Bayesian Methods for Measures of Agreement

335 Pages·2009·3.13 MB·English

by  Lyle D. Broemeling

Bayesian Methods
for Measures
of Agreement
© 2009 by Taylor & Francis Group, LLC
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Editor-in-Chief
Shein-Chung Chow, Ph.D.
Professor
Department of Biostatistics and Bioinformatics
Duke University School of Medicine
Durham, North Carolina, U.S.A.
Series Editors
Byron Jones Jen-pei Liu
Senior Director Professor
Statistical Research and Consulting Centre Division of Biometry
(IPC 193) Department of Agronomy
Pfizer Global Research and Development National Taiwan University
Sandwich, Kent, UK Taipei, Taiwan
Karl E. Peace Bruce W. Turnbull
Georgia Cancer Coalition Professor
Distinguished Cancer Scholar School of Operations Research
Senior Research Scientist and and Industrial Engineering
Professor of Biostatistics Cornell University
Jiann-Ping Hsu College of Public Health Ithaca, NY
Georgia Southern University
Statesboro, GA
© 2009 by Taylor & Francis Group, LLC
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Published Titles
1.Design and Analysis of Animal Studies in Pharmaceutical Development,
Shein-Chung Chow and Jen-pei Liu
2.Basic Statistics and Pharmaceutical Statistical Applications, James E. De Muth
3.Design and Analysis of Bioavailability and Bioequivalence Studies,
Second Edition, Revised and Expanded, Shein-Chung Chow and Jen-pei Liu
4.Meta-Analysis in Medicine and Health Policy, Dalene K. Stangl and Donald A. Berry
5.Generalized Linear Models: A Bayesian Perspective, Dipak K. Dey,
Sujit K. Ghosh, and Bani K. Mallick
6.Difference Equations with Public Health Applications, Lemuel A. Moyé
and Asha Seth Kapadia
7.Medical Biostatistics, Abhaya Indrayan and Sanjeev B. Sarmukaddam
8.Statistical Methods for Clinical Trials, Mark X. Norleans
9.Causal Analysis in Biomedicine and Epidemiology: Based on Minimal
Sufficient Causation, Mikel Aickin
10.Statistics in Drug Research: Methodologies and Recent Developments,
Shein-Chung Chow and Jun Shao
11.Sample Size Calculations in Clinical Research, Shein-Chung Chow, Jun Shao, and Hansheng
Wang
12.Applied Statistical Design for the Researcher, Daryl S. Paulson
13.Advances in Clinical Trial Biostatistics, Nancy L. Geller
14.Statistics in the Pharmaceutical Industry, Third Edition, Ralph Buncher
and Jia-Yeong Tsay
15.DNA Microarrays and Related Genomics Techniques: Design, Analysis, and Interpretation of
Experiments, David B. Allsion, Grier P. Page, T. Mark Beasley, and Jode W. Edwards
16.Basic Statistics and Pharmaceutical Statistical Applications, Second Edition,
James E. De Muth
17.Adaptive Design Methods in Clinical Trials, Shein-Chung Chow and Mark Chang
18.Handbook of Regression and Modeling: Applications for the Clinical and Pharmaceutical
Industries, Daryl S. Paulson
19.Statistical Design and Analysis of Stability Studies, Shein-Chung Chow
20.Sample Size Calculations in Clinical Research, Second Edition, Shein-Chung Chow,
Jun Shao, and Hansheng Wang
21.Elementary Bayesian Biostatistics, Lemuel A. Moyé
22.Adaptive Design Theory and Implementation Using SAS and R, Mark Chang
23.Computational Pharmacokinetics, Anders Källén
24.Computational Methods in Biomedical Research, Ravindra Khattree and
Dayanand N. Naik
25.Medical Biostatistics, Second Edition, A. Indrayan
26.DNA Methylation Microarrays: Experimental Design and Statistical Analysis,
Sun-Chong Wang and Arturas Petronis
27.Design and Analysis of Bioavailability and Bioequivalence Studies, Third Edition,
Shein-Chung Chow and Jen-pei Liu
28.Translational Medicine: Strategies and Statistical Methods, Dennis Cosmatos and
Shein-Chung Chow
29.Bayesian Methods for Measures of Agreement, Lyle D. Broemeling
© 2009 by Taylor & Francis Group, LLC
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Bayesian Methods
for Measures
of Agreement
Lyle D. Broemeling
Director
Broemeling & Associates Inc.
Medical Lake
Washington, U.S.A.
© 2009 by Taylor & Francis Group, LLC
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Library of Congress Cataloging-in-Publication Data
Broemeling, Lyle D., 1939-
Bayesian methods for measures of agreement / Lyle D. Broemeling.
p. cm. -- (Chapman & Hall/CRC biostatistics series ; 29)
Includes bibliographical references and index.
ISBN 978-1-4200-8341-5 (hardcover : alk. paper)
1. Bayesian statistical decision theory. 2. Clinical medicine--Decision making.
I. Title. II. Series.
QA279.5.B76 2009
519.5’42--dc22 2008049374
Visit the Taylor & Francis Web site at
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and the CRC Press Web site at
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© 2009 by Taylor & Francis Group, LLC
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Contents
Preface ..........................................................................................................xi
Acknowledgments ....................................................................................xiii
Author .........................................................................................................xv
1 Introduction to Agreement ................................................................1
1.1 Introduction ...........................................................................................1
1.2 Agreement and Statistics .....................................................................3
1.3 The Bayesian Approach .......................................................................5
1.4 Some Examples of Agreement ............................................................7
1.4.1 The Lennox Lewis–Evander Holyfi eld Bout ..........................7
1.4.2 Phase II Clinical Trials ............................................................10
1.4.3 Agreement on Tumor Size ......................................................10
1.4.4 Wine Tasting ............................................................................15
1.4.5 Forgery: Robinson versus Mandell .......................................21
1.5 Sources of Information .......................................................................22
1.6 Software and Computing ..................................................................23
1.7 A Preview of the Book ........................................................................24
Exercises ...............................................................................................30
References ............................................................................................31
2 Bayesian Methods of Agreement for Two Raters .........................35
2.1 Introduction .........................................................................................35
2.2 The Design of Agreement Studies ....................................................36
2.3 Precursors of Kappa ...........................................................................38
2.4 Chance Corrected Measures of Agreement ....................................41
2.5 Conditional Kappa ..............................................................................42
2.6 Kappa and Stratifi cation.....................................................................45
2.7 Weighted Kappa ..................................................................................49
2.8 Intraclass Kappa ..................................................................................51
2.9 Other Measures of Agreement ..........................................................55
2.10 Agreement with a Gold Standard ....................................................59
2.11 Kappa and Association ......................................................................62
2.12 Consensus ............................................................................................65
Exercises ...............................................................................................66
References ............................................................................................69
3 More than Two Raters ......................................................................71
3.1 Introduction .........................................................................................71
3.2 Kappa with Many Raters ...................................................................72
3.3 Partial Agreement ...............................................................................78
vii
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viii Contents
3.4 Stratifi ed Kappa ...................................................................................83
3.5 Intraclass Kappa ..................................................................................91
3.6 The Fleiss Generalized Kappa ..........................................................94
3.7 The G Coeffi cient and Other Indices ................................................97
3.8 Kappa and Homogeneity ...................................................................99
3.9 Introduction to Model Based Approaches ....................................100
3.10 Agreement and Matching ................................................................103
Exercises .............................................................................................104
References ..........................................................................................109
4 Agreement and Correlated Observations.....................................111
4.1 Introduction .......................................................................................111
4.2 An Example of Paired Observations ..............................................112
4.3 The Oden Pooled Kappa and Schouten Weighted Kappa...........118
4.4 A Generalized Correlation Model ..................................................119
4.5 The G Coeffi cient and Other Indices of Agreement.....................124
4.6 Homogeneity with Dependent Data ..............................................125
4.7 Logistic Regression and Agreement ..............................................130
Exercises .............................................................................................138
References ..........................................................................................142
5 Modeling Patterns of Agreement .................................................145
5.1 Introduction .......................................................................................145
5.2 Nominal Responses ..........................................................................147
5.3 Ordinal Responses ............................................................................167
5.4 More than Two Raters ......................................................................173
5.5 Other Methods for Patterns of Agreement ...................................177
5.6 Summary of Modeling and Agreement ........................................182
Exercises .............................................................................................183
References ..........................................................................................191
6 Agreement with Quantitative Scores ...........................................193
6.1 Introduction .......................................................................................193
6.2 Regression and Correlation .............................................................194
6.3 The Analysis of Variance .................................................................199
6.4 Intraclass Correlation Coeffi cient for Agreement ........................204
6.5 Agreement with Covariates .............................................................209
6.6 Other Considerations with Continuous Scores ............................212
6.6.1 Introduction............................................................................212
6.6.2 Bayesian Bland–Altman .......................................................213
6.6.3 More on Variance Components ...........................................215
6.6.4 Fixed Effects for Agreement ................................................216
6.6.5 Multivariate Techniques .......................................................220
Exercises .............................................................................................222
References ..........................................................................................233
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Contents ix
7 Sample Sizes for Agreement Studies ...........................................235
7.1 Introduction .......................................................................................235
7.2 The Classical and Bayesian Approaches to Power Analysis ......238
7.3 The Standard Populations: Classical and Bayesian
Approaches ........................................................................................239
7.4 Kappa, the G Coeffi cient, and Other Indices .................................245
7.5 The Logistic Linear Model ...............................................................252
7.6 Regression and Correlation .............................................................255
7.7 The Intraclass Correlation................................................................260
7.8 Bayesian Approaches to Sample Size .............................................266
Exercises .............................................................................................267
References ..........................................................................................271
Appendix A Bayesian Statistics ..........................................................273
A1 Introduction .......................................................................................273
A2 Bayes Theorem ..................................................................................274
A3 Prior Information ..............................................................................276
A4 Posterior Information .......................................................................278
A5 Inference .............................................................................................280
A5.1 Introduction............................................................................280
A5.2 Estimation ...............................................................................280
A5.3 Testing Hypotheses ...............................................................282
A5.3.1 Introduction ..............................................................282
A5.3.2 A Binomial Example ...............................................283
A5.3.3 Comparing Two Binomials .....................................284
A5.3.4 A Sharp Null Hypothesis for the Normal
Mean ..........................................................................284
A5.3.5 Comparing Two Normal Populations ...................285
A6 Predictive Inference .........................................................................286
A6.1 Introduction............................................................................286
A6.2 The Binomial ..........................................................................287
A6.3 Forecasting from a Normal Population..............................287
A7 Checking Model Assumptions .......................................................288
A7.1 Introduction............................................................................288
A7.2 Sampling from an Exponential, but Assuming a
Normal Population ................................................................289
A7.3 Speed of Light Study of Newcomb .....................................290
A7.4 A Poisson Population ............................................................292
A7.5 Measuring Tumor Size ..........................................................292
A7.6 Testing the Multinomial Assumption ................................293
A8 Sample Size Problems .......................................................................294
A8.1 Introduction............................................................................294
A8.2 The One Sample Binomial ...................................................295
A8.3 One Sample Binomial with Prior Information ..................296
A8.4 Comparing Two Binomial Populations .............................297
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x Contents
A9 Computing .........................................................................................298
A9.1 Introduction ...........................................................................298
A9.2 Direct Methods ......................................................................299
A9.3 Monte Carlo Markov Chain .................................................303
A9.3.1 Introduction ..............................................................303
A9.3.2 The Metropolis Algorithm .....................................303
A9.3.3 Gibbs Sampling ........................................................304
A9.3.4 The Common Mean of Normal Populations........305
A9.3.5 MCMC Sampling with WinBUGS .........................309
Exercises .............................................................................................312
References ..........................................................................................313
Appendix B Introduction to WinBUGS .............................................315
B1 Introduction .......................................................................................315
B2 Download ...........................................................................................316
B3 The Essentials ....................................................................................316
B3.1 Main Body ..............................................................................316
B3.2 List Statements .......................................................................316
B4 Execution ............................................................................................316
B4.1 The Specifi cation Tool ...........................................................318
B4.2 The Sample Monitor Tool .....................................................318
B4.3 The Update Tool .....................................................................318
B5 Output .................................................................................................319
B6 Examples ............................................................................................320
B6.1 Kappa ......................................................................................321
B6.2 Logistic Linear Model ...........................................................323
B7 Summary ............................................................................................325
References ..........................................................................................325
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