The aim of this unique volume is to help medical researchers design clinical trials to improve survival, remission durat
448 84 41MB
Pages [863] Year 1990
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.
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.
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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
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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
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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)
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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
H«
=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
b£
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
4«
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
7«
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
'
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
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'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
*
----- 2859" ' 307*“ “ *973" 2935 3396 5181
51'2 ""
1010
1237
433 449
952 1041
1235 1276
438 455
479 512
■851“ "951 '
1243
570
1049
1289
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” 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
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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
*'
*
1322 ■ IS2T" 3011 "' 1443
•
TOOT ' 1308 T W 1160 1564 2265
•
830
1954
928' 1088
2994
1158 1432
717"
983'
808
964
' '
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
• **
«*
1433 1441
143? 1489
1504 2265
458
0.15' '*** ***
T787
2023" "2531 2994
0.2 "■***
"2719
2477" 3033 2575 3619
717
.00
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0.25
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2000 2439
2725
2088
2807
3429
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2753
2946
0.3
***
2910 2948
3206
4556
0.35
***
"2987 3037
313-2 3364
4519 4869
0.4
*** ***
2969 3033
3435
5077
0.45"" ***
2874 2954
3100 3430
075
.75
.50 .25
.00
1.0
BIN
.75
DEL=.20
.50 .25
BIN
75
1.0
.50 .25
119
.00
BIN
.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
"
"
832
407
w r
421 440
447" 495
249 255
270
261
281 284
178
"132“
881
980 1081
175
802
186
191 183
*3 7 860
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
'
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
'
428 448
473 509
564 553
243 273
284 299
319 300
178 183
189 196
"
410 430
455” 546 491 530
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
125 129
134 108
154 159
145 171
179 153
"
4975 5077
799 845
911 1017
1234 1237
0.6
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'2307 2435
2447 3070
48-03 4869
751 798
844 968
llffff"" 1172
0.65
*** •**
2074 2213
2453 2860
4524 4556
693 739
802“ 1093 1081 901
0.7
*** *•*
1*37 1978
2177" 31"30 2611 4140
*23
668
724 815
983 964
• **
1596 1732
1940" 2321
347 584
635 709
843 821
283
299 319
347 322
0.8 “ « *
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"1338 1471
i'533" 3011 1985 2994
454 484
524 582
676 651
216 225
234 249
266 241
***
1184
347
394 429
482 456
3525" 3619
1082
1352 1588
2265
777
944"
1438 1432
846
93 93
149 171
2853 3239
' *** •»*
.50 .25
92 92
167 168
2524 2640
0.9
.75
121
296 456
***
0.85
1.0
153
287
'2721 2818
O': 75
.00
BIN
120
291
283
***
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
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454 459
467 478
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249
595
619 641
679 821
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742 777
841 964
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1443
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4519 4869
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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
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5077
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409
466
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4869
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976
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2102" 2468 2244 2899
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4556
748
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1095“ 1081
" 634' 677
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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 "™*“ **•
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*•*
HOT" 1354
586
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351 '" 397
2265
372
1206
1609
791 860
958
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1115
1432
431
482 456
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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
226
217
86
745
TABLE 7: ALPHA= 0.05 P0WER= 0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 2750
DEL=.0 2 FACT=
DEL=.05 .50 .25
DEL=.10 .0 0 BIN
DEL=.1S
DEL=.20
.5 0 .25
.0 0 BIN
1 .0 75
.5 0 .2 5
.0 0 BIN
1 .0 .75
.50 .25
.00 BIN
140 140
140 140
140 217
62 82
62 82
82 115
58 58
58 58
58 73
762 1076
233 233
233 235
235 310
123 125
125 125
125 153
82 82
62 82
62 93
1082 1098
lll6 1422
315 318
3 l9 321
322 390
161 161
161 163
163 186
"101 102
102 102
1E2 no
1332 1352
1376 1405
1442 1719
388 391
393 397
40b 458
192 194
1$4 194
195 213
118 118
120 120
120 124
102$2 11890
1555 1584
1622 1666
1724 1967
448 452
4 $6 460
" 465 514
216 219
219 221
223 235
132 132
133 133
133 135
8668 9073
9415 11616 10070 1321$
1727 1768
1818 1880
l$ 6 l 2164
496 50L
507 511
518 557
239 239
240 242
243 252
142 142
142 144
144 143
0 .3 5
9308 9573
1O0O4 13072 10826 1423$
1851 1902
1964 2041
2146 2313
531 538
"514" 551
560 588
252 254
256 257
2$$ 263
14$ 149
149 150
150 147
0.4
9475 9798
10322 14009 11300 14950
1930 1988
2062 2155
2280 2412
553 560
577
'587 606
260 263
264 ' 257 266 268
$410 9795
10401 14714 11520 15352
1965 2031
2113 2219
2363 2461
563 570
580 589
6bl 613
"2 6 3 264
766 269
268
0 .5
9159 9597
10277 14886 11508 15445
1961 2033
2l22 2236
2390 2461
$62 570
$79 589
" 601 606
25$ 260
264 266
267 263
0 .5 5
8761 9245
$960 14820 11285 15228
1921 1995
2088 2205
2363 2412
"548
535
556
575
587 588
250 252
256 257
8249 8761
9530 14418 10871 14703
1845 1921
2012 2127
2282 2313
522 531
$39 549
560 557
236 239
7646 8170
8946 13683 10273 13868
1737 1807
1895 2003
2150 2164
486 493
501 510
520 514
6966 7481
8231 9494
12614 12724
1$94 1660
1737 1835
1962 1967
438 445
0 .7 5
6209 6694
7389 8533
11212 11271
1418 1473
1538 1618
1721 1719
377 383
0. 8
5369 5797
6400 7371
9487 9509
12ol 1244
1295 1356
1431 1422
0 .8 5
4 4 l2 4757
5237 5974
7437 7438
940 969
1003 1041
1088 1076
0 .9
3275 3512
3825 4282
5066 5058
625 639
6 $6 673
692 681
0 .$ $
1806 1902
201$ 2172
2380 2368
1 .0 .75
.50 .25
.0 0 BIN
l 600 1811
1823 1838
1862 3481
390 391
393 393
395 681
” 377? 3808
3860 3942
40$2 6047
738 744
749 754
O .IS
$$53 5620
5726 5919
6328 8304
1057 1068
'G'.'T '
70o8 7115
72$2 7622
840$ 10251
0 .2 5
8110 8263
8519 9008
0 .3
PCONT: 0 .0 5 0 .1
0 .4 5
0 .4 0 .6 5 0 .7 '
1 .0 .75
1 .0 .75
REQUIRED NUMBER OF PATIENTS
153" ” T53~~ 154 149 153 154 153 153
154 " 154 154
147
14$ 149
150 150
1$3 143
25$ 252
142 142
T 4 r~ 144
146 135
240 242
24$ 235
132 133
133 133
135 124
216 218
219 221
225 213
120 120
120 122
122 110
'4'52 ' 467 459 458
192 194
1$4 195
186
102 104
104 104
104 93
3B8 395
400 390
161 161
163 164
164 153
'8 4 ” 84
85 85
85 73
305 309
312 318
321 310
125 125
125 126
126 115
221 223
22$ 226
217
228
771
197
"
"
'
CRC Handbook of Sample Size Guidelines for Clinical Trials
746
TABLE 7: ALPHA= 0.05 POWER= 0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 3000 DEL=.01
DEL=.02
DEL=.05 DEL=.10 DEL=.15 1 .0 75
.50 .2 5
.0 0 BIN
1 .0 .7 5
.50 .25
.0 0 BIN
"11'5 " 115 115 328
58 58
58 58
58 134
40 40
40 40
40 80
182 182
182 182
182 419
80 80
80 80
80 155
50 50
50 50
50 89
1862 3481
392 392
392 392
395 681
140 140
140 140
140 217
80 80
80 80
80 115
3868 3950
4093 6047
740 745
748 755
763 1076
230 235
235 235
235 310
122 125
125 125
175 153
5570 5642
5T50 5942
6328 8304
1060 1070
1085 "1 1 1 5 1100 1422
317' 317
320 320
320 390
160 160
163 163
163 186
32833 40298
7037 7150
7333 "TRIO 7663 10251
1337 1355
1378 1408
1442 1719
388 392
392 395
400 458
193 193
193 193
193 213
30595 31153 30782 32215
40310 46976
8155 8315
8578 9065
1562 1592
1630 1670
1723 1967
448 452
455 460
467 514
220 220
220 220
223 235
33215 33985 33475 35435
46678 52416
8927 9140
9493 11815 10150 13219
' 497“ "'5 0 8 500 512
520 557
238 238
242 242
242 252
34465 35488 34805 37385
51830 56620
9385 9658
10105 13075 10930 14239
53TT" 545 538 553
560 588
' ” 253' ' 253 ~ 237 ' 253 257 263
553 560
5'68' 575
587 606
'
.5 0 .25
.0 0 BIN
947 947
950 950
955 3648
347 347
347 350
350 1206
115 115
2095 2098
2105 2113
2128 6022
673 673
677 677
680 1793
0 .0 5
6340 6358
6392 6463
6647 12848
1805 1813
1825 1840
0 .1
13990 14128 14035 14368
15470 23235
3782 3820
0 .1 5
20905 21152 20987 21617
24437 32385
26882 26623 27617
0 .2 5 0 .3
PCONT =*** 0. 01 0 .0 2
0 .2
0 .3 5
***
•**
•**
1 .0 .75
.50 .25
1 .0 .75
1 .0 .7 5
FACT=
.00 BIN
.50 .25
.00 BIN
REQUIRED NUMBER OF PATIENTS
10250 11890
1738 " 1825 "1 7 6 0 ' 1780 1885 2164 ” '1 8 6 5 1915
1975 "TT47" 2050 2313
0 .4
34490 35822 ""55700" 34940 38222 59588
9568 9905
10442 14008 11425 14950
1948 ~ 2075 " 2282 2005 2162 2412
0. 45
33490 3518S 34063 38120
58258 61319
9520 9917
10540 14615 11657 15352
1985 2050
2128 2230
2360 2461
565 572
580 590
31660 33785 32390 37250
59477 61814
9287 9737
10430 14885 11660 15445
1982 2053
2140 2245
2390 2461
565 572
0 .5 5
29233 31820 30140 35770
59350 61072
8900 9395
10142 14822 11443 15228
1945 "2 1 0 5 "~"236'5 2015 2215 2412
0 .6
2643 5 29477 27530 33805
57875 59093
8402 8923
9700 14417 11030 14703
1870 1940
2027 2140
23477 26893 24740 31445
55063 55878
7802 8335
9115 13682 10430 13868
1760 1828
0 .7
20522 24163 21902 28750
50920 51427
7120 7640
8395 9643
12613 12724
0 .7 5
17657 21317 19070 25727
45457 45739
6355 6842
7535 8665
0 .8
14882 18332 16232 22337
38675 38815
5495 5927
0 .8 5
12115 15118 13303 18470
30602 30654
4517 4862
9175 11465 10097 13892
21250 21256
5627 6137
6865 8035
10633 10622
2570 2735
2945 3230
3662 3648
0 .5
0 .6 5
0.9
•**
***
•••
0 .9 5 0 .9 8 '
*»*
"
260" 260
265 265
598 613
265 265
268 “ 7 7 2 ' 268 268
580 590
602 606
260 260
265 265
550 557
568 575
587 588
2282 2313
523 535
542 550
560 557
238 238
242 242
245 235
1910 2015
2147 2164
490 497
505 512
520 514
215 220
220 223
223 213
1615 1678
1753 1843
1963 1967
440 445
452 460
467 458
193 193
193 197
197 186
11215 11271
1435 1487
1550 1625
1723 1719
380 385
388 395
400 390
160 163
163 163
163 153
6527 7480
9485 9509
1213 1255
1303 1360
1430 1422
305 310
313 317
320 310
125 125
125 125
125 115
5335
7435 7438
950
6055
977
1007 1045
1085 1076
220 223
223 227
227 217
3347 3580
3890 4330
5065 5058
628 643
658 673
692 681
1835 1930
2042 2185
2380 2368
'
268 268
268 263
“ 2 5 0 ' ~253~ 260 253 257 252
'
747
TABLE7: ALPHA* 0.05 POWER= 0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 3250 D E I*.01 FACT=
D E I*.02
1 .0 .75
.50 .25
.00 BIN
POONT=***
1 .0 .75
.50 .25
D E I* .05 .00 BIN
1 .0 .75
D E I* .10
D E I* .15
.50 .25
.0 0 BIN
1 .0 75
.50 .2 5
.00 BIN
1 .0 .75
.50 .25
.00 BIN
43 43
43 43
43 80
s r "” 31
REQUIRED NUMBER OF PATIENTS
0 .0 1
••• • **
948 948
948 953
953 3648
347 347
347 347
347 1206
116 116
114 116
116 328
57 59
'3 7 ' 59
59 134
0.&2
••• ***
2594 2099
2101 2115
2124 4022
472 677
677 677
680 1793
181 181
181 181
184 419
?9 79
79 79
79 155
***
4343 4364
6391 6470
"3449" 12848
1854" 1814
393 393
393 393
394 481
141 141
n r 141
141 217
742 745
750 753
751 1074
233 233
233 233
233 310
ITT-
1042 1075
1084 1099
1114 1422
3 l4 319
319 319
8407 10251
1343 1362
1384 1408
1441 1719
387 393
0 .5 5
1874 "18*3 ' 1842 3481
-
51
51
51 89
ffr
84 84
84 115
124
124 124
124 153
322 390
140 140
160 160
160 184
396 396
401 458
192 192
192 192
192 213
84
0.T
~***
0 .1 5
'*** ***
20724 21193 21014 21688
24437 32385
0 .2
••• »**
24524 26945 24669 27728
32834 40298
15.25
••• ***
30442 ■312*4 "40311 ' ” 8173" 8363 30845 32381 44976
9122
15 7 5 1 11890
1571 1598
"14341476
172 5 1947
449 452
458 461
466 514
217 217
222 222
222 235
0 .3
••• *•*
33283 34111 33559 35655
46674 52414
8984 9208
9569 11816 10227 13219
1749 1790
1834 1891
1961 2164
498 501
5d6 514
517 557
236 238
241 241
241 252
d .3 5
••• *•*
34550 35655 34919 37670
51832 56620
945 r 9744
10199 13571 11023 14239
1879 1928
1985 2058
2148 2313
“ 534 539
547 55d
'558 588
254 254
254 257
257 263
**•
34602 36040 35086 38572
55702 59588
9658 10552 14510 10007 11535 14950
1944 2021
2084 2172
2281 2412
558 563
571 579
588 606
243 243
243 266
266 268
0 .4 5
••• *•*
33632 35460 34252 38539
58259 61319
9626 10666 14414 10037 11784 15352
2004 2064
2142 2237
2362 2461
566 574
582 591
599 613
263 266
264 271
271 268
0 .5
•••
31644 34114 32627 37730
59478 61814
9406 15373"1 4 5 8 8 9869 11795 15445
"""2554" 2151" 2069 2256
2391 2461
“ 54T~ 574
582 591
599 606
243 243
263 266
266 263
•••
29464 32210 30434 36300
59351 61072
9038 9541
10292 14823 11589 15228
1944 2034
2 llS 2224
2362 2412
550 558
546 579
588 588
717” 254
254 257
257 252
•**
24718 29914 27874 34371
57877 59093
8542 9073
9853 14419 11177 14703
1891 1961
2042 2148
2281 2313
523” 534
542 550
558 557
258"' 241
• ••
23804 27348 25133 32026
55044 55878
7949 8485
9268 13480 10573 13848
1777 1847
1923 2021
2148 2164
490 498
556 509
***
20&87 24649 22317 29326
50917 51427
7241 7784
8542 9780
12613 12724
1631 1693
1764 1850
1961 1967
441 449
***
18032 21794 19489 26266
45449 45739
"4489 6977
7673 8786
11215 11271
1449 1501
1563 1631
1725 1719
•••
15245 18771 16629 22821
38672 38815
5617 6048
4444 '9487 7578 9509
1224 1265
1311 1368
***
12437 15492 13653 18869
30604 30654
4612 4959
"3125 6129
7437 7438
954 984
0 .9
*•* *•*
9428 11743 10362 14167
2 l2 4 9 21256
3415 3646
3946 4374
506? 5058
631 647
0 .0 5
•••
5766 6283
7oo4 8155
10633 10622
1863 1953
2061 2199
2378 2368
0 .9 8
•••
2619 2781
2984 3256
3659 3648
0 .4
d .S s 0 .4 0 .4 5 0 .7 0 .7 5 0 .8 0 .8 5
•** •••
• ••
1*552""14178 1 5 4 7 3 — 3792” 3881 14051 14403 23235 3829 3959
4092 6047
” 3 587" "5774“” 6327 5661 5961 8304 7 0 4 7 ' 7372 7185 7700
'
'
"
238
241
246 235
523 514
217 217
222 222
225 213
452 461
464 458
192 192
192 198
198 186
379 384
387 396
40l 390
145 140
165 165
165 153
1433 1422
306 311
3 l4 319
319 310
124 124
124 124
127 115
1013 1046
1086 1076
222 222
225 225
230 217
66l 677
493 681
CRC Handbook of Sample Size Guidelinesfor Clinical Trials
748
TABLE 7: ALPHA= 0.05 POWER=0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP= 3500 DEL=.01 FACT=
1 .0 .7 5
.5 0 .25
DEL=.02 .0 0 BIN
POONT=***
O'. 01 ” * •
1 .0 .7 5
.50 .2 5
DEL=.05 .0 0 BIN
1 .0 .7 5
DEL=.1 0
.50 .25
.0 0 BIN
1 .0 75
.50 .2 5
DEL=.15 .0 0 BIN
1 .0 .7 5
.50 .25
.00 BIN
REQUIRED NUMBER OF PATIENTS
347" 347
317 347
347 1206
IT*” "T14 114 116
328
ri4
"38 58
2104 ' 212*"" 2115 6022
676 676
676 676
680 1793
1T1 181
181 181
181 419
81 81
81 81
4408 6478
4447 12848
1808 1817
1831 1843
1861 3481
391 391
391 391
396 681
137 137
" 948' ' 951" ' 951 948 2097 2103
951” 3648
58" ' 58 58 134
41 41
41
41 80
’ 81' 155
50 50
50 50
50 89
137 143
143 217
81 81
81 81
81 115
233 233
233 310
125 " 125 125 125
125 153
318 ” 321' 321 390
150 160
140 143
r53 " 186
195 " f*5 195 213
0.02
* •
0.05
* ” ""'4350 • 4347
0.1
• •
flO ll" 14172 14044 14435
15473 23235
3803 3838
3888 3966
4092 6047
711 746
750 755
764 1076
233 233
0.15
• •
20945 21233 21041 21755
24436 32385
5606 5681
5795 5979
6329 8304
AT45 1079
1088 1100
m 7 1422
~31fi 318
0.5
* *
26559 27008 24711 27840
32833 40298
7099 7216
7405 7732
8406 10251
1350 1368
1388 1411
1441 1719
391 391
396 396
400 458
190 195
0.25
• *
30689 31334 30902 32535
40308 46976
8234 8411
8486 9173
10252 11890
1581 1607
1437 1477
1721 1967
452 452
458 461
514
2T4 “ 221“ 221 221
221 235
0.3
• •
33343 34236 T 7 5 7 8 33641 35869 52416
9o34 "TOO "ll'STT” 9269 10293 13219
1741 “ TB40""T9 57" ' 1796 1893 2164
239 239
242 242
2'42 252
0.35
• •
34635 35820 35032 37943
5l829 56620
9526 9823
10284 13075 11106 14239
1893 1940
1992 2042
2146 2313
"534” 540
251 256
256 "250 256 263
0.4
* •
34714 36254 35233 38908
55700 59588
9741 10660 14006 10103 11635 14950
1980 2033
2097 2174
2281 2412
5'57 544
571 580
583 606
0.45
* •
33778 35723 "58255 34443 38935 61319
9727 T0784 14615 10147 11897 15352
2018 2080
2155 "2350 2244 2441
■ ~ 5 7 r" 575
583 592
4or
0 .5
• •
32028 34437 32868 38188
59476 61814
9523 9995
10704 14816 11923 15445
2024 2088
2147 "23*1 2263 2441
— 545” 575
583 “ 501 592 404
0.55
• •
29691 32588 30724 36800
59348 61072
9l44 9475
10436 14820 11722 15228
r7 8 3 '"2137"~23"45 2050 2234 2412
0.4
• •
26991 30339 28213 34901
57878 59093
8477 9211
9998 14417 11311 14703
l9lO 1975
2059 2155
2281 2313
•
*
24126 27819 25509 32573
55046 55878
8082 8425
9412 13682 10704 13868
1796 1861
1934 2033
0.7
• •
21239 25110 22718 29861
50919 51427
7396 7925
8677 9902
12611 12724
1448 1709
0.75
* •
18395 22245 19891 26772
45450 45739
4412 7108
7799 8896
11211 11271
0.8
* *
15590 19186 17004 23269
38672 ' 5725 38815 4157
4752 7671
0.65
* •
12743 15&43 13976 19235
30601 30654
4701 5043
0 .*
* •
9663 12002 10608 14423
21251 21256
0.95
• •
5900 6416
7134 8266
10634 10622
0.98
• •
2443 2820
30l6 3278
3660 3648
0.45
5oi ' 510 " 5 1 9 505 513 557
'
545 “ 557 554 588
' 270 265
245 245
' 245 —248” 245 248
413
'
250 245
245 245
268 268 248 268 248 243
589 588
251 “ 754” 254 254
270 252
528 534
545 '5 4 3 554 557
237 ” 242" 239 242
212 " 235
2150 2144
493“ 496
505 “ 51* 513 514
2T4 221
221 221
225 213
1773 1858
1963 1967
443“ 449
452 461
466 456
190 195
195 195
195 184
1444 1511
1569 1639
1721 1719
382 388
391 396
400 390
i4o 143
143 143
f5T 153
9488 9509
1234 1275
131T 1429 1371 1422
30V 312
312 318
321 310
125 125
125 125
T25 " 115
5506 6192
7435 7438
965 991
"101T" 1088 1053 1076
221 225
225 225
230 217
3476 3704
3996 4413
5063 5058
636 650
1887 1975
2080 2211
2377 2368
662 674
494 481
55* ' 571 543 580
'
-
'
749
TABLE 7: ALPHA= 0.05 POWER= 0.8 EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP^ 3750 D E L :.01 FACT=
DEL=.02
.50 .25
.00 BIN
950 950
950 950
953 3648
350 350
350 350
350 1206
2097 2103
2 lb * 2116
212$ 6022
*72 678
*78 678
5353 6372
*409 6484
.00 BIN
1 .0 .75
.00 BIN
1 .0 75
.50 .25
.0 0 BIN
1 .0 .75
.50 .25
.00 BIN
115 115
" 115 115
'1 1 5 328
"59" 59
59
39“ 134
40 40
40 40
40 80
*76 1793
161 181
181 184
164 419
81 81
''1 1 81
6l 155
53 53
53 53
53 89
6644 '"T B IT ' 1B31 12848 1822 1844
1863 3481
391 391
391 397
397 681
138 138
136 138
138 217
81 81
81 81
Bl 115
"753 756
762 1076
231 231
231 237
237 310
125 125
125 125
125 153
REQUIRED NUMBER OF PATIENTS
O.Ol 1 M ' 44 4
b.OS "44 4' *** O .i
1 .0 .75
.50 .25
.50 .25
PCONT
0.0 2
DEL=.05 DEL=.10 DEL=.1S
1 .0 .75
'4 4 4
'
***
14022 14191 14078 14468
15?72 23235
36o9 3847
3697 3972
4090 6047
743 747
#*• ***
20965 21275 21068 21818
32385
5622 5697
5615 5997
6325 8304
1072 1081
1090 1103
ills 1422
316 316
322 322
322 390
162 162
162 162
1*2 186
444
***
26590 27072 26753 27944
32834 40298
7122 7250
7437 7759
8406 10251
1333 1372
1390 1413
14*1 1719
391 391
397 397
4oo 458
194 194
194 194
194 213
**• • ••
50734 31428 30968 32688
40309 46976
8275 8453
8734 9218
10253 11890
1567 1615
1*43 1681
1722 1967
453 456
456 462
46* 514
218 218
218 222
222 235
44 4
334b9 343*2 33728 36078
4**7$ 52416
9091 9331
9706 11815 10356 13219
'1 7 * 9 ' 1850 1806 1897
1'9S2 2164
500 503
'30