Clinical Trial Design: Bayesian and Frequentist Adaptive Methods

355 Pages·2012·6.54 MB·English

by  Guosheng Yin(auth.)

CLINICAL TRIAL DESIGN
WILEY SERIES IN PROBABILITY AND STATISTICS
Established by WALTER A. SHEWHART and SAMUEL S. WILKS
Editors: David J. Balding, Noel A. C. Cressie, GarrettM. Fitzmaurice,
Harvey Goldstein, Iain M. Johnstone, Geert Molenberghs, David W. Scott,
Adrian F. M. Smith, Ruey S. Tsay, Sanford Weisberg
Editors Emeriti: Vic Barnett, J. Stuart Hunter, Joseph B. Kadane, Jozef L. Teugels
A complete list of the titles in this series appears at the end of this volume.
CLINICAL TRIAL DESIGN
Bayesian and Frequentist
Adaptive Methods
Guosheng Yin
The University of Hong Kong
The University of Texas M. D. Anderson Cancer Center
WILEY
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Library of Congress Cataloging-in-Publkation Data:
Yin, Guosheng.
Clinical trial design: Bayesian and frequentist adaptive methods / Guosheng Yin.
p. ; cm. — (Wiley series in probability and statistics)
Includes bibliographical references and indexes.
ISBN 978-0-470-58171-1 (cloth)
I. Title. II. Series: Wiley series in probability and statistics.
[DNLM: 1. Clinical Trials as Topic—methods. 2. Bayes Theorem. 3. Statistics as Topic—methods.
QV771]
LC-classification not assigned
610.72'4—dc23 2011033589
Printed in the United States of America.
10 9 8 7 6 5 4 3 21
To my mother and
the memory of my father
CONTENTS
Preface xv
1 Introduction 1
1.1 What Are Clinical Trials? 1
1.2 Brief History and Adaptive Designs 2
1.3 Modern Clinical Trials 5
1.4 New Drug Development 7
1.5 Emerging Challenges 10
1.6 Summary 10
2 Fundamentals of Clinical Trials 13
2.1 Key Components of Clinical Trials 13
2.1.1 Protocol 13
2.1.2 Primary Objective 15
2.1.3 Eligibility Criteria and Accrual 15
2.1.4 Power and Sample Size 16
2.1.5 Blinding 17
2.1.6 Randomization 18
2.1.7 Parallel and Crossover Designs 19
vii
VU! CONTENTS
2.1.8 Data Collection 20
2.1.9 Adverse Events 20
2.1.10 Closeout 21
2.2 Pharmacokinetics and Pharmacodynamics 22
2.3 Phases I-IV of Clinical Trials 25
2.3.1 Phase I 25
2.3.2 Phase II 25
2.3.3 Phase III 26
2.3.4 Phase IV 26
2.4 Summary 27
Exercises 28
Frequentist versus Bayesian Statistics 29
3.1 Basic Statistics 29
3.1.1 Probability and Univariate Distributions 29
3.1.2 Multivariate Distributions 35
3.1.3 Copula 38
3.1.4 Convergence of Sequences of Random Variables 39
3.2 Frequentist Methods 41
3.2.1 Maximum Likelihood Estimation 41
3.2.2 Method of Moments 42
3.2.3 Generalized Method of Moments 43
3.2.4 Confidence Interval 44
3.2.5 Hypothesis Testing 46
3.2.6 Generalized Linear Model and Quasi-Likelihood 49
3.2.7 Random Effects Model 51
3.3 Survival Analysis 52
3.3.1 Kaplan-Meier Estimator 52
3.3.2 Log-Rank Test 56
3.3.3 Proportional Hazards Model 56
3.3.4 Cure Rate Model 58
3.4 Bayesian Methods 58
3.4.1 Bayes'Theorem 58
3.4.2 Prior Elicitation 61
3.4.3 Conjugate Prior Distribution 63
3.4.4 Bayesian Generalized Method of Moments 65
3.4.5 Credible Interval 66
3.4.6 Bayes Factor 67
3.4.7 Bayesian Model Averaging 68
CONTENTS ix
3.4.8 Bayesian Hierarchical Model 69
3.4.9 Decision Theory 71
3.5 Markov Chain Monte Carlo 72
3.5.1 Inversion Sampling 72
3.5.2 Rejection Sampling 72
3.5.3 Gibbs Sampler 73
3.5.4 Metropolis-Hastings Algorithm 73
3.6 Summary 74
Exercises 75
Phase 1 Trial Design 77
4.1 Maximum Tolerated Dose 77
4.2 Initial Dose and Spacing 79
4.3 3 + 3 Design 82
4.4 A + B Design 85
4.5 Accelerated Titration Design 87
4.5.1 Acceleration and Escalation 87
4.5.2 Modeling Toxicity with Random Effects 87
4.6 Biased Coin Dose-Finding Method 89
4.7 Continual Reassessment Method 90
4.7.1 Probability Model 90
4.7.2 Likelihood and Posterior 91
4.7.3 Dose-Finding Algorithm 93
4.7.4 Simulation Study 94
4.8 Bayesian Model Averaging Continual Reassessment Method 95
4.8.1 Skeleton of the CRM 95
4.8.2 BMA-CRM 96
4.8.3 Dose-Finding Algorithm 97
4.8.4 Simulation Study 97
4.8.5 Sensitivity Analysis 102
4.9 Escalation with Overdose Control 103
4.10 Bayesian Hybrid Design 105
4.10.1 Algorithm- versus Model-Based Dose Finding 105
4.10.2 Bayesian Hypothesis Testing 106
4.10.3 Dose-Finding Algorithm 109
4.10.4 Simulation Study 109
4.11 Summary 111
Exercises 112
X CONTENTS
Phase II Trial Design 115
5.1 Gehan's Two-Stage Design 117
5.2 Simon's Two-Stage Design 119
5.3 Bayesian Phase II Design with Posterior Probability 122
5.4 Bayesian Phase II Design with Predictive Probability 124
5.5 Predictive Monitoring in Randomized Phase II Trials 126
5.6 Predictive Probability with Adaptive Randomization 129
5.6.1 Bayesian Adaptive Randomization 129
5.6.2 Predictive Probability 130
5.6.3 Parameter Calibration 131
5.6.4 Simulation Study 133
5.6.5 Posterior versus Predictive Trial Monitoring 135
5.7 Bayesian Phase II Design with Multiple Outcomes 136
5.7.1 Bivariate Binary Outcomes 136
5.7.2 Stopping Boundaries 137
5.8 Phase I/II Design with Bivariate Binary Data 140
5.8.1 Motivation 140
5.8.2 Likelihood and Prior 141
5.8.3 Odds Ratio and Dose-Finding Algorithm 144
5.8.4 Numerical Comparison 147
5.9 Phase I/II Design with Times to Toxicity and Efficacy 149
5.9.1 Bivariate Times to Toxicity and Efficacy 150
5.9.2 Areas Under Survival Curves 151
5.9.3 Dose-Finding Algorithm 153
5.10 Summary 156
Exercises 156
Phase III Trial Design 159
6.1 Power and Sample Size 159
6.1.1 Statistical Hypothesis 160
6.1.2 Classification of Phase III Trials 161
6.1.3 Superiority versus Noninferiority 163
6.2 Comparing Means for Continuous Outcomes 164
6.2.1 Testing for Equality 164
6.2.2 Superiority Trial 168
6.2.3 Noninferiority Trial 169
6.2.4 Equivalence Trial 170
6.3 Comparing Proportions for Binary Outcomes 172
6.3.1 Testing for Equality 172
CONTENTS xi
6.3.2 Sample Size Formula with Unpooled Variance 175
6.3.3 Superiority Trial 176
6.3.4 Noninferiority Trial 177
6.3.5 Equivalence Trial 179
6.4 Sample Size with Survival Data 180
6.4.1 Comparison of Survival Curves 180
6.4.2 Parametric Approach under Exponential Distribution 181
6.4.3 Nonparametric Approach with Counting Process 183
6.5 Sample Size for Correlated Data 186
6.5.1 Linear Model with Continuous Data 186
6.5.2 Logistic Model with Binary Data 187
6.6 Group Sequential Methods 188
6.6.1 Multiple Testing 189
6.6.2 Pocock's Design 191
6.6.3 O'Brien and Fleming's Design 193
6.6.4 Information and Asymptotic Distribution 195
6.6.5 Stopping Boundary Computation 198
6.6.6 Sample Size and Inflation Factor 200
6.6.7 Futility Stopping Boundary 202
6.6.8 Repeated Confidence Intervals 204
6.7 Adaptive Designs 204
6.7.1 Motivation 204
6.7.2 Fisher's Combination Criterion 206
6.7.3 Conditional Power 207
6.7.4 Adaptive Group Sequential Method 209
6.7.5 Self-Designing Strategy 211
6.8 Causality and Noncompliance 213
6.8.1 Causal Inference and Counterfactuals 213
6.8.2 Noncompliance and Intent-to-Treat Analysis 214
6.8.3 Instrumental Variable Approach 216
6.9 Post-Approval Trial—Phase IV 218
6.9.1 Limitations of Phase I—III Trials 218
6.9.2 Drug Withdrawal 218
Exercises 220
7 Adaptive Randomization 223
7.1 Introduction 223
7.2 Simple Randomization 225
7.3 Permuted Block Randomization 226