Bayesian adaptive methods for clinical trials

Already popular in the analysis of medical device trials, adaptive Bayesian designs are increasingly being used in drug development for a wide variety of diseases and conditions, from Alzheimer's disease and multiple sclerosis to obesity, diabetes, hepatitis C, and HIV. Written by leading pioneers of Bayesian clinical trial designs, Bayesian Adaptive Methods for Clinical Trials explores the growing role of Bayesian thinking in the rapidly changing world of clinical trial analysis.

The book first summarizes the current state of clinical trial design and analysis and introduces the main ideas and potential benefits of a Bayesian alternative. It then gives an overview of basic Bayesian methodological and computational tools needed for Bayesian clinical trials. With a focus on Bayesian designs that achieve good power and Type I error, the next chapters present Bayesian tools useful in early (Phase I) and middle (Phase II) clinical trials as well as two recent Bayesian adaptive Phase II studies: the BATTLE and ISPY-2 trials. In the following chapter on late (Phase III) studies, the authors emphasize modern adaptive methods and seamless Phase II-III trials for maximizing information usage and minimizing trial duration. They also describe a case study of a recently approved medical device to treat atrial fibrillation. The concluding chapter covers key special topics, such as the proper use of historical data, equivalence studies, and subgroup analysis.

For readers involved in clinical trials research, this book significantly updates and expands their statistical toolkits. The authors provide many detailed examples drawing on real data sets. The R and WinBUGS codes used throughout are available on supporting websites.

Scott Berry talks about the book on the CRC Press YouTube Channel.

Author Notes

Scott M. Berry is the President and Senior Statistical Scientist at Berry Consultants, a statistical consulting group specializing in adaptive clinical trial design in pharmaceutical and medical device research and development.

Bradley P. Carlin is Mayo Professor in Public Health and Head of the Division of Biostatistics at the University of Minnesota.

J. Jack Lee is Professor of Biostatistics at the University of Texas M.D. Anderson Cancer Center.

Peter Müller is a Robert R. Herring Distinguished Professor in Clinical Research in the Department of Biostatistics at the University of Texas M.D. Anderson Cancer Center.

Foreword	p. xi
Preface	p. xiii
1 Statistical approaches for clinical trials	p. 1
1.1 Introduction	p. 1
1.2 Comparisons between Bayesian and frequentist approaches	p. 4
1.3 Adaptivity in clinical trials	p. 6
1.4 Features and use of the Bayesian adaptive approach	p. 8
1.4.1 The fully Bayesian approach	p. 8
1.4.2 Bayes as a frequentist tool	p. 10
1.4.3 Examples of the Bayesian approach to drug and medical device development	p. 12
2 Basics of Bayesian inference	p. 19
2.1 Introduction to Bayes' Theorem	p. 19
2.2 Bayesian inference	p. 26
2.2.1 Point estimation	p. 26
2.2.2 Interval estimation	p. 27
2.2.3 Hypothesis testing and model choice	p. 29
2.2.4 Prediction	p. 34
2.2.5 Effect of the prior: sensitivity analysis	p. 37
2.2.6 Role of randomization	p. 38
2.2.7 Handling multiplicities	p. 40
2.3 Bayesian computation	p. 42
2.3.1 The Gibbs sampler	p. 44
2.3.2 The Metropolis-Hastings algorithm	p. 45
2.3.3 Convergence diagnosis	p. 48
2.3.4 Variance estimation	p. 49
2.4 Hierarchical modeling and metaanalysis	p. 51
2.5 Principles of Bayesian clinical trial design	p. 63
2.5.1 Bayesian predictive probability methods	p. 64
2.5.2 Bayesian indifference zone methods	p. 66
2.5.3 Prior determination	p. 68
2.5.4 Operating characteristics	p. 70
2.5.5 Incorporating costs	p. 78
2.5.6 Delayed response	p. 81
2.5.7 Noncompliance and causal modeling	p. 82
2.6 Appendix: R Macros	p. 86
3 Phase I studies	p. 87
3.1 Rule-based designs for determining the MTD	p. 88
3.1.1 Traditional 3+3 design	p. 88
3.1.2 Pharmacologically guided dose escalation	p. 91
3.1.3 Accelerated titration designs	p. 92
3.1.4 Other rule-based designs	p. 92
3.1.5 Summary of rule-based designs	p. 92
3.2 Model-based designs for determining the MTD	p. 93
3.2.1 Continual reassessment method (CRM)	p. 94
3.2.2 Escalation with overdose control (EWOC)	p. 102
3.2.3 Time-to-event (TITE) monitoring	p. 105
3.2.4 Toxicity intervals	p. 109
3.2.5 Ordinal toxicity intervals	p. 113
3.3 Efficacy versus toxicity	p. 116
3.3.1 Trial parameters	p. 117
3.3.2 Joint probability model for efficacy and toxicity	p. 117
3.3.3 Defining the acceptable dose levels	p. 118
3.3.4 Efficacy-toxicity trade-off contours	p. 118
3.4 Combination therapy	p. 121
3.4.1 Basic Gumbel model	p. 122
3.4.2 Bivariate CRM	p. 126
3.4.3 Combination therapy with bivariate response	p. 127
3.4.4 Dose escalation with two agents	p. 129
3.5 Appendix: R Macros	p. 134
4 Phase II studies	p. 137
4.1 Standard designs	p. 137
4.1.1 Phase IIA designs	p. 138
4.1.2 Phase IIB designs	p. 140
4.1.3 Limitations of traditional frequentist designs	p. 142
4.2 Predictive probability	p. 142
4.2.1 Definition and basic calculations for binary data	p. 143
4.2.2 Derivation of the predictive process design	p. 146
4.3 Sequential stopping	p. 150
4.3.1 Binary stopping for futility and efficacy	p. 150
4.3.2 Binary stopping for futility, efficacy, and toxicity	p. 151
4.3.3 Monitoring event times	p. 154
4.4 Adaptive randomization and dose allocation	p. 155
4.4.1 Principles of adaptive randomization	p. 155
4.4.2 Dose ranging and optimal biologic dosing	p. 163
4.4.3 Adaptive randomization in dose finding	p. 167
4.4.4 Outcome adaptive randomization with delayed survival response	p. 168
4.5 Hierarchical models for phase II designs	p. 173
4.6 Decision theoretic designs	p. 176
4.6.1 Utility functions and their specification	p. 176
4.6.2 Screening designs for drug development	p. 179
4.7 Case studies in phase II adaptive design	p. 183
4.7.1 The Battle trial	p. 183
4.7.2 The I-SPY 2 trial	p. 189
4.8 Appendix: R Macros	p. 191
5 Phase III studies	p. 193
5.1 Introduction to confirmatory studies	p. 193
5.2 Bayesian adaptive confirmatory trials	p. 195
5.2.1 Adaptive sample size using posterior probabilities	p. 196
5.2.2 Futility analyses using predictive probabilities	p. 200
5.2.3 Handling delayed outcomes	p. 204
5.3 Arm dropping	p. 208
5.4 Modeling and prediction	p. 211
5.5 Prior distributions and the paradigm clash	p. 218
5.6 Phase III cancer trials	p. 221
5.7 Phase II/III seamless trials	p. 228
5.7.1 Example phase II/III trial	p. 230
5.7.2 Adaptive design	p. 231
5.7.3 Statistical modeling	p. 232
5.7.4 Calculation	p. 233
5.7.5 Simulations	p. 235
5.8 Case study: Ablation device to treat atrial fibrillation	p. 241
5.9 Appendix: R Macros	p. 247
6 Special topics	p. 249
6.1 Incorporating historical data	p. 249
6.1.1 Standard hierarchical models	p. 250
6.1.2 Hierarchical power prior models	p. 252
6.2 Equivalence studies	p. 260
6.2.1 Statistical issues in bioequivalence	p. 261
6.2.2 Binomial response design	p. 263
6.2.3 2 x 2 crossover design	p. 265
6.3 Multiplicity	p. 268
6.3.1 Assessing drug safety	p. 269
6.3.2 Multiplicities and false discovery rate (FDR)	p. 275
6.4 Subgroup analysis	p. 276
6.4.1 Bayesian approach	p. 276
6.4.2 Bayesian decision theoretic approach	p. 277
6.5 Appendix: R Macros	p. 280
References	p. 281
Author index	p. 297
Index	p. 303

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