Table of contents for Adaptive design theory and implementation using SAS and R / Mark Chang.

Bibliographic record and links to related information available from the Library of Congress catalog.

Note: Contents data are machine generated based on pre-publication provided by the publisher. Contents may have variations from the printed book or be incomplete or contain other coding.


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Preface vii
1. Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Adaptive Design Methods in Clinical Trials . . . . . . . . . 2
1.2.1 Group Sequential Design . . . . . . . . . . . . . . . . 3
1.2.2 Sample Size Reestimation . . . . . . . . . . . . . . . 4
1.2.3 Drop-Loser Design . . . . . . . . . . . . . . . . . . . 5
1.2.4 Adaptive Randomization Design . . . . . . . . . . . . 6
1.2.5 Adaptive Dose-Finding Design . . . . . . . . . . . . . 7
1.2.6 Biomarker-Adaptive Design . . . . . . . . . . . . . . 8
1.2.7 Adaptive Treatment-Switching Design . . . . . . . . 9
1.2.8 Clinical Trial Simulation . . . . . . . . . . . . . . . . 10
1.2.9 Regulatory Aspects . . . . . . . . . . . . . . . . . . . 11
1.2.10 Characteristics of Adaptive Designs . . . . . . . . . . 12
1.3 FAQs about Adaptive Designs . . . . . . . . . . . . . . . . . 13
1.4 RoadMap . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.4.1 Computer Programs . . . . . . . . . . . . . . . . . . 18
2. Classic Design 19
2.1 Overview of Drug Development . . . . . . . . . . . . . . . . 19
2.2 Two-Group Superiority and Noninferiority Designs . . . . . 21
2.2.1 General Approach to Power Calculation . . . . . . . 21
2.2.2 Powering Trials Appropriately . . . . . . . . . . . . . 26
2.3 Two-Group Equivalence Trial . . . . . . . . . . . . . . . . . 28
2.3.1 Equivalence Test . . . . . . . . . . . . . . . . . . . . 28
2.3.2 Average Bioequivalence . . . . . . . . . . . . . . . . 31
2.3.3 Population and Individual Bio-equivalence . . . . . . 34
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2.4 Dose-Response Trials . . . . . . . . . . . . . . . . . . . . . . 35
2.4.1 Uni?ed Formulation for Sample Size . . . . . . . . . 36
2.4.2 Application Examples . . . . . . . . . . . . . . . . . 38
2.4.3 Determination of Contrast Coeó cients . . . . . . . . 41
2.4.4 SAS Macro for Power and Sample Size . . . . . . . . 43
2.5 Maximum Information Design . . . . . . . . . . . . . . . . . 45
2.6 Summary and Discussion . . . . . . . . . . . . . . . . . . . 45
3. Theory of Adaptive Design 51
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.2 General Theory . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.2.1 Stopping Boundary . . . . . . . . . . . . . . . . . . . 54
3.2.2 Formula for Power and Adjusted P-value . . . . . . . 55
3.2.3 Selection of Test Statistics . . . . . . . . . . . . . . . 57
3.2.4 Polymorphism . . . . . . . . . . . . . . . . . . . . . . 58
3.2.5 Adjusted Point Estimates . . . . . . . . . . . . . . . 59
3.2.6 Derivation of Con?dence Intervals . . . . . . . . . . . 63
3.3 Design Evaluation - Operating Characteristics . . . . . . . . 64
3.3.1 Stopping Probabilities . . . . . . . . . . . . . . . . . 64
3.3.2 Expected Duration of a Adaptive Trial . . . . . . . . 65
3.3.3 Expected Sample Sizes . . . . . . . . . . . . . . . . . 65
3.3.4 Conditional Power and Futility Index . . . . . . . . . 66
3.3.5 Utility and Decision Theory . . . . . . . . . . . . . . 66
3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4. Method with Direct Combination of P-values 71
4.1 Method Based on Individual P-values . . . . . . . . . . . . 71
4.2 Method Based on the Sum of P-values . . . . . . . . . . . . 76
4.3 Method with Linear Combination of P-values . . . . . . . . 81
4.4 Method with Product of P-values . . . . . . . . . . . . . . . 81
4.5 Event-Based Adaptive Design . . . . . . . . . . . . . . . . . 93
4.6 Adaptive Design for Equivalence Trial . . . . . . . . . . . . 95
4.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5. Method with Inverse-Normal P-values 101
5.1 Method with Linear Combination of Z-Scores . . . . . . . . 101
5.2 Lehmacher and Wassmer Method . . . . . . . . . . . . . . . 104
5.3 Classic Group Sequential Method . . . . . . . . . . . . . . . 109
5.4 Cui-Hung-Wang Method . . . . . . . . . . . . . . . . . . . . 112
5.5 Lan-DeMets Method . . . . . . . . . . . . . . . . . . . . . . 113
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5.5.1 Brownian Motion . . . . . . . . . . . . . . . . . . . . 113
5.5.2 Lan-DeMets Error-Spending Method . . . . . . . . . 115
5.6 Fisher-Shen Method . . . . . . . . . . . . . . . . . . . . . . 118
5.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
6. Implementation of N-Stage Adaptive Designs 121
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
6.2 Nonparametric Approach . . . . . . . . . . . . . . . . . . . 121
6.2.1 Normal Endpoint . . . . . . . . . . . . . . . . . . . . 121
6.2.2 Binary Endpoint . . . . . . . . . . . . . . . . . . . . 127
6.2.3 Survival Endpoint . . . . . . . . . . . . . . . . . . . . 131
6.3 Error-Spending Approach . . . . . . . . . . . . . . . . . . . 137
6.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
7. Conditional Error Function Method 139
7.1 Proschan-Hunsberger Method . . . . . . . . . . . . . . . . . 139
7.2 Denne Method . . . . . . . . . . . . . . . . . . . . . . . . . 142
7.3 Müller-Schäfer Method . . . . . . . . . . . . . . . . . . . . . 143
7.4 Comparison of Conditional Power . . . . . . . . . . . . . . . 143
7.5 Adaptive Futility Design . . . . . . . . . . . . . . . . . . . . 146
7.5.1 Utilization of an Early Futility Boundary . . . . . . . 146
7.5.2 Design with a Futility Index . . . . . . . . . . . . . . 147
7.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
8. Recursive Adaptive Design 149
8.1 P-clud Distribution . . . . . . . . . . . . . . . . . . . . . . . 149
8.2 Two-Stage Design . . . . . . . . . . . . . . . . . . . . . . . 151
8.2.1 Method Based on Product of P-values . . . . . . . . 152
8.2.2 Method Based on Sum of P-values . . . . . . . . . . 153
8.2.3 Method Based on Inverse-Normal P-values . . . . . . 154
8.2.4 Con?dence Interval and Unbiased Median . . . . . . 155
8.3 Error-Spending and Conditional Error Principles . . . . . . 158
8.4 Recursive Two-Stage Design . . . . . . . . . . . . . . . . . . 161
8.4.1 Sum of Stagewise P-values . . . . . . . . . . . . . . . 162
8.4.2 Product of Stagewise P-values . . . . . . . . . . . . . 164
8.4.3 Inverse-Normal Stagewise P-values . . . . . . . . . . 164
8.4.4 Con?dence Interval and unbiased Median . . . . . . 165
8.4.5 Application Example . . . . . . . . . . . . . . . . . . 166
8.5 Recursive Combination Tests . . . . . . . . . . . . . . . . . 170
8.6 Decision Function Method . . . . . . . . . . . . . . . . . . . 173
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8.7 Summary and Discussion . . . . . . . . . . . . . . . . . . . 174
9. Sample Size Adjustment 177
9.1 Opportunity . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
9.2 Adaptation Rules . . . . . . . . . . . . . . . . . . . . . . . . 178
9.2.1 Adjustment Based on Eñect Size Ratio . . . . . . . . 178
9.2.2 Adjustment Based on Conditional Power . . . . . . . 179
9.3 SAS Macros for Sample-Size Reestimation . . . . . . . . . . 180
9.4 Comparison of Sample Size Reesimation Methods . . . . . . 183
9.5 Analysis of Adaptive Design with N-Adjustment . . . . . . 189
9.5.1 Design without Possible Early Stopping . . . . . . . 189
9.5.2 Design with Possible Early Stopping . . . . . . . . . 191
9.6 Trial Example: Prevention of Myocardial Infarction . . . . 192
9.7 Summary and Discussion . . . . . . . . . . . . . . . . . . . 195
10. Multiple-Endpoint Adaptive Trials 199
10.1Multiplicity Issues . . . . . . . . . . . . . . . . . . . . . . . 199
10.1.1 Statistical Approaches to the Multiplicity . . . . . . 200
10.1.2 Single Step Procedures . . . . . . . . . . . . . . . . . 203
10.1.3 Step-wise procedures . . . . . . . . . . . . . . . . . . 205
10.1.4 Gatekeeper Approach . . . . . . . . . . . . . . . . . . 207
10.2Multiple-Endpoint Adaptive Design . . . . . . . . . . . . . 209
10.2.1 Fractals of Gatekeepers . . . . . . . . . . . . . . . . . 209
10.2.2 Single Primary with Secondary Endpoints . . . . . . 210
10.2.3 Co-primary with Secondary Endpoints . . . . . . . . 215
10.2.4 Tang-Geller Method . . . . . . . . . . . . . . . . . . 216
10.2.5 Summary and Discussion . . . . . . . . . . . . . . . . 218
11. Drop-Loser and Add-Arm Designs 221
11.1 Opportunity . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
11.1.1 Impact Overall Alpha level and Power . . . . . . . . 221
11.1.2 Reduction In Expected Trial Duration . . . . . . . . 222
11.2Method with Week Alpha-Control . . . . . . . . . . . . . . 223
11.2.1 Contract Test Based Method . . . . . . . . . . . . . 223
11.2.2 Sampson-Sill?s Method . . . . . . . . . . . . . . . . . 224
11.2.3 Normal Approximation Method . . . . . . . . . . . . 225
11.3Method with Strong Alpha-Control . . . . . . . . . . . . . . 226
11.3.1 Bauer-Kieser Method . . . . . . . . . . . . . . . . . . 226
11.3.2 MSP with Single-Step Multiplicity Adjustment . . . 226
11.3.3 A More Powerful Method . . . . . . . . . . . . . . . 227
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11.4 Application of SAS Macro for Drop-Loser Design . . . . . . 228
11.5 Summary and Discussion . . . . . . . . . . . . . . . . . . . 232
12. Biomarker-Adaptive design 235
12.1 Opportunities . . . . . . . . . . . . . . . . . . . . . . . . . . 235
12.2 Design with Classi?er Biomarker . . . . . . . . . . . . . . . 237
12.2.1 Setting the Scene . . . . . . . . . . . . . . . . . . . . 237
12.2.2 Classic Design with Classi?er Biomarker . . . . . . . 239
12.2.3 Adaptive Design with Classi?er Biomarker . . . . . . 242
12.3 Challenges in Biomarker Validation . . . . . . . . . . . . . . 247
12.3.1 Classic Design with Biomarker Primary-Endpoint . . 247
12.3.2 Treatment-Biomarker-Endpoint Relationship . . . . . 247
12.3.3 Multiplicity and False Positive Rate . . . . . . . . . 249
12.3.4 Validation of Biomarkers . . . . . . . . . . . . . . . . 249
12.3.5 Biomarkers in Reality . . . . . . . . . . . . . . . . . 250
12.4 Adaptive Design with Prognostic Biomarker . . . . . . . . . 251
12.4.1 Optimal Design . . . . . . . . . . . . . . . . . . . . . 251
12.4.2 Prognostic Biomarker in Designing Survival Trial . . 252
12.5 Adaptive Design with Predictive Marker . . . . . . . . . . . 253
12.6 Summary and Discussion . . . . . . . . . . . . . . . . . . . 253
13. Adaptive Treatment Switching and Crossover 257
13.1 Treatment Switching and Crossover . . . . . . . . . . . . . . 257
13.2Mixed Exponential Survival Model . . . . . . . . . . . . . . 258
13.2.1 Mixed Exponential Model . . . . . . . . . . . . . . . 258
13.2.2 Eñect of Patient Enrollment Rate . . . . . . . . . . . 261
13.2.3 Hypothesis Test and Power Analysis . . . . . . . . . 263
13.3 Threshold regression . . . . . . . . . . . . . . . . . . . . . . 265
13.3.1 First Hitting Time Model . . . . . . . . . . . . . . . 265
13.4Mixture of Wiener Processes . . . . . . . . . . . . . . . . . 266
13.4.1 Running Time . . . . . . . . . . . . . . . . . . . . . . 266
13.4.2 First Hitting Model . . . . . . . . . . . . . . . . . . . 267
13.4.3 Mixture of Wiener Processes . . . . . . . . . . . . . . 267
13.4.4 Statistical Inference . . . . . . . . . . . . . . . . . . . 268
13.4.5 Latent Event Time Model for Treatment Crossover . 269
13.5 Summary and discussions . . . . . . . . . . . . . . . . . . . 271
14. Response-Adaptive Allocation Design 273
14.1 Opportunities . . . . . . . . . . . . . . . . . . . . . . . . . . 273
14.1.1 Play-the-Winner Model . . . . . . . . . . . . . . . . 273
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14.1.2 Randomized Play-the-Winner Model . . . . . . . . . 274
14.1.3 Optimal RPW Model . . . . . . . . . . . . . . . . . . 275
14.2 Adaptive Design with RPW . . . . . . . . . . . . . . . . . . 277
14.3 General Response-Adaptive Randomization (RAR) . . . . . 280
14.3.1 SAS Macro for M-Arm RAR with Binary Endpoint . 281
14.3.2 SAS Macro for M-Arm RAR with Normal Endpoint 283
14.3.3 RAR for General Adaptive Designs . . . . . . . . . . 285
14.4 Summary and Discussion . . . . . . . . . . . . . . . . . . . 286
15. Adaptive Dose Finding Trial 289
15.1 Oncology Dose-escalation Trial . . . . . . . . . . . . . . . . 289
15.1.1 Dose Level Selection . . . . . . . . . . . . . . . . . . 289
15.1.2 Traditional Escalation Rules . . . . . . . . . . . . . . 290
15.1.3 Simulations Using SAS Macro . . . . . . . . . . . . . 293
15.2 Continual Reassessment Method (CRM) . . . . . . . . . . . 295
15.2.1 Probability Model for Dose-Response . . . . . . . . . 296
15.2.2 Prior Distribution of Parameter . . . . . . . . . . . . 296
15.2.3 Reassessment of Parameter . . . . . . . . . . . . . . 297
15.2.4 Assignment of Next Patient . . . . . . . . . . . . . . 298
15.2.5 Simulations of CRM . . . . . . . . . . . . . . . . . . 298
15.2.6 Evaluation of Dose-escalation Design . . . . . . . . . 300
15.3 Summary and Discussion . . . . . . . . . . . . . . . . . . . 302
16. Bayesian Adaptive Design 305
16.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 305
16.2 Intrinsic Bayesian Learning Mechanism . . . . . . . . . . . 306
16.3 Bayesian Basics . . . . . . . . . . . . . . . . . . . . . . . . . 308
16.3.1 Bayes?Rule . . . . . . . . . . . . . . . . . . . . . . . 308
16.3.2 Conjugate Family of Distributions . . . . . . . . . . 310
16.4 Trial Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
16.4.1 Bayesian for Classic Design . . . . . . . . . . . . . . 311
16.4.2 Bayesian power . . . . . . . . . . . . . . . . . . . . . 313
16.4.3 Frequentist Optimization . . . . . . . . . . . . . . . . 314
16.4.4 Bayesian Optimal Adaptive Designs . . . . . . . . . 316
16.5 Trial Monitoring . . . . . . . . . . . . . . . . . . . . . . . . 320
16.6 Analysis of Data . . . . . . . . . . . . . . . . . . . . . . . . 322
16.7 Interpretation of Outcomes . . . . . . . . . . . . . . . . . . 324
16.8 Regulatory Perspective . . . . . . . . . . . . . . . . . . . . . 325
16.9 Summary and Discussions . . . . . . . . . . . . . . . . . . . 326
17. Planning, Execution, Analysis, and Reporting 329
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17.1 Validity and Integrity . . . . . . . . . . . . . . . . . . . . . 329
17.2 Study Planning . . . . . . . . . . . . . . . . . . . . . . . . . 330
17.3Working with Regulatory Agency . . . . . . . . . . . . . . . 330
17.4 Trial Monitoring . . . . . . . . . . . . . . . . . . . . . . . . 331
17.5 Analysis and Reporting . . . . . . . . . . . . . . . . . . . . 333
17.6 Bayesian Approach . . . . . . . . . . . . . . . . . . . . . . . 333
17.7 Clinical Trial Simulation . . . . . . . . . . . . . . . . . . . . 333
17.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335
18. Paradox - Debates in Adaptive Designs 337
18.1My Standing Point . . . . . . . . . . . . . . . . . . . . . . . 337
18.2 Decision Theory Basics . . . . . . . . . . . . . . . . . . . . . 338
18.3 Evidence Measure . . . . . . . . . . . . . . . . . . . . . . . 340
18.3.1 Frequentist P-Value . . . . . . . . . . . . . . . . . . . 340
18.3.2 Maximum Likelihood Estimate . . . . . . . . . . . . 340
18.3.3 Bayes Factor . . . . . . . . . . . . . . . . . . . . . . 341
18.3.4 Bayesian P-Value . . . . . . . . . . . . . . . . . . . . 342
18.3.5 Repeated Looks . . . . . . . . . . . . . . . . . . . . . 343
18.3.6 Role of Alpha in Drug Development . . . . . . . . . 343
18.4 Statistical Principles . . . . . . . . . . . . . . . . . . . . . . 344
18.5 Behaviors of Statistical Principles in Adaptive Designs . . . 350
18.5.1 Suó ciency Principle . . . . . . . . . . . . . . . . . . 350
18.5.2 Minimum Suó ciency Principle and Eó ciency . . . . 351
18.5.3 Conditionality and Exchangeability Principles . . . . 352
18.5.4 Equal Weight Principle . . . . . . . . . . . . . . . . . 353
18.5.5 Consistency of Trial Results . . . . . . . . . . . . . . 354
18.5.6 Bayesian Aspects . . . . . . . . . . . . . . . . . . . . 354
18.5.7 Type-I Error, P-value, Estimation . . . . . . . . . . . 355
18.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356
Appendix A Random Number Generation 359
A.1 Random Number . . . . . . . . . . . . . . . . . . . . . . . . 359
A.2 Uniformly Distributed Random Number . . . . . . . . . . . 359
A.3 Inverse CDF Method . . . . . . . . . . . . . . . . . . . . . . 360
A.4 Acceptance-Rejection Methods . . . . . . . . . . . . . . . . 360
A.5 Multi-Variate Distribution . . . . . . . . . . . . . . . . . . . 361
Appendix B Implementing Adaptive Designs in R 365
Bibliography 377

Library of Congress Subject Headings for this publication:

Clinical trials -- Design.
Clinical trials -- Computer simulation.
Clinical trials -- Statistical methods.
Adaptive sampling (Statistics).
SAS (Computer file).
R (Computer program language).
Clinical Trials -- methods.
Research Design.
Biometry -- methods.
Data Interpretation, Statistical.
Software.