Detection in Analytical Chemistry. Importance, Theory, and Practice 9780841214453, 9780841212084, 0-8412-1445-X

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ACS

SYMPOSIUM

SERIES

Detection in Analytical Chemistry Importance, Theory, and Practice Lloyd A. Currie,

EDITOR

Developed from a symposium sponsored by the Divisions of Analytical Chemistry, Environmental Chemistry, and Nuclear Chemistry and Technology at the 191st Meeting of the American Chemical Society, New York, New York, April 13-18, 1986

American Chemical Society, Washington, DC 1988

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

361

Library of Congress Cataloging-in-Publication Data Detection in analytical chemistry. ACS symposium series; 361 Includes bibliographies and indexes. 1. Chemistry, Analytic—Measurement—Congresses. I. Currie, Lloyd A., 1930. II. American Chemical Society. Division of Analytical Chemistry. III. American Chemical Society. Division of Environmental Chemistry. IV. American Chemical Society. Division of Nuclear Chemistry and Technology. V. American Chemica (191st: 1986: New York, N.Y.) VI QD75.4.M4D46 1988 ISBN 0-8412-1445-X

543

87-30735

Copyright © 1988 American Chemical Society All Rights Reserved. The appearance of the code at the bottom of the first page of each chapter in this volume indicates the copyright owner's consent that reprographic copies of the chapter may be made for personal or internal use or for the personal or internal use of specific clients. This consent is given on the condition, however, that the copier pay the stated per copy fee through the Copyright Clearance Center, Inc., 27 Congress Street, Salem, M A 01970, for copying beyond that permitted by Sections 107 or 108 of the U.S. Copyright Law. This consent does not extend to copying or transmission by any means—graphic or electronic—for any other purpose, such as for general distribution, for advertising or promotional purposes, for creating a new collective work, for resale, or for information storage and retrieval systems. The copying fee for each chapter is indicated in the code at the bottom of the first page of the chapter. The citation of trade names and/or names of manufacturers in this publication is not to be construed as an endorsement or as approval by ACS of the commercial products or services referenced herein; nor should the mere reference herein to any drawing, specification, chemical process, or other data be regarded as a license or as a conveyance of any right or permission, to the holder, reader, or any other person or corporation, to manufacture, reproduce, use, or sell any patented invention or copyrighted work that may in any way be related thereto. Registered names, trademarks, etc., used in this publication, even without specific indication thereof, are not to be considered unprotected by law. PRINTED IN THE UNITED STATES OF AMERICA

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

ACS Symposium Series M. Joan Comstock, Series Editor 1987 Advisory Board Harvey W. Blanch University of California—Berkele

Vincent D. McGinniss

Alan Elzerman Clemson University

W. H . Norton J. T. Baker Chemical Company

John W. Finley Nabisco Brands, Inc.

James C . Randall Exxon Chemical Company

Marye Anne Fox The University of Texas—Austin

E . Reichmanis AT&T Bell Laboratories

Martin L . Gorbaty Exxon Research and Engineering Co.

C . M . Roland U.S. Naval Research Laboratory

Roland F. Hirsch U.S. Department of Energy

W. D. Shults Oak Ridge National Laboratory

G . Wayne Ivie USDA, Agricultural Research Service

Geoffrey K. Smith Rohm & Haas Co.

Rudolph J. Marcus Consultant, Computers & Chemistry Research

Douglas B. Walters National Institute of Environmental Health

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

Foreword The ACS SYMPOSIUM SERIES was founded in 1974 to provide a

medium for publishing symposia quickly in book form. The format of the Series parallels that of the continuing ADVANCES IN CHEMISTRY SERIES except that, in order to save time, the papers are not typeset but are reproduced as they are submitted by the authors in camera-read form Paper reviewed unde the supervision of th Advisory Board and are selected to maintain the integrity of the symposia; however, verbatim reproductions of previously published papers are not accepted. Both reviews and reports of research are acceptable, because symposia may embrace both types of presentation.

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

Preface CHEMICAL MEASUREMENTS ARE CHARACTERIZED by three fundamental processes: detection, identification, and quantification. The first of these relates to the ultimate measurement capability as expressed in the detection limit. The invitation to organize a symposium on this topic carried the suggestion that we address the "true meaning" of detection limits. That charge, in fact, influenced the structure of the symposium and the content of this volume. The objectiv from both fundamental an in chemical measurement science. It is not intended to serve as a compendium of the current "detection limits" for a broad range of analytical methods. The "meaning" of detection and detection limits has been examined in two senses: (I) the basic scientific meaning as to exactly what is signified by the minimum detectable quantity of a chemical substance, and how that quantity is derived; and (2) the meaningfulness or usefulness of such detection limits in the context of external problems, such as those affecting society, industrial processes, or scientific research. It is timely and appropriate for these two sides of detection to be considered together, for the ability to detect prescribed amounts of chemical substances in the natural environment, foods, or manufactured products can have important effects on our economic or physical well-being. However, unless the technical significance of detection decisions and detection limits is fully defined, misleading or even dangerous conclusions can follow. Equally important is mutual understanding by the lay public and the technical community of their respective interpretations of detection. This text consists of an overview chapter and four principal sections. The first section addresses the issue of detection from the perspective of the well-informed but nonscientific public, that is, the most extensive user community of detection limits. The authors of Chapters 2 and 3, a former member of Congress and a former congressional subcommittee staff director, respectively, are eminently qualified to present the public view because they have both helped to shape that view and because they respond to the publics technological needs. The second section begins with a tutorial chapter, followed by six contributions treating fundamental characteristics of the chemical measurement process, which must be taken into account to derive meaningful detection limits. Included in this section

vn In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

are expositions on comparative detection limits, a matter of some importance in selecting chemical methods or in interpreting interlaboratory data. Five chapters make up the third section of the book. Selected examples illustrate the care and energy involved in devising methods of extreme sensitivity. Exhaustive method characterization and attention to a host of potential sources of error mark these contributions. These chapters, together with several chapters in the preceding section, also treat important areas of application. The text concludes with two panel discussions. The first reflects the overall focus of the book, in that it examines with some vigor "real-world" problems and needs for meaningful detection, both in the laboratory and in the regulatory environment. The second panel, comprising members of an international team working on coding environmental analytical data, shares some of the approaches and issues involved in preparing low-level chemical data for computerized dat distortion are quite significant in this regard because of problems of rounding and truncation and interpretation of the meaning of detection. The objectives of this book will have been met if improved communication on the subject of detection results. Such communication would be beneficial not only between the public and the technical community, but also within the technical community. As indicated in the overview chapter, the history of detection limits in analytical chemistry has been marked by an unfortunate degree of diversity in terminology and meaning and a lack of attention to the probabilities of both false negatives and false positives. At the same time, we should help the public understand that all detection limits must allow for these two types of error, and that "zero" detection limits cannot, in principle, be attained. DISCLAIMER This book was edited by Lloyd A. Currie in his private capacity. No official support or endorsement by the National Bureau of Standards is intended or should be inferred. L L O Y D A. CURRIE

Gaithersburg, MD 20899 September 1, 1987

V111

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

Chapter 1

Detection: Overview of Historical, Societal, and Technical Issues Lloyd A . Currie Center for Analytical Chemistry, National Bureau of Standards, Gaithersburg, M D 20899

Practical societa advances frequentl possessing s p e c i f i e d detection c a p a b i l i t i e s with acceptable p r o b a b i l i t i e s of false p o s i t i v e s and false negatives. The first part of t h i s overview introduces the basic concept of (chemical) detection, together with i t s applicability to selected s o c i e t a l problems such as the detection of natural hazards and the implementation of c e r t a i n regulations. Basic scientific measurement issues concerning assumptions and t h e i r validity, plus hypothesis t e s t i n g and decision theory as r e l a t e d to analyte detection are next introduced. Part two comprises a b r i e f historical review, h i g h l i g h t i n g major contributions to the concept and r e a l i z a t i o n of detection i n chemical applications. The current state of the art i s then considered. Part three i s the most extensive, as i t seeks to expose most of the technical issues involved i n deriving meaningful detection decisions and detection limits, considering the o v e r a l l Chemical Measurement Process. Those concerned p r i m a r i l y with s o c i e t a l or historical matters may wish to pass over t h i s part. Among the topics discussed are: systematic and model error; non-normal random error; the s p e c i a l problem of the blank; r e p l i c a t i o n vs Poisson variance; issues concerning complex data evaluation, c a l i b r a t i o n , and reporting -- including pitfalls associated with "black box" algorithms; OC curves; power of the t - t e s t ; and q u a l i t y . The section concludes with some new material on d i s c r i m i n a t i o n limits, lower and upper regulatory l i m i t s , multiple detection decisions, and univariate and m u l t i variate identification. A brief summary follows, bringing together historical, s o c i e t a l , and technical highlights. A concluding observation i s that a meaningful approach to p r a c t i c a l s o c i e t a l needs i s at hand, but that order must be brought out of the extant d i v e r s i t y of technical views on detection. T h i s chapter not subject to U . S . copyright Published 1988 A m e r i c a n C h e m i c a l Society

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

2

DETECTION IN ANALYTICAL CHEMISTRY The DETECTION LIMIT (Lp) i s one o f t h e most important c h a r a c t e r i s t i c s o f any Measurement P r o c e s s . Recognizing the e x i s t e n c e o f such l i m i t s i s c r u c i a l b o t h f o r s t r i c t l y s c i e n t i f i c endeavors, such as t h e s e a r c h f o r a new fundamental p a r t i c l e ( i l , and f o r v i t a l s o c i e t a l a p p l i c a t i o n s o f s c i e n t i f i c measurements, such as t h e d e t e c t i o n o f a p a t h o l o g i c a l s t a t e o r a hazardous l e v e l o f a heavy m e t a l . I n t h i s l a t t e r r e g a r d , i m p o r t a n t p r o g r e s s has been made i n c o n v e y i n g t o t h e p u b l i c and t h e i r p o l i c y makers t h a t i t i s a l a w o f measurement s c i e n c e t h a t t h e d e t e c t i o n c a p a b i l i t y o f a l l Measurement P r o c e s s e s must s t o p s h o r t o f z e r o , i n c l o s e analogy w i t h t h e T h i r d Law o f Thermodynamics. R e c o g n i t i o n t h a t Lq may n o t be z e r o , has a l l e v i a t e d e a r l i e r l e g i s l a t i v e problems, such as t h e d i c t u m t h a t no r e s i d u e o f p r o v e n a n i m a l c a r c i n o g e n s may be p r e s e n t i n c e r t a i n f o o d p r o d u c t s ( 2 ) . The f a c t , however, t h a t d e t e c t i o n l i m i t s c a n , a t a c o s t and w i t h t e c h n o l o g i c a l advances be made e v e r s m a l l e r h a s f o r c e d reexami nation o f regulatory issue potential detection capabilities c o n s i d e r a t i o n o f c o s t / b e n e f i t o r "acceptable r i s k " a l t e r n a t i v e s t o "no d e t e c t a b l e r e s i d u e " r e g u l a t o r y p o l i c y ( 3 ) . Such a l t e r n a t i v e s are mandatory i n l i g h t o f t h e fundamental p r i n c i p l e s o f d e t e c t i o n . D e f i n i n g a c c e p t a b l e l e v e l s o f r i s k ( 4 ) , whether i n a r e g u l a t o r y s e t t i n g o r w i t h r e s p e c t t o m e d i c a l d e c i s i o n s o r even i n terms o f governmental actions i n connection with potential natural d i s a s t e r s , i s p r i m a r i l y a s o c i o p o l i t i c a l matter. Although t h i s i s s u e i s o f c e n t r a l importance, i t t r a n s c e n d s t h e theme o f t h i s c h a p t e r , w h i c h i s t o examine t h e h i s t o r i c a l e v o l u t i o n and c u r r e n t s t a t e o f t h e a r t o f d e t e c t i o n from t h e p e r s p e c t i v e o f c h e m i c a l measurement s c i e n c e . I n o r d e r t o h i g h l i g h t t h e importance o f D e t e c t i o n D e c i s i o n s and Detection L i m i t s , and t o u n d e r l i n e the f a c t that the p r o b a b i l i t y o f d e t e c t i o n does n o t i m m e d i a t e l y pass from z e r o t o u n i t y a t t h e D e t e c t i o n L i m i t , we have p r e s e n t e d i n F i g . 1 s e v e r a l s i t u a t i o n s where v a l i d d e t e c t i o n d e c i s i o n s and adequate d e t e c t i o n l i m i t s a r e o f c o n s i d e r a b l e p r a c t i c a l importance. (The p r e s e n c e o f a f i n i t e r i s k o f e r r o r ( f a l s e negative) a t the detection l i m i t i . e . , t h e absence o f " c e r t a i n t y " i s t h e second a s p e c t o f t h e problem t h a t i s somewhat f o r e i g n t o t h e common u n d e r s t a n d i n g , t h e f i r s t being the f a c t that zero d e t e c t i o n l i m i t s a r e unattainable.) This f i g u r e introduces the Hypothesis Testing foundation f o r D e t e c t i o n , and i t demonstrates t h a t i t i s e s s e n t i a l f o r those o f us i n v o l v e d i n measurement s c i e n c e t o d e v e l o p a sound, common, and q u a n t i t a t i v e approach t o t h e f o r m u l a t i o n o f D e t e c t i o n L i m i t s . I n a d d i t i o n , t h i s f o r m u l a t i o n must be communicated i n an e f f e c t i v e manner b o t h w i t h i n t h e s c i e n t i f i c community and w i t h t h o s e who depend on o u r measurements f o r s o c i e t a l d e c i s i o n s and p o l i c y making. As a f i n a l i n t r o d u c t o r y n o t e , i t s h o u l d be o b s e r v e d t h a t from the p e r s p e c t i v e s o f b a s i c d i s c o v e r i e s i n S c i e n c e and t h e e a r l y d i s c e r n m e n t o f fundamental changes i n t h e G l o b a l Environment (e.g.,

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

1. CUtfRIE

Overview of Historical, Societal, and Technical Issues

H Y P O T H E S E S

••• •• •

CO 1 2 2-4 2+ >1

F i n a l l y , i t i s i m p o r t a n t t o note t h a t the l i m i t o f d e t e c t i o n w i l l be l a r g e r under some c o n d i t i o n s i n which a measurement i n v o l v e s consumption of a sample. For example, a mass s p e c t r o m e t e r equipped w i t h a s i n g l e d e t e c t o r i s sometimes used t o measure more than one mass-to-charge r a t i o i n a g i v e n sample so as t o i n c r e a s e one's c o n f i d e n c e i n the i d e n t i f i c a t i o n o f the a n a l y t e . I f the s p e c t r o m e t e r spends e q u a l time on each o f t h r e e masses (and the s w i t c h i n g time i s n e g l i g i b l e ) , the q u a n t i t y o f sample must be t h r e e times l a r g e r i n o r d e r t o a t t a i n the same d e t e c t i o n l i m i t as t h a t f o r the s i m i l a r

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

5. ROGERS

Interlaboratory Aspects of Detection Limits

99

procedure t h a t measures o n l y one mass f o r the same t o t a l time. We s h a l l see l a t e r t h a t such a t r a d e - o f f of improved s e l e c t i v i t y and reliability for a higher detection limit w i l l usually be desirable. SELECTIVITY ASPECTS S e l e c t i v i t y i s g e n e r a l l y i n v e r s e l y r e l a t e d t o the r e l a t i v e amount of i n t e r f e r e n c e one can expect from a p a r t i c u l a r s p e c i e s (above a g i v e n l e v e l ) i n a t t e m p t i n g t o measure a n o t h e r s o u g h t - f o r s p e c i e s . B e f o r e g o i n g f a r t h e r , one should r e c a l l t h a t the e x t e n t of an i n t e r f e r e n c e i s u s u a l l y expressed i n terms of i t s c o n c e n t r a t i o n or amount t h a t w i l l produce the same s i g n a l as the u n i t amount of the s o u g h t - f o r species. I t i s i m p o r t a n t t o note t h a t use of the standard a d d i t i o n or i n t e r n a l standard method t o e s t i m a t e the amount of a s o u g h t - f o r specie provide compensatin f o r an i n t e r f e r e n c e t h a The e x t e n t of s i g n a l fro taken i n t o account and s u b t r a c t e d by measuring a b l a n k t h a t c o n t a i n s a known amount of the i n t e r f e r i n g s p e c i e s i n the presence of a l l other s p e c i e s except the s o u g h t - f o r species. However, as will be p o i n t e d out below, t h i s p o s s i b i l i t y i s r u l e d out i f c o m p l e t e l y unknown substances are i n v o l v e d because one i s unable t o prepare an a p p r o p r i a t e b l a n k . I t i s worth n o t i n g t h a t i n c l a s s i c a l q u a n t i t a t i v e a n a l y s i s , which u s u a l l y d i d not i n v o l v e a n a l y s e s of t r a c e amounts, the problem of unknown i n t e r f e r e n c e s was a t t a c k e d by u s i n g two methods t h a t were as n e a r l y independent as p o s s i b l e . In t h a t way, the chance t h a t an i n t e r f e r e n c e would g i v e the same response f o r each method was m i n i m a l . In c o n t r a s t , t h e r e i s an example i n c l i n i c a l c h e m i s t r y which c l e a r l y s u f f e r s from a l a c k of s e l e c t i v i t y i n the a c c e p t e d method. F i g u r e 2 (11) shows t h a t the use of the determination of sugar i n serum as a method f o r d i a g n o s i n g d i a b e t e s i s c l e a r l y unsatisfactory. The d i s t r i b u t i o n f o r sugar c o n t e n t i n s e r a o f d i a b e t i c s d i s t i n c t l y o v e r l a p s the d i s t r i b u t i o n f o r those who are not. Hence, s i g n i f i c a n t f r a c t i o n s o f both f a l s e p o s i t i v e s and f a l s e n e g a t i v e s w i l l be o b t a i n e d over a r e l a t i v e l y wide range of sugar c o n c e n t r a t i o n . A s i m i l a r c o n c l u s i o n would have been reached i f sugar were indeed a h i g h l y s e l e c t i v e b a s i s f o r d i a g n o s i n g d i a b e t e s but t h e r e was a second unknown substance p r e s e n t i n some s e r a t h a t c o n t r i b u t e d an i n t e r f e r i n g "sugar s i g n a l " . Hence, the use of two "independent" procedures should enhance one's c o n f i d e n c e i n the results. The s i t u a t i o n i n v o l v i n g the completely u n i d e n t i f i e d source of i n t e r f e r e n c e becomes i n c r e a s i n g l y i m p o r t a n t as the c o n c e n t r a t i o n or amount of s o u g h t - f o r substance d e c r e a s e s (.2) • Donaldson (12) p o i n t e d out t h i s p r i n c i p l e , which can be i l l u s t r a t e d u s i n g 99.999% water t h a t c o n t a i n s 10 p a r t s per m i l l i o n o f t o t a l i m p u r i t y . If we make the s i m p l i f y i n g assumption t h a t a l l i m p u r i t i e s are p r e s e n t at the same l e v e l , we c a l c u l a t e t h a t 10 i m p u r i t i e s can be p r e s e n t at the 1 ppm l e v e l , 10^ a t the 1 p a r t per b i l l i o n l e v e l or 10^ at 1 p a r t per t r i l l i o n . The l a s t f i g u r e c o r r e s p o n d s q u i t e c l o s e l y t o the e s t i m a t e d t o t a l of known c h e m i c a l s p e c i e s . Hence, when one i s faced w i t h the t r a c e a n a l y s i s of a complete unknown, such

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

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- DISTRIBUTION OF T H O S E WITH D I A B E T E S

DISTRIBUTION OF T H O S E WITHOUT 0 I A 8 E T E S

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5. ROGERS

Interlaboratory Aspects of Detection Limits

101

as the water i n a drainage ditch from an i n d u s t r i a l plant, the approach to s e l e c t i v i t y of estimating the extent of interference based on a few known species i s t o t a l l y inadequate. One can get a feeling for the r e a l i t y of such interferences from unusual examples that came to l i g h t that relate to my service with a team of consultants to advise the Dow Chemical Company concerning the adequacy of their procedures for analyzing dioxins. The overall procedure used by Dow involved multiple high-resolution steps (13); an i n i t i a l l i q u i d - l i q u i d extraction followed successively by l i q u i d chromatography, gas chromatography, and, f i n a l l y , a few selected ions i n mass spectrometry. One of their chemists remarked that they found, quite by accident, when using highly p u r i f i e d nitrogen to evaporate a solvent from a sample p r i o r to mass spectrometric measurement of the dioxin, high e r r a t i c values were obtained unless they f i r s t passed the nitrogen through a column packed with s i l i c a g e l That seemingly unnecessary step removed the unidentified interference attention only recently fish that had been extracted, and "cleaned up" by liquid chromatography before being analyzed by mass spectrometry using three different mass-to-charge r a t i o s , unexpectedly high results were obtained. By recording the entire spectrum over a wide range of masses, the selected masses were found to be s i t t i n g on top of a very broad high background which the chemist speculated might have been a large glyceride, unanticipated and unidentified, that broke up into a broad continuum of different masses i n the range of interest. (Telephone conversation with Lewis Shadoff i n July 1986) A third example from the laboratory of V e i l l o n has recently been described, together with i t s h i s t o r i c a l background (14). In b r i e f the graphite furnace measurements of chromium using atomic absorption spectrometry, were confounded with an unidentified species in urine samples that was contributing a background signal which was inadequately corrected for when using a deuterium lamp source. V e i l l o n showed a linear plot r e l a t i n g the magnitude of the background signal to the apparent chromium concentration i n the urine. He estimated that erroneous values had been reported i n the l i t e r a t u r e for more than 10 years! E a r l i e r , mention was made of the c l a s s i c a l way of insuring higher s e l e c t i v i t y by doing two unrelated determinations i n p a r a l l e l . The Dow determinations of dioxins cited above are examples i n which selectivity was increased by performing multiple, relatively high-resolution steps i n one quantitative procedure, but they s t i l l encountered unexpected interferences. There are also other examples of procedures consisting of multiple high-resolution steps such as those in mass spectrometry-mass spectrometry, mass spectrometry-infrared, and other "hyphenated" techniques which also increase one's confidence i n the r e s u l t s . However, i t i s clear that we need a way to estimate the s e l e c t i v i t y of such techniques when a large number of species, most of them unknown, might be present. This aspect w i l l be addressed more f u l l y l a t e r .

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REGULATORY/CONTROL LIMITS FOR TRACE AMOUNTS The term " r e g u l a t o r y l i m i t " u s u a l l y i m p l i e s t h a t a governmental body has s e t t h e l i m i t whereas t h e term " c o n t r o l l i m i t " i s u s u a l l y associated with process specifications f o r private or non-governmental purposes. I t i s the w r i t e r ' s impression t h a t , i n a r r i v i n g a t such l i m i t s , t h e u s u a l p r a c t i c e i s t o : ( a ) use t h e most s e n s i t i v e p r o c e d u r e , ( b ) t e s t t h e procedure w i t h known o r l i k e l y i n t e r f e r e n c e s , ( c ) use d a t a from i n t r a l a b o r a t o r y s t u d i e s t o e s t i m a t e t h e RSD f o r use i n c a l c u l a t i n g t h e d e t e c t i o n limit f o r the p r o c e d u r e , (d) use a q u a l i t y a s s u r a n c e procedure t h a t employs samples o f unknown c o n c e n t r a t i o n s w h i c h , however, a r e known t o the a n a l y s t t o be s t a n d a r d s , and (e) a p p l y g u i d e l i n e s o f the American Chemical S o c i e t y i n s e l e c t i n g the " r e g i o n s o f d e t e c t i o n " and " r e g i o n s of q u a n t i t a t i o n " (_3) . In c o n t r a s t , a g e n e r a l p r o t o c o l recommended b t h AOAC that has long been used by t h from t h e above approach s e l e c t e d f o r use may o r may n o t be the most s e n s i t i v e one a v a i l a b l e . Second, t h e RSD o b t a i n e d from t h e pooled r e s u l t s has been r e c o g n i z e d as u s u a l l y b e i n g a p p r o x i m a t e l y double t h a t o f t h e v a l u e obtained in a single laboratory. The f a c t t h a t a l o n g time p e r i o d may be r e q u i r e d t o reach t h a t minimum m u l t i p l e o f an i n t r a l a b o r a t o r y v a l u e has a l s o been r e c o g n i z e d . The American N a t i o n a l Standards I n s t i t u t e (ANSI), a f t e r much d e l i b e r a t i o n , has added a n o t h e r c o n c e p t , t h a t o f an A c c e p t a b l e Minimum D e t e c t i o n Amount (AMDA) f o r use i n i n t e r l a b o r a t o r y s t u d i e s . A l t h o u g h i t has been d i s c u s s e d i n more d e t a i l by ( B r o d s k y , A. , N u c l e a r R e g u l a t o r y Commission, Washington, D.C., u n p u b l i s h e d d a t a . ) , the AMDA, i n b r i e f , i s t h e MDA t h a t i s o b t a i n a b l e i n p r a c t i c e by competent a n a l y t i c a l s c i e n t i s t s u s i n g the best state-of-the-art at e c o n o m i c a l l y a f f o r d a b l e c o s t s t o t h e customer. Where p o s s i b l e , the AMDA has been e s t a b l i s h e d a t l e a s t s e v e r a l times h i g h e r than the MDA, i f t h e h i g h e r v a l u e i s adequate f o r p r o t e c t i o n purposes. In essence, t h e AMDA p e r m i t s the f l e x i b i l i t y for different l a b o r a t o r i e s t o use cheaper and more r a p i d procedures when they are a v a i l a b l e and meet t h e l i m i t . In the w r i t e r ' s opinion, t h i s concept has been i m p l i c i t , i f n o t e x p l i c i t , i n t h e s e l e c t i o n o f procedures by the AOAC and i n EPA r e g u l a t i o n s . The AMDA concept o f ANSI i s a t t r a c t i v e , and t h e w r i t e r would l i k e t o expand upon i t . F i r s t , i f t h e RSD and t h e MDA have been based on i n t r a l a b o r a t o r y s t u d i e s , a procedure f o r e s t i m a t i n g t h e i n t e r l a b o r a t o r y RSD and t h e AMDA c o u l d be done by a p p l y i n g an appropriate s e r i e s o f approximate c o r r e c t i o n s shown i n T a b l e 1. Such c o r r e c t i o n s c o u l d be a p p l i e d t o e i t h e r t h e o r i g i n a l procedure f o r which an AMDA was t o be s t a t e d o r t o the a l t e r n a t e l e s s s e n s i t i v e procedure which was t o be used f o r t h e AMDA. Of c o u r s e , i f an AOAC-type i n t e r l a b o r a t o r y study were conducted t o determine a pooled RSD, o n l y the c o r r e c t i o n s f o r v a r i a b l e s n o t i n c l u d e d i n the AOAC-type study would be used. To a p p l y t h e AMDA concept t o c r i t i c a l r e g u l a t o r y d e c i s i o n s , i t would be easy t o adopt t h e c l a s s i c a l concept o f r e q u i r i n g a n a l y s e s by two as n e a r l y independent methods as p o s s i b l e . T h i s would be an i m p o r t a n t s t a r t i n t h e d i r e c t i o n o f a d d r e s s i n g t h e q u e s t i o n s of p o s s i b l e c o n t r i b u t i o n s t o t h e measured s i g n a l s by unsuspected

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and unrecognized interferences. However, since the second procedure w i l l r a r e l y be as sensitive as the f i r s t , adoption of the second procedure w i l l provide a basis for deciding more e x p l i c i t l y the minimum multiple that should be applied by ANSI i n c a l c u l a t i n g the detection l i m i t on going from an MDA to the AMDA (or to a second, confirmatory AMDA procedure). The use of such a double-check w i l l also contribute to the r e l i a b i l i t y through having another test of the s e l e c t i v i t y . Remember that the usual way of discussing s e l e c t i v i t y and interferences i s to work with species that are known or suspected to be present. However desirable that exercise may be, i t i s , unfortunately, u n r e a l i s t i c i n dealing with most environmental samples and, possibly, many c l i n i c a l samples. If one r e c a l l s the large number of possible interferences that might be present when making an analysis at the low part per b i l l i o n l e v e l , a new approach to thinking about possible interferences and estimating s e l e c t i v i t y of a procedure appears to be needed. hopeless, undefined proble of Kaiser (15). Let us assume that one can do a computerized search of physical properties of a l l known organic and inorganic substances so that one can, for example, assemble l i s t s of their molecular weights, b o i l i n g points, mass-to-charge r a t i o s of positive (or negative) molecular ions, major bands in the infrared, and so forth. Then, i t should be possible to plot a d i s t r i b u t i o n of the frequencies with which d i f f e r e n t values are found along the axis of each property. Taking the b o i l i n g point at atmospheric pressure i n degrees Kelvin as an example of one property, i t would then be possible to estimate f i r s t the number of compounds that had b o i l i n g points between 300°K and 350°K (or any other desired range) and, second, what f r a c t i o n of the t o t a l possible number of species to which that corresponded. Hence, i f a d i s t i l l a t i o n were performed over that range, one would be making an estimate of the number of possible compounds that might be present. If a second property were employed i n the o v e r a l l analysis, such as a positive molecular ion spectrum in mass spectrometry, a similar estimate could be made of that d i s t r i b u t i o n . (For example, Harvan et a l . (16) reported that there were 700 elemental compositions within 0.2 dalton of the mass for tetrachlorodioxin that s a t i s f i e d the c r i t e r i a for valence, contained four chlorine atoms and, i n addition, only C,H,N,0 and S atoms.) It should then be possible to calculate for the n_ properties involved in a given o v e r a l l procedure a "volume" i n •n-dimensional space which would provide an estimate of the number of possible interferences present. That number, when viewed i n terms of the t o t a l number of compounds considered could provide a basis for estimating the s e l e c t i v i t y of the o v e r a l l procedure. To c i t e a s p e c i f i c example, a computerized search of the current Heilbron compilation, published by Chapman and H a l l , was made using the Lockheed Dialog system. That f i l e currently includes 150,000 organic compounds. F i r s t , a boiling-point range between 200 and 220°C was examined, and a f t e r less than 5 seconds of search time, 1321 compounds were reported as having been found. Second, molecular weight was searched between 300 and 305. Again, a f t e r less than 5 seconds of search, 1492 compounds were found. F i n a l l y , a search

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for the compounds found i n both l i s t s took less than 2 seconds to come up with a t o t a l of 6. Hence, when suitable properties are available and the software permits, appropriate searches can be made very quickly. It i s important to note that i m p l i c i t assumptions are made in doing such a calculation. The f i r s t i s that the compounds i n the c o l l e c t i o n are representative of the entire body of organic compounds. If so. one can make the following extrapolation. If there are 1.5 x 10° compounds estimated to e x i s t , one can extrapolate to 60 possible " h i t s ; i f 1.5 x 10 compounds are assumed, 600 " h i t s " are estimated. If further assumptions are made that (a) the i n t e r v a l i s small r e l a t i v e to the width of the o v e r a l l d i s t r i b u t i o n and (b) the d i s t r i b u t i o n of b o i l i n g points i s uniform across the 20° i n t e r v a l , then, i f one can j u s t i f i a b l y narrow the range of b o i l i n g points to 10°C instead of 20°, the number of estimated " h i t s " could b reduced t 300 t f th 1.5 10 compounds. Clearly, assumption t o t a l number of compound property parameter w i l l have i t s own c h a r a c t e r i s i t i c a b i l i t y to impart s e l e c t i v i t y , especially when combined with one or more other parameters, the use of additional parameters should produce significant reductions in the estimated number of "hits". Unfortunately, the number of compounds that can be searched for specific infrared bands, mass-to-charge ratios of ions, gas chromatographic retention indices, and l i q u i d chromatographic indices i s much smaller than 150,000 species. However, one can expect the data bases for a l l types of compounds - organic, inorganic, and metal lorganic - to grow quickly during the next few years. Although one can foresee disagreements about the t o t a l to be used for the number of possible species, this should not be a major deterrent to the use of this approach for estimating r e l a t i v e s e l e c t i v i t i e s of different properties and the gains to be made from an improved precision of measurements. (For example, many oligomeric series, e. g., those of polystyrene terminated with butyl, as well as the corresponding series terminated with other a l k y l groups, w i l l quickly add many species to the estimated t o t a l . Improvements i n precision and accuracy with which properties can be measured w i l l usually conteract that increase by reducing the percentage of " h i t s " . However, i n special cases, such as i n high resolution mass spectrometry, of large organic compounds, where isotopic species can e a s i l y double or treble the number of major molecular ions that should be detectable within 5 millimass units, greater resolution does not necessarily insure a better qualitative or quantitative r e s u l t . (17A)) In any case, the approximate approach to the estimation of o v e r a l l s e l e c t i v i t y of the type outlined here should be useful to the analyst for comparing two o v e r a l l procedures. 11

7

7

In a l i g h t e r vein, i t would be of interest for a chemist to find out, for example, the mean value for the b o i l i n g point of a l l chemicals (ruling out those that decompose as well as a few extremes l i k e l i q u i d helium and magnesium oxide). Similarly, i t would be interesting to speculate about the mean value i n the d i s t r i b u t i o n of v i b r a t i o n a l frequencies or of negative molecular ions. Before concluding this discussion of s e l e c t i v i t y , one must r e a l i z e that there are situations i n which the analyst might l i k e

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to have two methods that exhibited as nearly the same s e l e c t i v i t y as possible for a wide variety of compounds. That s e l e c t i v i t y goal, which represents the opposite extreme to the e a r l i e r one, has been represented schematically (19) i n Figure 3 which shows the scopes of d i f f e r e n t procedures for determining the organic carbon content of water. Instead, to a greater or lesser extent that depends on the selections made, the reported carbon content i s a function of the types of compounds present and the procedure employed for the determination. CONCLUSIONS F i r s t , i t i s clear that any stated minimum detection l i m i t for a procedure used for interlaboratory measurements should incorporate the RSD that includes a l l known sources of interlaboratory uncertainty. Second, because the sought-for substanc for minimizing the e f f e c t get larger i t would be highly desirable that, i n c r i t i c a l regulatory decisions, a minimum of two as nearly independent procedures as possible be used. In that case, the less sensitive procedure would be the one that would have to be used to establish the AMDA. At that point, one would then apply the recommended c r i t e r i a of the American Chemical Society Committee to calculate values for the "region of detection" and "region of quantitation" (3). Third, a basis has been presented for a general approach for estimating and reporting s e l e c t i v i t y for a sample i n which a large number of unsuspected and unknown interferences may occur. The approach depends upon n-dimensional screens of the properties of the sample i t s e l f (e.g., s o l u b i l i t y ) and of those involved i n the i s o l a t i o n and measurement procedures. F i n a l l y , i t i s important to note that this discussion has focussed almost e n t i r e l y on uncertainties a r i s i n g largely from chemical sources. These always assume p r i o r c a l i b r a t i o n against a primary chemical standard and, frequently, additional internal references, except in c l i n i c a l chemistry where the rule has not yet been universally adopted (20). However, f a i l u r e s to control the laboratory environment (21) and to calibrate instruments properly (22 and correspondence from G. N. Bowers, J r . on May 15, 1984.) (e.g., wavelength, detector response, instrument and room temperatures, flow rate, resistance between electrodes) and computer algorithms (23-27) (e.g., peak deconvolution, curve-fitting, multivariate analysis) are also major sources of uncertainty and error. It seems clear that one must not assume that the use of costly complex instrumentation, including those incorporating on-line computers for instrument control, data a c q u i s i t i o n and data analysis, eliminates the need for careful environmental controls, frequent c a l i b r a t i o n of the c r i t i c a l components of the instrumentation against primary standards, and c a l i b r a t i o n (validation) of the algorithms for analyses of data.

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KEY

A r e a h-Sulfite, nitrite A r e a i - N o n b i o d « g r a d a b l « organics

F i g u r e 3. Schematic diagram o f m a t e r i a l s measured by c h e m i c a l oxygen demand (COD) as r e l a t e d t o t o t a l o r g a n i c m a t e r i a l s . (Reproduced w i t h p e r m i s s i o n from Ref. 19. C o p y r i g h t 1973 American Water Works A s s o c i a t i o n . )

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ACKNOWLEDGMENT The w r i t e r wishes t o thank the U. S. Department o f Energy, Department of B a s i c E n e r g i e s , C o n t r a c t No. DE-AS09-76ER00854, f o r l o n g - t e r m support o f h i s r e s e a r c h which has l e d t o awareness o f t h e problems d i s c u s s e d i n t h i s paper.

LITERATURE CITED 1. 2.

3. 4.

5. 6. 7.

8. 9. 10. 11.

12. 13. 14. 15. 16.

Rogers, L. B. J. Chem. Ed. 1986, 63, 3. Ad Hoc Subcommittee Dealing with the Scientific Aspects of Regulatory Measurements, ACS Joint Board/Council Committee on Science, Improving the R e l i a b i l i t y and Acceptability of Analytical Chemical Data used for Public Purposes May 10, 1982; see also Chem. Eng. News 1982, 60(23), 44. ACS Committee on Environmental Improvement Principles of Environmental Analysi MacDougall, D.; Crummett Nordberg, R. The Sampling Situation and the Analytical Result Symposium on Trace Analysis of Drugs and Related Compounds in Complex Mixtures, Stockholm, Sweden, November 18, 1981; Abstracted in Acta Pharm. Suecica 1982, 19(1), 51; see also: Borgå, O., Idem. 52. Hershenson, H. M.; and Rogers, L. B. Anal. Chem. 1952, 24, 219; see also, Rogers, L. B. J. Chem. Ed. 1952, 29, 612. Data shown in Figure 4 of reference 1. di Domencio, A . ; Merli, F.; Boniforti, L.; Camoni, I . ; Di Muccio, A . ; Taggi, F . ; Vergori, L.; Colli, G.; Elli, G.; Gorni, A.; Grassi, P.; Invernizzi, G.; Jemma, A . ; Luciani, L . ; Cattabeni, F . ; De Angelis, L . ; G a l l i , G.; Chiabrando, C.; Faneli, R. Anal. Chem. 1979, 51, 735.. Horwitz, W.; Kamps, L. R.; Boyer, K. W. J. Assoc. Off. Anal. Chem. 1980, 63, 1344. Garfield, F. M. Quality Assurance Principles for Analytical Laboratories, Association of Official Analytical Chemists, Arlington, VA, 1984. Liddle, J . A . ; through Maugh, T. H . , II Science, 1982, 215, 490. Weinstein, M. C. Med. Decis. Making 1981, 1, 309 through Lusted, L. B. Recent Advances in Analytical Methodology in the Life Sciences, L. A. Beaver, Ed.; U. S. Food and Drug Administration, Office of Science Coordination, Washington, D.C., 1982; p. 13. Donaldson, W. T. Environ. Sci. Technol. 1977, 11, 348-351. Nestrick, T. J.; Lamparski, L. L . ; Stehl, R. H. Anal. Chem. 1979, 51, 1453, 2273.; see also Hummell, R. A . ; Shadoff, L. A. Anal. Chem. 1980, 52, 191. Veillon, C. Anal. Chem. 1986, 58, 851A; see also Guthrie, B. E . ; Wolf, W. R.; Veillon, C. Anal. Chem. 1978, 50, 1900. Kaiser, H. Spectrochim. Acta 1978, Part B, 33B, 551; see also Trehy, M. L.; Yost, R. A . ; Dorsey, J . G. Anal. Chem. 1986, 58, 14. Harvan, D. J.; Hass, J . R.; Schroeder, J . L.; Corbett, B. J. Anal. Chem., 1981, 53, 1755..

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17.

Kateman, K; Pijpers, F. W. In Chemical Analysis; Elving, P.J.; Winefordner, J . D.: Wiley, New York, 1981, Vol 60, p.155. 17A. Mahle, N. H.; Shadoff, L. H. Biomed. Mass Spectrom. 1982, 9, 45; see Table 9 and the related discussion. 18. Analytical Reference Service Training Program, Report of Water Metals, No. 2, U. S. Dept. of Health, Education and Welfare, Robert A. Taft Sanitary Engineering Center, Cincinnati, OH, 1962. 19. Stevens, A. A; Symons, J . M. Proc. Amer. Water Works Assoc. Water Quality Technology Conference, 1973, pp. xxiii-1 to xxiii-26. 20. Bowers, G. N., Jr.; McComb, R. B. Clin. Chem, 1984, 30, 1128. 21. de Haseth, J . A. Appl. Spectrosc. 1982, 36, 544. 22. Horwitz, W. J . Assoc. Off. Anal. Chem. 1984, 67, 1053. 23. Meglen, R. R. Practical Consideration for Acceptance of Pattern Recognition and Othe Chemometri Method 100th AOAC Annual Meeting, Scottsdale 24. Sprouse, J . F. Spectroscopy, , 1(6), 25. Gritton, V. Calibration Curves for Flame AAS - A Study No. 123, Div. Anal. Chem., Natl. Mtg. Amer. Chem. Soc., Anaheim, CA, Sept. 11, 1986. 26. Marshall, A. G.; Chen, L . ; Cottrell, C. E. Limits to Precision in Measurement of Peak Height, Position, and Width in Fourier Transform Spectrometry No. 67, Div. Anal. Chem., Natl. Mtg. Am. Chem. Soc., Anaheim, CA, Sept. 10, 1986. 27. Rothman, L. D. Chromatogr. Forum 1986, 1(2), 13. RECEIVED November 13, 1986

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

Chapter 6

Comparison of Detection Limits in Atomic Spectroscopic Methods of Analysis Michael S. Epstein Inorganic Analytical Research Division, National Bureau of Standards, Gaithersburg, MD 20899

The compariso fundamental part of many decision-making processes for the analytical chemist. Despite numerous efforts to standardize methodology for the calculation and reporting of detection limits, there is still a wide divergence in the way they appear i n the literature. This paper discusses valid and invalid methods to calculate, report, and compare detection limits using atomic spectroscopic techniques. Noises which limit detection are discussed for analytical methods such as plasma emission spectroscopy, atomic absorption spectroscopy and laser excited atomic fluorescence spectroscopy. The c o m p a r i s o n o f d e t e c t i o n l i m i t s i s a fundamental p a r t o f most decision-making processes f o r the a n a l y t i c a l chemist. whether t h e d e c i s i o n i n v o l v e s t h e purchase o f a new i n s t r u m e n t o r t h e d e s i g n o f a t r a c e a n a l y s i s p r o t o c o l , t h e f i g u r e - o f - m e r i t [1] w h i c h i n f l u e n c e s the c h o i c e w i l l most l i k e l y be t h e d e t e c t i o n l i m i t . S i n c e one o r more o f t h e t e c h n i q u e s b e i n g compared i s o f t e n u n f a m i l i a r , t h e d e c i s i o n w i l l be b a s e d on i n f o r m a t i o n t h a t can be r e t r i e v e d from t h e literature, both from m a n u f a c t u r e r a d v e r t i s i n g and t h e open scientific literature. Unfortunately, despite the e f f o r t s of o r g a n i z a t i o n s such as t h e I n t e r n a t i o n a l U n i o n o f Pure and A p p l i e d C h e m i s t r y (IUPAC) t o s t a n d a r d i z e methodology t o c a l c u l a t e and r e p o r t d e t e c t i o n l i m i t s [ 2 ] , t h e r e i s s t i l l a wide d i v e r g e n c e i n t h e way t h a t d e t e c t i o n l i m i t s appear i n p r i n t . W h i l e t h e r e i s h o p e f u l l y no d e l i b e r a t e attempt on t h e p a r t o f a u t h o r s and m a n u f a c t u r e r s t o b i a s d e t e c t i o n l i m i t s towards a p a r t i c u l a r technique, t h e manner o f calculating and r e p o r t i n g c a n l e a d t o a m i s i n t e r p r e t a t i o n o f d e t e c t i o n l i m i t s by the c a r e l e s s o r u n f a m i l i a r reader. I f the d e t e c t i o n l i m i t methodology i s n o t w e l l documented, a c o m p a r i s o n c a n be b i a s e d by s e v e r a l o r d e r s o f magnitude. I t i s impossible t o completely eliminate bias i n detection limit comparisons, particularly when comparing detection capabilities i n r e a l sample m a t r i c e s . However, i f t h e b a s i c

This chapter not subject to U.S. copyright Published 1988 American Chemical Society

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p r i n c i p l e s b e h i n d t h e t e c h n i q u e s t o be compared a r e u n d e r s t o o d and we a r e aware o f t h e common ways i n w h i c h d e t e c t i o n l i m i t comparisons can be m i s i n t e r p r e t e d , r e a s o n a b l y v a l i d c o n c l u s i o n s c a n be drawn. Thus, t h i s d i s c u s s i o n w i l l c o n c e n t r a t e i n g e n e r a l on v a l i d and i n v a l i d ways t o compare d e t e c t i o n l i m i t s and i n s p e c i f i c d e t a i l about l i m i t i n g n o i s e s w h i c h determine those d e t e c t i o n l i m i t s u s i n g several o f t h e most common atomic spectroscopic techniques, i n c l u d i n g flame and plasma e m i s s i o n s p e c t r o s c o p y , atomic a b s o r p t i o n s p e c t r o s c o p y , and l a s e r - e x i t e d atomic f l u o r e s c e n c e s p e c t r o s c o p y . B e f o r e d e t e c t i o n l i m i t s a r e d i s c u s s e d i n any d e t a i l , i t i s n e c e s s a r y t o d e f i n e t h e scope o f t h e p r o c e s s t o w h i c h t h e d e t e c t i o n l i m i t a p p l i e s . F o r example, t h e d e t e c t i o n l i m i t d e t e r m i n e d f o r an element i n t h e absence o f c o n c o m i t a n t s (i.e., i n pure water s o l u t i o n ) i s l i k e l y t o be s i g n i f i c a n t l y l e s s t h a n t h e d e t e c t i o n l i m i t d e t e r m i n e d f o r a complete a n a l y t i c a l p r o t o c o l w h i c h i n c l u d e s s a m p l i n g , sample p r e p a r a t i o n and a n a l y s i s The former which i s the type o f d e t e c t i o n l i m i may be r e f e r r e d t o a i n s t r u m e n t a l n o i s e sources w h i c h a r e i n h e r e n t i n t h e a n a l y t i c a l i n s t r u m e n t used. Fundamental d e t e c t i o n l i m i t s a r e o f t e n o f l i m i t e d v a l u e t o t h e p r a c t i c i n g a n a l y t i c a l chemist who must determine t h a t element i n r e a l and o f t e n v e r y complex m a t r i c e s . The l a t t e r type o f d e t e c t i o n l i m i t , r e f l e c t i n g t h e e n t i r e a n a l y t i c a l p r o t o c o l , may be r e f e r r e d t o as m e t h o d o l o g i c a l . Methodological d e t e c t i o n l i m i t s are a l s o o f l i m i t e d v a l u e s i n c e they i n c l u d e many v a r i a b l e s w h i c h cannot be e a s i l y reproduced. The d e t e c t i o n l i m i t s t o be d i s c u s s e d here w i l l be c a l l e d i n s t r u m e n t a l and w i l l be d e f i n e d as f a l l i n g between fundamental and m e t h o d o l o g i c a l i n t h a t they w i l l c o n s i d e r v a r i a t i o n s i n d u c e d by t h e i n s t r u m e n t a l o n e and by t h e i n t e r a c t i o n o f t h e sample w i t h the instrument, but w i l l not consider the e n t i r e a n a l y t i c a l scheme w h i c h i n c l u d e s b l u n d e r s and c o n t a m i n a t i o n i n t h e s a m p l i n g and sample p r e p a r a t i o n p r o c e s s . I t i s noteworthy t h a t i n s t r u m e n t a l d e t e c t i o n l i m i t s w i l l approach fundamental d e t e c t i o n l i m i t s when t h e sample m a t r i x i s s i m p l e o r when n o i s e r e d u c t i o n methods s p e c i f i c t o sample-matrix-induced noises are a p p l i e d . While the d i s c u s s i o n w i l l d e a l w i t h atomic rather than m o l e c u l a r s p e c t r o s c o p i c methods, many o f t h e p o i n t s t o be made w i l l a p p l y t o b o t h atomic and m o l e c u l a r methods. The major d i f f e r e n c e between t h e n o i s e c h a r a c t e r i s t i c s o f t h e two methods i s u s u a l l y t h e dynamic o r f l o w i n g s t a t e o f an atomic system, such as a h i g h temperature flame o r plasma, compared t o t h e s t a t i c s t a t e o f a m o l e c u l a r system i n w h i c h t h e sample u s u a l l y i s p l a c e d i n a s m a l l transparent cuvette. The dynamic s t a t e o f t h e atomic system generates an a n a l y t e s i g n a l - c a r r i e d n o i s e w h i c h i s p r o p o r t i o n a l t o a n a l y t e s i g n a l magnitude and thus becomes l i m i t i n g a t h i g h a n a l y t e concentrations. (A s i g n a l - c a r r i e d n o i s e i s one whose magnitude i s a c o n s t a n t p e r c e n t a g e o f t h e a m p l i t u d e o f a s i g n a l , w h i c h may be due to background o r t o t h e a n a l y t e . Thus, an a n a l y t e s i g n a l - c a r r i e d n o i s e i s a f l u c t u a t i o n i n t h e phenomenon caused by t h e a n a l y t e , where t h e phenomenon i s used as a measure o f t h e a n a l y t e c o n c e n t r a t i o n , such as a b s o r p t i o n o r e m i s s i o n o f e l e c t r o m a g n e t i c radiation). The s t a t i c s t a t e o f t h e m o l e c u l a r system l i m i t s t h e magnitude o f a n a l y t e s i g n a l - c a r r i e d n o i s e s , e x c e p t where t h e s t a t i c s t a t e i s d i s t u r b e d ( i . e . , v i b r a t i o n , c e l l p o s i t i o n changes, e t c . ) o r where r a d i a t i o n source f l u c t u a t i o n s a r e s i g n i f i c a n t a t h i g h a n a l y t e concentrations ( i . e . , molecular fluorescence spectrophotometry).

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B i a s In D e t e c t i o n L i m i t Comparisons There a r e s e v e r a l ways t h a t d e t e c t i o n l i m i t i n f o r m a t i o n can be presented i n o r d e r t o b i a s the o b s e r v e r . Again, i t must be emphasized t h a t i n most cases s u f f i c i e n t i n f o r m a t i o n w i l l be p r e s e n t e d i n a f i g u r e or i n the accompanying t e x t t o a l l o w the knowledgeable reader to properly interpret detection limit comparisons. R e a l or A r t i f i c i a l D e t e c t i o n L i m i t s . C e r t a i n l y , one o f the most common ways t o r e p o r t d e t e c t i o n l i m i t s i s i n "pure aqueous s o l u t i o n . " whether the a n a l y t i c a l c o n d i t i o n s or the i n s t r u m e n t a t i o n used i s c a p a b l e o f those d e t e c t i o n l i m i t s when r e a l samples are analyzed i s another question. T h i s source o f b i a s i s most o f t e n e n c o u n t e r e d when a new a n a l y t i c a l technique i s developed. An example i s the e a r l development f flam atomi fluorescenc spectroscopy (FAFS), wher consumption b u r n e r i C e r t a i n l y no one would attempt r e a l sample a n a l y s i s i n such a flame because o f i t s t u r b u l e n t f l o w and poor d i s s o c i a t i o n c h a r a c t e r i s t i c s . More r e a l i s t i c d e t e c t i o n l i m i t s are on the o r d e r o f 200 pg/mL i n an a i r - a c e t y l e n e flame [4] . I n flame atomic a b s o r p t i o n s p e c t r o s c o p y (FAAS), t i n d e t e c t i o n l i m i t s are s i g n i f i c a n t l y b e t t e r («4x) in a cool air-hydrogen flame t h a n i n h o t t e r flames as a r e s u l t o f i n c r e a s e d s e n s i t i v i t y and lower flame background e m i s s i o n [ 5 ] . The use o f the s a m p l i n g b o a t [6] i n FAAS a l s o improves d e t e c t i o n l i m i t s f o r many elements by an o r d e r o f magnitude because o f i n c r e a s e d sample t r a n s p o r t e f f i c i e n c y . However, n e i t h e r o f these t e c h n i q u e s i s w i d e l y used i n FAAS, s i n c e b o t h e x h i b i t s i g n i f i c a n t chemical i n t e r f e r e n c e s w i t h r e a l samples. Recently developed techniques, such as i n d u c t i v e l y - c o u p l e d plasma mass s p e c t r o m e t r y (ICP-MS) [7] and l a s e r enhanced i o n i z a t i o n s p e c t r o s c o p y (LEIS) [8] e x h i b i t s i m i l a r sample-related degradation of d e t e c t i o n l i m i t s . C e r t a i n l y , most t e c h n i q u e d e t e c t i o n l i m i t s s u f f e r somewhat when r e a l samples are a n a l y z e d and n o i s e s induced by the sample m a t r i x become limiting. The e x t e n t o f t h i s e f f e c t w i l l v a r y , however, from t e c h n i q u e t o t e c h n i q u e , and w i l l u s u a l l y d i m i n i s h as the method reaches m a t u r i t y . Detection Limit Criterion. The c r i t e r i o n used t o d e f i n e the d e t e c t i o n l i m i t , or perhaps as i m p o r t a n t , the p r o t o c o l used t o measure i t , can be c r i t i c a l i n e s t a b l i s h i n g a v a l i d d e t e c t i o n l i m i t . C u r r i e [9] has d e s c r i b e d the wide v a r i a t i o n i n d e t e c t i o n l i m i t definitions for radiochemical measurements reported in the literature. IUPAC [2] recommends the d e t e c t i o n l i m i t , c , be defined as the concentration of an analyte equal to a background-corrected s i g n a l , x-^ - xg, t h r e e times the estimated s t a n d a r d d e v i a t i o n o f a s i n g l e d e t e r m i n a t i o n u s i n g 20 measurements o f the b l a n k . L

X

L

c

L

=

X

B

+

k s

B

= ks /m B

where

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

W (2)

DETECTION IN ANALYTICAL CHEMISTRY

112 x xg sg c L

L

— — *

uncorrected signal blank measure estimated standard deviation of the blank measure detection l i m i t , which i s the concentration derived from the smallest measure ( x ) that can be detected with reasonable confidence. - numerical factor chosen i n accordance with the confidence l e v e l desired. - analytical sensitivity L

k m

As pointed out by Long and Winefordner [10], the use of k-3 allows a confidence l e v e l of 99.86% for a normal d i s t r i b u t i o n of xg, or an 89% confidence l e v e l for a non-normal d i s t r i b u t i o n . While xg w i l l often be normally d i s t r i b u t e d when instrumental noise limits detection, the presence of analyte contamination i n the blank, either i n the sample preparation process or as a series of discrete events ( i . e . , Na or Fe measurement process, w i l a d i s t r i b u t i o n may be bimodal or skewed depending on the source and c h a r a c t e r i s t i c s of the contaminant. Long and Winefordner [10] have also presented several examples of the influence of measurement protocol on c-^. The use of values of k < 3 or the use of the standard deviation of the mean or pooled standard deviation rather than the standard deviation of a single measurement, can lead to C L values which deviate by an order of magnitude from the IUPAC model. Measurement protocols which include the error i n the a n a l y t i c a l s e n s i t i v i t y as well as the error i n the blank can also cause C L to deviate s i g n i f i c a n t l y from the IUPAC model, which assumes a well-defined s e n s i t i v i t y . F i n a l l y , the presence of very low frequency noise or d r i f t may not be incorporated into the IUPAC d e f i n i t i o n of detection l i m i t [11]. The c a l i b r a t i o n scheme used for r e a l samples may be spread out over a longer time period than was used for the determination of the detection l i m i t and thus noises which were i n s i g n i f i c a n t during the detection l i m i t measurement may be encountered. Ideally, a technique detection l i m i t should be determined using the measurement protocol employed for r e a l sample analysis. A n a l y t i c a l Blank. I f the detection l i m i t i s not measured from the true a n a l y t i c a l blank, a c r i t i c a l part of the detection l i m i t determination has been ignored. Since the emphasis i n this discussion i s on "instrumental" rather than "methodological" detection l i m i t s , only blanks r e s u l t i n g from the instrumentation w i l l be considered. Although method blanks can c e r t a i n l y be l i m i t i n g , p a r t i c u l a r l y for elements such as Fe, Na, and Ca which are common i n the laboratory environment, they are not as predictable as instrumental contamination blanks, since variations i n laboratory procedures and design w i l l be much greater than variations i n instrument design. For example, i n FAFS one can s i g n i f i c a n t l y improve a detection l i m i t i n a s i t u a t i o n l i m i t e d by flame scatter of source r a d i a t i o n by making measurements with no water being introduced into the flame. By eliminating the scattering species, unvaporized water droplets, the detection l i m i t i s improved. S i m i l a r l y , one can measure a graphite furnace atomic absorption

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s p e c t r o s c o p y (GFAAS) d e t e c t i o n l i m i t w i t h o u t a c t u a l l y a t o m i z i n g a b l a n k sample, assuming the n o i s e t o be independent o f the a t o m i z e r . T h i s i s c e r t a i n l y an i n v a l i d assumption when d e t e r m i n i n g an element whose most s e n s i t i v e a b s o r p t i o n l i n e l i e s i n the v i s i b l e r e g i o n o f the spectrum, such as barium, where t h e r m a l e m i s s i o n from the g r a p h i t e tube i s s i g n i f i c a n t , or where c o n t a m i n a t i o n i n the tube i s l i m i t i n g , such as when z i n c i s determined. For t h e s e elements, p u b l i s h e d d e t e c t i o n l i m i t s may be i n v a l i d , u n l e s s t h e y were measured under a c t u a l a n a l y s i s c o n d i t i o n s . The m o r a l i s thus t o measure the b l a n k under c o n d i t i o n s as s i m i l a r as p o s s i b l e t o the a n a l y s i s c o n d i t i o n s used. Instrument N o i s e C h a r a c t e r i s t i c s . Depending on the f r e q u e n c y domain spectrum o f the s i g n a l from the a n a l y t i c a l i n s t r u m e n t , t h a t i s , i f the n o i s e i s w h i t e ( s h o t ) o r 1/f ( f l i c k e r ) i n n a t u r e [ 1 ] , the i n t e g r a t i o n time o r tim constant d fo th detectio limit d e t e r m i n a t i o n may have a I n cases where s h o t n o i s a l l wavelengths o r FAAS above 230 nm, o r ICP e m i s s i o n s p e c t r o s c o p y (ICP-ES) below 250 nm, the d e t e c t i o n l i m i t can be improved as the s q u a r e - r o o t o f the i n t e g r a t i o n time. In f l i c k e r noise l i m i t e d c a s e s , t h e r e may be l i t t l e or no improvement i n the d e t e c t i o n l i m i t w i t h an i n c r e a s e i n the i n t e g r a t i o n time. [12,13] The improvement i n d e t e c t i o n l i m i t f o r an i n c r e a s e o f i n t e g r a t i o n time w i l l be u l t i m a t e l y l i m i t e d by the s i g n i f i c a n c e o f v e r y low f r e q u e n c y d r i f t and the a v a i l a b i l i t y o f l a r g e volumes o f sample s o l u t i o n . Measurement U n i t s . Perhaps the most o b v i o u s y e t c o n f u s i n g a s p e c t o f many d e t e c t i o n l i m i t comparisons i s the use o f " r e l a t i v e " v e r s u s "absolute" u n i t s . R e l a t i v e u n i t s r e f l e c t a mass p e r u n i t volume, such as micrograms per m i l l i l i t e r , w h i l e a b s o l u t e u n i t s r e f l e c t a mass o n l y , such as micrograms. O b v i o u s l y , " r e l a t i v e " and " a b s o l u t e " u n i t s s h o u l d n o t be d i r e c t l y compared. However, a b s o l u t e u n i t s can be c o n v e r t e d i n t o r e l a t i v e u n i t s and v i c e v e r s a , employing the volume o f s o l u t i o n u t i l i z e d by a p a r t i c u l a r t e c h n i q u e . Nonetheless, how that conversion i s done or how i t i s documented can s i g n i f i c a n t l y b i a s the o b s e r v e r . Table I i l l u s t r a t e s s e v e r a l examples, t a k e n from the s c i e n t i f i c l i t e r a t u r e , o f the use o f d e t e c t i o n l i m i t v a l u e s i n a t a b l e f o r comparison purposes. I n each case the a u t h o r p r o v i d e s adequate i n f o r m a t i o n f o r the i n f o r m e d reader t o make an accurate comparison. Nevertheless, the c o n c l u s i o n s drawn by the c a r e l e s s o r u n i n f o r m e d r e a d e r who does not r e a d o r u n d e r s t a n d the f o o t n o t e s or the t e x t w h i c h d e s c r i b e s the t a b l e , can be b i a s e d by s e v e r a l o r d e r s o f magnitude. T a b l e l a , p r e s e n t s a comparison o f FAAS and GFAAS d e t e c t i o n l i m i t s [14]. Without r e a d i n g the t e x t which r e f e r s t o the t a b l e , one i s impressed by the s i g n i f i c a n t , 3 t o 4 o r d e r s o f magnitude, improvement u s i n g the g r a p h i t e f u r n a c e . However, the t e x t c l e a r l y i n d i c a t e s t h a t b o t h flame and g r a p h i t e f u r n a c e d e t e c t i o n l i m i t s assume a 1 mL sample volume which, w h i l e c e r t a i n l y v a l i d i n a flame, i s n o t v a l i d f o r a g r a p h i t e f u r n a c e s i n c e the maximum sample volume i s u s u a l l y about 50 t o 100 /xL. Some systems, l i k e the c a r b o n r o d a t o m i z e r [ 1 5 ] , can o n l y accommodate 1 t o 2 /iL o f s o l u t i o n . Thus, f o r a v a l i d comparison, the g r a p h i t e f u r n a c e d e t e c t i o n l i m i t s must be degraded by one t o two o r d e r s o f magnitude.

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DETECTION IN ANALYTICAL CHEMISTRY Table l a .

D e t e c t i o n L i m i t s R e p o r t e d f o r Atomic A b s o r p t i o n

D e t e c t i o n L i m i t (zxg/mL) Nonflame Flame 6 x 10" 0.02 4 x 10" 0.002 1 x 10" 0.004 2 x 10" 0.0008

Element Ba Ca Fe Mn

6

7

5

7

"...the l i m i t s are based on a s i g n a l - t o - n o i s e r a t i o = 2 c r i t e r i o n and the assumption t h a t a volume o f 1 mL i s the minimum r e q u i r e d f o r a d e t e r m i n a t i o n . For example, i f an a b s o l u t e d e t e c t i o n l i m i t i s g i v e n ( e . g . , nonflame a t o m i z e r ) as 10"^ g, t h i s i s e x p r e s s e d as a c o n c e n t r a t i o n a l d e t e c t i o n l i m i t o f 0.001 /xg/mL. One must b e a r i n mind t h a t most c u r r e n t nonflame a t o m i z e r s cannot h a n d l e samples l a r g e r t h a n , say, 0.1 mL cannot h a n d l e samples ( f o mL. The 1 mL c r i t e r i o n . .. i s thus more f o r the purpose o f d i r e c t comparison than f o r the v e r y l o w e s t p o s s i b l e d e t e c t i o n l i m i t s . . . " R e p r i n t e d from [14] by p e r m i s s i o n o f J o h n W i l e y and Sons, c o p y r i g h t 1976. Source: Wiley.

Reproduced w i t h p e r m i s s i o n from Ref. 14.

Copyright

1976

I n T a b l e l b [16] a b s o l u t e r a t h e r t h a n r e l a t i v e d e t e c t i o n l i m i t s are compared f o r s e v e r a l t e c h n i q u e s . U n l e s s one l o o k s a t the f o o t n o t e s however, i t i s not obvious t h a t the d e t e c t i o n l i m i t f o r one method i s based on a 1 /xL sample s i z e , a n o t h e r on a 5 /iL sample s i z e and another on a 1 mL sample s i z e , thus b i a s i n g the c a r e l e s s o b s e r v e r o f t h i s t a b l e by 2 t o 3 o r d e r s o f magnitude. Table l b . Absolute D e t e c t i o n L i m i t s U s i n g Atomic F l u o r e s c e n c e S p e c t r o m e t r y and S e v e r a l Other Methods

Element Ag Cd Mg Ni

AFS 0.4 0.0015 1 5

D e t e c t i o n L i m i t s (pg) AAS 0.2 0.1 0.06 10

AEICP 200 70 3 200

AFS = Atomic f l u o r e s c e n c e s p e c t r o m e t r y - 1 /xL sample s i z e AAS = Atomic a b s o r p t i o n s p e c t r o m e t r y - 5 /xL sample s i z e AEICP = Plasma e m i s s i o n u s i n g the ICP - 1 mL sample s i z e [16] R e p r i n t e d from [16] by p e r m i s s i o n o f Pergamon J o u r n a l s L t d . Source: Reproduced w i t h p e r m i s s i o n from Ref. 16. C o p y r i g h t 1979 Pergamon P r e s s . F i n a l l y , i n Table l c [17] a comparison i s made of d e t e c t i o n l i m i t s f o r carbon f u r n a c e atomic e m i s s i o n s p e c t r o s c o p y (CFAES), flame e m i s s i o n s p e c t r o s c o p y ( F E S ) , and CFAAS. Note t h a t s e n s i t i v i t i e s are used as p s e u d o - d e t e c t i o n l i m i t s f o r CFAAS. These are not r e a l l y s e n s i t i v i t i e s as d e f i n e d by IUPAC [ 1 8 ] , but are c h a r a c t e r i s t i c c o n c e n t r a t i o n s , s i n c e they r e p r e s e n t a c o n c e n t r a t i o n e q u i v a l e n t to an absorbance of 0.0044. Furthermore, n o i s e In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

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measurements are n o t made i n the c a l c u l a t i o n o f t h i s parameter, so the t r u e d e t e c t i o n l i m i t w i l l l i k e l y be much s m a l l e r , p a r t i c u l a r l y in the case o f CFAAS, where t r a n s m i s s i o n flicker noise is negligible. T a b l e l c . D e t e c t i o n L i m i t s U s i n g Carbon Furnace Atomic E m i s s i o n S p e c t r o m e t r y and Other Techniques

Element

Mo Si Be

CFAES

0.016 0.088 0.46

D e t e c t i o n L i m i t s (ttg/mL) Flame e m i s s i o n

0.03 10 10

CFAAS

0.005 0.01 0.0002

CFAES = Carbon f u r n a c e atomi of s o l u t i o n CFAAS = Carbon f u r n a c e atomi a b s o r p t i o spectrometry y i n /xg/mL/0.0044 A - based on a 20 fih a l i q u o t o f s o l u t i o n R e p r i n t e d from [17] by p e r m i s s i o n o f E l s e v i e r S c i e n c e P u b l i s h e r s Source: Reproduced w i t h p e r m i s s i o n from Ref. 17. Copyright 1978 Elsevier Scientific. Now, l e t us summarize the q u e s t i o n s t h a t s h o u l d be c o n s i d e r e d when comparing d e t e c t i o n l i m i t s . F i r s t , what i s the n o i s e bandwidth ( d e f i n e d by the i n t e g r a t i o n time o r time c o n s t a n t f o r each measurement) o f each instrument? Were the measurements made under s i m i l a r c o n d i t i o n s and, when u s i n g a method such as ICP-ES [12,13], does i t make any d i f f e r e n c e ? Second,' are we d e a l i n g w i t h a b s o l u t e o r r e l a t i v e u n i t s and have the u n i t s been c o r r e c t l y c o n v e r t e d t o a l l o w a v a l i d comparison? T h i r d , does sample-induced n o i s e , t h a t i s n o i s e r e s u l t i n g from components i n the sample m a t r i x , s i g n i f i c a n t l y degrade d e t e c t i o n limits? T h i s may be more s i g n i f i c a n t f o r some t e c h n i q u e s than others. For example, s c a t t e r or m o l e c u l a r a b s o r p t i o n i n FAAS, when compensated f o r by a background c o r r e c t i o n method such as Zeeman s p l i t t i n g o r a continuum s o u r c e , w i l l u s u a l l y r e s u l t i n o n l y a s m a l l i n c r e a s e i n shot n o i s e due to a t t e n u a t i o n of primary source i n t e n s i t y and no s i g n i f i c a n t change i n d e t e c t i o n l i m i t s w i l l o c c u r . The same m a t r i x components i n an ICP-ES system, w h i c h i s f l i c k e r n o i s e l i m i t e d , may show a f a r more s i g n i f i c a n t d e g r a d a t i o n of d e t e c t i o n l i m i t when f l i c k e r i n the sample m a t r i x e m i s s i o n becomes the l i m i t i n g n o i s e . F o u r t h , does the s e n s i t i v i t y of the t e c h n i q u e d e c r e a s e i n the p r e s e n c e of the sample m a t r i x ? O f t e n c o n d i t i o n s w h i c h f a v o r the b e s t d e t e c t i o n l i m i t s , such as low b a c k g r o u n d e m i s s i o n or h i g h sample i n t r o d u c t i o n r a t e s a l s o r e s u l t i n r e d u c e d sample d i s s o c i a t i o n and t h u s d e c r e a s e d a n a l y t e s e n s i t i v i t y when a complex sample m a t r i x i s present. Are d e t e c t i o n l i m i t s d e t e r m i n e d under u n r e a l i s t i c c o n d i t i o n s or w i t h a p p a r a t u s u n s u i t a b l e f o r r e a l sample a n a l y s i s ? F i f t h , a r e we d e a l i n g w i t h c o n d i t i o n s o p t i m i z e d f o r a s i n g l e element or m u l t i e l e m e n t a n a l y s i s ? Compromise c o n d i t i o n s degrade d e t e c t i o n l i m i t s b u t improve the i n f o r m i n g power of the method ( i . e . , the t o t a l amount of i n f o r m a t i o n about a sample t h a t can be o b t a i n e d from an a n a l y t i c a l method).

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

DETECTION IN ANALYTICAL CHEMISTRY

116

Sixth and f i n a l l y , what c r i t e r i a were detection l i m i t and how was i t calculated?

used

to

define

the

Noises Which Limit Detection Let us now look b r i e f l y into the three major classes of a n a l y t i c a l spectrometric methods: emission, absorption, and fluorescence. Noises w i l l be defined, and examples of how and when they l i m i t detection w i l l be given. Table II l i s t s the major noises which l i m i t detection for the three atomic spectroscopic techniques to be discussed. Detailed d e f i n i t i o n s of these noises may be found i n the paper by Epstein and Winefordner [1]. TABLE I I . Noises Which Limit Detection i n Atomic Spectroscopic Methods

PMT shot noise induced by dark current, atomizer background emission, or sample matrix emission. Electronics noise (including RF) Atomizer background intensity fluctuations induced by atomizer gases, sample matrix components, or contamination.

ABSORPTION PMT shot noise induced by the radiation source, atomizer background emission, or sample matrix emission. Electronics noise Radiation source intensity fluctuations Atomizer transmission fluctuations induced by flame or furnace gases, sample matrix components, or contamination.

FLUORESCENCE PMT shot noise induced by dark current, atomizer background emission, sample matrix emission, or scattered r a d i a t i o n source intensity. Electronics noise (including RF) Radiation source intensity fluctuations carried by scatter, contamination fluorescence, or broadband fluorescence from flame and furnace gases or from sample matrix components. Atomizer background intensity fluctuations induced by flame or furnace gases, sample matrix components, or contamination.

Every spectrometric system consists of four of the components shown i n Figure 1: (a) a source of atoms; (b) a spectrometer to isolate the radiation whose intensity and frequency contains information about the analyte; (c) a photodetector to convert photons to e l e c t r i c current; and (d) a signal processing scheme to

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

(Absorption)

SOURCE

RADIATION

CELL

Figure 1.

DETECTION

NON-OPTICAL

VAPOR

ATOMIC

(Fluorescence)

SOURCE

R ADI A T I O N

DETECTOR

OPTICAL

Components of an a n a l y t i c a l spectrometric system.

SPECTROMETER PROCESSING

S IGNAL

118

DETECTION IN ANALYTICAL CHEMISTRY

decode the i n f o r m a t i o n s t o r e d i n the r a d i a t i o n . In emission methods, the h i g h temperature o f the atom s o u r c e p r o v i d e s e x c i t a t i o n energy t o promote e l e c t r o n t r a n s i t i o n s , w h i l e i n a b s o r p t i o n and f l u o r e s c e n c e methods, e x t e r n a l r a d i a t i o n s o u r c e s a r e u s e d t o induce the e l e c t r o n t r a n s i t i o n s o f the a n a l y t e atoms. A l l o f these i n s t r u m e n t components can r e s u l t i n n o i s e w h i c h l i m i t s d e t e c t i o n . S p e c t r o s c o p i c t e c h n i q u e s which use n o n - o p t i c a l d e t e c t i o n , such as LEIS o r p h o t o a c o u s t i c s p e c t r o s c o p y , a r e c h a r a c t e r i z e d by n o i s e s o u r c e s s i m i l a r t o f l u o r e s c e n c e , s i n c e the i n f o r m a t i o n - c a r r y i n g phenomenon i s energy r e l e a s e f o l l o w i n g a b s o r p t i o n . R a t h e r than r a d i a t i o n a l d e a c t i v a t i o n o f the e x c i t e d s t a t e , i n LEIS the energy release mechanism i s flame ion current g e n e r a t i o n , and in photoacoustic spectroscopy, it is thermal or collisional deactivation. E m i s s i o n N o i s e Sources N o i s e s i n the e m i s s i o n t e c h n i q u e a r e the s i m p l e s t to understand d i r e c t c u r r e n t plasma (DCP become p o p u l a r i n r e c e n t y e a r s . The n o i s e s w h i c h l i m i t d e t e c t i o n u s i n g t h e s e e m i s s i o n s o u r c e s are e a s i l y c h a r a c t e r i z e d . W i t h v e r y low o p t i c a l throughput, such as when narrow s l i t w i d t h s a r e used i n the f a r UV, p h o t o m u l t i p l i e r dark c u r r e n t n o i s e may be s i g n i f i c a n t . However, i n most c a s e s , s h o t n o i s e i n d u c e d by the s o u r c e background r a d i a t i o n , o r f l i c k e r n o i s e c a r r i e d by the s o u r c e background are l i m i t i n g . The background i n t e n s i t y may r e s u l t from argon e m i s s i o n i n the s o u r c e o r may be i n d u c e d by i n t e r a c t i o n o f the s o u r c e w i t h the sample m a t r i x . I n the case o f f l i c k e r n o i s e , t h a t i s , the f l u c t u a t i o n i n the background i n t e n s i t y , the n o i s e u s u a l l y r e s u l t s from t e m p o r a l v a r i a t i o n s i n the sample t r a n s p o r t system o r the e x t e r n a l gas f l o w s . The major q u e s t i o n when comparing d e t e c t i o n l i m i t s u s i n g e m i s s i o n t e c h n i q u e s i s whether the s i g n a l - t o - b a c k g r o u n d r a t i o (SBR) o r the s i g n a l - t o - n o i s e r a t i o (SNR) was used as the measure o f d e t e c t i o n l i m i t . The SBR r e q u i r e s a measure o f the c o n c e n t r a t i o n c o r r e s p o n d i n g t o a m u l t i p l e o f the background i n t e n s i t y , r a t h e r than the n o i s e , and thus r e q u i r e s o n l y one measurement o f background. The measurement o f background i s u s u a l l y made i n the presence o f the a n a l y t e - c o n t a i n i n g sample by measuring a t a w a v e l e n g t h slightly o f f s e t from the wavelength o f the a n a l y t e i n t e n s i t y maximum. I n a m u l t i e l e m e n t system, i t i s thus much s i m p l e r t o m o n i t o r i n s t r u m e n t performance by measuring the SBR f o r each c h a n n e l , r a t h e r t h a n the SNR, w h i c h would r e q u i r e m u l t i p l e measurements. The d e t e c t i o n l i m i t i s t h e n c a l c u l a t e d by assuming t h a t the b a c k g r o u n d - c a r r i e d f l i c k e r n o i s e i s l i m i t i n g and t h a t t h e r e i s a c o n s t a n t r e l a t i v e s t a n d a r d d e v i a t i o n o f the background e m i s s i o n , u s u a l l y about one p e r c e n t . The l i m i t a t i o n t o t h i s procedure has been c l e a r l y p o i n t e d out by Boumans [ 1 9 ] , who d e s c r i b e s the r e l a t i o n s h i p o f the relative s t a n d a r d d e v i a t i o n o f the background t o the f l i c k e r n o i s e and shot n o i s e components by the f o l l o w i n g e q u a t i o n : (RSD)

B

where (RSD)

B

= (a

2 B

+ g/Vx )^

2

B

= observed r e l a t i v e s t a n d a r d d e v i a t i o n o f the background e m i s s i o n .

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

O)

6.

EPSTEIN

Comparing Detection Limits

119

ag = f l i c k e r f a c t o r i n d u c e d by v a r i a t i o n s i n i n s t r u m e n t a l components such as n e b u l i z e r o r gas flow controls. xg — measured background s i g n a l i n u n i t s o f anode current. g - photomultiplier gain f$ — c o n s t a n t c o e f f i c i e n t w h i c h i n c l u d e s components due to the e f f e c t i v e system n o i s e b a n d w i d t h , the e l e c t r o n i c charge, and g a i n f l u c t u a t i o n s due t o secondary e l e c t r o n e m i s s i o n . The v a l i d i t y o f assuming a c o n s t a n t s t a n d a r d d e v i a t i o n o f the background e m i s s i o n depends on the dominance o f background f l i c k e r noise. W i t h t h a t n o i s e , w h i c h Boumans p o i n t s out i s l i m i t i n g a t w a v e l e n g t h s g r e a t e r t h a n 300 nm, the SNR and thus the d e t e c t i o n l i m i t can be c h a r a c t e r i z e d b th SBR d i v i d e d b flicke factor ag the f i r s t term i f u n c t i o n of a p a r t i c u l a depends on the s t a b i l i t y o f v a r i o u s i n s t r u m e n t components. Thus, as l o n g as f l i c k e r n o i s e i s l i m i t i n g and the f l i c k e r f a c t o r does not change, the a p p r o x i m a t i o n i s v a l i d . D e v i a t i o n s from the a s s u m p t i o n occur a t s h o r t e r w a v e l e n g t h s , where the spectrometer optical t h r o u g h p u t and plasma background i n t e n s i t y d e c r e a s e . The background s h o t n o i s e i n t e n s i t y , r e p r e s e n t e d by the second term i n Boumans' e q u a t i o n , ( g ^ / x g ) ^ , w i l l make a s i g n i f i c a n t c o n t r i b u t i o n t o the v a r i a t i o n o f the background i n t e n s i t y , and the s i m p l e r e l a t i o n s h i p o f f l i c k e r f a c t o r t o SNR mentioned p r e v i o u s l y b r e a k s down. Thus, d e t e c t i o n l i m i t s c a l c u l a t e d from SBR's w i t h o u t c o n s i d e r a t i o n o f shot n o i s e may be i n e r r o r . A b s o r p t i o n N o i s e Sources. N o i s e s i n atomic a b s o r p t i o n s p e c t r o s c o p y a r e more complex than i n e m i s s i o n . When a source o f r a d i a t i o n i s i n t r o d u c e d , whose a t t e n u a t i o n c a r r i e s the a n a l y t e i n f o r m a t i o n , s e v e r a l new l i m i t i n g n o i s e s o u r c e s are i n t r o d u c e d . F l i c k e r noise due t o e m i s s i o n from the h i g h temperature atomic v a p o r c e l l i s not as s i g n i f i c a n t as i t i s i n e m i s s i o n t e c h n i q u e s , because atomic a b s o r p t i o n uses source m o d u l a t i o n t o d i s c r i m i n a t e a g a i n s t such n o i s e by encoding the a n a l y t e i n f o r m a t i o n s i g n a l a t a h i g h frequency. Shot n o i s e i s s t i l l observed as a r e s u l t o f background e m i s s i o n from the flame o r from sample m a t r i x components, b u t no s i g n i f i c a n t f l i c k e r n o i s e i s measured. However, new n o i s e s a r e s h o t and f l i c k e r from the r a d i a t i o n s o u r c e , flame t r a n s m i s s i o n f l i c k e r n o i s e w h i c h becomes l i m i t i n g a t wavelengths l e s s t h a n 230 nm, and m o l e c u l a r a b s o r p t i o n o r s c a t t e r n o i s e from sample m a t r i x components. A l l o f the f l i c k e r n o i s e s can be e f f e c t i v e l y e l i m i n a t e d by the use of double-beam o p t i c s i n c o n j u n c t i o n w i t h a background c o r r e c t i o n system such as Zeeman s p l i t t i n g or a w e l l - a l i g n e d ( o r wavelength-modulated) continuum s o u r c e . Thus the u l t i m a t e l i m i t i n g n o i s e i n atomic a b s o r p t i o n i s source shot n o i s e , w h i c h can be r e d u c e d ( r e l a t i v e t o t o t a l source i n t e n s i t y o r I ) by i n c r e a s i n g the source i n t e n s i t y , up t o the p o i n t o f o p t i c a l s a t u r a t i o n . Table I I I presents some examples o f l i m i t i n g n o i s e s in d i f f e r e n t atomic a b s o r p t i o n d e t e r m i n a t i o n s . These measurements are a c o m p i l a t i o n o f i n f o r m a t i o n from s e v e r a l s o u r c e s , b u t p r i m a r i l y from the work o f I n g l e [20,21] u s i n g a v e r y s i m p l e , single-beam Q

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

DETECTION IN ANALYTICAL CHEMISTRY

120

atomic absorption spectrometer. Aluminum in a nitrous oxide-acetylene flame i s l i m i t e d by flame transmission f l i c k e r and source f l i c k e r . The flame transmission f l i c k e r r e s u l t s from absorption by molecular species (e.g., OH). Barium i n a similar flame, but with a double-beam instrument, i s l i m i t e d only by source induced shot noise. The double-beam system reduces the source f l i c k e r noise component. Calcium i n an air-acetylene flame i s l i m i t e d by both source f l i c k e r and shot noise, while i n the hotter nitrous oxide-acetylene flame, flame emission shot noise becomes greater than the source shot noise. The flame emission shot noise results from the intense molecular emissions of CN and CH i n the higher temperature flame. Copper i s l i m i t e d by both source f l i c k e r and shot noise at a one second integration time, but l i m i t e d by only f l i c k e r noise at a ten second integration time, a r e s u l t of the reduction of the shot noise component. An increase i n integration time w i l l improve the detection l i m i t i n a shot noise l i m i t e d case Table I I I . Dominant

Element

Wavelength (nm)

Flame type

Limiting noise (Absorbance)

= FT

{R

X X

(T)|

(7)

( T ) i s real and even for real processes, S(OJ) i s also r e a l and:

Because R and even,

+ 00 S(OJ)

=

[

J

R

xx

(T)

COS

CUT

dx = 2

Jf

R

xx

(T)

COS

COT

dT

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

(8)

7. SMIT AND STEIGSTRA

Noise and Detection Limits

133

F i n a l l y , the physical r e a l i z a b l e one-sided PSD function G(to) i s defined as: oo

G(o)) = 4

j

R

X X

(T)

cos OJT dr

(9)

0 The energy of the signal can be calculated from G(co): oo

E[x (t)] = J 2

G(u>) do) = R^CO)

(10)

0 2

2

E [ x ( t ) ] i s the mean square value i(/ of the signal x ( t ) . I f the mean of x ( t ) i s not zero, f o instanc i f x(t) i nois with Direct Current (DC) component t o t a l energy. However, variations of the signal and not i n the mean value which can be estimated and corrected. Therefore, i n the following we assume a mean value of zero, i n which case E [ x ( t ) ] becomes the variance a . Some d e f i n i t i o n s from l i n e a r system theory are required. The weighting function h(t) i s the response (output) of a l i n e a r system applied to an impulse s i g n a l , t h e o r e t i c a l l y a Dirac-delta function 6 ( t ) , or more precisely, a 6-distribution with the properties: 2

2

+ oo

6(t) dt (ID 6(t) = 0

(t + 0)

The FT of the impulse response i s the complex frequency response H(joj). Suppose x(t) with a PSD = G (OJ) i s the input signal of a l i n e a r system with a complex frequency response H(jio) and suppose y(t) i s the r e s u l t i n g output. Then i t can be proved (J_) that the PSD of y ( t ) i s given by: X

2

G (u>) = |H(jco)| G

y

x

(o>)

(12)

Variance of Integrated Noise The system functions, mentioned i n the previous paragraph, can be determined for an integrator. The response of an integrator applied to an impulse 6(t) i s the value 1 ( t > 0 ) , as follows from the d e f i n i t i o n of the 6-distribution (Equation 11). The FT can e a s i l y be calculated, r e s u l t i n g i n :

H(jO)) = FT | h ( t ) | = J

h(t) e

j U ) t

dt = J

-joot

dt =

J _

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

(13)

DETECTION IN ANALYTICAL CHEMISTRY

134

A c c o r d i n g t o E q u a t i o n 12 we c a n c a l c u l a t e t h e PSD o f t h e o u t p u t , assuming a s t o c h a s t i c i n p u t s i g n a l w i t h known PSD: G (0)) = |H(ja))| G (co) = - L (u>) y x ^2 x

(14)

2

G

At f i r s t s i g h t , i t appears p o s s i b l e t o c a l c u l a t e , w i t h o u t any p r o blem, t h e v a r i a n c e o f t h i s o u t p u t s i g n a l by i n t e g r a t i n g the c a l c u l a ted output PSD over the 0)-range from zero t o (see E q u a t i o n 10): 0 0

?

k V

=

°° i f - L G (co)dco J u)

(15)

x

2

However, t h i s i s n o t c o r r e c t , as a l r e a d y i s shown i n p r e v i o u s papers ( 6 , 7 ) . A s i g n a l i s neve a l i m i t e d time i n t e r v a l In r e a l i t y , t h e impulse response h ( t ) o f an i n t e g r a t o r i s n o t 1, b u t i s g i v e n by: h(t)

= 1

(0 1 2 ) and i n f i n i t e i s n e g l i g i b l e . The v a l u e o f t h e i n t e g r a l w i t h i n t e g r a t i o n l i m i t s 0 and i s TT/2. The f i n a l r e s u l t i s : T

00

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

DETECTION IN ANALYTICAL CHEMISTRY

136

k

a

2

- a

I

2

& n u)

(25)

Q

In this p a r t i c u l a r case the variance of the integrated noise i s proportional to the integration i n t e r v a l and to the variance a of the o r i g i n a l baseline noise. We note that a and COQ 22£ independent, reducing COQ means reducing o . Noise with a strong 1/f character i s much more r e a l i s t i c (7), p a r t i c u l a r l y i n chromatography. The PSD of 1/f (or 1 /to) noise i s proportional to 1/to. Because of the s i n g u l a r i t y in co=0, a s l i g h t l y modified model i s more r e a l i s t i c . Such a PSD might be: n

A R E

n

n

G(u)) = K/oj£

0 < oo < u>£ (26)

G(oj) =

K/00

< co

0)£

co^ i s a fixed (low)

frequency

Substitution i n Equation 19 gives:

k2 a

m

2 T

JL

f

2

2

sin (o)T/2)

J

(a)T/2)

Q

r" s i n ( 0 T / 2 ) 2

d a ) T / 2

+

2

2

k

t

2

t

J

(a)T/2)

d ( ( 0 T / 2 )

( 2 y )

3

For low values of u)£ the f i r s t term i s approximately KT , the i n t e gral i n the second term has to be calculated numerically. An important conclusion i s that i n case of 1/f ( f l i c k e r ) noise the variance o\ i s proportional to T . A treatment i n the frequency domain i s not always optimal. For instance, calculations with non-stationary stochastic processes are d i f f i c u l t . Moreover, the PSD i s mostly determined by Fourier transforming the ACF, therefore an expression using d i r e c t l y the ACF avoids Fourier transforming. The derivation happens to be not d i f f i cult. Assuming a random signal n(t) with mean value y, we write the random v a r i a b l e : 2

b I - J n(t)dt

b E[I] = f

E[n(t)] = \i

y(t)dt

(28)

Now we write: b I

2

b

- J n(ti)dti J n(t )dt 2

a

(29)

2

a

using two dummy (time) variables t i and t . The integration l i m i t s are independent and the iterated integral can be written as a double i n t e g r a l : 2

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

7. SMIT AND STEIGSTRA

Noise and Detection Limits

137

b b I

= J Jn(t )n(t )dt dt

2

1

2

1

(30)

2

a a Taking the expected value and interchanging the expected value procedure and the integration gives: b b 2

E[I ]

= f |E[n(t )n(t )]dt dt 1

2

1

(31)

2

a a b b R(ti,t )dt!dt 2

2

= a

2

(32)

a a More or less naturally th usable expression. I f , assumed, then we get: T 2

E[I ]

-

f

2

T ~ 2

,

y

ergodicity

T 2

j

R(t -t )dt dt 1

2

1

2

(33)

T "2

T T assuming an integration i n t e r v a l from - — to — . Equation 33 can be simplified to: T 2

E[I ]

= 2j

(T-T)R(T)dT

(34)

0 T = ti - t . 2

The proof, being purely mathematical, i s omitted (j6). As a f i n a l r e s u l t we have two expressions (Equations 19 and 34) with certain r e s t r i c t i o n s quite usable i n practice. One can prove that the expressions e s s e n t i a l l y are the same and they can be derived from one another. Figures 4 and 5 show some t y p i c a l types of noise: f i r s t order noise, i . e . white noise bandlimited by a simple f i r s t order f i l t e r with time constant T i , and noise with a strong 1/f component, o r i g i nating from an Inductively Coupled Plasma - Atomic Emission Spectrograph (ICP-AES). The ACF of f i r s t order noise i s : -Kl R ( T ) = a* exp - — -

n

Ti

Substitution i n Equation 34 r e s u l t s i n :

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

(35)

138

DETECTION IN ANALYTICAL CHEMISTRY

Figure 4.

ACF, PSD

and record of f i r s t order noise.

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

7. SMIT AND STEIGSTRA

Noise and Detection Limits

139

noise I C P

0.0 (

)

eg o

a

0.00

4.00

8.00

12.00

16.0

1

T (XIO ) 40.00

r

noise I C P

PSD

32.00 24.00

I >< X a!

16.00 8.00 0.00 -8.00 0.00

1.60

320 Freq. U

4.80

6.40

1

I0 )

F i g u r e 5. ACF, PSD and r e c o r d o f n o i s e o f an I n d u c t i v e l y Plasma - Atomic E m i s s i o n S p e c t r o g r a p h .

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

Coupled

DETECTION IN ANALYTICAL CHEMISTRY

140

o\

= a*

j^2TT

1+

2Tf jexp (-^-)

- l J J

(36)

In chromatography T » T i , and the expression can be simplified to: 2

a ? . « a . 2TTi l n

(37) 2

Again, the variance i s proportional to T, a and T i are not independent. Figure 6 shows the r e s u l t of the computer c a l c u l a t i o n of the error variance as a function of the integration time. The o r i g i n of the noise i s a Flame Ionisation Detector (FID). The ACF i s estimated from a limited number of baseline noise data points, r e s u l t i n g i n a confidence i n t e r v a l derived with the B a r t l e t t formula (4,8). An i n t e r e s t i n g question i s : Is f i l t e r i n g p r i o r to integration useful, p a r t i c u l a r l y i decreasing cut-off frequenc of the baseline noise an , decreasing cut-off frequency r e s u l t s i n a distorted peak; the peak width i s increasing and implying that an increasing integration time i s needed to avoid systematic errors; as i s shown, t h i s i s not favorable. A study carried out with f i r s t order and second order f i l t e r s has shown that f i l t e r i n g p r i o r to integration i s not advisable, as the second effect dominates (6). Optimum Integration Limits Another interesting question i s : Is i t possible to determine optimal peak integration i n t e r v a l s on the basis of known or even unknown peak shapes and known noise characteristics? And i f an optimum integration i n t e r v a l can be estimated, what i s the error variance? As i s extensively shown i n a previous paper (9), i t happens to be possible i n some cases to determine optimum integration l i m i t s . As an example l e t us consider a symmetric peak with, f o r instance, a Gaussian peak shape with known peak maximum. Decreasing the i n t e gration i n t e r v a l means decreasing the random error i n the peak area estimate, as i s shown. But the systematic error i s increasing; the peak i s not completely integrated and the r e s u l t i n g area w i l l be biased. Figure 7 shows a signal x ( t ) composed of a peak s(t) (dashed line) and noise n ( t ) . 1^ i s the true peak area and !«, i s t h e peak area estimate, taken as the area of the noisy peak within the i n t e gration i n t e r v a l divided by the normalized integrated peak f r a c t i o n I ( T ) = I (T)/Ioo> being the f r a c t i o n of the peak area i n the i n t e r v a l T divided by the true peak area. This i s equal to the shaded part of the small peak with unit area. We want to minimize P 2 ( T ) , i . e . the expected value of the squared difference between the true area and the estimate: n o r m

S

°I y (T) = E | I - I 1 2

I

00

( T )

=

= error variance

00 I

„

„ «

norm

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

(38)

7.

SMIT AND STEIGSTRA

Figure 7. interval.

Noise and Detection Limits

141

Noisy peak and normalized peak with optimum integration

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

142

DETECTION IN ANALYTICAL CHEMISTRY

μ (Τ) has t o be m i n i m i z e d w i t h r e s p e c t t o T. The n o r m a l i z e d i n t e g r a ­ ted peak a r e a i n case o f a known peak shape i s known, and we have d e r i v e d an e x p r e s s i o n f o r t h e i n t e g r a t e d n o i s e v a r i a n c e . As u s u a l , we can determine the d e r i v a t i v e , s e t t i n g i t e q u a l t o z e r o and t h e d e s i r e d r e s u l t can be c a l c u l a t e d . T h i s p r o c e d u r e l e a d s t o : 2

da* (T) I'(T)

In

- 2σ*

dT

(T)

d

I

(

'

η

T

)

(39)

dT

case of symmetric peaks: u+^T

R ( T )

K S " T~ f

=

=

s ( t ) d ( t )

( 4 0 )

u-^T An e x p r e s s i o n f o r the v a r i a n c e i s known ( E q u a t i o n

σ*

I

34):

Τ (Τ) = 2 Γ (Τ - τ) R (τ)άτ Ι ηη

(41)

ο Hence, u s i n g E q u a t i o n s Γ s ( t ) d t . ÎΤ R u+^T J J u-^T 0 n

40 and 41 E q u a t i o n 39 can be w r i t t e n a s :

(τ)άτ = 2 fΤ ( T - ) R n J T

n

n

(τ)άτ . [ s ( u + i T ) ]

(42)

0

E v a l u a t i o n g e n e r a l l y l e a d s t o a minimum f o r some v a l u e o f T. S i m i l a r e q u a t i o n s can be d e r i v e d f o r asymmetric peaks ( 9 ) . The f i n a l r e s u l t i n case o f a G a u s s i a n peak w i t h f i r s t o r d e r noise i s :

e r f [ - J L - U

X e x p i - ^ l

V T .

)

(43)

= s t a n d a r d d e v i a t i o n o f t h e peak. This r e l a t i o n i s s a t i s f i e d i f : Τ

opt

«2.8

σ

(44)

ρ

The c o r r e s p o n d i n g 5.6 σ μ (Τ

J

2

°

p t

2

error variance i s : Τ

σ

? - J L ± ~

2

erf (0.99)

8

o

2 n

T

(45)

σ

X

P

Τ = time c o n s t a n t of the f i r s t o r d e r n o i s e , χ

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

7.

SMIT AND STEIGSTRA

Noise and Detection Limits

143

A remarkable r e s u l t i s t h a t i n t h i s p a r t i c u l a r case the optimum i n t e g r a t i o n i n t e r v a l i s independent of the time c o n s t a n t and of the v a r i a n c e of the n o i s e . Of c o u r s e , the r e s u l t i n g e s t i m a t i o n e r r o r depends on b o t h parameters. The t h e o r y can be extended t o skewed peaks w i t h known or unknown shape, o t h e r k i n d s of n o i s e , e t c . A d e t a i l e d treatment i s g i v e n i n ( 9 ) . Integration Variance

after Baseline Correction

The e x p r e s s i o n s d e r i v e d so f a r are o n l y v a l i d i f the n o i s e i s assumed to be s t a t i o n a r y . However, i t i s u n f o r t u n a t e t h a t t h i s i s not always the case. P a r t i c u l a r l y i n a technique l i k e chromatography, a nons t a t i o n a r y b a s e l i n e d r i f t i s o f t e n p r e s e n t due t o , f o r i n s t a n c e , s t r i p p i n g of the column, c o n t a m i n a t i o n of d e t e c t o r s , e t c . The nons t a t i o n a r y d r i f t , not t o be confused w i t h s t a t i o n a r y low frequency noise with properties define i p r o b a l i s t i c o n s i d e r e d as a d e t e r m i n i s t i Baseline d r i f t correctio indispensabl par goo chromatographic d a t a p r o c e s s i n g p r o c e d u r e . The f o l l o w i n g q u e s t i o n s have t o be answered: - What i s the i n f l u e n c e of u n c o r r e c t e d d r i f t on the e s t i m a t e d ACF, which i s used to c a l c u l a t e s t a t i s t i c a l q u a n t i t i e s l i k e the i n t e g r a ­ t i o n error variance? - What i s the i n t e g r a t i o n v a r i a n c e a f t e r d r i f t c o r r e c t i o n ? A complete treatment i s beyond the scope of t h i s paper, but an i n t r o ­ d u c t i o n w i t h a s i m p l i f i e d , but p r a c t i c a l l y r e l e v a n t example, w i l l be g i v e n here. The s i m p l e s t case i s a l i n e a r b a s e l i n e d r i f t and the r e s u l t i n g model of the n o i s y d r i f t i n g b a s e l i n e i s : x(t)

(46)

= n ( t ) + a + bt

where a and b are c o n s t a n t s . Τ Τ A f i n i t e measurement time from - γ to γ i s chosen, w h i c h i s not important f o r the d e r i v a t i o n . The e s t i m a t i o n of the ACF i s now d e f i n e d as: m

Τ (47) Τ 2 E v a l u a t i o n of t h i s i n t e g r a l g i v e s : true

ACF

R* (τ) = R (τ) xx xx

systematic e r r o r + a

2

random e r r o r

+

(48)

Ρ and Q are s t o c h a s t i c f u n c t i o n s of τ, b o t h w i t h an expected v a l u e zero:

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

of

144

DETECTION IN ANALYTICAL CHEMISTRY

Ρ(τ)

n(t)dt +

Τ =

Q(T)

r2

1

[

L

1

n(t) t dt +

Τ ' 2

(49)

n(t + x)dt

(Τ-τ)

Τ ,2" Γ n(t)dt + ^ J

- τ

T

Ζ

-1

2

n(t + T ) t d t

4

(50)

However, assuming Τ » τ, t h e i r v a r i a n c e can be d e t e r m i n e d as t h e r a t h e r simple expression: Τ-τ 8 J

2

E[P (T)]!

(Τ-τ-t

and

Ε [Q (τ )] « (2 ( Τ-τ ) / 3 ) J " ( t ) dt

(52)

2

As an example, t h e e q u a t i o n s 2

f o r f i r s t o r d e r n o i s e w i l l be g i v e n : (53)

2

E [ P ] = 8σ τ /(Τ-τ) η

E[Q

2

= 2σ

2

η

(54)

τ (Τ-τ)/3 η

A c l o s e l o o k a t E q u a t i o n 48 l e a d s t o t h e f o l l o w i n g c o n c l u s i o n c o n ­ c e r n i n g t h e e f f e c t o f u n c o r r e c t e d l i n e a r d r i f t . The e s t i m a t e d ACF c o n t a i n s two s y s t e m a t i c components, each p r o p o r t i o n a l t o a and b r e s p e c t i v e l y , and two s t o c h a s t i c components, p r o p o r t i o n a l t o a and b. A f i n a l c o n c l u s i o n can be d e r i v e d from t h e f o r m u l a e : a c o n s i d e r a b l e e r r o r i n the e s t i m a t i o n o f t h e ACF and d e r i v e d q u a n t i t i e s can be expected i f b a s e l i n e d r i f t i s n o t c o r r e c t e d . T h i s l e a d s us t o t h e r e m a i n i n g q u e s t i o n , the d e t e r m i n a t i o n o f t h e i n t e g r a t i o n v a r i a n c e after baseline d r i f t correction. Many c o r r e c t i o n p r o c e d u r e s a r e known: l i n e a r and e x p o n e n t i a l f i t t i n g , p o l y n o m i a l a p p r o x i m a t i o n ( b o t h o r t h o g o n a l and n o n - o r t h o g o n a l ) , e t c . I n t h i s paper the d e s c r i p t i o n w i l l be r e s t r i c t e d t o the v e r y o f t e n used l i n e a r e x t r a p o l a t i o n , a g a i n assuming a l i n e a r b a s e l i n e d r i f t . L e t us c o n s i d e r a n o i s y peak w i t h a l i n e a r d r i f t i n g b a s e l i n e . The u s u a l p r o c e d u r e i s as f o l l o w s ( F i g u r e 8). Two time i n t e r v a l s w i t h a time d u r a t i o n T a r e s e l e c t e d on b o t h s i d e s o f t h e peak. Now each i n t e r v a l i s f i t t e d w i t h a s t r a i g h t l i n e . To s i m p l i f y t h e e q u a t i o n s the f o l l o w i n g i n t e g r a l s a r e d e f i n e d : 2

c

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

2

7. SMIT AND STEIGSTRA

Noise and Detection Limits

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

145

DETECTION IN ANALYTICAL CHEMISTRY

146 T 1

1

T

2

= Jx(t)dt

I

2

Τι»

3

= J x(t)dt

Ti

T

I

3

= J x(t)dt T

2

(55)

3

The l e n g t h o f t h e i n t e g r a t i o n i n t e r v a l s a r e T , T^ and T , r e s p e c t i ­ v e l y . The b a s e l i n e d r i f t c o r r e c t e d i n t e g r a l i s : c

I = I

Τ - - i

2

c

(I1 + I3) (56) 2T

The

c v a r i a n c e of t h e c o r r e c t e d i n t e g r a l can be c a l c u l a t e d :

Γ

di.i

2

+ ι .ι )τ 2

/(ΐ

3

2 ι ) τ \ ~| 2

1

+

3

Ε

(

τ.\

2

2TJ

τ. -(Ε[ΙΙ.Ι ]+Ε[Ι .Ι ]) ^ 2

2

3

+

τ? + Ε[Ι

1 Β

Ι ] —

(57)

3

The f i r s t t h r e e e x p e c t e d v a l u e s can be d e t e r m i n e d by a l r e a d y d e s c r i ­ bed o r d i n a r y "σ|" c a l c u l a t i o n s . The o t h e r t h r e e a r e a c t u a l l y c r o s s terms. E v a l u a t i o n leads to a r a t h e r complicated formula, but nevertheless i t i s g e n e r a l l y u s a b l e f o r a l l k i n d s of n o i s e w i t h known ACF. As an example t h e r e s u l t f o r f i r s t o r d e r n o i s e w i l l be g i v e n :

σ

2

I

= σ

2

2T.X -2x

2

n

(l - e x p ( - T . / x ) ) n

" «p(- W )

2

.

η

e x p ( - Τ./τ ) 2 (l - e x p ( - T ^ ) η

+

-T / r j l -L

exp(-

(l - e x p ( - T / x ) ) c

n

T./tJ).

(58)

E q u a t i o n 58 i s g r a p h i c a l l y d i s p l a y e d i n F i g u r e 9, showing σ-j- as a f u n c t i o n of T^ w i t h t h e c o r r e c t i o n i n t e r v a l as a parameter. A remarkable r e s u l t i s that the curves are c r o s s i n g . A c a r e f u l i n s p e c t i o n of E q u a t i o n 58 and F i g u r e 9 l e a d s t o t h e f o l l o w ­ i n g statement: I f a s i g n a l w i t h l i n e a r d r i f t i n g b a s e l i n e and f i r s t o r d e r b a s e l i n e n o i s e i s i n t e g r a t e d , then the optimum b a s e l i n e c o r r e c ­ t i o n i n t e r v a l i s i n f i n i t e i f t h e i n t e g r a t i o n time i s g r e a t e r than f o u r times the time c o n s t a n t o f t h e n o i s e ; o t h e r w i s e , the optimum c o r r e c t i o n i n t e r v a l i s z e r o . I n t h e l a s t case the use o f two c o r r e c ­ t i o n p o i n t s on b o t h s i d e s o f a peak i s s u f f i c i e n t .

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

7.

SMIT AND STEIGSTRA

Noise and Detection Limits

147

τ. ι F i g u r e 9. Standard d e v i a t i o n o f t h e i n t e g r a t e d n o i s e a f t e r d r i f t c o r r e c t i o n v e r s u s the i n t e g r a t i o n t i m e , w i t h t h e c o r r e c t i o n i n t e r v a l w i d t h as a parameter.

American Chemical Society Library 16thChemistry; S t , N.W. In Detection in1155 Analytical Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987. Washington, D.C 20036

DETECTION IN ANALYTICAL CHEMISTRY

148 Discussion and Conclusions

In case of a stable and stationary chromatographic system, the derived general theory i s certainly usable for calculating quantitat i v e l y uncertainties and detection l i m i t s i n signal integrating methods l i k e chromatography. However, an extensive analysis of the detector noise i s required and the use of a computer with a data acquisition system and special software i s inevitable. If a d r i f t i n g baseline i s present and possibly corrected, the formulae become rather complicated and are not d i r e c t l y usable i n d a i l y practice. An extension to other kinds of noise, i . e . the more r e a l i s t i c 1/f or f l i c k e r noise leads to even more complicated f o r mulae. Nevertheless, i t i s possible to determine quantitatively detection l i m i t s i n case of the application of some s p e c i f i c baseline d r i f t correction procedure, i f the measurement conditions are well defined and stable and from an a p r i o r i analysis effects influencing th g y i s obtained.

Literature Cited 1. 2. 3. 4. 5. 6. 7. 8. 9.

Bendat, J. S.; Piersol, A. G. Measurement and Analysis of Random Data; Wiley: New York, 1966. Box, G. E. P.; Jenkins, G. M. Time Series Analysis; Holden-Day: San Francisco, 1976. Papoulis, A. The Fourier Integral and its Applications; McGraw-Hill: New York, 1962. Jenkins, G. M.; Watts, D. G. Spectral Analysis and its Applications; Holden-Day: San Francisco, 1969. Beauchamp, K.; Yuen, C. Digital Methods for Signal Analysis; Allen & Unwin: London, 1979. Smit, H. C.; Walg, H. L. Chromatographia 1975, 8, 311. Smit, H. C.; Walg, H. L. Chromatographia 1976, 9, 483. Duursma, R. P. J . ; Smit, H. C. Anal. Chim. Acta 1981, 133, 67. Laeven, J. M.; Smit, H. C. Anal. Chim. Acta 1985, 176, 77.

RECEIVED

January 21, 1987

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

Chapter 8

Establishing Clinical Detection Limits of Laboratory Tests Mark H. Zweig Clinical Pathology Department, Clinical Center, National Institutes of Health, Bethesda, MD 20892

Fundamental clinical laboratory test performance can be described in terms of accuracy, or the ability to correctly classify subjects into clinically relevant subgroups. Receiver operating characteristic (ROC) curves demonstrate the limits of a given test to detect the alternative states of interest over the complete spectrum of operating conditions, providing a comprehensive and pure index of accuracy. Obtaining valid data for ROC analysis requires attention to the following important steps: (1) define carefully the specific clinical question to be addressed; (2) choose subjects who are representative of the population to which the test is ultimately to be applied; (3) perform all tests being evaluated on all subjects; (4) determine the "true" diagnosis by rigorous and complete means independent of the test(s) being studied; and (5) evaluate and compare test performance at all decision levels using ROC curves. Swets and Pickett ( 1 ) divide t e s t performance into a discrimination or accuracy aspect and a decision or e f f i c a c y aspect. Accuracy, on the one hand, r e f e r s to the a b i l i t y of the test to c l a s s i f y , to c o r r e c t l y discriminate between alternative c l i n i c a l states of the subjects under study ( i . e . , signals vs. noise, disease vs. non-disease, chest pain with myocardial i n f a r c t i o n vs. chest pain without i n f a r c t i o n , blood i n stools due to malignancy vs. blood i n stools from other conditions). This i s accuracy or correctness r e l a t i v e to truth, as best as we can determine that truth. We can express accuracy as c l i n i c a l s e n s i t i v i t y and s p e c i f i c i t y . E f f i c a c y , on the other hand, i s a measure of the actual p r a c t i c a l value of the diagnostic information or c l a s s i f i c a t i o n - how much

This chapter not subject to U.S. copyright Published 1988 American Chemical Society

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

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b e n e f i t t h e t e s t p r o v i d e s r e l a t i v e t o i t s r i s k s and c o s t s . E v a l u a t i n g o r o p t i m i z i n g e f f i c a c y i n v o l v e s d e c i s i o n t h e o r y and c o n s i d e r a t i o n of the complexities of c l i n i c a l u t i l i t y , r a t h e r than j u s t accuracy. T h i s i s p a r t o f a symposium on d e t e c t i o n l i m i t s . In this paper I w i l l c o n s i d e r l i m i t s i n terras o f c l i n i c a l d e t e c t i o n r a t h e r t h a n a n a l y t i c a l d e t e c t i o n . By c l i n i c a l d e t e c t i o n I mean a c c u r a c y or the d i s c r i m i n a t i n g a b i l i t y r e f e r r e d t o i n the preceding p a r a g r a p h . T h i s a b i l i t y o f a t e s t , e x p r e s s e d as s e n s i t i v i t y and s p e c i f i c i t y , i s n i c e l y d e s c r i b e d and a p p r e c i a t e d u s i n g t h e r e c e i v e r o p e r a t i n g c h a r a c t e r i s t i c (ROC) c u r v e because i t p r o v i d e s a pure index of accuracy, of d i s c r i m i n a t i o n a b i l i t y . I t deals w i t h s i g n a l d e t e c t i o n and t h e a b i l i t y t o d i s t i n g u i s h s i g n a l f r o m noise. The i n d e x o f a c c u r a c y p r o v i d e d i s independent o f any d e c i s i o n c r i t e r i o n w h i c h might be a p p l i e d o r o f any b i a s w h i c h t h e system might have towar d e c i s i o n aspect, which s e p a r a t e d o u t so as n o i n t r i n s i c a b i l i t y o f t h e t e s t t o d i s c r i m i n a t e among v a r i o u s s t a t e s . The i n f l u e n c e o f v a r i o u s d e c i s i o n f a c t o r s ( p r e v a l e n c e , u t i l i t i e s ) on t h e o p e r a t i o n and u l t i m a t e e f f i c a c y o f t h e t e s t i s a d d r e s s e d by c l i n i c a l d e c i s i o n a n a l y s i s . The f o r m a l t o o l o f c l i n i c a l d e c i s i o n a n a l y s i s j o i n s the estimates of the p r o b a b i l i t i e s o f t e s t outcomes ( t r u e p o s i t i v e s , f a l s e p o s i t i v e s , e t c . ) p r o v i d e d by ROC a n a l y s i s w i t h d e c i s i o n f a c t o r s so as t o e s t a b l i s h t h e d e c i s i o n c r i t e r i o n f o r t e s t s and t o choose t h e s e t and o r d e r o f d i a g n o s t i c and t h e r a p e u t i c s t e p s t o be t a k e n t o o p t i m i z e t h e outcome i n terms o f y e a r s o f l i f e , q u a l i t y o f l i f e , c o s t s , resource u t i l i z a t i o n , e t c . (2-3). The b a s i c j o b o f a c l i n i c a l l a b o r a t o r y t e s t i s t o p r o v i d e i n f o r m a t i o n about t h e c l i n i c a l s t a t e o f p a t i e n t s f o r h e a l t h c a r e management p u r p o s e s . The g o a l then i s t o s u b d i v i d e o r c l a s s i f y s e e m i n g l y s i m i l a r s u b j e c t s i n t o c l i n i c a l l y r e l e v a n t management subgroups. Suppose we a r e t a l k i n g about p e o p l e who come t o an emergency room w i t h a c u t e c h e s t p a i n . Some w i l l t u r n o u t t o be h a v i n g a h e a r t a t t a c k and some won't. L a b o r a t o r y t e s t s h e l p d i v i d e o r c l a s s i f y t h o s e p a t i e n t s i n t o subgroups - t h a t i s , l a b t e s t s h e l p t o d i s t i n g u i s h t h o s e who p r o b a b l y a r e h a v i n g a h e a r t a t t a c k from those who a r e n ' t . The q u e s t i o n i s , what i s t h e l i m i t of t h e a b i l i t y o f t h e t e s t t o i d e n t i f y o r d e t e c t s u b j e c t s h a v i n g a h e a r t a t t a c k among t h o s e w i t h c h e s t p a i n ? What a r e t h e l i m i t s o f t h e t e s t ' s powers t o d e t e c t a c c u r a t e l y t h e c l i n i c a l s t a t e o f each i n d i v i d u a l i n t h e group? T h i s i s a s i g n a l d e t e c t i o n t h e o r y i s s u e . Most d i a g n o s t i c t e s t s a r e i m p e r f e c t and, p a r t i c u l a r l y when we use a b i n a r y approach - r e s u l t s a r e e i t h e r " p o s i t i v e " o r " n e g a t i v e " - t h e r e a r e some m i s c l a s s i f i c a t i o n e r r o r s , i n a c c u r a c i e s . Some s u b j e c t s w i t h t h e c o n d i t i o n o f i n t e r e s t w i l l be m i s s e d o r some w i t h o u t t h e c o n d i t i o n w i l l be m i s t a k e n l y c o n s i d e r e d a f f e c t e d , o r b o t h w i l l happen. The a b i l i t y o f a t e s t to properly i d e n t i f y or c l a s s i f y subjects o r conditions of i n t e r e s t can be e x p r e s s e d as t h e s e n s i t i v i t y and s p e c i f i c i t y o f t h e t e s t . F o r c l i n i c a l purposes t h e s e a r e d e f i n e d as f o l l o w s : SENSITIVITY (TRUE POSITIVE RATE): F r a c t i o n o f a l l a f f e c t e d

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

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Establishing Clinical Detection Limits of Laboratory Tests

subjects i n whom the test result i s p o s i t i v e ; "test p o s i t i v i t y i n the presence of the disease." SPECIFICITY (TRUE NEGATIVE RATE): Fraction of a l l unaffected subjects i n whom the test result i s negative; "test negativity i n the absence of the condition." These inaccuracies i n terms of s e n s i t i v i t y and s p e c i f i c i t y can be s t a t i s t i c a l l y represented by the ROC curve. This paper w i l l discuss basic test performance i n terms of accuracy, but w i l l not deal with actual a p p l i c a t i o n of a test. The l a t t e r involves choosing decision levels ( i . e . , reference values, cut-offs, normal l i m i t s , etc.) and involves measures of u t i l i t y which are beyond the scope of fundamental test performance. I w i l l describe a set of p r i n c i p l e s or elements important f o r evaluating test performance and comparing tests to one another (4,5). I w i l l p a r t i c u l a r l y emphasize the power and convenience of ROC curves, an extremely e f f e c t i v e t o o l for assessing and comparin usefulness of ROC curve members of various biomedica d i s c i p l i n e years, t o o l has received l i t t l e attention from the c l i n i c a l laboratory community. SiRnal/Noise Discrimination:

H i s t o r i c a l Perspectives

The ROC curve apparently had i t s origins i n e l e c t r o n i c signal detection theory. Much of t h i s arose i n the 1940's and 1950's from analysis of radar systems. During WWII, radar operators watched screens f o r b l i p s which might indicate enemy a i r c r a f t f o r the purpose of deciding when to mobilize f i g h t e r squadrons to intercept. The problem was to d i s t i n g u i s h between signals from h o s t i l e planes and noise from clouds, flocks of b i r d s , etc. They realized that i n interpreting the radar signals they saw there was always a trade-off between s e n s i t i v i t y and s p e c i f i c i t y as the s e n s i t i v i t y increased so did the rate of f a l s e p o s i t i v e s . That i s , i f they lowered the threshold f o r which b l i p s they interpreted as s i g n i f y i n g enemy planes, they f a l s e l y i d e n t i f i e d clouds and migrating b i r d s , etc., as planes more often. S p e c i f i c i t y declined and they scrambled interceptor squadrons unnecessarily. On the other hand, r a i s i n g the threshold f o r c a l l i n g a b l i p " p o s i t i v e " (enemy bombers) meant not responding to the a r r i v a l of enemy a i r c r a f t in some instances (false negatives). They were experiencing the trade-off between s e n s i t i v i t y and s p e c i f i c i t y inherent i n t e s t systems. Figure 1 shows hypothetical signals and noise i n the form of peaks. Imagine t h i s i s radar information and the r e a l planes give peaks I, I I , and I I I . I f interceptor planes are sent up when the signal exceeds c r i t e r i o n C, then two r e a l signals, I and I I , w i l l be missed. However, i f c r i t e r i o n A i s used so as to catch a l l three r e a l signals of enemy a i r c r a f t , a number of noise a r t i f a c t s w i l l be incorrectly c l a s s i f i e d as p o s i t i v e s (false p o s i t i v e s ) .

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Signal/Noise Discrimination i n the C l i n i c a l Laboratory Figure 2 i l l u s t r a t e s t h i s i n the form of serum myoglobin concentrations obtained 5 hours after the onset of chest pain from patients admitted to a coronary care u n i t with the suspicion of myocardial i n f a r c t i o n . This test has been proposed by some as a marker f o r heart attacks. Some of these patients turned out to have a heart attack ( s o l i d bars) and some didn't (hatched bars). Because of the overlap between "signals" and "noise," any decision c r i t e r i o n we choose w i l l r e s u l t i n some m i s c l a s s i f i c a t i o n s . We could choose any of various decision l e v e l s , each giving a d i f f e r e n t s e n s i t i v i t y / s p e c i f i c i t y combination - a l l of the possible combinations comprising the trade-offs available with t h i s test. This spectrum of trade-offs constitutes the detection l i m i t of t h i s t e s t and i s represented by the ROC curve. We have defined th as s e n s i t i v i t y and th as s p e c i f i c i t y and can expres percentage decimal f r a c t i o n s . A perfect test would exhibit both a s e n s i t i v i t y and s p e c i f i c i t y of 100% or 1.0. Tests are rarely perfect. I t would be rather unusual f o r a test to exhibit a s e n s i t i v i t y and a s p e c i f i c i t y of 100% at the same time. Often we hear or read that a p a r t i c u l a r test has a p a r t i c u l a r s e n s i t i v i t y or s p e c i f i c i t y . In r e a l i t y , as noted with radar and serum myoglobin, there i s n t j u s t one s e n s i t i v i t y or s p e c i f i c i t y f o r a t e s t , but rather a continuum of s e n s i t i v i t i e s and s p e c i f i c i t i e s . By varying the decision l e v e l (or "decision point," "upper limit-of-normal," "cutoff value," "reference value," e t c . ) , any s e n s i t i v i t y from 0 to 100% can be obtained. Each of these s e n s i t i v i t i e s w i l l have a corresponding s p e c i f i c i t y . Sensitivity and s p e c i f i c i t y occur, then, i n p a i r s . The test's accuracy i s r e f l e c t e d i n the pairs that can occur; not a l l pairs are possible f o r a p a r t i c u l a r t e s t . A given test w i l l have one set of s e n s i t i v i t y - s p e c i f i c i t y pairs i n one c l i n i c a l s i t u a t i o n , but may have a d i f f e r e n t set of pairs when applied to another c l i n i c a l s i t u a t i o n where the group tested i s d i f f e r e n t . The spectrum of p a i r s exhibited by a t e s t i n a given c l i n i c a l setting characterizes or describes the accuracy of the test. Often test users i m p l i c i t l y assume one s e n s i t i v i t y - s p e c i f i c i t y p a i r characterizes a t e s t because they accept a conventional, often a r b i t r a r i l y chosen, upper-limit-of-normal as the single correct decision l e v e l f o r that test for a l l circumstances. They accept the corresponding s e n s i t i v i t y - s p e c i f i c i t y p a i r as the correct one f o r the t e s t . This, however, i s actually only one of multiple possible operating points for the t e s t . When the concept of varying the decision l e v e l (operating point) to generate a spectrum of s e n s i t i v i t y - s p e c i f i c i t y pairs i s understood, then the issue becomes: How good are the pairs? Also, which p a i r ( s ) works the best for the circumstances i n which the test i s to be used? f

T

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

8.

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Establishing Clinical Detection Limits of Laboratory Tests

F i g u r e 1:

Diagra a rada r e p r e s e n t s i g n a l s from a i r c r a f t , w h i l e a l l o t h e r peaks r e p r e s e n t n o i s e . L i n e s A, B, C, and D r e p r e s e n t i n c r e a s i n g d e c i s i o n l e v e l t h r e s h o l d s , which r e s u l t s i n s u c c e s s i v e l y lower t r u e - and f a l s e - p o s i t i v e r a t e s .

500 Γ CD :200

< F ζ

100

LU

υ Ζ Ο ο ω

3

50

20

Ο > 10 Έ Έ D ce

LU CO

INDIVIDUAL PATIENTS F i g u r e 2:

Serum m y o g l o b i n c o n c e n t r a t i o n s f o r 54 p a t i e n t s w i t h chest pain admitted to a c o r o n a r y c a r e u n i t . M y o g l o b i n was measured 5 h o u r s a f t e r the o n s e t of p a i n . Solid bars: acute myocardial i n f a r c t . C r o s s h a t c h e d b a r s : no i n f a r c t .

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154 ROC

Curves:

Derivation

To answer these questions, we f i r s t need a way to represent and deal with a l l these d i f f e r e n t possible operating points and t h e i r resultant performance c h a r a c t e r i s t i c s ( s e n s i t i v i t y / s p e c i f i c t y p a i r s ) . The ROC curve graphically displays the entire spectrum of a given test's performance for a p a r t i c u l a r sample group of affected and unaffected subjects. Figure 3 contains a hypothetical frequency d i s t r i b u t i o n histogram at the top and the and the corresponding ROC curve below. The ROC curve plots the true p o s i t i v e (TP) rate or percentage as a function of the f a l s e p o s i t i v e (FP) rate or percentage as the decision l e v e l i s varied. The true p o s i t i v e rate i s the same as s e n s i t i v i t y and i s equal to the number of affected individuals with a " p o s i t i v e " r e s u l t divided by the t o t a l number of affected i n d i v i d u a l s . The true p o s i t i v e rate i s also equal t 1 - f a l s negativ (FN) rate Th f a l s e p o s i t i v e rate i s nevertheless have a " p o s i t i v e related to s p e c i f i c i t y , or the a b i l i t y of the test to c o r r e c t l y i d e n t i f y unaffected individuals ( s p e c i f i c i t y = true negative (TN) rate = number of unaffected individuals with "negative" r e s u l t s / t o t a l number of unaffected individuals = 1 - f a l s e p o s i t i v e r a t e ) . Both the TP and FP rates depend on the decision l e v e l chosen. Both rates also depend on the c l i n i c a l s e t t i n g , as r e f l e c t e d by the study population chosen. The FP rate i s influenced by the type of nondiseased subjects included i n the study group. I f , for example, the nondiseased subjects are a l l healthy blood donors who are free of any signs or symptoms of disease, the test may appear to have a much lower rate than i f the nondiseased subjects are persons who c l i n i c a l l y resemble those who a c t u a l l y have the disease. Like the FP rate, the TP rate also depends on the study group. A test used to detect cancer may have a higher TP rate when applied to patients who have active or advanced disease than when applied to patients having stable or limited disease. This dependence of TP and FP rates on the study population i s the reason why an ROC curve must be generated f o r each c l i n i c a l situation. Each point on the ROC curve represents a p a i r of true and f a l s e p o s i t i v e rates corresponding to some decision l e v e l . In Figure 3 , the l e f t hand curve of the frequency histogram (top) represents results from unaffected individuals and the right hand curve i s derived from affected individuals. The ROC curve i s derived from the data i n the frequency histogram, so the f i r s t step i s to obtain the t e s t results from both the affected group and the unaffected group. True p o s i t i v e rates are calculated using the results from the affected i n d i v i d u a l s , while f a l s e p o s i t i v e rates are generated from the unaffected individuals' data. The ROC curve i s constructed by varying the decision l e v e l from the highest test r e s u l t down to zero, r e s u l t i n g i n true and f a l s e p o s i t i v e rates which vary continuously. The decision l e v e l at point a i n Figure 3 i s higher than any observed results (see top), so at that decision l e v e l none of the r e s u l t s are " p o s i t i v e " and both true and f a l s e p o s i t i v e rates are zero (see bottom). As the

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

8. ZWEIG

Establishing Clinical Detection Limits of Laboratory Tests

unaffected

False Positive Rate (%)

Figure 3:

Top: Hypothetical frequency d i s t r i b u t i o n curve. Bottom: Receiver operating c h a r a c t e r i s t i c (ROC) curve corresponding to data i n top panel, generated by varying the decision l e v e l and then p l o t t i n g the r e s u l t i n g pairs of true and f a l s e p o s i t i v e rates. Arrows at a to e mark points corresponding to decision l e v e l s i n top panel. The curve from c to d d e s c r i b e s t h e test's performance i n the c r u c i a l overlap region.

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156

decision l e v e l i s lowered from a to b, some of the affected individuals have p o s i t i v e results but none of the unaffected individuals do, so the true p o s i t i v e rate r i s e s while the f a l s e p o s i t i v e rate remains zero. Point c shows the highest true p o s i t i v e rate achievable (with t h i s data) with the f a l s e p o s i t i v e rate s t i l l at zero. This i s the edge of the overlap region (c to d). At c the ROC curve leaves the Y axis because i f the decision l e v e l i s lowered any further, some unaffected individuals have f a l s e l y p o s i t i v e r e s u l t s . At decision l e v e l d, a l l affected individuals have p o s i t i v e test r e s u l t s , so the true p o s i t i v e rate reaches 100%, at the expense of some percentage of f a l s e p o s i t i v e s . This i s the other edge of the c r u c i a l overlap region. The portion of the curve from c to d (where i t has l e f t the Y axis but not yet intercepted the true p o s i t i v e = 100% horizontal l i n e ) describes the overlap region. From decision l e v e l d to e, f a l s e p o s i t i v e rates increas unaffected individuals ROC

Curves:

Interpretation

The complete ROC curve summarizes the c l i n i c a l accuracy of the test by displaying the paired true and f a l s e p o s i t i v e rates for a l l possible decision l e v e l s . Good c l i n i c a l performance of a test i s characterized by a high true p o s i t i v e rate and a low f a l s e p o s i t i v e rate. Accordingly, as test performance improves, the ROC curve w i l l move upward (toward higher true p o s i t i v e rates) and to the l e f t (toward lower f a l s e p o s i t i v e r a t e s ) . A perfect test would achieve a 100% true p o s i t i v e rate with no f a l s e p o s i t i v e s . Thus, i t s ROC curve would r i s e v e r t i c a l l y to the (0,100) point i n the upper l e f t comer and then move h o r i z o n t a l l y to the right along the horizontal l i n e representing true p o s i t i v e rate = 100% to the (100,100) point i n the upper right corner. Conversely, for a c l i n i c a l l y useless t e s t , which gives s i m i l a r results for subjects with and without the condition, the true and f a l s e p o s i t i v e rates would be i d e n t i c a l for any given decision l e v e l . Therefore, the ROC curve would be a diagonal between the lower l e f t and upper r i g h t corners, representing the l i n e where the true p o s i t i v e rate always equals the f a l s e p o s i t i v e rate. Because the curve i s usually above the diagonal, i t starts out at the lower l e f t with the TP rate ( s e n s i t i v i t y ) increasing faster than the f a l s e p o s i t i v e rate. At some point the slope begins to f a l l and the f a l s e p o s i t i v e rate starts increasing faster than the true p o s i t i v e rate - i n other words, gains i n s e n s i t i v i t y come at the cost of increasingly larger costs in terms of n o n s p e c i f i c i t y . This imposes a p r a c t i c a l l i m i t on the usable s e n s i t i v i t y of the test - where that l i m i t i s depends on the r e l a t i v e u t i l i t y or benefits and the costs of true and f a l s e r e s u l t s and gets us beyond detection and into decision issues. The ROC curve can also be constructed as a p l o t of true p o s i t i v e rate ( s e n s i t i v i t y ) versus true negative rate ( s p e c i f i c i t y ) instead of versus f a l s e p o s i t i v e rate

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

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Establishing Clinical Detection Limits of Laboratory Tests

( 1 - s p e c i f i c i t y ) . T h i s produces a m i r r o r image of the c u r v e shown i n F i g u r e 3, f l i p p i n g t h e c u r v e t o the r i g h t s i d e w i t h the p e r f e c t p o i n t b e i n g the upper r i g h t hand c o r n e r i n s t e a d of the upper l e f t hand c o r n e r . The ROC c u r v e , t h e n , p r o v i d e s a comprehensive p i c t u r e of t h e t e s t ' s accuracy at a l l p o s s i b l e operating p o i n t s ( d e c i s i o n l e v e l s ) . I t does t h i s w i t h o u t the need t o choose a d e c i s i o n l e v e l o r e s t a b l i s h a normal range i n advance. Comparing T e s t s B e s i d e s b e i n g v a l u a b l e i n e v a l u a t i n g a s i n g l e t e s t by d e m o n s t r a t i n g the complete spectrum of i t s i n t r i n s i c performance, t h e ROC c u r v e i s e x t r e m e l y u s e f u l i n comparing t e s t s t o one a n o t h e r . Even i f we a r e e v a l u a t i n g o n l y a s i n g l e new t e s t , comparisons t o e x i s t i n process. ROC c u r v e s p r o v i d d e m o n s t r a t i n g the r e l a t i v y multipl , comparing them a t e v e r y TP r a t e by p l o t t i n g the ROC c u r v e s f o r a l l the t e s t s on t h e same graph. I f the ROC c u r v e f o r one t e s t i s u n i f o r m l y above and t o the l e f t o f the ROC c u r v e f o r a second t e s t , t h e f i r s t t e s t w i l l have a lower FP r a t e t h a n t h e second t e s t has f o r any g i v e n TP r a t e . The ROC c u r v e s of F i g u r e 4 i l l u s t r a t e t h e a m b i g u i t y i n v o l v e d i n comparing t e s t s a t j u s t one d e c i s i o n l e v e l o r o p e r a t i n g p o i n t . C o n s i d e r the case i n w h i c h t e s t A has a TP r a t e of 98% and a FP r a t e of 30%, w h i l e t e s t Β has a TP r a t e of 70% and a FP r a t e of 2%. I f the c l i n i c a l performance of the two t e s t s were e q u i v a l e n t , t h e y would s h a r e a s i n g l e ROC c u r v e . This s i t u a t i o n i s i l l u s t r a t e d i n F i g u r e 4, l e f t . T e s t Β c o u l d have a c h i e v e d t h e same TP and FP r a t e s as t e s t A i f a d i f f e r e n t d e c i s i o n l e v e l had been used. I n f a c t e i t h e r t e s t c o u l d have a c h i e v e d any of t h e p a i r s of TP and FP r a t e s on the common ROC c u r v e s i m p l y by c h a n g i n g the d e c i s i o n l e v e l . Thus, the two t e s t s may i n f a c t s h a r e a s i n g l e ROC c u r v e but i n i t i a l l y appear t o p e r f o r m d i f f e r e n t l y because t h e two d e c i s i o n l e v e l s used p l a c e the t e s t s a t d i f f e r e n c e p o i n t s on the c u r v e , i . e . , t h e o p e r a t i n g c o n d i t i o n s were not comparable. On t h e o t h e r hand, t h e two t e s t s may a c t u a l l y perform very d i f f e r e n t l y , with t e s t Β c l e a r l y s u p e r i o r , as i l l u s t r a t e d i n F i g u r e 4, c e n t e r . R e g a r d l e s s of the d e c i s i o n l e v e l chosen f o r t e s t A, i t can not a c h i e v e a TP r a t e of 70% w i t h a FP r a t e of o n l y 2%, as d i d t e s t B. I n f a c t , when t e s t A*s TP r a t e i s 70%, i t s FP r a t e i s 10%. S i m i l a r l y , t h e t r u e - and f a l s e p o s i t i v e r a t e s g i v e n o r i g i n a l l y would be e q u a l l y c o n s i s t e n t w i t h t h e s i t u a t i o n shown i n F i g u r e 4, r i g h t , where t e s t A i s c l e a r l y s u p e r i o r . These examples i l l u s t r a t e how t h e use of ROC c u r v e s a v o i d s the a m b i g u i t y w h i c h may o c c u r when t e s t s a r e compared u s i n g o n l y one d e c i s i o n l e v e l f o r each.

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F i g u r e 4. H y p o t h e t i c a l r e c e i v e r o p e r a t i n g c h a r a c t e r i s t i c (ROC) c u r v e s showing t h r e e p o s s i b l e r e l a t i o n s between t e s t s A and B. I n each c a s e , t e s t A e x h i b i t s a t r u e p o s i t i v e r a t e o f 98% and a f a l s e p o s i t i v e r a t e o f 30%, w h i l e t e s t Β e x h i b i t s a t r u e p o s i t i v e r a t e o f 70% and a f a l s e p o s i t i v e r a t e o f 2%. L e f t p a n e l : Both t e s t s have i d e n t i c a l ROC c u r v e s , and t h u s , e q u i v a l e n t d i a g n o s t i c accuracy. Middle panel: Test Β has a b e t t e r ROC c u r v e . Right panel: Test A has a b e t t e r c u r v e .

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Figures 5 and 6 are examples of real ROC curves and i l l u s t r a t e how the ROC curve can represent individual t e s t accuracy as well as compare the accuracy of multiple tests to one another. Four analytes were measured. Creatine kinase (CK) i s a serum enzyme, found primarily i n heart and other muscles, which has been used f o r some years as an early marker for necrosis. Peak serum concentrations usually occur within the f i r s t 12-24 hours a f t e r the onset of i n f a r c t i o n . CK-MB i s an isoenzyme of CK which i s more s p e c i f i c f o r heart muscle than i s t o t a l CK and thus has become popular i n the l a s t 10 years. CK-BB, another isoenzyme of CK found i n the heart, has also been examined as a possible marker f o r myocardial i n f a r c t i o n . Myoglobin, a heme containing protein found i n muscle, i s released into the serum with muscle injury. Serum concentrations of myoglobi t r i s e a r l i e tha C i n patients with myocardia a f t e r the onset of ches these four markers of myocardial injury i n patients suspected of having a heart attack sampled 8 hours a f t e r the onset of chest pain. Myoglobin occupies the left-most p o s i t i o n of the tests, and achieves the best r a t i o of true positives to f a l s e positives, with good absolute s e n s i t i v i t y (high true p o s i t i v e rate) and s p e c i f i c i t y (low f a l s e p o s i t i v e rate) simultaneously. From the ROC curve, one can make two judgements. F i r s t , myoglobin achieves the best accuracy of the four tests. Second, myoglobin probably has potential as a early marker of myocardial i n f a r c t i o n because i t ' s ROC curve l i e s quite close to the i d e a l location, the upper l e f t hand corner. This indicates that i t can achieve high true p o s i t i v e and low f a l s e p o s i t i v e rates at the same time. How best to use this test c l i n i c a l l y and which decision l e v e l ( i . e . , where on the ROC curve to operate) to select requires c l i n i c a l decision analysis with consideration of the costs of f a l s e results, the alternative tests or procedures available, the costs of the alternatives, and the u t i l i t i e s of the various possible outcomes (2,3). The ROC curve displays the spectrum of s e n s i t i v i t y / s p e c i f i c i t y pairs achievable; these pairs are the raw data needed to make the selection of decision l e v e l . In Figure 6, the patients are sampled at 18 hours after the onset of chest pain. Myoglobin's accuracy has decreased while that of the three other tests has markedly increased to a close-to-perfect l e v e l . This r e f l e c t s the fact that the serum concentration of myoglobin i s not increased as much or as often at 18 hours compared to 8 hours after the onset of pain. Therefore, i t i s not as good at discriminating between patients having and not having an i n f a r c t i o n . CK and i t s isoenzymes, on the other hand, are near peak concentrations i n those patients with i n f a r c t s and lower i n those without i n f a r c t s , and thus are very accurate i n discriminating. In t h i s study, the "true" diagnosis or gold standard was established by review of electrocardiographic data, c l i n i c a l course, and serum lactate dehydrogenase isoenzymes, as

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In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

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Establishing Clinical Detection Limits of Laboratory Tests

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well as scintigraphic findings where available. To avoid introduction of bias, the c l a s s i f i c a t i o n of patients was made without consideration of the results of any of the four tests being evaluated. A given study provides an estimate of the ROC curve for that t e s t and patient population. The confidence l i m i t s around the ROC curve can be calculated (8,9). Furthermore, the area under the ROC curve can be calculated f o r each test so as to derive a quantitative index of the test's individual accuracy and i t s r e l a t i o n to the other tests being evaluated (8,9). ROC curves can also be used to examine the impact of a n a l y t i c a l improvements on c l i n i c a l accuracy. Figure 7 shows d i s t r i b u t i o n s of test results and the corresponding ROC curves, based on simulated data. For both the affected and the unaffected patients, the b i o l o g i c a l v a r i a b i l i t y of the marker being measured has a standard deviatio have a mean test r e s u l a mean test result of 12 a n a l y t i c a imprecisio SD of 4 units, there i s considerable overlap i n test results between the affected and unaffected patients. The corresponding ROC curve shows the poor c l i n i c a l performance of the test. If an improved a n a l y t i c a l system reduces the imprecision of the measurement from 4 to 2 units, the overlap i n test results i s considerably reduced. The dramatic s h i f t of the ROC curve upward and to the l e f t r e f l e c t s the improved c l i n i c a l performance of the test. If the a n a l y t i c a l imprecision i f again halved, reducing i t s standard deviation from 2 to 1, another s i g n i f i c a n t improvement i n c l i n i c a l performance occurs. In this example, i n which the b i o l o g i c a l overlap between the two groups of patients was small, the precision of the a n a l y t i c a l system became the p r i n c i p a l factor i n determining the c l i n i c a l performance of the test; substantial improvements i n c l i n i c a l accuracy occurred as the a n a l y t i c a l p r e c i s i o n improved. In contrast, Figure 8 shows the s i t u a t i o n i n which the b i o l o g i c a l overlap i s greater. In t h i s example, the b i o l o g i c a l v a r i a t i o n i n each group has an SD of 4 u n i t s , r e s u l t i n g i n considerable i n t r i n s i c overlap i n the test results of the two groups. The figure shows t h i s extensive overlap and the poor ROC curve for an a n a l y t i c a l SD of 4. Decreasing the a n a l y t i c a l imprecision (from 4 to 2 to 1) provides only a minor improvement i n c l i n i c a l accuracy. Thus, when the b i o l o g i c a l overlap of the two groups i s large, even severalfold improvements i n a n a l y t i c a l p r e c i s i o n may have l i t t l e e f f e c t on the c l i n i c a l accuracy of the t e s t , as r e f l e c t e d i n the ROC curve. P r i n c i p l e s of Test Evaluation Once we have the basic performance data describing detection and the l i m i t s of detection as represented by the ROC curve, then we can go on to decision analysis. This involves structuring the c l i n i c a l problem i n the form of a decision tree, estimating u t i l i t i e s and costs of various outcomes, choosing decision levels

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In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

8. ZWEIG

Establishing Clinical Detection Limits of Laboratory Tests

for using the t e s t . However, obtaining v a l i d data f o r the ROC curve i n the f i r s t place requires attention to several common-sense p r i n c i p l e s which are suprisingly often overlooked. Table I has a l i s t or recipe for designing a good study to evaluate the detection power of a test. The ideal study i s prospective and i s usually harder, longer and more expensive than the type of evaluation commonly done, but an "inexpensive'* c l i n i c a l evaluation may prove more costly i n the long run i f i t s erroneous conclusions lead to improper test u t i l i z a t i o n or improper patient management.

Table I. 1. 2. 3. 4. 5.

P r i n c i p l e s of a Good Evaluation of a Laboratory Test DEFINE CLINICAL QUESTION TEST WILL BE USED FOR SELECT APPROPRIATE SUBJECTS TO STUDY CLASSIFY PERFORM AL EVALUATE

The f i r s t and most important element on this l i s t i s defining s p e c i f i c a l l y and c a r e f u l l y the c l i n i c a l question or problem at which the test i s to be directed. I t ' s not enough to say "Let's look at this test for p r o s t a t i c cancer or coronary artery disease and see how well i t does." We need to define precisely what question of relevance to patient management i s being addressed and how that test w i l l be used i n practice. Do we want to screen large numbers of people for cancer or use the test to e s t a b l i s h the stage of cancer once we know i t ' s there, or do we want to predict response to a p a r t i c u l a r therapy, or assess response to a p a r t i c u l a r therapy? I t may provide a l l these functions but with varying effectiveness and requiring d i f f e r i n g decision levels. Each of these roles must be evaluated separately because the populations are d i f f e r e n t , conditions are d i f f e r e n t , goals are d i f f e r e n t , and ROC curves may be d i f f e r e n t . If you think about these issues, c a r e f u l l y and s p e c i f i c a l l y defining what you are trying to establish, the rest starts f a l l i n g into place. The second element i s selecting appropriate subjects. Once you have defined the question, you've pointed the way toward the proper subjects. I f you want to use a tumor marker to i d e n t i f y colon cancer among middle aged people with bowel obstruction, occult blood loss, or unexplained anemia, then you need to look at the test performance i n that group of subjects. Healthy young people aren't relevant and neither i s a reference range based on them. There's no point i n doing conventional normal ranges i f healthy young volunteers aren't the ones f o r whom the test i s intended. Number three concerns establishing the true diagnosis: Once you've got a group of people with bowel signs or symptoms suggestive that cancer i s possible, then you must separate them into 2 groups, those who r e a l l y do have carcinoma of the colon and those who don't. This provides a gold standard f o r calculation of

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DETECTION IN ANALYTICAL CHEMISTRY

TP r a t e s , FP r a t e s , e t c . T h i s d i a g n o s i s needs t o be a c c u r a t e as w e l l as independent of a l l t e s t s b e i n g e v a l u a t e d . To t h e e x t e n t t h a t e i t h e r a c c u r a c y o r independence i s l a c k i n g , t h e r e s u l t s o f t h e e v a l u a t i o n w i l l be b i a s e d and m i s l e a d i n g . C o n s i d e r the h y p o t h e t i c a l s i t u a t i o n i n F i g u r e 9. The c l i n i c a l q u e s t i o n i s , "Has t h i s p a t i e n t p r e s e n t i n g a t the emergency room w i t h an a c u t e p s y c h i a t r i c d i s o r d e r used m a r i j u a n a r e c e n t l y ? " The r o u t i n e t e s t i s s e n s i t i v e enough t o d e t e c t o n l y 70% of t h e r e c e n t drug u s e r s ; 30% of t h e m a r i j u a n a u s e r s have f a l s e l y n e g a t i v e r e s u l t s . The r o u t i n e t e s t a l s o s u f f e r s from v a r i o u s i n t e r f e r e n c e s , l e a d i n g t o f a l s e p o s i t i v e r e s u l t s i n 30% of n o n - u s e r s . T e s t I r e p r e s e n t s a new t e s t which i s b e i n g e v a l u a t e d . I n a c t u a l i t y i t m a n i f e s t s e x c e l l e n t s e n s i t i v i t y and s p e c i f i c i t y , g i v i n g p o s i t i v e r e s u l t s i n a l l r e c e n t m a r i j u a n a u s e r s and n e g a t i v e r e s u l t s i n a l l n o n - u s e r s . I f , however, i n s t e a d of i n d e p e n d e n t l y and a c c u r a t e l y d e t e r m i n i n g t h e drug-use s t a t u s of each p a t i e n t t h e p a t i e n t s a r e s i m p l y c l a s s e d as u s e r s o r non-user r e s u l t s , T e s t I w i l l appea o f t h e p a t i e n t s . I n t h i s case a p e r f e c t t e s t appears t o p e r f o r m p o o r l y s i m p l y because t h e c l i n i c a l q u e s t i o n was n o t answered a c c u r a t e l y f o r each p a t i e n t ; i . e . , the " g o l d s t a n d a r d " used f o r comparison was inadequate. The o p p o s i t e b i a s can a l s o r e s u l t from use of inadequate g o l d standards. T e s t I I i n F i g u r e 9 performs even more p o o r l y t h a n t h e r o u t i n e t e s t , y i e l d i n g f a l s e n e g a t i v e r e s u l t s i n 40% of the m a r i j u a n a u s e r s and f a l s e p o s i t i v e r e s u l t s i n 40% of the n o n - u s e r s . I f , however, t h e r o u t i n e t e s t ' s r e s u l t s a r e a c c e p t e d as c o r r e c t and T e s t I I i s judged on t h i s b a s i s , T e s t I I w i l l appear t o m i s c l a s s i f y o n l y 10% of the p a t i e n t s — and w i l l have a b e t t e r apparent performance than T e s t I ! T h i s can o c c u r i n s e v e r a l ways i n c l i n i c a l p r a c t i c e . In e v a l u a t i n g a t e s t f o r a c u t e m y o c a r d i a l i n f a r c t i o n , i f the p a t i e n t s a r e c l a s s i f i e d on t h e b a s i s of EKG d a t a a l o n e o r even a c o m b i n a t i o n of h i s t o r y , EKG f i n d i n g s and some c a r d i a c enzyme r e s u l t s (a " r o u t i n e workup"), t h e d i a g n o s i s may s t i l l be i n a c c u r a t e and, t h u s , d i s t o r t the apparent performance of t h e new t e s t . I n t h e case of a cancer tumor maker, i f the g o l d s t a n d a r d ( d i a g n o s i s o r s t a g i n g , e t c . ) i s based upon c l i n i c a l f i n d i n g s r a t h e r than s u r g i c a l and/or t i s s u e d a t a , t h e n t h e g o l d s t a n d a r d may be i n a c c u r a t e and b i a s t h e apparent v a l u e of t h e marker. I f an a m n i o t i c f l u i d marker f o r f e t a l l u n g m a t u r i t y i s compared t o an e x i s t i n g i m p e r f e c t marker, then even i f t h e new marker i s p e r f e c t , i t w i l l appear i m p e r f e c t . The g o l d s t a n d a r d a g a i n s t which t h e new marker s h o u l d be compared i s the a c t u a l p r e s e n c e o r absence of r e s p i r a t o r y d i s t r e s s syndrome i n those newborns d e l i v e r e d w i t h i n a s h o r t time of measurement of the marker. Because t h e v a l i d i t y of a c l i n i c a l e v a l u a t i o n ' s c o n c l u s i o n s i s c r i t i c a l l y dependent on t h e a c c u r a t e d e t e r m i n a t i o n of t h e answer t o t h e c l i n i c a l q u e s t i o n f o r each s u b j e c t , r o u t i n e c l i n i c a l diagnoses are l i k e l y t o be inadequate f o r t e s t e v a l u a t i o n s t u d i e s . D e f i n i t i v e d e t e r m i n a t i o n of a p a t i e n t ' s t r u e c l i n i c a l subgroup may r e q u i r e such p r o c e d u r e s as b i o p s y , s u r g i c a l e x p l o r a t i o n , a u t o p s y e x a m i n a t i o n , a n g i o g r a p h y , o r l o n g term f o l l o w - u p of response t o t h e r a p y and c l i n i c a l outcome.

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

ZWEIG

Establishing Clinical Detection Limits of Laboratory Tests

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H y p o t h e t i c a l performances o f t h r e e t e s t s f o r m a r i j u a n a u s e i n two subgroups o f p a t i e n t s , one w h i c h has used m a r i j u a n a r e c e n t l y and one w h i c h has n o t . Assumes t h a t t h e r o u t i n e t e s t g i v e s c o r r e c t r e s u l t s i n 70% o f subjects.

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

DETECTION IN ANALYTICAL CHEMISTRY

170

The next item i s performing a l l tests being evaluated on a l l the subjects being used. This may sound reasonable but i s very often overlooked. I f the specimens or subjects aren't i d e n t i c a l for a l l tests being examined, observed differences i n test performance could simply be r e f l e c t i o n s of differences i n the subjects rather than true differences i n performance. The last element i s evaluating and comparing tests using ROC curves, extensively discussed above. The ROC analysis i s a powerful tool which provides a pure index of accuracy, of discrimination c a p a b i l i t y , c l e a r l y describing the limits of c l i n i c a l detection possible for a given test i n a given c l i n i c a l setting. Adherence to the recipe i n Table I, including ROC analysis, should maximize the likelihood of obtaining a v a l i d assessment of laboratory test accuracy.

Literature Cited 1. Swets, J.Α., and Pickett, Diagnosti Systems. Methods from Signal Detection Theory; Academic Press: New York, 1982; Chapter 1. 2. McNeil, B.J.; Keeler, E.; Adelstein, S.J. N. Engl. J. Med. 1975, 293, 211-215. 3. Weinstein, C.; Feinberg, H.V. Clinical Decision Analysis; W.B. Saunders Co.: Philadelphia, 1980. 4. Zweig, M.H.; Robertson, E.A. Clin. Chem. 1982, 28, 1272-1276. 5. Robertson, Ε.Α.; Zweig, M.Η.; Van Steirteghem, A.C. Clin. Pathol. 1983, 79, 78-86.

Amer. J.

6. Metz, C.E. Semin. Nucl. Med. 1978; 8, 283-298. 7. Turner, D.A. J. Nucl. Med. 1978, 19, 213-220. 8. Beck, J.R.; Shultz, E.K. 13-20.

Arch. Pathol. Lab. Med. 1986, 110,

9. McNeil, B.J.; Hanley, J.A. Med. Dec. Making. 1984, 4, 137-150. RECEIVED December 24, 1986

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

Chapter 9

Perspectives on Detection Limits for Nuclear Measurements in Selected National and International Programs 1

2

Lloyd A. Currie and Robert M. Parr 1

Center for Analytical Chemistry, National Bureau of Standards, Gaithersburg, MD 20899 International Atomic Energy Agency, A-1400 Vienna, Austria 2

Issues involving the definition and practical significance of Detection Limits are discussed in the light of US and international programs in which the concept plays a central role. The US program relates to the "Lower Limit of Detection" (LLD) which forms a part of the Technical Specifications for nuclear power reactors, as required by the US Nuclear Regulatory Commission for measurements of effluent and environmental radioactivity. The programs of the International Atomic Energy Agency, which are oriented toward coordinated research and technical cooperation, similarly require common understanding and use of the "Limit of Detection" (LOD) as a practical and meaningful performance characteristic for measurements of trace elements in bioenvironmental matrices. Efforts to meet the needs of these two programs to formulate realistic and practicable detection limits will be reviewed, with special focus on problems-in-common such as the treatment of the blank, decision criteria, algorithm and assumption dependence, and the reporting of subliminal results. Detection limits have p r a c t i c a l s i g n i f i c a n c e i n a number o f important s o c i e t a l contexts, where measurement p r o c e s s e s must p o s s e s s adequate d e t e c t i o n c a p a b i l i t y t o meet s p e c i f i c d i a g n o s t i c , r e g u l a t o r y , o r r e s e a r c h needs. Two such c o n t e x t s , where s p e c i f i c r e q u e s t s were made t o f o r m u l a t e m e a n i n g f u l and r e l i a b l e approaches to d e t e c t i o n l i m i t s , i n v o l v e d : a) t h e r e q u i r e m e n t s o f t h e U. S. N u c l e a r R e g u l a t o r y Commission [NRC] f o r t h e d e t e c t i o n o f e f f l u e n t and e n v i r o n m e n t a l r a d i o a c t i v i t y , and b) t h e r e q u i r e m e n t s o f t h e I n t e r n a t i o n a l Atomic Energy Agency [IAEA] f o r t h e d e t e c t i o n o f t r a c e elements i n a wide range o f b i o e n v i r o n m e n t a l matrices. The NRC p r o j e c t r e l a t e d d i r e c t l y t o t h e f o r m a l r e g u l a t o r y r e q u i r e m e n t , as set f o r t h i n the t e c h n i c a l s p e c i f i c a t i o n s f o r operating nuclear power r e a c t o r s , t h a t t h e r a d i o a c t i v i t y measurement p r o c e s s e s have d e t e c t i o n l i m i t s meeting s p e c i f i e d s t a n d a r d s f o r t h e purpose o f p r o t e c t i n g t h e p u b l i c from e x c e s s i v e r e l e a s e s . T y p i c a l r e q u i r e m e n t s 0097-6156/88/0361-0171 $06.75/0 © 1988 American Chemical Society

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

DETECTION IN ANALYTICAL CHEMISTRY

172

f o r t h e "Lower L i m i t o f D e t e c t i o n " [LLD] a r e g i v e n i n T a b l e I (1) . The IAEA e f f o r t was f o c u s s e d on measurements o f e s s e n t i a l and t o x i c t r a c e elements i n b i o e n v i r o n m e n t a l samples g l o b a l l y , as found i n t h e i r l a b o r a t o r y i n t e r c o m p a r i s o n and c o o r d i n a t e d r e s e a r c h programs. D e t e c t i o n c a p a b i l i t i e s i n t h i s case r e l a t e d i r e c t l y t o t h e a b i l i t y to d e t e c t d e f i c i e n c i e s ( o f e s s e n t i a l elements) o r e x c e s s e s ( o f t o x i c elements) i n foods o r b i o l o g i c a l samples from d i f f e r e n t g e o g r a p h i c a l regions. F i g u r e 1, w h i c h i s drawn from t h e IAEA's c u r r e n t l i s t o f a v a i l a b l e r e f e r e n c e m a t e r i a l s , i n d i c a t e s some t y p i c a l m a t r i c e s and elements o f i n t e r e s t ( 2 . 3 ) . Concentrations v a r i e d widely with element and m a t r i x ; by way o f i l l u s t r a t i o n , c e r t i f i e d v a l u e s on a d r y w e i g h t b a s i s i n sample H-8 (horse k i d n e y ) ranged from 0.91 mg/kg f o r Hg t o 12.6 g/kg f o r C I . The two p r o j e c t s shared some f e a t u r e s i n common. R e l i a b l e and comparable measures o f d e t e c t i o n c a p a b i l i t i e s were r e q u i r e d on a c o n t i n u i n g b a s i s among many l a b o r a t o r i e s and they h a d t o be d e v e l oped i n a manner t h a t woul a b r o a d range o f a n a l y t e matrices. D e t e c t i o n l i m i t s had t o be a b s o l u t e i n t h e sense t h a t a c t u a l c o n c e n t r a t i o n o r r a d i o a c t i v i t y l e v e l s may be l i n k e d t o s p e c i f i c n u t r i t i o n a l o r h e a l t h e f f e c t s . A t t h e o u t s e t o f each study it was o b s e r v e d t h a t v a r y i n g d e f i n i t i o n s and e v a l u a t i o n s o f d e t e c t i o n l i m i t s were i n use, w i t h t h e r e s u l t t h a t s t a t e d d e t e c t i o n l i m i t s were n o t o n l y non-comparable b u t i n some c a s e s i n e r r o r by o r d e r s o f magnitude. Such d i s c r e p a n c i e s a r e a l r e a d y most s e r i o u s from a s c i e n t i f i c o r m e t r o l o g i c a l s t a n d p o i n t , b u t they invite dangerous m i s i n t e r p r e t a t i o n and c o n f u s i o n when v i e w e d by t h e l a y p u b l i c o r i n t e r p r e t e d by s p e c i a l i n t e r e s t groups. Approach t o NRC and IAEA S t u d i e s I n i t i a l States. An o u t l i n e o f t h e approach t a k e n f o r each study, t o g e t h e r w i t h an i n d i c a t i o n o f t h e i n i t i a l d e t e c t i o n l i m i t d e f i n i t i o n s i n use by t h e two o r g a n i z a t i o n s i s g i v e n i n T a b l e I I . A p a r t from t h e d i f f e r e n c e i n t e r m i n o l o g y - - Lower L i m i t o f D e t e c t i o n [LLD], and L i m i t o f D e t e c t i o n [LOD] -- t h e f o r m u l a t i o n s d i f f e r i n c o e f f i c i e n t s and i n u n d e r l y i n g p r i n c i p l e s . ( F o r t h e purposes o f t h i s c h a p t e r we s h a l l r e p r e s e n t t h e d e t e c t i o n l i m i t by t h e s i n g l e symbol Lp . ) The i n i t i a l NRC e x p r e s s i o n e x p l i c i t l y r e c o g n i z e s t h e two h y p o t h e s i s t e s t i n g e r r o r s , (5%) f a l s e p o s i t i v e s and f a l s e n e g a t i v e s , though w i t h a t r i v i a l r o u n d i n g e r r o r [4.66 r a t h e r than 4.65]. The i n i t i a l IAEA f o r m u l a t i o n , w h i c h was t a k e n from K e i t h (4), e x p l i c i t l y t a k e s i n t o account o n l y t h e f a l s e p o s i t i v e e r r o r , but a t a g r e a t l y reduced ( 1 - s i d e d ) s i g n i f i c a n c e l e v e l (as l i t t l e as 0.13% i n contrast to 5%). T h i s i s a problem: ignoring false n e g a t i v e s does n o t make them go away! I n f a c t , n e a r l y a l l such f o r m u l a t i o n s i n v i t e f a l s e n e g a t i v e s a t a r a t e o f 50%. The i n i t i a l NRC and IAEA f o r m u l a t i o n s d i f f e r e d a l s o w i t h r e s p e c t t o t h e denominator. That i s , R e f e r e n c e 4 t r e a t s d e t e c t i o n i n terms o f " s i g n a l s " , t h e denominator w h i c h c o n v e r t s from s i g n a l u n i t s to concentration being only implied. I n c o n t r a s t , the denominator f o r t h e LLD shows e x p l i c i t l y f a c t o r s f o r d e t e c t o r E ( f f i c i e n c y ) , sample V(olume), c h e m i c a l Y ( i e l d ) , and r a d i o a c t i v e D(ecay). The e s t i m a t e d s t a n d a r d d e v i a t i o n o f t h e b l a n k ( s ) i s t h e B

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

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In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

MATRIX

ELEMENTS OR NUCLIDES REFERENCED

Trace elements: Br, Ca,Cl,Cu,Fe,K,Mg,Mn, P,Rb,Zn

Trace elements: Ba, Environmental levels Ca,CI,Cr,Cu,Hg,Mg,Μη, Mo,Na,Nl,Pb,Sr

Rye flour

Cotton cellulose

v-e

V-9

v

Milk ponder

A-14

Sr-90, Cs-137 Na K, Ca

Trace elements : Br,Ca, Normal levels Cu,Fe,K,Na,Rb,S,Se,Zn

Freeze dried ani­ mal blood

A-13

Environmental levels

Environmental levels

5mBq/g (0.14 pCl/g) 55mBq/g (1.48 pCi/g)

Ra-226 Sr-90

Animal bone

Environmental levels

A-12

v

Milk powder

Trace elements: Ca Cl,Cu,Pe,Hg,K,Mg,Mn, Na,P,Rb,Zn

CONCENTRATION OR ACTIVITY LEVEL

A-ll

BIOLOGICAL MATERIALS ( t e r r e s t r i a l )

SAMPLE CODE

25 g

50 g

250 g

25 g

80 g

25 g

SAMPLE SIZE (1 UNIT)

CRM

RM

CRM

CRM

CRM

RM

SAMPLE"

or

CLASS

Non-certlfled information values f o r : Al,Br,Cd,Pe,Ga, Hf,Ll,S,Sc,Se,Sm,Sn,Th,U,V

Non-certifled information values f o r : Al,Au,Ba,Cd,Co,Cs, Mo,Na,S,Sb

Non-certifled information value for Sr (total)

Non-certlfled information values f o r : Mg,Nl,P,Pb

Non-certified information values f o r : Ag, A l , As, Au, B,Ba, Br, Cd, Cr, Ce, F, I, L l , Pb, Pt, Sb, Se, S i , Sn, Sr, T l , U, V

REMARKS

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In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987. Normal levels

Normal levels

Normal levels

See remarks

Trace elements: Br, Ca,Cl,Cs,Cu,Fe,Hg,K, Mg,Mn,Na,Rb,Se,Zn

Animal bone ( i n c l u - Trace elements: Ba, ding mineral and Br,Ca,Cl,Fe,K,Mg,Na, organic components) P,Pb,Sr,Zn

Trace elements: Br, Ca,Cd,Cl,Cu,Pe,Hg, K,Mg,Mn,Mo,Na,P,Rb, Se,Zn

Multielement

Animal muscle

Horse kidney

Mixed human diet

H-5

H-8

H-9

30 g

30 g

30 g (2 v i a l s )

20 g (2 v i a l s )

50 g

RM

RM

RM

CRM

CRM

Representative of diet consumed i n Finland. Available from March 1986

Cd concentration similar to human levels Non-certified information values f o r : Co,Cs,S,Sr

Non-certifled information values f o r : Al,Cs,Su,Hf,La, Mn,Sb,Se,Sm,Th

F i g u r e 1. B i o l o g i c a l R e f e r e n c e and C e r t i f i e d R e f e r e n c e M a t e r i a l s a v a i l a b l e f r o m t h e I n t e r n a t i o n a l A t o m i c Energy Agency. (Reproduced w i t h p e r m i s s i o n f r o m R e f . 2. C o p y r i g h t 1986, 1987 I n t e r n a t i o n a l A t o m i c Energy Agency.)

* RM for Reference Material, CRM f o r C e r t i f i e d Reference Material

Environmental levels

H-4

t

Trace elements: Ag, As,Ba»Br,Ca Cd,Ce,Co Cr,Cu,F,Fe,Ga,Hg,I,K Mg,Mo,Na,Nl,P,Pb,Si Sn,U,V,Zn

Hay (powder)

V-10

DETECTION IN ANALYTICAL CHEMISTRY

176

Table I I .

Detection Limits:

P r a c t i c a l Needs

N u c l e a r R e g u l a t o r y Commission [NRC]; I n t e r n a t i o n a l Atomic Energy Agency [IAEA] APPLICATION: NRC

IAEA

Detection limits specified in the Technical Specifications f o r n u c l e a r power r e a c t o r s f o r t h e d e t e c t i o n o f e f f l u e n t and e n v i r o n m e n t a l r a d i o a c t i v i t y . Detection l i m i t toxic] i n bioenvironmental R e s e a r c h Programs]

matrices.

[Coordinated

OBJECTIVE: Method-independent definition samples. ["cookbook" manual]

INITIAL STATE

(a

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formulation;

real

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NRC -- LLD = 4 . 6 6 s /(E«V»Y^D) B

IAEA -- LOD - 3 s

B

APPROACH: NRC

L i t e r a t u r e r e s e a r c h ; s i t e v i s i t s t o a s s e s s problems and practices. [NRC r e g i o n a l o f f i c e s ; power r e a c t o r ; contracting labs]

IAEA -- M u l t i d i s c i p l i n a r y 1985]

consultants'

m e e t i n g [IAEA HQ,

Dec.

s represents t h e s t a n d a r d d e v i a t i o n o f t h e background o r b l a n k . Other symbols i n d i c a t e : Efficiency, Volume, Y i e l d , and Decay f a c t o r , resp. B

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

9. CURRIE & PARR

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177

s c a l i n g parameter i n b o t h e x p r e s s i o n s , though l i t t l e guidance i s given f o r i t s determination. A l s o t h e NRC d e f i n i t i o n i s s l i g h t l y ambiguous i n s t a t i n g t h a t s i s "the standard d e v i a t i o n o f the background...or... o f a b l a n k sample as a p p r o p r i a t e " ( 1 ) . Neither approach explicitly t r e a t s p o s s i b l e non-normality, degrees o f freedom, u n c e r t a i n t i e s i n t h e denominator [overall calibration f a c t o r ] , s y s t e m a t i c e r r o r , o r t h e a p p l i c a t i o n t o multicomponent systems which e x h i b i t i n t e r f e r e n c e and m a t r i x e f f e c t s and o f t e n r e q u i r e more s o p h i s t i c a t e d c o m p u t a t i o n a l p r o c e d u r e s . E f f e c t s o f t h e r e l a t i v e l y s i m p l i s t i c f o r m u l a t i o n s a r e seen, f o r example, i n T a b l e I and F i g u r e s 2 and 3. I n the t a b l e , we see t h a t o n l y two o f t h e r a d i o n u c l i d e s l i s t e d a r e commonly measured by " s i m p l e c o u n t i n g " where a s i g n a l minus background o p e r a t i o n o b t a i n s . F a r more commonly LLD's must be determined f o r multicomponent gamma r a y s p e c t r o m e t r y , which may i n v o l v e r e l a t i v e l y c o m p l i c a t e d computat i o n s and a t t e n d a n t assumptions r e g a r d i n g i n t e r f e r i n g components, b a s e l i n e shapes, e t c i s o l a t e d gamma r a y peaks n o t always c o n s i s t e n t and erroneous d e t e c t i o n l i m i t s f o l l o w . One p r a c t i c a l i l l u s t r a t i o n o f the p i t f a l l s attending the a p p l i c a t i o n of the " s i m p l e c o u n t i n g " e x p r e s s i o n t o r e l a t i v e l y s i m p l e gamma r a y s p e c t r o m e t r y has been d e s c r i b e d by R e i c h e l ( 5 ) . I n t h i s i n v e s t i g a t i o n , commercial spectrum a n a l y s i s s o f t w a r e was employed t o c a l c u l a t e t h e d e t e c t i o n l i m i t s o f Hg-203 (279 keV) and Cr-51 (320 keV) on a Compton continuum from i n t e r f e r i n g Co-60. The recommended d e t e c t i o n l i m i t o p t i o n which "has a p r o b a b i l i t y o f 95% o f [a peak] b e i n g d e t e c t e d , " produced d e t e c t i o n l i m i t s o f 1557 and 1511 counts f o r Hg-203 and Cr-51, r e s p e c t i v e l y . Y e t when peaks f o r these two n u c l i d e s were added t o t h e continuum a t l e v e l s o f about 1580 and 1910 c o u n t s , r e s p e c t i v e l y , from a mixed s o u r c e , n e i t h e r was d e t e c t e d by t h e s o f t w a r e , though b o t h were c l e a r l y v i s i b l e t o even an u n t r a i n e d eye! See F i g u r e 2. The t h i r d peak a t 310 keV, d e r i v i n g from t h e Co-60 Compton i n t e r a c t i o n s , was a l s o u n d e t e c t e d . The peaks remained u n d e t e c t e d u n t i l t h e i r l e v e l s were a p p r o x i m a t e l y t w i c e t h e presumed d e t e c t i o n l i m i t s , a t which p o i n t a good r e s u l t was o b t a i n e d f o r Hg-203, b u t a poor one [ t o o s m a l l ] f o r Cr-51. This l a t t e r r e s u l t no doubt f o l l o w e d from an erroneous b a s e l i n e assumption, even though the program o p t i o n f o r "double peak e v a l u a t i o n " was chosen. F i g u r e 3 i l l u s t r a t e s t h e problem f a c e d b y t h e IAEA i n t h e b r o a d e r c o n t e x t o f t h e i r t r a c e element l a b o r a t o r y i n t e r c o m p a r i s o n program. These d a t a show t h e r e p o r t e d r e s u l t s o f 16 l a b o r a t o r i e s f o r measurements o f a r s e n i c i n t h e h o r s e k i d n e y i n t e r c o m p a r i s o n sample (H-8), based on v a r i o u s v e r s i o n s o f atomic a b s o r p t i o n spectrometry, o p t i c a l emission spectrometry, neutron activation a n a l y s i s , and i n d u c e d X-ray e m i s s i o n a n a l y s i s . The o b j e c t i v e o f t h e h o r s e k i d n e y i n t e r c o m p a r i s o n was t o a s s e s s (and r e f i n e ) a n a l y t i c a l methods f o r t h e d e t e r m i n a t i o n o f e s s e n t i a l and t o x i c t r a c e elements i n t h i s s u r r o g a t e f o r human k i d n e y ( 7 ) . K i d n e y , as the main t a r g e t organ which accumulates t o x i c elements, was o f s p e c i a l i n t e r e s t w i t h r e s p e c t t o cadmium. Horse k i d n e y , which c o n t a i n s s i m i l a r l e v e l s o f cadmium t o the human k i d n e y c o r t e x , was s e l e c t e d f o r t h e development and maintenance o f methods h a v i n g a demonstrated l e v e l o f q u a l i t y t o a s s u r e r e l i a b l e b i o l o g i c a l m o n i t o r i n g o f t h i s element. Participants were i n v i t e d t o a n a l y z e some 24 a d d i t i o n a l t r a c e elements, however, B

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

DETECTION IN ANALYTICAL CHEMISTRY

178

F. Reichel (IAEA, 1985)

95% Confidence Level

250

300

350

Channel (keV)

F i g u r e 2. Non-detected, y e t q u i t e v i s i b l e gamma r a y peaks o f Hg-203 and Cr-51 from IAEA p r a c t i c a l e x a m i n a t i o n o f s o f t w a r e performance ( 5 ) . The continuum, shown dashed b e n e a t h t h e Hg-203 and Cr-51 peaks, i s due t o Co-60.

10*

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5

10

4

10

X2

X2

3

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A5

a.

10

2

AS

?9 9

«

99

9

S9

99

1

10

10°

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?

-I

I

40 30 36

I

I

3

52

I

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L

27 25 38 54 73 35 61

J

6

I

I

L

12 10 29

Lab. Code No.

F i g u r e 3. I n t e r l a b o r a t o r y r e s u l t s f o r As, from t h e IAEA i n t e r c o m p a r i s o n o f cadmium and o t h e r elements i n h o r s e k i d n e y (H-8) ( 7 ) . F i l l e d c i r c l e s r e p r e s e n t q u a n t i t a t i v e r e s u l t s ( u n c e r t a i n t i e s n o t e x c e e d i n g c i r c l e d i a m e t e r ) ; open c i r c l e s correspond t o reported detection l i m i t s .

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

9.

CURRIE & PARR

179

Perspectives on Detection Limits

most o f w h i c h are shown i n F i g u r e 1. R e s u l t s f o r cadmium, a t a l e v e l o f about 190 mg/kg were q u i t e s a t i s f a c t o r y , b u t the much lower concentrations o f a r s e n i c p r e s e n t e d d i f f i c u l t i e s . The 5 filled c i r c l e s i n f i g u r e 3 r e p r e s e n t " q u a n t i t a t i v e " r e s u l t s -- i e , those whose r e p o r t e d u n c e r t a i n t i e s do not exceed the d i a m e t e r o f the circle. These are c l e a r l y i n c o n s i s t e n t , by more t h a n t h r e e o r d e r s o f magnitude. Open c i r c l e s r e p r e s e n t " d e t e c t i o n l i m i t s " f o r nond e t e c t e d [ND] r e s u l t s ; t h e i r s p r e a d exceeds f o u r o r d e r s o f magni­ tude. The c r o w n i n g i n c o n s i s t e n c y i s the f a c t t h a t a r s e n i c has been "measured" by some l a b o r a t o r i e s a t l e v e l s c o n s i d e r a b l y i n excess o f the d e t e c t i o n l i m i t s o f o t h e r s r e p o r t i n g ND -- c l e a r l y a l o g i c a l impossibility. To d e r i v e a c t u a l l e v e l s and e s t a b l i s h q u a l i t y measurement f o r t r a c e elements i n f o o d s t u f f s , m a t e r i a l s such as m i l k powder (A-11) and r e p r e s e n t a t i v e r e g i o n a l d i e t a r y b l e n d s (eg, USDIET-1) have been provided (8.9). Consistency o f i n t e r l a b o r a t o r y r e s u l t s among "independent" a n a l y t i c a o f such m a t e r i a l s or th n a t u r e o f the i n i t i a l measurement problem i s i l l u s t r a t e d by the r e s u l t s o f the m i l k powder ( A - l l ) i n t e r c o m p a r i s o n , where the means, r e l a t i v e ranges (max/min, d i m e n s i o n l e s s ) and medians o f 17 atomic a b s o r p t i o n s p e c t r o s c o p y [AAS] and 7 r a d i o c h e m i c a l n e u t r o n a c t i v a t i o n a n a l y s i s [RNAA] l a b o r a t o r y r e s u l t s f o r manganese were as f o l l o w s .

[AAS] [RNAA]

mean (mg/kg)

max/min

median (mg/kg)

3.99 0.295

279 4.8

0.67 0.26

(95% (0.45 (0.12

-

CI) 1.27) 0.58)

I t i s i n t e r e s t i n g t o note t h a t the r a t i o o f means (AAS/RNAA) i s 13.5, whereas the r a t i o o f medians i s b u t 2.6. Reliability is i n c r e a s e d t h r o u g h the use o f the median as a r o b u s t statistic, e s p e c i a l l y when the number o f r e p l i c a t e s η (here, l a b o r a t o r i e s ) i s r e l a t i v e l y large. (When n>8, the 95% CI o f the median does not d i r e c t l y depend upon the extremes, so some a d d i t i o n a l , a u t o m a t i c o u t l i e r p r o t e c t i o n i s afforded.) I t i s n o t e w o r t h y , however, t h a t a l a r g e number o f r e p l i c a t e s does not guarantee q u a l i t y ! The r e l a ­ t i v e l y few RNAA measurements y i e l d a more r e l i a b l e r e s u l t t h a n would a v e r y e x t e n s i v e s e t o f AAS measurements ( r e p r e s e n t a t i v e o f t h i s p a r t i c u l a r intercomparison). The b a s i c i s s u e i s one o f contamina­ t i o n and i n t e r f e r e n c e , as i m p l i e d f o r example by the skewness r e p r e s e n t e d i n the r a t i o o f mean t o median. T h i s "blank" i s s u e i s b r o u g h t out a t t h i s p o i n t i n our d i s c u s s i o n because i t i s p r o b a b l y the s i n g l e most i m p o r t a n t l i m i t a t i o n t o r e l i a b l e measurement and r e l i a b l e d e t e c t i o n f o r l o w - l e v e l , multicomponent measurements i n complex m a t r i c e s . As such, i t has been a major c o n s i d e r a t i o n i n a d d r e s s i n g the q u e s t i o n o f " r e a l sample" d e t e c t i o n l i m i t s f o r b o t h r a d i o l o g i c a l and t r a c e element measurements i n bioenvironmental samples. Experts and Concerned Groups. The foregoing observations i n v o l v i n g d i v e r s e f o r m u l a t i o n s and i n t e r p r e t a t i o n s f o r r a d i o l o g i c a l d e t e c t i o n l i m i t s , and d i v e r s e and d i s c r e p a n t i n t e r l a b o r a t o r y r e s u l t s

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

180

DETECTION IN ANALYTICAL CHEMISTRY

f o r low l e v e l t r a c e element measurements - - l e d the NRC and the IAEA, r e s p e c t i v e l y , t o q u e s t i o n the v a l i d i t y or a t l e a s t the u n i v e r s a l i t y o f d e t e c t i o n l i m i t f o r m u l a t i o n s as t h e n a p p l i e d . In o r d e r t o address the q u e s t i o n i n an e f f i c i e n t manner the two o r g a n i z a t i o n s employed problem s o l v i n g approaches o f demonstrated e f f e c t i v e n e s s : v i z . , (a) s i t e v i s i t s and f i e l d i n t e r v i e w s w i t h each o f the a f f e c t e d s e c t o r s [NRC], and (b) an i n t e n s i v e workshop i n v o l v i n g e x p e r t s r e p r e s e n t i n g each o f the r e s p e c t i v e a n a l y t i c a l disciplines [IAEA, ( 1 0 ) ] . The importance o f t h e s e approaches d e s e r v e s emphasis, f o r i t t r a n s c e n d s the p a r t i c u l a r s c i e n t i f i c problem under c o n s i d e r a t i o n . I n the case o f the NRC, f o r example, the v a r y i n g needs and p e r c e p t i o n s o f the u t i l i t i e s and their o p e r a t o r s , the c o n t r a c t ( r a d i o l o g i c a l ) l a b o r a t o r i e s , the c r o s s - c h e c k ( c o n t r o l ) l a b o r a t o r y , the i n s p e c t o r s , and NRC h e a d q u a r t e r s p e r s o n n e l c o u l d not o t h e r w i s e have been d i s c e r n e d . As a r e s u l t i t was p o s s i b l e t o i d e n t i f y and t o some e x t e n t s o r t out measurement from p o l i c y i s s u e s , and attemp l i m i t c o n c e p t s and t e r m i n o l o g i n t e r p r e t a t i o n . A summary o f the f i n d i n g s o f the NRC s i t e v i s i t s i s given i n Table I I I . Table I I I .

NRC

Findings

* LLD Manual Needed - - f o r d i v e r s e backgrounds * Wide r a n g i n g nomenclature and [LLD, MDA, ...]

formulations

* Socio-political-economic issues [ b i a s e d r e p o r t i n g ( p u b l i c p e r c e p t i o n s ) , LLD r e q u i r e m e n t s minor components when h i g h i n t e r f e r e n c e l e v e l s , . . . ] * Detection decisions: *

Blank:

ambiguity

f a l s e negatives in

o f t e n e x c l u d e d from

initial

draft

ranged from 5% t o

for

50%

document, b l a n k v a r i a t i o n s

LLD

* Non-counting e r r o r s g e n e r a l l y ignored,

e s p e c i a l l y sampling

* Simple c o u n t i n g f o r m u l a t i o n o n l y [ s i g n a l - b l a n k ] ; i n a p p l i c a b l e to many cases o f n u c l e a r s p e c t r o m e t r y * Gamma s p e c t r o m e t r y : multiple detection decisions; occasionally h i d d e n , c h a n g i n g a l g o r i t h m s ; erroneous parameters * Appropriate

[ l o w - l e v e l ] and double b l i n d QA

samples needed

The c a l l i n g together o f complementary or m u l t i d i s c i p l i n a r y teams o f e x p e r t s i s a t r a d i t i o n i n a number o f i n t e r n a t i o n a l o r g a n i z a t i o n s , such as the IAEA. S i n c e the IAEA o b j e c t i v e w i t h r e s p e c t t o d e t e c t i o n l i m i t s was e x p l i c i t y "method independent", such an approach was mandatory. That i s , e x p e r t knowledge c o n c e r n i n g the n a t u r e and s o u r c e s o f e r r o r , such as the b l a n k , m a t r i x e f f e c t s , and d e t e c t o r c h a r a c t e r i s t i c s f o r the methods o f i n t e r e s t (NAA, AAS,

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

9. CURRIE & PARR

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ICP,...) was e s s e n t i a l so t h a t t h e approach t o d e t e c t i o n l i m i t s would a t l e a s t be b r o a d enough t o encompass t h e c h a r a c t e r i s t i c s o f t h e s e p a r t i c u l a r methods. A t h e o r e t i c a l f o r m u l a t i o n was n o t enough; a common, p r a c t i c a l approach t o d e t e c t i o n , s u i t a b l e f o r t h e s e s e v e r a l methods o f t r a c e a n a l y s i s was c a l l e d f o r . T a b l e IV g i v e s the c o m p o s i t i o n and o b j e c t i v e s o f t h e IAEA t a s k f o r c e . Outcomes The b a s i c c o n c e p t s o f d e t e c t i o n d e c i s i o n s and d e t e c t i o n l i m i t s , based upon h y p o t h e s i s t e s t i n g as o u t l i n e d e a r l i e r i n t h i s volume, n e c e s s a r i l y s e r v e d as t h e f o u n d a t i o n f o r t h e NRC and IAEA programs. For t h e p r o b a b i l i s t i c p a r t o f t h e problem, f a l s e p o s i t i v e s and f a l s e n e g a t i v e s were t a k e n e q u a l t o 0.05 i n each case. T h i s means t h a t f o r normal random e r r o r s , t h e d e t e c t i o n d e c i s i o n i s made once t h e o b s e r v e d s i g n a l exceed 1.645 time t h s t a n d a r d f th n u l l s i g n a l [standard e r r o r larger f o r paired observations] freedom i s s m a l l , o f c o u r s e , t h e ζ-statistic i s r e p l a c e d by Student's-t. F o r s i m p l e measurements t h e d e t e c t i o n l i m i t i s j u s t twice t h i s c r i t i c a l l e v e l . In addition to this r e l a t i v e l y straight­ f o r w a r d n o r m a l , " s t a t i s t i c a l " t r e a t m e n t o f d e t e c t i o n , however, i t was n e c e s s a r y t o pay a t t e n t i o n t o t h e s p e c i a l c h a r a c t e r i s t i c s o f t h e r e a l measurement p r o c e s s e s i n v o l v i n g t h e d e t e c t i o n o f low l e v e l s o f mixed r a d i o n u c l i d e s , and t r a c e c o n c e n t r a t i o n s o f m u l t i p l e elements i n complex m a t r i x m a t e r i a l s . T h i s m a t t e r , w h i c h was an e x p l i c i t com­ ponent o f b o t h p r o j e c t s , cannot be overemphasized. I f one c a l c u ­ l a t e s s t a t i s t i c a l d e t e c t i o n l i m i t s f o r i n t e r f e r e n c e - f r e e measure­ ments i n pure s o l u t i o n s , e s t i m a t e d d e t e c t i o n l i m i t s w i l l be t o o low, o f t e n by o r d e r s o f magnitude. S i m i l a r l y , d e t e c t i o n l i m i t s w h i c h a r e p r e d i c t e d f o r an a l t e r a t i o n o r o p t i m i z a t i o n o f a measurement p r o c e s s w i l l be u n r e a l i s t i c a l l y o p t i m i s t i c i f one a p p l i e s j u s t a s i m p l e s t a t i s t i c a l f o r m u l a t o c a l c u l a t e t h e change i n d e t e c t i o n l i m i t , eg, w i t h i n c r e a s e d r e p l i c a t i o n o r i n c r e a s e d c o u n t i n g time. Unless t e s t s are made w i t h known o r common m a t e r i a l s comparable i n c o m p o s i t i o n t o the samples o f i n t e r e s t , these erroneous e s t i m a t e s w i l l n o t be exposed. NRC S p e c i a l T o p i c s . The e s t i m a t i o n o f p r a c t i c a l , r e a l sample d e t e c t i o n l i m i t s r e q u i r e s a t t e n t i o n t o a l l o f the sources o f e r r o r t h a t must be f a c e d i n d e r i v i n g c o n f i d e n c e , o r more c o r r e c t l y , u n c e r t a i n t y i n t e r v a l s (11). I n t h e NRC s t u d y , s p e c i a l a t t e n t i o n was g i v e n t o t h e f o l l o w i n g : a) bounds f o r uncompensated s y s t e m a t i c e r r o r i n t h e background and c a l i b r a t i o n f a c t o r , b) n o n - P o i s s o n random e r r o r ( t h a t w h i c h exceeds " c o u n t i n g s t a t i s t i c s " ) , c ) d e c o n v o l u t i o n and model e r r o r connected w i t h a l p h a o r gamma-ray spectrum a n a l y s i s o f multicomponent m i x t u r e s , and d) s p e c i a l l i m i t a t i o n s from t h e nonnormality o f the Poisson distribution f o r extreme low-level c o u n t i n g , such as o c c u r s w i t h m o n i t o r i n g o f a c t i n i d e s o r o t h e r a l p h a emitters. Each o f these f a c t o r s r e q u i r e d extension o f the "simple-counting" expression o r i g i n a l l y found i n t h e d r a f t NRC Technical S p e c i f i c a t i o n s [see t a b l e I I ] . A full discussion, supplemented w i t h a p p r o p r i a t e f o r m u l a s , r e f e r e n c e s , and examples may be found i n Ref. 12; and one o f t h e more b r o a d l y a p p l i c a b l e r e s u l t s w i l l be t r e a t e d h e r e . I n t a b l e V we g i v e an e x t e n s i o n o f the

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T a b l e IV. C o n s u l t a n t s ' M e e t i n g on L i m i t o f D e t e c t i o n Dates and P l a c e 2-4 December 1985;

IAEA H e a d q u a r t e r s ,

Vienna

Participants Austria:

W. Wegscheider

Belgium:

J.P. Op de Beeck R. Van G r i e k e n

F.R.G.

M. S t o e p p l e r

U.S.A.

L.A.

IAEA

R.M. P a r r ( S c i e n t i f i c F. R e i c h e l R. Schelenz H. V e r a - R u i z

Curri Secretary)

METHODS Topics

· A c t i v a t i o n A n a l y s i s and gamma-ray ( J . P . Op de Beeck; F. R e i c h e l )

spectrometry

• XRF and PIXE (R. Van G r i e k e n ) • AAS (M. S t o e p p l e r ) • ICP-AES (W. Wegscheider) • Voltammetry and o t h e r methods (M. S t o e p p l e r ) GOALS General d i s c u s s i o n • Method-independent d e t e c t i o n (LoD)

definition

of

the

limit

of

• P r a c t i c a l d e t e r m i n a t i o n and use o f t h e LoD • Special problems a n a l y t i c a l methods • Decision making n e a r t h e LoD

and

associated

reporting

with

of

individual

data

P r e p a r a t i o n o f meeting r e p o r t

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

below

or

9. CURRIE & PARR

Perspectives on Detection Limits

183

T a b l e V. D e s i g n and O p t i m i z a t i o n (LJJ ) V a r i a t i o n s w i t h background (B) and C o u n t i n g Time ( t ) ( a )

LLD

t«r Β < 1 1


SE - 18.8, w i t h 9 degrees o f freedom.) The complemen­ t a r y q u e s t i o n i s : "What i s the s m a l l e s t c o n c e n t r a t i o n o f Zn t h a t c o u l d be d e t e c t e d w i t h 95% p r o b a b i l i t y , g i v e n the above c r i t i c a l level?" The answer, namely the e s t i m a t e d d e t e c t i o n l i m i t f o r the measurement p r o c e s s under c o n s i d e r a t i o n , i s a p p r o x i m a t e l y t w i c e the c r i t i c a l l e v e l o r 72.4 mg/kg. Note t h a t 71.5 i s an experimental outcome (which we t e s t e d f o r s t a t i s t i c a l s i g n i f i c a n c e ) , whereas 72.4 i s a measure o f the i n h e r e n t d e t e c t i o n c a p a b i l i t y o f the measurement process. An upper l i m i t f o r Lp may be computed u s i n g the upper l i m i t f o r σ/s. U s i n g χ w i t h 10 degrees o f freedom, we f i n d a v a l u e o f 1.59 f o r t h i s r a t i o ( 1 - s i d e d , 5% s i g n i f i c a n c e l e v e l ) , hence an upper l i m i t f o r Lp o f 115 mg Zn/kg bone. The t r u e d e t e c t i o n l i m i t i s l i k e l y (95% chance) s m a l l e r t h a n t h i s v a l u e , b u t a more p r e c i s e e s t i m a t e o f σ would be r e q u i r e d t o b e t t e r d e t e r m i n e i t . A s t i l l more c o n s e r v a t i v e v a l u e , i n c o r p o r a t i n g the Gauss i n e q u a l i t y where [ t + ( 1 . bjlj})' ]a r e p l a c e s 2to , would r a i s e t h i s upper l i m i t f o r the d e t e c t i o n l i m i t by an a d d i t i o n a l 8%, t o 124 mg/kg. The major c o n s t r a i n t on p r e c i s e knowledge o f the d e t e c t i o n l i m i t i s thus knowledge o f σ ; f o r n o r m a l l y d i s t r i b u t e d d a t a , w i t h s b a s e d on r e p l i c a t i o n , the u n c e r t a i n t y range ( a t the 90% c o n f i d e n c e l e v e l ) f o r σ/s f a l l s below a f a c t o r o f 2 once the number o f r e p l i c a t e s exceeds a dozen. Q

B

2

1

Q

Q

Ό

Two points merit emphasis i n the above e x e r c i s e : a) The s t a t i s t i c a l c o n f i d e n c e i n t e r v a l f o r the outcome Js b a s e d on S and i t s SE ( u s i n g a 2 - s i d e d S t u d e n t ' s - t ) ; SE b u t n o t S i s u s e d a l s o f o r the e s t i m a t i o n o f 1^ . b) The c o n f i d e n c e i n t e r v a l , and and Lp (and i t s upper l i m i t ) are c o r r e c t f o r n o r m a l l y d i s t r i b u t e d random errors. P a i r e d Τ, Β comparisons and a moderate number o f r e p l i c a t e s t e n d t o make t h e s e assumptions r e a s o n a b l y good; t h i s i s an i m p o r t a n t p r e c a u t i o n , g i v e n the w i d e l y v a r y i n g b l a n k d i s t r i b u t i o n s o f such d i f f i c u l t measurements. Perhaps the most i m p o r t a n t consequence o f the p a i r e d c o m p a r i s o n i n d u c e d symmetry, i s t h a t the e x p e c t e d v a l u e f o r the n u l l s i g n a l [Β - B'] w i l l be z e r o -- i e , u n b i a s e d . S y s t e m a t i c e r r o r bounds, some deeper implications of paired A

A

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

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comparisons, and d i s t r i b u t i o n f r e e t e c h n i q u e s a r e t r e a t e d i n t h e extended d i s c u s s i o n o f t h e above example ( 1 0 ) . C o n s i d e r a t i o n o f r e a s o n a b l e s y s t e m a t i c e r r o r bounds f o r t h e b l a n k and o v e r a l l c a l i b r a t i o n f a c t o r l e d t o a f i n a l d e t e c t i o n l i m i t [upper l i m i t f o r ] o f about 140 mg/kg. Use o f t h e median as a more a s s u m p t i o n - f r e e e s t i m a t o r y i e l d e d a 95% c o n f i d e n c e i n t e r v a l e x t e n d i n g from -3 ( e r g o , 0) t o 150 mg/kg. (The n u m e r i c a l v a l u e s f o r t h i s s i m u l a t e d example were i n s p i r e d b y a c t u a l IAEA i n t e r c o m p a r i s o n d a t a f o r Zn i n a n i m a l bone [H-5], as r e p o r t e d i n T a b l e I o f Ref. 6.) G e n e r a t i n g a u t h e n t i c b l a n k s f o r measurement i s another m a t t e r . The c e n t r a l importance o f t h e b l a n k f o r r e l i a b l e a n a l y t e d e t e c t i o n , and t h e c o m p l e x i t y o f t h e b l a n k i n multicomponent t r a c e element a n a l y s i s o f b i o e n v i r o n m e n t a l m a t r i c e s a r e such t h a t t h e IAEA gave t h i s matter s p e c i a l a t t e n t i o n . A t h r e e f a c e t e d approach was devised, comprising the " i d e a l blank," the " s i m u l a t i o n or surrogate b l a n k , " and f i n a l l y " p r o p a g a t i o n o f t h e b l a n k . " F u l l discussion i n c l u d i n g method s p e c i f i a b r i e f exposition follows which r e f l e c t s t h e sample and t h e measurement p r o c e s s i n e v e r y r e s p e c t save one: t h e absence o f t h e a n a l y t e o f i n t e r e s t . For r e l a t i v e l y s i m p l e m a t r i c e s and r e l a t i v e l y l o w l e v e l s o f i n t e r f e r e n c e , t h e i d e a l b l a n k may be approached. F a i l i n g t h i s , one must d e v i s e s u r r o g a t e b l a n k s which c l o s e l y s i m u l a t e t h e r e a l sample. T h i s p r o c e s s , as w e l l as t h e a l t e r n a t i v e b l a n k p r o p a g a t i o n t e c h n i q u e , r e q u i r e s t r u e e x p e r t i s e i n t h e r e l e v a n t a n a l y t i c a l s c i e n c e as opposed t o s t a t i s t i c s . Remembering t h a t t h e " b l a n k e f f e c t " -- i e , t r u e a n a l y t e b l a n k t o g e t h e r w i t h u n r e s o l v e d interférants -- may be a s s o c i a t e d w i t h t h e sample, i t s e l f , d i s s o l u t i o n p r o c e d u r e s , r e a g e n t s , and i n s t r u m e n t a l (and even s o f t w a r e ) a r t i f a c t s , we note t h a t a good s u r r o g a t e b l a n k r e q u i r e s t h e i n t r o d u c t i o n o f a n a l y t e o r interférant a t t h e same s t a g e s o f t h e measurement p r o c e s s and i n t h e same amounts as o c c u r w i t h t h e a c t u a l sample. Spectral interf e r e n c e s , m a t r i x e f f e c t s , r e c o v e r i e s , s e n s i t i v i t i e s , and r e a g e n t q u a n t i t i e s and sample s i z e s s h o u l d be s u f f i c i e n t l y s i m i l a r . The a l l o w a b l e degree o f d e p a r t u r e , a g a i n i s a sample-method s p e c i f i c s c i e n t i f i c i s s u e which must be determined b y t h e r e s p e c t i v e e x p e r t s , perhaps w i t h t h e a i d o f e x p e r i m e n t a l ruggedness t e s t s . An i n t e r e s t i n g i l l u s t r a t i o n o f t h e s u b t l e t y o f s u r r o g a t e b l a n k p i t f a l l s i s found i n t h e a n a l y s i s o f t r a c e elements i n m i l k by neutron a c t i v a t i o n a n a l y s i s . Knowledge o f t r a c e c o n s t i t u e n t s o f m i l k , e s p e c i a l l y human m i l k , i s o f c o n s i d e r a b l e importance i n IAEA c o o p e r a t i v e r e s e a r c h programs i n v o l v i n g g l o b a l t r e n d s i n human h e a l t h and n u t r i t i o n ( 3 . 8 ) . L a c k i n g s u f f i c i e n t i n f o r m a t i o n r e g a r d i n g 1) b a s e l i n e i n t e r f e r e n c e i n NAA u s i n g gamma r a y s p e c t r o m e t r y , and 2) t r a c e element c o m p o s i t i o n o f presumably s i m i l a r b i o l o g i c a l m a t e r i a l s , one might s e l e c t cows' m i l k as a p o t e n t i a l s u r r o g a t e . Such a c h o i c e would be m i s l e a d i n g f o r a number o f a c t i v a t e d gamma e m i t t e r s , however, because cows' m i l k c o n t a i n s phosphorus a t conc e n t r a t i o n s which exceed those i n human m i l k b y about a f a c t o r o f 10, and t h e b r e m s s t r a h l u n g from t h e h i g h energy b e t a e m i t t i n g n e u t r o n a c t i v a t i o n p r o d u c t P-32 would cause a much i n c r e a s e d i n s t r u mental b a s e l i n e c o n t r i b u t i o n which would n o t be r e p r e s e n t a t i v e o f the t r u e , human m i l k b l a n k ( 1 5 ) . F o r o t h e r methods, such as AAS o r XRF, t h i s problem would n o t a r i s e .

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

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Space does n o t p e r m i t a d e t a i l e d d i s c u s s i o n o f t h e p r o p a g a t i o n approach t o t h e b l a n k and i t s v a r i a b i l i t y , b u t i n essence i t c o n s i s t s o f c o n s i d e r i n g each s e q u e n t i a l s t e p o f t h e measurement p r o c e s s , t o g e t h e r w i t h t h e i n t r o d u c t i o n and p r o p a g a t i o n o f a n a l y t e b l a n k and interférants through each s t e p , t a k i n g i n t o account t h e r e s p e c t i v e r e c o v e r i e s . I n t h e f i n a l , i n s t r u m e n t a l measurement s t e p p e r t u r b a t i o n s o f t h e response (shape and s e n s i t i v i t y ) f o r a n a l y t e , interférants, and m a t r i x a b s o r p t i o n and s c a t t e r i n g must a l l be considered. P r o p a g a t i o n o f components o f t h e b l a n k thus r e p r e s e n t s an e x c e l l e n t independent approach t o d e v i s i n g a s u r r o g a t e b l a n k . I t s s u c c e s s , however, depends upon t h e e s t i m a t i o n o f a p p r o p r i a t e r e c o v e r y and s e n s i t i v i t y f a c t o r s f o r t h e t h r e e t r o u b l e makers: a d v e n t i t i o u s a n a l y t e , interférants, and m a t r i x e f f e c t s . Excellent e x p e r i m e n t a l t e c h n i q u e s w h i c h may h e l p i n t h e t a s k i n c l u d e m u l t i p l e s t a n d a r d a d d i t i o n s , i s o t o p e d i l u t i o n , and m u l t i p l e sample a d d i t i o n s (16) . R e p o r t i n g o f Low-Level Data R e p o r t i n g and q u a l i t y i s s u e s t r a n s c e n d t h e s p e c i f i c NRC and IAEA programs, and they a r e t r e a t e d i n some d e t a i l elsewhere i n t h i s volume. L o w - l e v e l d a t a a r e f a r more s u b j e c t t o i n f o r m a t i o n l o s s and b i a s than d a t a c o r r e s p o n d i n g t o l a r g e s i g n a l s . T h i s f o l l o w s because o f a tendency t o r e p o r t o b s e r v a t i o n s w h i c h a r e n o t s t a t i s t i c a l l y s i g n i f i c a n t as z e r o , o r " t r a c e " , o r as v a r i o u s types o f upper l i m i t s . A v e r a g i n g o r combining o r even comparing s e t s o f r e s u l t s so reported i s e i t h e r impossible or not p o s s i b l e without b i a s . Worse s t i l l , t h e same r e s u l t s c o u l d be r e p o r t e d a c c o r d i n g t o d i f f e r e n t p r e s c r i p t i o n s , l e a d i n g a t t h e v e r y l e a s t t o m i s c o n c e p t i o n s by t h e lay public. The recommendation g i v e n b o t h t h e NRC and t h e IAEA was t h a t observed v a l u e s and t h e i r u n c e r t a i n t i e s be r e p o r t e d , t o g e t h e r with appropriate detection l i m i t i n f o r m a t i o n , even when t h e detection d e c i s i o n i s negative. Q u a l i t y c o n t r o l o r c r o s s check samples a t low l e v e l s a r e e s s e n t i a l f o r a s s u r i n g q u a l i t y measurements i n these same concentration regions. I n t e r n a l , known c o n t r o l s i n s i m i l a r m a t r i c e s and h a v i n g s i m i l a r i n t e r f e r e n c e s s h o u l d be t h e f i r s t s t e p toward attaining control. C e r t i f i e d , n a t u r a l m a t r i x m a t e r i a l s are the b e s t , f o r one c a n then t e s t n o t j u s t c o n s i s t e n c y o r i n t e r l a b o r a t o r y c o m p a r a b i l i t y , but a l s o accuracy. Use o f e x t e r n a l , b l i n d c o n t r o l samples, perhaps i n c l u d i n g l a b o r a t o r y i n t e r c o m p a r i s o n s , may be t h e o n l y way t o r e l i a b l y a s s e s s performance under r o u t i n e c o n d i t i o n s (17) . S i m i l a r l y , t e s t d a t a s e t s can be most i m p o r t a n t f o r a l g o r i t h mic q u a l i t y assurance o f low l e v e l multicomponent spectrometry (18.19) . I t was f e l t t h a t t h e o b j e c t i v e s o f b o t h t h e NRC and IAEA programs c o u l d be b e t t e r met by t a k i n g c a r e f u l measures t o a s s u r e t r u l y b l i n d c o n t r o l samples t h a t would be f a i t h f u l s u r r o g a t e s w i t h r e s p e c t t o a n a l y t e c o n c e n t r a t i o n and m a t r i x c o m p o s i t i o n f o r t h e samples and a n a l y t e s o f concern. D i s t r i b u t i o n o f b l i n d blanks c o u l d f u r t h e r assure v a l i d claims concerning d e t e c t i o n l i m i t s . Conclusion The NRC and IAEA programs share the common p r a c t i c a l g o a l o f s e e k i n g t o e s t a b l i s h a c c u r a t e v a l u e s f o r t h e d e t e c t i o n l i m i t performance

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

9. CURRIE & PARR

Perspectives on Detection Limits

189

c h a r a c t e r i s t i c f o r t h e i r r e s p e c t i v e measurement p r o c e s s e s f o r t r a c e r a d i o n u c l i d e s and t r a c e elements, r e s p e c t i v e l y . The d r i v i n g f o r c e s f o r e s t a b l i s h i n g m e a n i n g f u l d e t e c t i o n l i m i t s f o r t h e a c t u a l measure­ ment p r o c e s s were, i n t h e f i r s t case f o r r a d i o l o g i c a l m o n i t o r i n g t o prevent the r e l e a s e o f r a d i o a c t i v i t y l e v e l s o f environmental c o n c e r n , and i n t h e second, t o i n c r e a s e o u r knowledge o f c o n c e n t r a ­ t i o n s and g e o g r a p h i c v a r i a t i o n s o f e s s e n t i a l and t o x i c t r a c e elements i n b i o l o g i c a l and e n v i r o n m e n t a l samples. D e t e c t i o n l i m i t f o r m u l a t i o n s w h i c h appeared s i m i l a r , b u t w h i c h were f u n d a m e n t a l l y d i f f e r e n t , were i n i t i a l l y found. I n b o t h cases the e x p r e s s i o n s were a l s o somewhat l i m i t e d i n a p p l i c a b i l i t y , i n t h a t they d i d n o t e x p l i c i t l y t r e a t s y s t e m a t i c e r r o r s , o r those a s s o c i a t e d w i t h many o f t h e " r e a l - l i f e " problems o f l o w - l e v e l measurement such as o v e r l a p p i n g peaks, m a t r i x e f f e c t s , b l a n k i n t r o d u c t i o n a t v a r i o u s s t a g e s o f measurement, i n s t r u m e n t a l a r t i f a c t s , o r non-normal random errors. A s y n o p s i s o f t h e i s s u e s t o g e t h e r w i t h an i n d i c a t i o n o f the c r u c i a l r o l e o f s c i e n t i f i b e n e f i t s o f sound measuremen d e r i v a t i o n o f meaningful d e t e c t i o n l i m i t s . I n F i g u r e 4, t o be c o n t r a s t e d w i t h F i g u r e 3, we i l l u s t r a t e a "success s t o r y . " Here, the improvement i n measurement q u a l i t y has made p o s s i b l e t h e d i s c r i m i n a t i o n o f s i g n i f i c a n t geographical v a r i a t i o n s i n the trace Table V I .

Outcome and D e s i d e r a t a

NRC -- Method-independent o f o r m u l a t i o n ; a t t e n t i o n t o n o n - c o u n t i n g random and s y s t e m a t i c e r r o r . S p e c i a l t r e a t m e n t f o r few counts IAEA -- P a i r e d o b s e r v a t i o n s ; r e p o r t an adequate number o f " i d e a l " b l a n k s ; use o f " t " , c e n t r a l l i m i t theorem, and σ/s ( l i m i t ) Q

1.

Sound, c o n c e p t u a l b a s i s [not ad hoc]

2.

Method-independent t e r m i n o l o g y , f o r m u l a t i o n

3.

Responsible r e p o r t i n g [low-level

4.

Use o f t h e f u l l power o f s t a t i s t i c s [hypothesis t e s t i n g , robust e s t i m a t i o n , e r r o r propagation...]

5.

GOOD SCIENCE

data]

Knowledge o f t h e Measurement P r o c e s s i n place of empiricism ["local" matrix c a l i b r a t i o n and l a r g e r e p l i c a t i o n s , a r e costly] E x p e r t knowledge r e : simulation components o f t h e b l a n k .

blank,

propagation

of

Special a t t e n t i o n to error bounds [ i n c l u d i n g m o d e l - e r r o r ] , v a l i d a t i o n , c o n t a m i n a t i o n , i n t e r f e r e n c e , and m a t r i x e f f e c t s A n a l y t i c a l Q u a l i t y A s s u r a n c e v i a l o w - l e v e l C e r t i f i e d Reference M a t e r i a l s , and S i m u l a t i o n T e s t Data [ a l g o r i t h m i c QA].

In Detection in Analytical Chemistry; Currie, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

190

DETECTION IN ANALYTICAL CHEMISTRY

100

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