" "3 SIT " "595— 631 1904 2452 3678

581 754

884 873

1 "300 " 3 3 0 " 313 351

380 362

0 .7

' 1591" 1903" "333 4" 1715 2244 3342

6 l6 682

794 778

261 ' 2 9 3 “ 279 311

335 316

470" ' 538 500 592

581 662

228 " 2 4 7 ” 280 260 238 262

2431" " ' 3 9 r ~ 444 484 2417 414

545 526

... 181 '" 195 ' 2 l5 194 188 204

0.75

«"'■' 1393 1*B 5~ 2927" *** 1510 1997 2922

0 .8

***

0.85

*«'■" 952 ' 1158 1036 1360

1847" 1829

0.9

*** ***

1177 1156

1183 1287

580 736

1441 1706

814 935

538" 571

294 311

330 355

389 368

-

245 242

178 183

l9o 197

207 187

155 160

155 171

179 158

128 132

135 140

145" " 124

“ 155' 158

_ r i .5„-

161 166

' 155 ' 166 148 160

CRC Handbook of Sample She Guidelinesfor Clinical Trials

640

TABLE 6: ALPHA* 0.025 POWER* 0.9 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP* 450

D E L = .OS FACT=

D E L - .10

1.0 .75

.50 .25

.00 BIN

PCONT=***

1.0 .75

.50 .25

D E L * . 15 .00 BIN

1.0 .75

DEL=.20

DEL=.25

.50 .25

.00 BIN

1.0 75

.50 .25

.00 BIN

1.0 .75

.50 .25

.00 BIN

REQUIRED NUMBER OF PATIENTS

0.05

*** **•

636 640

645 654

671 1156

230 231

234 236

239 368

136 136

137 138

13* 194

96 96

97 97

98 124

75 75

75 75

0.1

••• • ••

1164 1172

n r r 1217

1295 1829

'"371 375

381 388

400 526

201 203

206 208

212 260

134 135

13'6 138

139 158

99 100

10O 101

io2 107

0.15

••• • *»

1616 1630

1'657 1715

2417

1 8*8

488 496

507 523

546 662

7F5~~'" 263"" 259 269

276 316

1"64 166

" 1'67‘ 171

174 187

118 119

120 122

123 124

0.2

«*

1971 1993

2034 2126

2448 2922

" Tffl " 611 593 636

679 778

298 303

311 320

332 362

186 191

194 199

203 211

133 135

136 139

141 138

0.25

*** *•*

” 2726 2257

2314 2445

3342

'650 667

691 728

"791 873

3T 0 " 338

3*3" 360

378 400

206 210

215 220

277 229

14* 146

149 151

154 148

0 .3

*** ***

“ 73'85 2427

2503 2675

3331 3678

” 698 720

750 798

~8B2 946

353 363

375 391

414 428

219 224

229 236

245 242

151 154

157 160

164 154

0.35'

*** • *»

2458 2512

2610 2824

3648 3930

726 752

789 847

950 999

367 379

393 412

43* 446

226 232

239 247

257 250

155 158

162 166

170 158

0.4

•••

' 2457 2525

2645 2901

3876 4098

737 768

8l0 876

996 1030

373 386

402 424

455 456

229 235

243 252

263 253

156 159

163 167

172 158

0.45

r** *•*

7596 2479

Z721 2916

4014 4182

'102U" 1041

372 386

404 427

460 456

227 234

242 251

263 250

1ST 157

161 166

171 154

0.5

■»** ***

2288 2386

2549 2874

4061 4182

"717 753

803 880

364 ' 397 421 379

456 446

221 228

236 246

258 242

149 152

156 160

166 148

0.55""*** *•*

2147 2258

2437 2785

40i' 0 .7 0 .7 5 0 .8 0 .8 5 0 .9

• **

20 1 ~ T 1 A 215 213

101 103

85 73

"'

'

723

TABLE 7: ALPHA= 0.05 POWER= 0.8 EXPECTED ACCRUAL THRU MINIMUM F0LL0W-UP= 550

DEL*.0 2 FACT=

DEL*.05

1 .0 .75

.50 .25

.00 BIN

*•*

1764 1768

1777

1673

395

138

3481

380 382

385

1794

389

681

***

3672 3681

3699 3751

4092 6047

699 707

717 734

5367 5383

5415 5509

6328 8304

990

£721

PCONT=***

0 . 05 0 .1 0 .1 5

•••

**•

***

1 .0 .75

.50 .25

DEL*.10 .00 BIN

DEL*.15

DEL*.20

.50 .25

.0 0 BIN

1 .0 75

.50 .2 5

.0 0 BIN

1 .0 .75

.50 .25

.00 BIN

138

139 140

140 217

81 81

81 82

82 115

57 57

57 58

58 73

762 1076

224 226

229

235 310

121 122

123 124

125

232

153

80 81

81 81

82 93

1011 1047

1117 1422

299 303

308 314

322 390

155

158

157

160

163 186

99 100

101 ' "103 " 102 110

1 .0 .75

REQUIRED NUMBER OF PATIENTS

'

»**

6795 6940

8409 10251

1199 1221

1254 1314

1441 1719

360 367

375 386

400 458

183 186

188 192

173 " '

115

117 '

6745

213

116

118

••• ***

7697 7733

7803 8012

10253 11890

1365 1396

1443 T 7 5 T 1529 1967

408 418

430 445

465 514

205

212 217

222 235

127 128

130 132

134

209

0.3

•••

6303

11616

1478 1518

1960 2164

443 455

491

519 557

221 226

231 236

243 252

135 137

139 142

"144

13219

1581 1693

471

8352

8449 8734

0 .3 $

**• • **

8 566 8630

8759 9135

13073 14239

1542 1592

1669 1809

2147 2313

467 481

500 525

559 588

232 237

243 250

259 263

141 143

145 "1 5 1 148 147

0 .4

••• ***

8523 8607

8775 9257

14009 14950

1564 1624

1716 1880

2281 2412

479

515

496

546

587 606

236 244

250 258

268 268

143 146

148 ” 155 149 151

•••

8223 8331

8547 9147

n a i4 15352

1551

1727 1909

2362 2461

482 500

524 555

600 613

239 245

252 261

271'

1620

268

143 145

148 ” 155 147 151

••• • **

7716 7854

8126 8853

14886 15445

1510 1587

1702 1902

2390 2461

' 475 495

520 553

600 606

235 241

249 257

268 263

140 142

148

•••

7057 7232

7568 8418

14820 15228

1445 1528

1651 1859

2343 2412

461 481

506 539

587 588

226 233

240

2OT 252

131

138

145 "

249

136

142

135

6305 6522

6924 7879

14419 14703

1361 1447

1573 1784

2263 2313

438 457

482 514

561 557

213 220

226 235

235

124 127

129 132

135 124

5517 5777

6237 7262

13682 13868

1261 1348

1677

2l4 9 2164

407 426

449 479

520 514

196 202

208 215

213

113 114

117 119

122 110

•••

4743 5037

5534 6584

12613 12724

1348 1540

1962 1967

369 385

4d6

1230

432

467 458

' ITT" 179

184 190

19? 186

96 100

101 103

105 93

••• • **

4 0 l2 4322

4826 5847

11213 11271

1017 1093

1200 1369

1?22 1719

322 335

352 373

401 390

148 151

” 155 160

165 153

80 81

83 84

85 73

*** •**

3328 3630

4107 5043

9486 9509

870 935

1025 1163

1431 1422

265 276

288 302

321 310

114 118

121 124

115

0 .8 5

**• • **

2671 ' 3355 2939 4144

7436 7438

698 748

815 914

1087 1076

197 203

211 219

229 217

0 .9

••• ***

1993 2201

5046 5058

490 520

559 612

493 681

***

1180 " m r 2380 1293 1726 2368

0 .2 0 .2 5

0 .4 5 0 .5 0 .5 5 0 .6 0 .6 5 0 .7 0 .7 5 0 .8

0 .9 5

•••

••• *•* ***

2516 3090

1147

1472

224

127

145

120 124 135 143

'

152 143

CRC Handbook of Sample Size Guidelines for Clinical Trials

724

TABLE 7: ALPHA= 0.05 POWER= 0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 600

DEL= .0 2 FACT=

DEL=.0 5DEL=.10

1 .0 .7 5

.5 0 .25

.00 BIN

.50 .25

.0 0 BIN

1 .0 75

.50 .2 5

.0 0 BIN

1 .0 .7 5

.50 .25

.00 BIN

1745 1770

1778 1797

1863 3481

381 383

386 390

395 681

138 138

139 140

140 217

81 81

62 82

82 ' 115

57 57

58 58

58 73

3674 3685

3704 3760

4092 6047

701 709

719 736

762 1076

225 227

229 232

235 310

121 122

123 124

12? 153

80 81

~ 81 82

82 93

5372 5389

5424 5525

6326 8304

980 995

ld i6 1051

1117 1422

300 304

309 315

322 390

156 157

159 161

163 186

100 100

101 102

n o

0 .2

6727 6754

6808 6965

8408 10251

1205 1228

1262 1 4 4 1 1321 1719

362 369

377 387

40b 458

184 186

189 192

195 213

115 116

117 118

120 124

0 .2 5

7707 7745

7822 8048

10253 11890

1374 1405

1454 1539

1724 1967

411 420

432 446

466 514

206 209

213 217

222 235

127 128

130 132

134 135

0 .3

8316 8369

8475 8783

11615 13219

1489 1530

1594 1706

1960 2164

447 459

474 493

519 557

223 227

232 237

243 252

136 138

140 142

144 143

0 .3 5

8563 8653

8794 9199

13073 14239

1556 1607

1687 1825

2147 2313

471 485

503 527

559 588

234 239

244 251

259 263

142 143

146 148

151 147

"

0 .4

8546 8638

8*21 9338

14009 14950

1582 1643

1737 1899

2281 2412

484 501

521 548

586 606

240 245

251 259

268 268

144 146

149 152

155 149

"

8252 8371

8605 9246

14614 15352

1571 1642

1749 1931

2362 2461

488 506

529 " 600 556 613

241 247

253 262

271 268

143 146

149 152

155 147

'

0 .5

7753 7904

8198 8968

14*66 ' 15445

1532 1611

1728 1925

2389 2461

481 501

525 " 601 556 606

23 7 243

250 258

268 263

140 143

145 148

152 143

0 .5 5

7105 7295

7655 8548

14*21 15228

1469 1554

1677 1884

2363 2412

467 486

511 542

587 588

228 235

241 250

259 252

134 ' 139 1 4 5 136 142 135

0 .6

6365 6598

7026 8020

14419 14703

1387 1474

1600 1808

2283 2313

444 463

487 ’ 518

560 557

215 221

228 236

245 235

125 127

130 132

135 124

5590 5866

6350 7409

13682 13868

1287 1374

1499 1701

2149 2164

413 431

453 482

520 514

198 203

209 216

224 213

113 115

n '7 119

122 110

4826 5135

5653 6731

12613 12724

1172 1255

1373 1561

1962 1967

374 390

410 434

467 458

176 180

185 191

107 186

98 100

101 103

105 93

4101 4424

4943 5987

11213 11271

1040 1116

1222 1388

1722 1719

326 339

' 355 " 401 375 390

149 152

156 160

165 153

80 82

83 84

73

0 .8

3416 3727

4217 5169

9487 9509

889 954

1043 1178

1430 1422

268 278

290 304

321 310

116 119

121 124

127 115

0 .8 5

2750 3025

3449 4248

7436 7438

713 763

829 924

1087 1076

199 205

212 220

229 217

0 .9

2054 2267

2566 3162

5066 5058

499 529

566 617

692 681

121* 1328

1491 1757

23813 2368

POONT = * * • 0 .0 5 0 .1

44 4

0 .1 5

0 .4 5

0. 65

***

** *

0 .7 0 .7 5

TO '

0. 95 ***

1 .0 .75

.50 .25

.00 BIN

1 .0 .75

DEL=.1 5 DEL=.20

REQUIRED NUMBER OF PATIENTS

103

"

725

TABLE 7: ALPHA= 0.05 POWER= 0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 650

DEL*.02 FACT=

DEL-.05

1 .0 .7 5

.50 .25

.00 BIN

1 .0 .75

.50 .25

DEL=.10 .00 BIN

1 .0 .75

DEL=.1S

.50 .25

.0 0 BIN

1 .0 75

DEL=.20

.50 .2 5

.0 0 BIN

1 .0 .75

.50 .25

.00 BIN

REQUIRED NUMBER OF PATIENTS

POONT=*** d.0 5

••• ***

1767 1771

1780 1800

1863 3481

381 384

387 390

395 681

138 138

T59140

141 217

81 81

81 82

82 115

57 58

58 58

58 73

O .i

*** ***

3677 3688

3709 3768

4092 6047

704 711

721 737

762 1076

226 228

230 232

236 310

122 123

123 124

125 153

81 81

81 81

82 93

***

5376 5395

5433 5541

6328"" 8304

985 999

1020 1055

1117 1422

302 305

310 315

322 390

156 158

159 161

163 186

lo o 101

101 102

103 110

• **

***

6734 6763

6821 "8409 6991 10251

1 2 1 1 " 1269 1234 1327

1441 1719

364 371

379 388

400 458

18$ 187

189 192

195 213

116 116

117 119

120 124

***

7717

7842 8085

10252

" 1382' 1414

1464 1548

1724 1967

414 423

434 448

465 514

2t)1

7758

210

214 218

222 235

128 129

i3d 132

133 135

8330 8387

8501 8832

II8I'6~

1500 1543

1607 1719

1960 2164

451 462

476 495

519

13219

557

224 228

232 237

244 252

136 138

14b 142

144 143

"S«Oi 8677

8827 9263

13073

1570

14239

1623

1703 1841

2147 2313

476 489

507 529

559 588

236 240

245 251

259 263

142 144

146 149

151 147

8569 8668

14009 14950

1598 1661

1756 1917

2281 2412

' "439 505

525 551

587 606

242 247

253

9417

260

268 268

145 147

149 152

155 149

0.15 0.2 0.25 ff.3

0.35 0 .4 0.45 0 .5

***

*** ***

*** *** *** *** • **

8662 9341

14615"........1'571 " l7*d 15352 1663 1952

2362 2461

493 510

532 561

600 613

242 248

255

8410

262

271 268

145 146

149 152

1$$ 147

•**

7*91 7954

8270 9079

1751 1947

2389 2461

487 506

$29 559

601 606

239 244

251 259

268 263

141 143

146 149

152 143

7153 7357

7741

14886 " 1554 ' 15445 1634 I4 8 2 f - - n9215228 1578

1702

2363 2412

515

1906

*** •**

6424 6674

7125

1625 1831

•**

***

5661 T 4 5 1 T 13682 5953 7548 13868

1311" 1523 1399 1723

■**■* •**

4907

5765

5230

6868

*** »**

""41'87 4520

*** " 8282

0". 55 O .i

0.65 0 .7 ' 0.75

0"; j — w

• **

0.85 0.9 0.95

11890

*** ***

'

3500 3819

8672 8154

1441T 14703

545

58 7 588

230 236

243 250

259 252

135 137

140 142

145 135

2283 2313

450 468

491 521

561 557

217 223

229 236

245 235

126 128

130 132

135 124

2149 2164

418 436

""457“

521 514

2do 205

210 216

224 213

"Tl"4 116

l id

484

120

122 110

12613" .....T I7 5 1279 12724

1396 1581

1962 1967

... . 379

413 437

467

177

394

458

181

186 191

197 186

99 100

102 103

105 93

11213 11271

1061 1137

1243 1405

1722

6118

1719

330 343

358 377

401 390

150 153

157 161

16$ 153

81 82

83 84

85 73

4320

9487

907

5286

9509

972

1060 1191

1431 1422

271 281

292 305

321 310

il7 119

122 124

127 115

1087 1076

" 201

213 220

229 217

' 5055“

2824

3537

3106

4344

7436 7438

' *” ■ 2112 *** 2328

2651 3230

5058

***

1411 1499

491

" 472“

— 72T — 841 777

934

5067 " ■■508— 574

1245" '1573" 2381 1360 1786 2368

537

622

692 681

207

CRC Handbook of Sample Size Guidelines for Clinical Trials

726

TABLE 7: ALPHA= 0.05 POWER=Q.8 EXPECTED ACCRUAL THRU MINIMUM F0LL0W-UP= 700

DEL=.02 FACT=

DEL=.05

1 .0 .7 5

.50 .25

.0 0 BIN

••• *•*

1768 1773

1781 1802

1663 3481

362 384

387 390

395 681

**•

3680 3691

3714 3776

4092 6047

705 713

?23 738

***

$380 5401

5441 5556

6326 8304

988 1003

*•*

6741 6772

6835 7015

8409 10251

0 .2 5

••• ***

7?26 7771

7661 8120

0 .3

••• ***

8343 8405

0 .3 5

••• *** ***

O .i 0 .1 5 0 .2

0 .4

.50 .25

.00 BIN

DEL=.15

DEL= .2 0

.50 .25

.00 BIN

1 .0 75

.50 .2 5

.0 0 BIN

1 .0 .7 5

138 138

139 140

m " 217

61 81

82 82

82 115

51 58

'58 58

-3 8 ' 73

762 1076

226 228

230 233

236 310

12 2 123

123 124

125 153

81 81

81 82

82 93

1024 1058

1117 1422

303 306

3 ll 316

323 390

156 158

139 161

163 186

100 100

101 102

1217 1241

1276 1332

1441 1719

366 372

360 388

400 458

185 187

190 192

195 ' 213

116 117

117 ~ r a r 119 124

10253 11890

1390 1423

1473 1556

1724 1967

416 425

436 449

465 514

208 211

214 218

2T T 235

128 129

131 132

134 135

8526 8880

11816 13219

1511 1554

1620 1730

1960 2164

453 465

479 496

519 557

225 229

233 238

243 252

"1 3 T ” 138

140 142

144 143

8618 8700

8864 9324

13073 14239

1563 1637

1718 1854

2147 2313

479 493

509 531

559 588

236 241

246 252

259 263

8592 8699

6911 9494

14009 14950

1614 1678

1773 1933

2281 2412

493 509

529 553

586 606

243 248

254 260

POONT=*** 0 .0 5

1 .0 .75

DEL= .1 0 1 .0 .75

.50 .25

.00 BIN

REQUIRED NUMBER OF PATIENTS

"

'

tot-

143 145

147 " T 5 1 149 147

268 268

145 147

150 ' 152

"'

T55' " 149

0 .4 5

•••

8311 8449

8719 9433

14614 15352

1609 "T79'0 1682 1969

2362 2461

498 515

536 563

600 613

"244 250

256 263

27i 268

145 1 4 ? 147 152

0 .5

••• ***

7829 8003

8339 9185

14886 15445

1574 1655

1773 1966

2389 2461

492 510

533 562

600' 606

” 240 246

252 260

268 263

142' 144

0 .5 5

•••

7200 7418

7824 8790

14821 15228

1514 1601

1724 1926

2363 2412

478 496

519 548

557 588

'232 237

244 251

260 252

' 135' 138

6483 6747

?220 8280

14419 14703

1433 1522

1648 1851

2283 2313

454 473

495 " 551' ' 523 557

219 224

230 237

T 45 235

126 128

130“ 133

135 124

116 120

122 110

0 .6

• ••

'

145“ 149

155 147 152 143

140“ " 145 142 135

0 .6 5

•••

5731 6037

6562 7678

13682 13868

1333 1422

1546 1742

2149 2164

423 440

460 486

520 514

201 206

211 217

224 213

114 116

0 .7

•••

4986 5321

5873 6998

12613 12724

1216 1300

141*7 1599

1962 1967

383 398

416 438

467 458

178 182

187 192

197 186

99 ~T02~ 101 103

105 93

0 .7 5

••• *•*

4269 4612

5160 6240

11213 11271

1081 1157

1262 1420

1722 1719

334 346

361 378

4oi 390

151 154

157 161

165 153

81 82

86 73

0 .8

••• ***

3579 3907

4418 5395

9487 9509

924 989

1076 1203

1430 1422

274 283

294 306

32i 310

118 120

122 124

127 115

0 .8 5

•••

2895 3181

3620 4433

7436 7438

740 789

852 942

1087 1076

202 208

214 221

229 217

0 .9

••• • **

2166 2385

2712 3291

S066 5058

515 544

579 626

693 681

0 .0 5

••• • **

1275 1390

1552 1812

2380 2368

83 84

■"

110

727

TABLE 7: ALPHA= 0.05 P0WER= 0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 750

DEL=.02

DE1=.05

DEL=.10

1 .0 .75

.50 .25

.00 BIN

*

1769 1774

1783 1804

1863 3481

383 385

387 391

395 681



3682 3694

3719 3784

4092 6047

707 715

725 740

o '.T r-5

* •

5385 5406

5450 5572

6328 8304

992 1006

or. 2

* *

6747 6781

6848 7039

8409 10251

0 .2 5

* •

7736 7784

7880 8154

0 .3

f •

0 .3 5 b. 4

FACT=

.50 .25

.00 BIN

1 .0 .75

DEL=.20

.50 .25

.00 BIN

1 .0 75

.50 .2 5

.0 0 BIN

1 .0 .75

.50 .25

.00 BIN

139 139

139 140

141' 217

81 81

*2 82

82 115

"17“ 57

57 58

58 73

762 1076

227 229

230 233

235 310

122 123

124 124

125 153

81 81

81 82

32 93

1028 1061

1117 1422

304 307

3 ll 317

323 390

157 158

160 161

163 186

100 100

io r 102

102 110

1222 1246

1281 1338

144T 1719

368 373

380 389

400 458

186 188

190 192

195" 213

116 117

118 119

120 124

10253 11890

1398 1432

14*2 1564

1724 1967

418 427

437 450

466 514

209 212

2T5" 218

222 235

128 130

131 132

134 135

8356 8422

8554" 11816 8926 13219

1521 1565

1631 1740

1960 2164

456 468

481 498

519 557

226 229

234 238

2w 252

138 139

140 142

"144 143

* *

8636 8724

8899 9384

13073 14239

1596 1651

1732 1867

2 l47 2313

483 496

512 533

559 588

238 242

247 252

259 263

143 145

147 149

151 147

■* •

8615 8730

8956 9568

T4009 14950

1629 1694

1790 1948

2281 2412

498 “ 53T 513 555

587 606

244 249

254 261

268 268

146 148

'T50“ 152

155 149

l

*

8341 8488

8775 9521

14614 15352

1626 1700

1809 1986

2362 2461

502 519

'W 565

600 613

245 ~~257" 250 263

27F 268

145 147

150 152

155 147

s •

7867 8053

*408 9287

14*86 15445

1593 1675

1793 1984

2389 2461

497 514

536 564

601 606

242 ~ 253“ 247 260

263 263

142 144

146 149

152 143

a ;55" "s 1

*

7248 7479

7906 8903

14821 15228

1534 1622

1745 1945

2363 2412

482 500

522 550

587 588

233 “ 244 239 251

259 252

136 138

140 143

145 135

b .6



6541 6819

7312 8401

14419 14703

1454 1543

1669 1870

2283 2313

459 477

499 525

560 557

220 225

231 237

244 235

127 129

130 133

135 124



5800 6119

6661 7802

13683 13868

1354 1443

1566 1760

2149 2164

427 444

464 489

520 514

202 207

212 217

224 213

115' 116

118 120

122 110

5062 "597'5“ 12613 5409 7120 12724

1236 1321

1436 1615

1962" 1967

386 401

419 440

467 458

179 183

187 " 197 192 186

100 101

102 104

105 93



4348 4700

5260 6355

11213 11271

1099 1175

1279 1434

1722 1719

337 349

363 380

400 390

l5 2 154

158 161

165 153

61 82

83 84

85 73

t •

3655 3990

4510 5497

94*6 9509

940 1004

1090 1214

1430 1422

276 285

295 307

321 310

113 “ 122

127 115

*

2961 3253

369* 4516

7436 7438

752 800

862 949

1087 1076

204 209

215

229 217

0 .9

* •

2218 2440

276$ 3348

5066 5058

522 550

585 630

693 681

0 .9 5

s

1302 1418

1379 1836

2380 2368

POONT=



0 .05

*

o .r

0 .4 5

O '

D. 65

0 /7 ' "~J * *

0 .7 5 0 .8



0 .8 5



1 .0 .75

DEI=.15

REQUIRED NUMBER OF PATIENTS

221

"

"

120

124

CRC Handbook of Sample Size Guidelines for Clinical Trials

728

TABLE 7: ALPHA= 0.05 POWER= 0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 800

DEL=.0 2

DEL=.05

.50 .25

.0 0 BIN

1*770 1775

1785 1806

1863

383

388

395

3481

385

391

681

3685 3698

3724 3792

4092 6047

709 716

727 741

762

227

1076

229

231 ~ 235" 233 310

***

5389 5412

5458 5586

6328 8304

995 1010

1031 1064

1117 1422

304 308

312 317

••• ***

6754

6861 7063

8409 10251

1228

1237

1252

1342

1441 1719

369 375

382

6790

390

***

7746 7797

7899 8188

10253 11890

1405 1440

1490 1571

1724

420

439

1967

429

•** ***

8369 8440

8580 8972

11816 13219

1530 1575

1512 "T960 1749 2164

•••

• **

8653 8747

8933 9442

13073 14239

1608 1664

1745 1878

0.4

••• ***

8638 8760

9000 9640

14009 14950

1643 1709

0.45

••• *•*

8371 8527

8831 "T4315 9607 15352

1642 1718

0 .5

••• »**

7904 8102

8476 9384

14886 15445

1611 1694

••• ***

7295 7539

7985 9010

14821 15228

1554 1641

••• ***

6599 6890

7401 8515

14703

1474 1564

••• ***

5867 6198

6757 7919

13682 13868

••• **•

5136 5493

6073 7235

12613

••• • »*

4424 4785

••• • t* **•

0 .0 5

.0 0 BIN

1 .0 .7 5

.5 0 .2 5

.0 0 BIN

81

82 82

82 115

57 58

58

81

58

58 73

0.1

124'

125 153

81 81

"8T

124

82

82 93

0 .1 5

161

163 186

100 101

101 102

103 110

d .2

190 193

195 213

116 117

118

188

120 124

0 .2 5

466 514

210 212

215 219

222 235

129 130

131 1 3 4 ' 132 135

0 .3

483 499

519 557

227

234 239

243 252

138 139

l'4'l'' 1 4 4

230

0 .3 5

142

143

486 499

5IT " 534

559 588

239 243

248 253

259 263

144'

147

151

145

149

147

2281 2412

501 516

534 557

587 606

245

255 '

26TT

146

150 “ 155

250

261

268

148

152

506 522

542 567

600 613

247

27r 268

150 ' ■155

252

257 264

146

2001

2362 2461

148

152

147

1812 2000

2390 2461

501 518

539 566

601 606

243 248

254

268 263

T43" 145

147 149

143

0 .5 5

17J5- 2363

486

526

1962

2412

246

260

552

587 588

235

504

240

252

252

135' 138

140 "T45 143 135

0 .6

1689 1886

2283 2313

463 481

$01 527

561 557

232

245 235

127 129

131 “ 135 133 124

0 .6 $

1374 1463

1586 1776

2149 2164

431 447

115 117

118 ~T 22 120 110

0 .7

12724

1255 1339

1455 1630

1962 1967

390 404

0 .7 5

5356 6463

11213 11271

1116 1192

1295 1447

1722 1719

339 351

365

401

' '152

381

390

155

158 161

165 153

0.8

3728 4069

4597 5593

9487 9509

954 1018

1102 "1431 1224 1422

278 287

297 308

321 310

119 121

123 125

127 115

0 .8 $

3025 3322

3771 4594

7436 7438

763 811

872 956

1087 1076

205 210

216 222

229 217

0 .7

•••

2267 2491

2823 3401

5066 5058

529 556

590 633

593 681

0 .9 5

•••

1328 1444

1605 1858

2380 2368

•••

••• •••

•••

***

.00 BIN

.50 .25

.0 0 BIN

1 .0 75

138

139

139

140

141 217

122 123

323 390

157 159

160

400 458

451

459 470

2147 2313

1805 1961

1826

DEL=.20

.50 .2 5

PCONT=***

.50 .25

DEL=.15

1 .0 .7 5

FACT=

1 .0 .75

DEL=.10 1 .0 .75

REQUIRED NUMBER OF PATIENTS

14419

"'*57'"'■"521 490

514

421

467 458

442

186

"

22T

226

261

238

"■ "203 “T I 3 "

"~Z7T 213

208

218

180 184

188 “T 9 7 192 186

"''TOO-

119

149

152

101

102 “ 105 104 93

82 83

84

n

85 73

729

TABLE 7: ALPHA= 0.05 PQWER=0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 850

DEL*.02 F1CT=

DEL*.05

1 .0 .7 5

.50 .25

.0 0 BIN

1771 1777

1787 1808

1863 3481

383 385

388 391

395 681

**•

**•

3487 3701

3728 3799

4092 6047

71 i 718

726 742

***

•••

5373 “ 3 4 5 7 ' 6328 5418 5601 8304

998 1013

***

***

6761 6799

'6874 7086

8400 10251

1233 1257

1292 1346

i'44r "

**•

7753 7809

7917 8221

15253 11890

1412 1447

83'82‘ ■86W 8457 9016

11815 13219

POONT=*** 0 .0 $ 0 .1 0 .1 5 5 .2 d . 25 0 .3

DEL*.10

•••

1 .0 .75

.50 .25

.00 BIN

1 .0 .75

DEL*.15 .50 .2 5

.0 0 BIN

1 .0 .75

.50 .25

82 82

62 115

57 57

$7 57

“ 57 73

122 123

123 124

125 153

61 81

82 82

62 93

323 390

157 158

i6d 161

163 186

15l 101

152 102

103 110

383 390

400 458

187 189

i9d 193

19$ 213

ll7 117

118 119

120 124

422 430

440 451

46$ 514

210 213

215 219

222 235

129 130

131 133

134 135

1965' 2164

' 461 ' 472

484 499

519 557

227 231

235 239

243 252

136 139

"1*1" 142

144 143

240 243

246 253

259 263

1*4 146

1*7 149

151 147

246 251

256 261

268 268

147 148

131 153

155 149

7*5"" 253

258 264

271 268

1*6” 148

151 153

155” 147

244 249

255 261

769 263

143 145

147 150

152 143

236 241

246 253

250 252

137 139

H I

.50 .25

.0 0 BIN

1 .0 75

138 139

139 140

140 217

' 82" 82

762 1076

22? 229

231 233

236 310

1 0 3 5 ' T117 1066 1422

3TJ3 309

312 317

1719

371 376

1498 1577

1724 1967

13*5 1585

1651 1757

••• **•

8671 8771

8967 9499

13073 14239

1619 1676

1757 1889

2146 2313

488 501

516' 535

560 588

0 .4

•••

8661 8790

9o44 9709

14od9 14950

"" 1537 1723

1820 1974

2281 2412

35*"" 537” 559 519

587 606

••• **•

8400 8566

8886 9689

14614 15352

1658 1734

1842 2015

2362 2461

'315' 526

3*3" 569

6 oo 613

•••

79'*1‘ "8542 8150 9478

14886 15445

1628 1711

1829 2015

2390" 2461

“ 7 3 1 1 “ 8557 7598 9113

14821 15228

1572 1660

1784 1977

0 .5 0 .5 $

***

.00 BIN

REQUIRED NUMBER OF PATIENTS

0 .3 5

0 .4 5

DEL*.20

" 551 521

542" “ 505“ 567 606

2363 2412

491 508

528 554

587 588

"

"

'

"

142

1*3“ 135

••• ***

6653 6959

7486 8624

14419 14703

1493 1583

1758 1902

2283 2313

467 484

5d4 529

561 557

222 227

232 238

244" 235

128 129

"131 133

” 133" 124

5". 65"

*« *»*

'5932 6275

6849 8030

13683 13868

1303 1481

1603 1790

2149 2164

*33 450

469 492

$20 514

254 206

213 218

224 213

116 117

110 120

122 110

0.7

•••

5207 5574

6167 7344

12613 12724

1273 1357

1471 1643

1962 1967

303 407

424 443

467 458

161 185

186 192

197 186

100 102

ld3 104

105 93

0 .7 5

••• »*•

4497 4866

5446 6565

11213 ' 11271

1 1 3 2 ' "1359 1208 1459

1722 1719

342 354

36? 382

151 390

153 156

158 162

165 153

82 83

84 85

65 73

0 .8

••• • ••

3797 4145

4685 5683

9487 9509

968 1031

1114 1233

1430 1422

280 289

296 309

321 310

IT T 121

123 124

127 115

0 .6 5

**• •**

3086 3387

3841 4667

7437" 7438

773 820

880 962

1087 1076

206 211

216 222

220 217

**• **•

2813 2539

2873 3451

5066 5058

535 562

594 636

692 681

• **

"1352 1468

1629 1878

2380 2368

0 .6

0 .0 d .95

'

'"

CRC Handbook of Sample Size Guidelinesfor Clinical Trials

730

TABLE 7: ALPHA= 0.05 P0WER= 0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 900

FACT=

1 .0 .7 5

.50 .25

.0 0 BIN

POONT= • **

1 .0 .7 5

.50 .25

DEL= .15

DEL= .10

DEI = .05

DEL= .02

.0 0 BIN

1 .0 .75

DEL= .20

.50 .25

.0 0 BIN

1 .0 75

.50 . 25

.0 0 BIN

1 .0 .7 5

" ”57" 57

.50 .25

.00 BIN

57 57

57“ 73

REQUIRED NUMBER OF PATIENTS

o .o r

1'772" 1786 "ITTC3" 1778 1810 3481

384 386

366 392

395 681

138 139

140 140

I4T 217

61 82

62 82

82 115

0 .1

3690 3704

3*733 3806

4092 6047

712 720

729 743

762 1076

228 230

231 233

233 ' 310

123 123

124 125

125 153

81 81

61 82

62 93

**•

53$8 5424

5175 5615

6328 8304

1001 1016

1037 7 1 1 7 1068 1422

306 309

313 317

323 390

158 159

160 162

163 186

TOO 101

101 102

102 110

***

5768 6808

6688 7108

6408 10251

1237 1262

1297 1350

1"441 1719

371 377

383 390

399 458

167 189

191 193

"775 213

117 117

116 ■■HIT 119 124

7765 7822

793’T 8253

10252 11890

141$ 1454

1504 7 7 2 4 1583 1967

424 432

441 452

465 514

210 213

216 219

222 235

" 129 130

131 132

134" " 135

o. lS 0 .2 0 . 25



0.3

• ••

63*6 8475

8632 9059

11816 13219

1548 1594

1761 "7961"' 1765 2164

454 474

486 501

519 557

228 231

235 239

243 252

'138 140

141 143

144 143

0. 35

• •• • **

8688 8794

9001 9554

13073 14239

1630 1667

1769 "~2T4'7 1899 2313

491 504

518 536

559 588

240 244

249 253

259 263

144 146

147 149

'1 7 1 147

0 .4

8684 8821

9088 9777

14009 14950

1670 1737

1633 1985

2281 2412

507— 539 522 560

586 606

247 252

257 262

268 268

147 149

151 153

155 149

0 .4 5

8429 8605

8940 9768

14615 15352

1673 1749

1657 2027

2362 2461

513 528

548 570

600 613

249 253

259 264

7 7 1 ■' 268

7979 8198

8607 9568

14886 15445

1644 1728

1845 2029

2390 2461

506 525

545 569

600 606

245 250

255 262

759 263

"144" 145

147 149

152 143

7388 7656

6137

14820 15228

1589 1677

18od

9212

1991

2363 2412

494 511

531 556

567“ ■ ’ ' 237 588

242

247 253

260 252

137 139

ur 143

rre 135

6711 7026

7*7(5 8728

14419 14703

1511 1601

1725 1916

2283 2313

470 487

506 531

560 557

224 228

233 239

715 235

126 129

131 133

135 124

5996 6350

6938 8136

13682 13868

1410 1499

162(3 1804

2149 2164

43U 453

471 493

521 514

205 209

213 218

724 213

116 117

119 120

T22 110

5276 5653

6257 7448

12612 12724

1289 1373

1487 1656

1962 1967

396 410

425 444

467 ” ' 458

~"T82 185

169 193

797 186

''

100“ 101

102 104

IU5 93

4567 4943

5534 6662

11213 " 11271

714ff" 1323“ 1722 1223 1469 1719

344 356

368 383

401 390

154 156

159 162

755 153

'..... "82 83

63

85 73

0 .6

3864 4217

4759 5769

9467 9509

981 1043

1125 1242

1431 1422

282 290

299 309

321 310

119 121

123 125

127 115

0 .6 5

3144 3449

3908 4735

7436 7438

783 829

888 968

1087 1076

207 212

217 223

22$ 217

0 .9

2357 2586

2921 3497

5067 5056

540 567

599 639

693 661

1376 1491

1650 1696

2361 2366

0 .5

***

0. 55 0 .6

• ••

0 .6 5 0 .7 0 .7 5

0 .9 5

• ••

*•*

TM

"

14 7— 151 149 153

84

r55‘ " 147

731

TABLE 7: ALPHA= 0.05 POWER= 0.8 EXPECTED ACCRUAL THRU MINIMUM F0LL0W-UP= 950

DEL=.02 FACT=

DEL=.05

1 .0 .75

.50 .25

.00 BIN

***

1773 1779

1790 1812

1863 3481

384 386

388 391

395 681

0 .1

***" ***

3692 3707

3738 3813

4092 6047

713 721

730 743

0 .1 $

m *•*

5402 5429

5484 5628

6328 8304

1003 1019

* •*

" 5774 6817

6901 7129

8409 10251

0755

ill ** *

7774 7835

7956 8284

073

***' * •*

8409 8493

b. 35

ill ***

074

DEL=,20

.00 BIN

1 .0 75

.50 .25

.0 0 BIN

1 .0 .75

139 139

i4d 140

141 217

82 82

82 82

82 115

57 58

' 58 58

58 73

762 1076

' 22T" 230

231 234

235 310

122 123

124 124

125 153

81 82

82 82

82 93

1040 1070

1117 1422

306 310

314 318

323 390

158 159

160 162

163 186

101 101

102 102

103 110

1242 1267

1302 1354

1440 1719

372 378

384 391

400 458

188 189

191 193

196 213

116 117

ll8 119

120 124

10252 11890

1426 1461

1511 1588

1724 1967

425 433

442 452

466 514

211 213

216 219

222 235

129 130

131 133

134 135

8658 9101

11816 13219

1557 1603

1670 1773

1960 2164

466 476

487 501

51'9 557

229 232

235 239

243 252

139 140

141 143

144 143

6706 8817

9035 9608

13073 14239

1 6 4 1 " 1780 1698 1907

2147 2313

494 506

520" 538

559 588

241 245

249 254

258 263

144 146

148 149

151 147

ill " • **

8707 8851

9131 9842

14009 14950

1682 1750

1845 1996

2281 2412

510 "75*0" 524 561

587 606

2*8 253

'2 5 7 “ 262

268 268

147 ' 1 5 1 " 149 153

154 149

0 .4 5

III * *♦

'8459 8643

8993 9844

14615 15352

1687 1763

1872 2040

2362 2461

515 531

549 572

600 613

249 254

"259“ 265

271 268

147 " n r 149 153

155 147

075

ill ** »

8016 8246

8670 9654

14865 15445

1660 1743

1860 2042

2389 2461

511 527

547 571

600 606

246 251

256 262

258 263

144 146

147 150

152 143

0 .5 5

i l l ■'

7433 7713

8210 9306

14821 15228

1606 1694

1816 2005

2363 2412

497 514

533 557

587 588

238 242

247 253

260 252

13B 139

1*T" 143

145 135

075

ill ** *

6765 7093

7651 8827

14419 14703

1527 1617

1741 1929

2282 2313

*7*"" 509 532 490

561 557

224 229

234 239

245 235

128 130

13l 133

135 124

0 .6 5

l l 'i '

6058 6423

7023 8237

13682 13868

1427 1515

1635 1817

2149 2164

441 456

473 495

52b 514

206 210

214 219

224 213

116 117

119 120

122 110

0 .7

III

5343 5729

6343 7546

12612 " 12724

n o r -

1389

1501 1667

1962 1967

399 412

427 445

467 458

1 32 186

190 193

197 186

101 102

103 104

105 93

4635 5018

5617 6755

11213 11271

ll6 l 1236

1336 1478

1722 1719

347 357

369 384

40l 390

154 156

159 162

165 153

82 83

84 84

85 73

12o 121

123 125

127 115

0 . 05

072

0 .7 5

m

ill

*M

.50 .25

.00 BIN

DEL=.15

.50 .25

PCX)NT=***

1 .0 .75

DEL=.10 1 .0 .75

i i 'i “

3928 4286

483$ 5850

9487 9509

993 1055

1135 1249

1431 1422

"2 3 3 " " 291

300 310

321 310

0 .6 5

i 1 i'

32oo 3508

3971 4801

7436 7438

792 837

695 973

1067 1076

208 213

217 223

229 217

0 .9

* fT "' • **

2400 2630

2966 3541

5067 5058

545 571

602 641

692 681

1397 1512

1671 1913

23 8 l 2368

• *»

.00 BIN

REQUIRED NUMBER OF PATIENTS

b. 6

0793“ i l l

.50 .25

...

CRC Handbook of Sample Size Guidelinesfor Clinical Trials

732

TABLE 7: ALPHA= 0.05 PQWER=0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 1000

DEL=.0 2

DEL=.1 5

DEL=.10

DEL=.05

DEL=.20

.50 .25

.00 BIN

1 .0 75

.5 0 . 25

.0 0 BIN

1 .0 .7 5

.5 0 .2 5

.0 0 BIN

139 140

140 140

141 217

81 81

82 82

82 115

58 58

58 58

58 73

762 1076

228 230

231 233

235 310

123 123

124 125

125 153

8l 81

81 82

82 93

1043 1072

1117 1422

3U7“ 310

314 318

323 390

158 160

160 161

163 186

101 101

101 102

103 110

11246 1271

1306 1357

1441 1719

373 379

385 391

400 458

188 190

191 193

195 213

"117" 118

118 119

120 124

10253 11890

1431 1467

1518 1593

1724 1967

427 435

443 453

466 514

211 214

214 219

222 235

130 131

131 133

134 135

8483 9142

11816 13219

1545 1612

l4"78 1779

1940 2144

468 477

489 502

519 557

230 233

236 240

243 252

139 " 1 4 1 140 143

"144 143

8724 8840

9069 9660

13073 14239

1651 1708

1790 1916

2146 2313

194" ' 521 508 538

560 588

242 246

250 254

259 263

143" 146

148 150

••• **•

8730 8881

0173 9905

14009 14950

1494 1762

1858 2005

2281 2412

513 526

543 562

586 606

249 253

258 263

268 268

14F 150

151 153

“ 155 149

0 .4 5

••• ***

8468 8681

9045 9919

14615 15352

1700 1777

1885 2051

2342 2441

51?" 534

551 573

600 613

251 255

26(3 265

271 268

148 150

151 153

155 147

0 .5

•••

8053 8293

8733 9738

14886 15445

1475 1759

1875 2054

2390 2441

515 530

549 572

601 606

247 251

254 262

268 263

145 146

148 150

152 143

7479 7769

8281 9397

14821 15228

1621 1710

1831 2017

2343 2412

' 5DB 516

534 558

587 588

2 3 ?"- 248 243 253

260 252

138 140

141 143

T45 135

.00 BIN

.5 0 .2 5

.0 0 BIN

T774 1780

1791 1813

1843 3481

385 386

389 392

395 681

o . i — »■**■■ "3S?5 *•* 3711

3742 3819

4092 6047

715 722

731 745

0 .1 5

**«■ *•*

3*04 5435

5177 5641

6326 8304

1006 1021

0 .2

••• ***

6781 6826

6914 7151

8409 10251

***

7784 7848

7975 8315

• ••

8422 8510

0 .3 5

*** ***

0 .4

0 .2 5 0 .3

0 .5 5

*** ***

• **

1 .0 .75

REQUIRED NUMBER OF PATIENTS

POONT=*** 0 .0 5

1 .0 .7 5

.50 .25

1 .0 .7 5

FACT=

'

151 ' ' 147

0 .4

•••

6820 7157

17*0 8923

14419 14703

1343 1633

1754 1941

2283 2313

477 493

511 533

561 557

225 230

234 239

245 235

129 130

131 133

"1 3 5 " 124

0 .6 5

••• • ••

4119 6493

7106 8334

13483 13868

1443 1531

1451 1828

fcl49 2144

458

475 496

521 514

207 211

215 219

224 213

116 118

119 120

122 110

5409 5801

4426 7641

12613 12724

1321 1403

1315 1478

1962 1967

401 414

429 446

467 458

183 186

190 193

197 186

101 102

103 104

105 93

83 83

84 85

85 73

0 .7 0 .7 5

•••

4701 5091

5597 6842

11213 11271

T175 1250

1348 1488

1722 1719

349 359

371 385

401 390

155 157

160 162

165 153

0 .8

•••

3090 4353

4907 5926

9484 9509

1004 1065

1145 1254

1431 1422

285 293

30l 310

321 310

lio 122

123 125

127 115

0 .8 5

••• • ••

3253 3565

4031 4862

7434 7438

800 845

90S 977

1087 1076

209 213

218 223

229 217

0 .9

••• *»*

2440 2672

3010 3581

5066 5058

550 575

606 643

693 681

0 .9 5

*** *•»

1418 1533

icto

2380 2368

1929

733 TABLE 7: ALPHA* 0.05 P0WER=0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 1100

DEL-. 02 FACT=

DEL*.05

0. 05 0 .1 0 .1 5 0 .2

*** 444

3751 " 4b92

717

3831

6047

725

4*4 ' * •*

5115 5447

5509 ■ 5 3 7 9 5666 8304

— 6795 • ** 6843

5940 ■T409 7191

10251

8759 8887

9135 9759

074

44 4 *»•

8775 "9257

fT * ** *

0.95

124 125

125 153

81 81

81 82

82 93

314 318

323 390

158 159

160 162

163 186

101 101

102

103 110

386 392

400 458

188 190

192 193

213

117 118

118 119

235

380

1 .0 .75

.00 BIN

io n

1047 1075

1027

"

1251

1314 1363

1280

1076

im

"

445 " 466

195

""

222

102

i3r

120 124

130 131

133

133 135

139” 140

142 143

144 143

145

148 149

147

151" 153

155" 149

151

1529 1602

1724 1967

43d 437

455

514

213 214

217 219

1627

1693 1791

1960 2164

471 480

4 9l 503

519 557

230 233

236 240

243 252

13073 14239

1669 1728

1809 1930

2146 2313

500 511

525 540

559 588

243 247

250 254

258 263

14008 10026 14950

1716 1785

1880 2023

2281 2412

518 531

546 564

"587 606

250 254

2 58 263

268 268

8546 8757

9147

14614 10059 15352

1726 1803

19d9 ' 2352 2070 2461

"524 538

555

600 613

252 257

261 265

271 268

148

576

150

153

155 147

44 4 * •*

8126 8386

8853 9896

14886 15445

1702 1786

1902 2075

2390 2461

520 535

553 574

600 606

249 253

257 263

268 263

145 147

148 150

143

44 4

7568 7879

8416 9569

14821 15228

1651 1739

1859 2039

2363 2412

506 521

539 561

587 588

240 244

249 254

259 252

138 140

142 143

135

“T J4 * •*

6924 7281

7879 9102

14419 14703

1573 1662

1784 1963

2282 2313

482 497

245

557

226 230

235

535

239

235

129 131

132 133

135 124

444 • **

6237

7262 8515

13682 13868

1472 1560

1677 1849

2149 2164

449 463

478

6628

498

521 514

208 212

215 219

224 213

117 118

119 120

122" " 110

5534 5941

6584 7816

12613 12724

1348 1430

1539 1697

1962 1967

406 418

432 448

467 458

184 187

191 194

197 186

101 103

103 104

105 93

4826

5847 7006

11213 11271

1200 1273

1369 1504

1722 1719

352 362

373 386

401 390

155 158

159 162

165 153

82 83

84 85

85 73

"5043

$486 9509

id24 1085

1163 1269

1431 1422

287 295

302 312

321 310

12l 122

124 125

126 115

210

219

229

214

** * IT I

8941

"

5228

0 .9

123 123

375

757

3700 3717

44 4 ** *

0 .8 $

235 310

1719

734 746

***

0 .3 5

O .i

"58 73

1441

395 681

8733 T1816" 9220 13219

0 .7 5

58 58

308 312

389 392

8545

0 .7

57 58

1422

385 387

7R49

0 .6 5

82 115

232 234

1816

**•

0 .6

82 82

229 230

.00 BIN

REQUIRED NUMBER OF PATIENTS

4T4 '

0 .5 5

81 82

140 217

1783

1863 3481

8374

0 .5

.50 .25

140 140

1794

7873

0 .4 5

1 .0 .75

139 139

1776

7803 TOT T~ 10253'

0 .3

.0 0 BIN

1 .0 75

.00 BIN

DEL*.20

.50 .2 5

.00 BIN

.50 .25

441 • **

0.25

.50 .25

DEL*.15

.50 .25

1 .0 .75

PCONT =*•*

1 .0 .75

DEL=.10

III ** *

,- n o7 4479

6069

11890

1443 1479

1551

"

11 1 ***

3354 ” 1114 4975

7436 7438

815 859

914

3672

985

1087 1076

11 1 ***

2 5 l6 2750

3b90 3656

5066 5058

559

612' 647

692 681

* •*

1156 1570

1726 1957

2380 2368

583

511"" 560

224

217

"

147 ”

141“ 150 '

151

i'57" 145" "

CRC Handbook of Sample Size Guidelinesfor Clinical Trials

734

TABLE 7: ALPHA= 0.05 POWEFU 0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 1200

DEL=.0 2 FACT-

1 .0 .7 5

.50 .25

DEL=.0 5 .0 0 BIN

***' •**

0 .1

***

1 7 7 7 ' 17 97 1785 1819

18*3 3481

.0 0 BIN

1 .0 .75

.50 .25

.0 0 BIN

1 .0 75

.50 .2 5

.0 0 BIN

1 .0 .7 5

.50 .25

.0 0 BIN

3841

•** “ 5TO" 5525 • ** 5458 5689

' 385" 388

390 392

681

139 139

139 140

140 217

82 82

82 82

82 115

$8 58

58 58

58 73

232 234

8l

395

727

747

762 1076

229 231

235 310

123 124

124 124

124 153

81

82 82

82 93

1016 1031

1051 1078

1117 1422

309 '" 315"" 322 319 312 390

159 160

1*0

8304

161

163 186

lo i 101

lb2 102

103 110

570'-T 37*0” "4092"" 3724

0 .1 5

.50 .25

REQUIRED NUMBER OF PATIENTS

POONT=*** 0 .0 3

1 .0 .7 5

DEL=.10DEL=.15DEL=.20

6047 ~6TTS~

719— 73*

0 .2

***

6808 6861

6965 7229

8408 10251

12*1 1287

1321 "T441 1368 1719

376 382

387 393

40o 458

189 190

1$2 193

195 213

117 118

118 119

120 124

0 .2 5

••• • **

7822 7899

8048 8429

10252 11890

1454 1490

1539 1609

1*23 1967

432 439

44* 455

4*6 514

213 215

217 220

222 235

130 131

132 133

133 135

0 .3

••• • **

8475 8580

8783 "1181'5 9295 13219

1594 1642

1706 1801

1960 2164

'474 —493” 482 505

519 557

232 234

237 240

243 252

139 140

142 142

143

0 .3 5

••• • ••

8794 8932

91$$ 9853

13073 14239

1*87 1745

1825 1944

2146 2313

503 514

$26 541

559 588

244 247

25o 254

259 263

145 147

148 150

151 147

0 .4

••• • •*

8821 9000

9338 14008 10139 14950

1737 1805

189$ 2038

2281 2412

521 534

" 548 565

' 58* 606

148 150

151 153

1$4 149

• **

8605 8830

924* "T4*14 10191 15352

1749 1826

l$ 3 l 2088

2362 2461

529 542

$58 577

"600 613

••• *•*

8198 8476

8968 14886 10043 15445

1728 1811

1925 2094

2389 2461

525 539

55* 576

601 606



d . 55

•••

7655 7984

8548 "T4821 9727 15228

1677 1765

1884 2058

2363 2412

511 526

542 562

587 588

-

d .6

•••

*•*

*026 7400

8020 T4419 9268 14703

1600 1689

1808 1983

2283 2313

487 501

517 537

**•

6350 6757

7409 8682

13682 13868

1498 1585

1*01 1867

2149 2164

453 466

5653 6073

673d 7978

12613 12724

1373 1454

15*1 1713

1$62 1967

4943 5356

598* 7155

11213 11271

1222 1294

1388 1518

4217 4597

5169 "9487 6199 9509

1043 1102

0 .4 5 0 .5

0 .6 5 0 .7 o .7 i 0 .8

•••

*** ••• •••

'

251

759

255

263

2*8 2*8

144*

253

7*2

271 ' '......148

151

257

266

268

150

153

250 254

738 263

268 263

145 147

148 "151" 150 143

241 245

730 254

"259 252

139 140

142 143

135

5*0 557

228 232

235 240

244 235

130 130

"TO 133

135 124

48l 499

520 514

209 212

21* 220

223 213

117 118

119 121

121 110

409 421

434 449

4*7 458

185 188

"T O 194

1$7 186

lo i 102

103 104

105 93

1722 1719

355 364

375 387

400 390

---- 156

130 163

135 153

82 83

84 85

85 73

1177 1279

1430 1422

290 296

3b4 312

321 310

121 122

211 215

22o 224

229 217

0 .8 5

•••

3448 3771

4248 5077

7436 7438

829 871

924 992

1087 1076

0.9

••• »**

2586 2822

3162 3724

5066 5058

566 589

*17 650

*$2 681

0 .9 5

••• »**

1491 1605

175* 1982

238b 2368

158

"T O 125

127 115

154 147

735

TABLE 7: ALPHA= 0.05 POWER= 0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 1300

DEL*. 02 F1CT=

DEI*. OS

1 .0 .7 5

.50 .25

.00 BIN

pcont=***

1 .0 .75

.50 .25

DEL*. 10 DEL*.15DEL*.20 .00 BIN

1 .0 .75

.50 .25

.0 0 BIN

1 .0 75

.5 0 .2 5

.0 0 BIN

1 .0 .75

.50 .25

82 82

82 115

58 58

58 58

"58" 73

81 81

81 82

82 93

.00 BIN

REQUIRED NUMBER OF PATIENTS

0 .o 5

*•* *•*

177? 1787

lSOo 1821

1863 3481

387 388

390 393

395 681

139 140

140 141

~T 4r~ 217

61 81

0 .1

••• **•

3709 3730

3748 3852

4092 6047

721 728

737 747

742 1074

230 231

232 234

236 310

123 123

"121" 124

173 153

0 .1 5

** H II

DEI = .02

.00 BIN

1 .0 .75

DEI

DEI,= .20

.50 .25

.00 BIN

1 .0 75

.50 . 25

.00 BIN

1 .0 .7 5

.50 .25

.0 0 BIN

1'40

83 115

58 58

58 58

58 73

81 83

83 83

83 93

REQUIRED NUMBER OF PATIENTS

l'8'2tf"~1 8 6 2 "

390

392

395

140

1808

1837

3481

392

393

681

140

140 140

217

83 83

83 83

3764 3796

3846 3933

1 5 9 2 “" 6047

736 742

748 754

762 1076

233 233

234 234

236 310

124 124

124 124

"124 153

5533 5596

5699 5893

6327

1052 1065

1079 1096

1117 1422

315 317

318 320

323 390

“ 161 161

162

8304

162

162 186

101 101

102 102

102” ' 110

6977 7077

7248 7577

8409 10251

1323 1345

1370 1401

1440 1719

387 390

393 396

399 458

192 193

193 195

195 213

118 118

118 120

124

8067 8211

8456 8940

10252 11890

1543 1574

1614 1662

1724 1967

416 451

217

461

218

220 221

'2 2 1

514

8808 9001

9331 9979

11815 13219

1712 1754

1806 1873

1961 2164

493 499

506 512

518

"'2 3 7 239

240 242

9231 9481

9898 13073 10712 14239

1833 1886

1949 2034

2146 2313

527 536

549

542

559 588

251 252

9377 9687

10193 1 4 0 0 9 11167 14950

1909 1970

2046 ' 2231' 2145 2412

549 558

567 576

""587 606

" 259

9293 9662

10254 17 6 1 5 11367 15352

"1942

2362 2461

559 568

577

2011

2096 2208

9024 9446

10114 174886 11340 15445

1936 2011

2102 2223

2390

558 567

577

8611 9079

9802 14820" 11109 15228

1895 1971

2067 2190

2364 2412

8087 8589

9346

14418 10690 14703

1820 1896

1992 2114

7479 7993

8761 13683 10095 13868

1712 1786

1876 1992

6801

8054 9327

12612 " 12724

1639

1824

7224 8383

11214 11271

1396 1454

1524

6533 5227 5654

6259 7245

9487 9509

1184 1231

1349

4296 4643

5126

7436 7436

929 961

995

5881

0.9

3196 3434

3751“ "5067' 4226

620 636

5775""

1773 1871

1993 T 3 ir r " 2154 2368

0705 0 .1

• •• **r

5715 0 .2

•**

0 .2 5 0 .3 0 .3 5 0 .4

• ••

0. 45 0 .5 0 .5 5

*•*

0 .6 0 .6 5 0 .7

T798

7308

6054

0 .7 5 0 .8 0 .8 5

***

*•*

5058

1571

2461

589 589

'

1 33

133

133

133

' 142 142

143

252

U S-

143

143

256

259 263

149

151

147

264 265

T68 268

151 152

152 154

154

261

599 613

262 264

267 268

271 268

" 151 152

152 154

154

601 606

” 259

2'68

261

264 265

263

148 149

149 151

143

254 258

259 252

142 143

143 145

135

245 235

133

133 " 134

136

134

124

"27"4 213

120 120

120 121

121' 110

557

254

513"

564

587

552

574

588

249 252

2283 2313

520 527

561

557

736

240

548

239

242

2149 2164

483 492

499 511

520

217 218

220

514

1962 1967

436 442

449 456

1721 1719

376 381

1431 1422

304 309

1037

1087 1076

220 221

652

692

671

681

\m

1611

1264

"

456 T 6 5

?39

221

'

12C3—

235

213 "

148

'

149

134 135

151

149 147

151 145 "

467

---- 192

193

458

192

195

196 186

102 104

104 104

106 93

387 393

""i u r '

161 162

162 164

165 153

84 84

84

390

86 73

312

317

321 310

124 124

124 126

126 115

224

229