Bayesian Adaptive Methods for Clinical Trials (Chapman & Hall CRC Biostatistics Series)

307 Pages·2010·2.86 MB·English

by  Scott M. Berry

Bayesian
Adaptive Methods
for Clinical Trials
K11217_FM.indd 1 6/18/10 2:08:02 PM
Published Titles
Editor-in-Chief
1. Design and Analysis of Animal Studies in 19. Statistical Design and Analysis of Stability
Shein-Chung Chow, Ph.D. Pharmaceutical Development, Studies, Shein-Chung Chow
Professor Shein-Chung Chow and Jen-pei Liu 20. Sample Size Calculations in Clinical Research,
2. Basic Statistics and Pharmaceutical Statistical Second Edition, Shein-Chung Chow,
Department of Biostatistics and Bioinformatics
Applications, James E. De Muth Jun Shao, and Hansheng Wang
Duke University School of Medicine
3. Design and Analysis of Bioavailability and 21. Elementary Bayesian Biostatistics,
Durham, North Carolina, U.S.A. Bioequivalence Studies, Second Edition, Revised Lemuel A. Moyé
and Expanded, Shein-Chung Chow and 22. Adaptive Design Theory and Implementation
Jen-pei Liu Using SAS and R, Mark Chang
4. Meta-Analysis in Medicine and Health Policy, 23. Computational Pharmacokinetics, Anders Källén
Dalene K. Stangl and Donald A. Berry 24. Computational Methods in Biomedical Research,
Series Editors
5. Generalized Linear Models: A Bayesian Ravindra Khattree and Dayanand N. Naik
Perspective, Dipak K. Dey, Sujit K. Ghosh, 25. Medical Biostatistics, Second Edition,
Byron Jones Jen-pei Liu and Bani K. Mallick A. Indrayan
Senior Director Professor 6. Difference Equations with Public Health 26. DNA Methylation Microarrays: Experimental
Statistical Research and Consulting Centre Division of Biometry Applications, Lemuel A. Moyé and Design and Statistical Analysis,
Asha Seth Kapadia Sun-Chong Wang and Arturas Petronis
(IPC 193) Department of Agronomy
7. Medical Biostatistics, Abhaya Indrayan and 27. Design and Analysis of Bioavailability and
Pfizer Global Research and Development National Taiwan University
Sanjeev B. Sarmukaddam Bioequivalence Studies, Third Edition,
Sandwich, Kent, U.K. Taipei, Taiwan
8. Statistical Methods for Clinical Trials, Shein-Chung Chow and Jen-pei Liu
Mark X. Norleans 28. Translational Medicine: Strategies and
9. Causal Analysis in Biomedicine and Statistical Methods, Dennis Cosmatos and
Karl E. Peace Bruce W. Turnbull
Epidemiology: Based on Minimal Sufficient Shein-Chung Chow
Georgia Cancer Coalition Professor
Causation, Mikel Aickin 29. Bayesian Methods for Measures of Agreement,
Distinguished Cancer Scholar School of Operations Research
10. Statistics in Drug Research: Methodologies and Lyle D. Broemeling
Senior Research Scientist and and Industrial Engineering Recent Developments, Shein-Chung Chow 30. Data and Safety Monitoring Committees in
Professor of Biostatistics Cornell University and Jun Shao Clinical Trials, Jay Herson
Jiann-Ping Hsu College of Public Health Ithaca, New York 11. Sample Size Calculations in Clinical Research, 31. Design and Analysis of Clinical Trials with Time-
Georgia Southern University Shein-Chung Chow, Jun Shao, and to-Event Endpoints, Karl E. Peace
Hansheng Wang 32. Bayesian Missing Data Problems: EM, Data
Statesboro, Georgia
12. Applied Statistical Design for the Researcher, Augmentation and Noniterative Computation,
Daryl S. Paulson Ming T. Tan, Guo-Liang Tian, and Kai Wang Ng
13. Advances in Clinical Trial Biostatistics, 33. Multiple Testing Problems in Pharmaceutical
Nancy L. Geller Statistics, Alex Dmitrienko, Ajit C. Tamhane,
14. Statistics in the Pharmaceutical Industry, and Frank Bretz
Third Edition, Ralph Buncher and Jia-Yeong Tsay 34. Bayesian Modeling in Bioinformatics,
15. DNA Microarrays and Related Genomics Dipak K. Dey, Samiran Ghosh, and
Techniques: Design, Analysis, and Interpretation Bani K. Mallick
of Experiments, David B. Allsion, Grier P. Page, 35. Clinical Trial Methodology, Karl E. Peace
T. Mark Beasley, and Jode W. Edwards and Ding-Geng (Din) Chen
16. Basic Statistics and Pharmaceutical Statistical 36. Monte Carlo Simulation for the Pharmaceutical
Applications, Second Edition, James E. De Muth Industry: Concepts, Algorithms, and Case
17. Adaptive Design Methods in Clinical Trials, Studies, Mark Chang
Shein-Chung Chow and Mark Chang 37. Frailty Models in Survival Analysis,
18. Handbook of Regression and Modeling: Andreas Wienke
Applications for the Clinical and Pharmaceutical 38. Bayesian Adaptive Methods for Clinical Trials,
Industries, Daryl S. Paulson Scott M. Berry, Bradley P. Carlin, J. Jack Lee,
and Peter Muller
K11217_FM.indd 2 6/18/10 2:08:03 PM
Published Titles
Editor-in-Chief
1. Design and Analysis of Animal Studies in 19. Statistical Design and Analysis of Stability
Shein-Chung Chow, Ph.D. Pharmaceutical Development, Studies, Shein-Chung Chow
Professor Shein-Chung Chow and Jen-pei Liu 20. Sample Size Calculations in Clinical Research,
2. Basic Statistics and Pharmaceutical Statistical Second Edition, Shein-Chung Chow,
Department of Biostatistics and Bioinformatics
Applications, James E. De Muth Jun Shao, and Hansheng Wang
Duke University School of Medicine
3. Design and Analysis of Bioavailability and 21. Elementary Bayesian Biostatistics,
Durham, North Carolina, U.S.A. Bioequivalence Studies, Second Edition, Revised Lemuel A. Moyé
and Expanded, Shein-Chung Chow and 22. Adaptive Design Theory and Implementation
Jen-pei Liu Using SAS and R, Mark Chang
4. Meta-Analysis in Medicine and Health Policy, 23. Computational Pharmacokinetics, Anders Källén
Dalene K. Stangl and Donald A. Berry 24. Computational Methods in Biomedical Research,
Series Editors
5. Generalized Linear Models: A Bayesian Ravindra Khattree and Dayanand N. Naik
Perspective, Dipak K. Dey, Sujit K. Ghosh, 25. Medical Biostatistics, Second Edition,
Byron Jones Jen-pei Liu and Bani K. Mallick A. Indrayan
Senior Director Professor 6. Difference Equations with Public Health 26. DNA Methylation Microarrays: Experimental
Statistical Research and Consulting Centre Division of Biometry Applications, Lemuel A. Moyé and Design and Statistical Analysis,
Asha Seth Kapadia Sun-Chong Wang and Arturas Petronis
(IPC 193) Department of Agronomy
7. Medical Biostatistics, Abhaya Indrayan and 27. Design and Analysis of Bioavailability and
Pfizer Global Research and Development National Taiwan University
Sanjeev B. Sarmukaddam Bioequivalence Studies, Third Edition,
Sandwich, Kent, U.K. Taipei, Taiwan
8. Statistical Methods for Clinical Trials, Shein-Chung Chow and Jen-pei Liu
Mark X. Norleans 28. Translational Medicine: Strategies and
9. Causal Analysis in Biomedicine and Statistical Methods, Dennis Cosmatos and
Karl E. Peace Bruce W. Turnbull
Epidemiology: Based on Minimal Sufficient Shein-Chung Chow
Georgia Cancer Coalition Professor
Causation, Mikel Aickin 29. Bayesian Methods for Measures of Agreement,
Distinguished Cancer Scholar School of Operations Research
10. Statistics in Drug Research: Methodologies and Lyle D. Broemeling
Senior Research Scientist and and Industrial Engineering Recent Developments, Shein-Chung Chow 30. Data and Safety Monitoring Committees in
Professor of Biostatistics Cornell University and Jun Shao Clinical Trials, Jay Herson
Jiann-Ping Hsu College of Public Health Ithaca, New York 11. Sample Size Calculations in Clinical Research, 31. Design and Analysis of Clinical Trials with Time-
Georgia Southern University Shein-Chung Chow, Jun Shao, and to-Event Endpoints, Karl E. Peace
Hansheng Wang 32. Bayesian Missing Data Problems: EM, Data
Statesboro, Georgia
12. Applied Statistical Design for the Researcher, Augmentation and Noniterative Computation,
Daryl S. Paulson Ming T. Tan, Guo-Liang Tian, and Kai Wang Ng
13. Advances in Clinical Trial Biostatistics, 33. Multiple Testing Problems in Pharmaceutical
Nancy L. Geller Statistics, Alex Dmitrienko, Ajit C. Tamhane,
14. Statistics in the Pharmaceutical Industry, and Frank Bretz
Third Edition, Ralph Buncher and Jia-Yeong Tsay 34. Bayesian Modeling in Bioinformatics,
15. DNA Microarrays and Related Genomics Dipak K. Dey, Samiran Ghosh, and
Techniques: Design, Analysis, and Interpretation Bani K. Mallick
of Experiments, David B. Allsion, Grier P. Page, 35. Clinical Trial Methodology, Karl E. Peace
T. Mark Beasley, and Jode W. Edwards and Ding-Geng (Din) Chen
16. Basic Statistics and Pharmaceutical Statistical 36. Monte Carlo Simulation for the Pharmaceutical
Applications, Second Edition, James E. De Muth Industry: Concepts, Algorithms, and Case
17. Adaptive Design Methods in Clinical Trials, Studies, Mark Chang
Shein-Chung Chow and Mark Chang 37. Frailty Models in Survival Analysis,
18. Handbook of Regression and Modeling: Andreas Wienke
Applications for the Clinical and Pharmaceutical 38. Bayesian Adaptive Methods for Clinical Trials,
Industries, Daryl S. Paulson Scott M. Berry, Bradley P. Carlin, J. Jack Lee,
and Peter Muller
K11217_FM.indd 3 6/18/10 2:08:03 PM
Bayesian
Adaptive Methods
for Clinical Trials
Scott M. Berry
Berry Consultants
College Station, Texas
Bradley P. Carlin
University of Minnesota
Minneapolis, Minnesota
J. Jack Lee
The University of Texas
MD Anderson Cancer Center
Houston, Texas
Peter Müller
The University of Texas
MD Anderson Cancer Center
Houston, Texas
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Library of Congress Cataloging‑in‑Publication Data
Bayesian adaptive methods for clinical trials / Scott M. Berry ... [et al.].
p. ; cm. -- (Chapman & Hall/CRC biostatistics series ; 38)
Includes bibliographical references and indexes.
Summary: “As has been well-discussed, the explosion of interest in Bayesian methods over the
last 10 to 20 years has been the result of the convergence of modern computing power and elcient
Markov chain Monte Carlo (MCMC) algorithms for sampling from and summarizing posterior
distributions. Practitioners trained in traditional, frequentist statistical methods appear to have been
drawn to Bayesian approaches for three reasons. One is that Bayesian approaches implemented with
the majority of their informative content coming from the current data, and not any external prior
information, typically have good frequentist properties (e.g., low mean squared error in repeated use).
Second, these methods as now readily implemented in WinBUGS and other MCMC-driven software
packages now offer the simplest approach to hierarchical (random effects) modeling, as routinely
needed in longitudinal, frailty, spatial, time series, and a wide variety of other settings featuring
interdependent data. Third, practitioners are attracted by the greater flexibility and adaptivity of
the Bayesian approach, which permits stopping for elcacy, toxicity, and futility, as well as facilitates
a straightforward solution to a great many other specialized problems such as dosing, adaptive
randomization, equivalence testing, and others we shall describe. This book presents the Bayesian
adaptive approach to the design and analysis of clinical trials”--Provided by publisher.
ISBN 978-1-4398-2548-8 (hardcover : alk. paper)
1. Clinical trials--Statistical methods. 2. Bayesian statistical decision theory. I. Berry, Scott M. II.
Series: Chapman & Hall/CRC biostatistics series ; 38.
[DNLM: 1. Clinical Trials as Topic. 2. Bayes Theorem. QV 771 B357 2011]
R853.C55B385 2011
615.5072’4--dc22 2010022618
Visit the Taylor & Francis Web site at
http://www.taylorandfrancis.com
and the CRC Press Web site at
http://www.crcpress.com
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To
Our families
Contents
Foreword xi
Preface xiii
1 Statistical approaches for clinical trials 1
1.1 Introduction 1
1.2 Comparisons between Bayesian and frequentist approaches 4
1.3 Adaptivity in clinical trials 6
1.4 Features and use of the Bayesian adaptive approach 8
1.4.1 The fully Bayesian approach 8
1.4.2 Bayes as a frequentist tool 10
1.4.3 Examples of the Bayesian approach to drug and
medical device development 12
2 Basics of Bayesian inference 19
2.1 Introduction to Bayes’ Theorem 19
2.2 Bayesian inference 26
2.2.1 Point estimation 26
2.2.2 Interval estimation 27
2.2.3 Hypothesis testing and model choice 29
2.2.4 Prediction 34
2.2.5 Effect of the prior: sensitivity analysis 37
2.2.6 Role of randomization 38
2.2.7 Handling multiplicities 40
2.3 Bayesian computation 42
2.3.1 The Gibbs sampler 44
2.3.2 The Metropolis-Hastings algorithm 45
2.3.3 Convergence diagnosis 48
2.3.4 Variance estimation 49
2.4 Hierarchical modeling and metaanalysis 51
2.5 Principles of Bayesian clinical trial design 63
2.5.1 Bayesian predictive probability methods 64
viii CONTENTS
2.5.2 Bayesian indifference zone methods 66
2.5.3 Prior determination 68
2.5.4 Operating characteristics 70
2.5.5 Incorporating costs 78
2.5.6 Delayed response 81
2.5.7 Noncompliance and causal modeling 82
2.6 Appendix: R Macros 86
3 Phase I studies 87
3.1 Rule-based designs for determining the MTD 88
3.1.1 Traditional 3+3 design 88
3.1.2 Pharmacologically guided dose escalation 91
3.1.3 Accelerated titration designs 92
3.1.4 Other rule-based designs 92
3.1.5 Summary of rule-based designs 92
3.2 Model-based designs for determining the MTD 93
3.2.1 Continual reassessment method (CRM) 94
3.2.2 Escalation with overdose control (EWOC) 102
3.2.3 Time-to-event (TITE) monitoring 105
3.2.4 Toxicity intervals 109
3.2.5 Ordinal toxicity intervals 113
3.3 Efficacy versus toxicity 116
3.3.1 Trial parameters 117
3.3.2 Joint probability model for efficacy and toxicity 117
3.3.3 Defining the acceptable dose levels 118
3.3.4 Efficacy-toxicity trade-off contours 118
3.4 Combination therapy 121
3.4.1 Basic Gumbel model 122
3.4.2 Bivariate CRM 126
3.4.3 Combination therapy with bivariate response 127
3.4.4 Dose escalation with two agents 129
3.5 Appendix: R Macros 134
4 Phase II studies 137
4.1 Standard designs 137
4.1.1 Phase IIA designs 138
4.1.2 Phase IIB designs 140
4.1.3 Limitations of traditional frequentist designs 142
4.2 Predictive probability 142
4.2.1 Definition and basic calculations for binary data 143
4.2.2 Derivation of the predictive process design 146
4.3 Sequential stopping 150
4.3.1 Binary stopping for futility and efficacy 150
4.3.2 Binary stopping for futility, efficacy, and toxicity 151
CONTENTS ix
4.3.3 Monitoring event times 154
4.4 Adaptive randomization and dose allocation 155
4.4.1 Principles of adaptive randomization 155
4.4.2 Dose ranging and optimal biologic dosing 163
4.4.3 Adaptive randomization in dose finding 167
4.4.4 Outcome adaptive randomization with delayed
survival response 168
4.5 Hierarchical models for phase II designs 173
4.6 Decision theoretic designs 176
4.6.1 Utility functions and their specification 176
4.6.2 Screening designs for drug development 179
4.7 Case studies in phase II adaptive design 183
4.7.1 The BATTLE trial 183
4.7.2 The I-SPY 2 trial 189
4.8 Appendix: R Macros 191
5 Phase III studies 193
5.1 Introduction to confirmatory studies 193
5.2 Bayesian adaptive confirmatory trials 195
5.2.1 Adaptive sample size using posterior probabilities 196
5.2.2 Futility analyses using predictive probabilities 200
5.2.3 Handling delayed outcomes 204
5.3 Arm dropping 208
5.4 Modeling and prediction 211
5.5 Prior distributions and the paradigm clash 218
5.6 Phase III cancer trials 221
5.7 Phase II/III seamless trials 228
5.7.1 Example phase II/III trial 230
5.7.2 Adaptive design 231
5.7.3 Statistical modeling 232
5.7.4 Calculation 233
5.7.5 Simulations 235
5.8 Case study: Ablation device to treat atrial fibrillation 241
5.9 Appendix: R Macros 247
6 Special topics 249
6.1 Incorporating historical data 249
6.1.1 Standard hierarchical models 250
6.1.2 Hierarchical power prior models 252
6.2 Equivalence studies 260
6.2.1 Statistical issues in bioequivalence 261
6.2.2 Binomial response design 263
6.2.3 2×2 crossover design 265
6.3 Multiplicity 268