Sách Adaptive design methods in clinical trials (biostatistics)

Thiết kế thích nghi hiện đang dần trở thành một xu hướng trong thử nghiệm lâm sàng. Cuốn sách này bàn về các vấn đề liên quan đến phương pháp thiết kế thích nghi trong thử nghiệm. Sách gồm các phần 1 Introduction 1 1.1 What Is Adaptive Design? . . . . . . . . . . . . . . . . 3 1.2 Regulatory Perspectives . . . . . . . . . . . . . . . . . 6 1.3 Target Patient Population . . . . . . . . . . . . . . . . 8 1.4 Statistical Inference . . . . . . . . . . . . . . . . . . . 10 1.5 Practical Issues . . . . . . . . . . . . . . . . . . . . . . 11 1.5.1 Moving target patient population . . . . . . 12 1.5.2 Adaptive randomization . . . . . . . . . . . . 13 1.5.3 Adaptive hypotheses . . . . . . . . . . . . . . 14 1.5.4 Adaptive doseescalation trials . . . . . . . . 15 1.5.5 Adaptive group sequential design . . . . . . 15 1.5.6 Adaptive sample size adjustment . . . . . . 16 1.5.7 Adaptive seamless phase IIIII design . . . 17 1.5.8 Adaptive treatment switching . . . . . . . . 18 1.5.9 Bayesian and hybrid approaches . . . . . . 18 1.5.10 Clinical trial simulation . . . . . . . . . . . . 19 1.5.11 Case studies . . . . . . . . . . . . . . . . . . 19 1.6 Aims and Scope of the Book . . . . . . . . . . . . . . . 20 2 Protocol Amendment 23 2.1 Actual Patient Population . . . . . . . . . . . . . . . . 23 2.2 Estimation of Shift and Scale Parameters . . . . . . 26 2.2.1 The case where µActual is random and σActual is fixed . . . . . . . . . . . . . . . . 28 2.3 Statistical Inference . . . . . . . . . . . . . . . . . . . 31 2.3.1 Test for equality . . . . . . . . . . . . . . . . . 33 2.3.2 Test for noninferioritysuperiority . . . . . . 34 2.3.3 Test for equivalence . . . . . . . . . . . . . . . 34 2.4 Sample Size Adjustment . . . . . . . . . . . . . . . . 35 2.4.1 Test for equality . . . . . . . . . . . . . . . . . 35 2.4.2 Test for noninferioritysuperiority . . . . . . 36 2.4.3 Test for equivalence . . . . . . . . . . . . . . . 37 2.5 Statistical Inference with Covariate Adjustment . . 38 2.5.1 Population and assumption . . . . . . . . . . 382.5.2 Conditional inference . . . . . . . . . . . . . . 39 2.5.3 Unconditional inference . . . . . . . . . . . . 40 2.6 Concluding Remarks . . . . . . . . . . . . . . . . . . . 43 3 Adaptive Randomization 47 3.1 Conventional Randomization . . . . . . . . . . . . . . 48 3.2 TreatmentAdaptive Randomization . . . . . . . . . . 52 3.3 CovariateAdaptive Randomization . . . . . . . . . . 55 3.4 ResponseAdaptive Randomization . . . . . . . . . . 58 3.5 Issues with Adaptive Randomization . . . . . . . . . 70 3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . 73 4 Adaptive Hypotheses 75 4.1 Modifications of Hypotheses . . . . . . . . . . . . . . 76 4.2 Switch from Superiority to NonInferiority . . . . . . 78 4.3 Concluding Remarks . . . . . . . . . . . . . . . . . . . 87 5 Adaptive DoseEscalation Trials 89 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 89 5.2 CRM in Phase I Oncology Study . . . . . . . . . . . . 91 5.3 Hybrid FrequentistBayesian Adaptive Design . . . 93 5.4 Simulations . . . . . . . . . . . . . . . . . . . . . . . . 100 5.5 Concluding Remarks . . . . . . . . . . . . . . . . . . . 104 6 Adaptive Group Sequential Design 107 6.1 Sequential Methods . . . . . . . . . . . . . . . . . . . 108 6.2 General Approach for Group Sequential Design . . . 112 6.3 Early Stopping Boundaries . . . . . . . . . . . . . . . 114 6.4 Alpha Spending Function . . . . . . . . . . . . . . . . 122 6.5 Group Sequential Design Based on Independent pValues . . . . . . . . . . . . . . . . . . . . . . . . . . 123 6.6 Calculation of Stopping Boundaries . . . . . . . . . . 125 6.7 Group Sequential Trial Monitoring . . . . . . . . . . 128 6.8 Conditional Power . . . . . . . . . . . . . . . . . . . . 133 6.9 Practical Issues . . . . . . . . . . . . . . . . . . . . . . 135 7 Adaptive Sample Size Adjustment 137 7.1 Sample Size Reestimation without Unblinding Data . . . . . . . . . . . . . . . . . . . . . 138 7.2 Cui–Hung–Wang’s Method . . . . . . . . . . . . . . . 140 7.3 Proschan–Hunsberger’s Method . . . . . . . . . . . . 142 7.4 Muller–Schafer Method . . . . . . . . . . . . . . . . . 146 7.5 Bauer–Kohne Method ¨ . . . . . . . . . . . . . . . . . . 1467.6 Generalization of Independent pValue Approaches . . . . . . . . . . . . . . . . . . . . . . . . 148 7.7 InverseNormal Method . . . . . . . . . . . . . . . . . 157 7.8 Concluding Remarks . . . . . . . . . . . . . . . . . . . 158 8 Adaptive Seamless Phase IIIII Designs 161 8.1 Why a Seamless Design Is Efficient . . . . . . . . . . 161 8.2 StepWise Test and Adaptive Procedures . . . . . . . 162 8.3 Contrast Test and Naive pValue . . . . . . . . . . . . 163 8.4 Comparison of Seamless Designs . . . . . . . . . . . 165 8.5 DroptheLoser Adaptive Design . . . . . . . . . . . . 167 8.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . 171 9 Adaptive Treatment Switching 173 9.1 Latent Event Times . . . . . . . . . . . . . . . . . . . 174 9.2 Proportional Hazard Model with Latent Hazard Rate . . . . . . . . . . . . . . . . . . . . . . . . 177 9.2.1 Simulation results . . . . . . . . . . . . . . . . 179 9.3 Mixed Exponential Model . . . . . . . . . . . . . . . . 181 9.3.1 Biomarkerbased survival model . . . . . . . 182 9.3.2 Effect of patient enrollment rate . . . . . . . 184 9.3.3 Hypothesis test and power analysis . . . . . . 187 9.3.4 Application to trials with treatment switch . . . . . . . . . . . . . . . . . . . . . . . 189 9.4 Concluding Remarks . . . . . . . . . . . . . . . . . . . 193 10 Bayesian Approach 195 10.1 Basic Concepts of Bayesian Approach . . . . . . . . . 195 10.1.1 Bayes rule . . . . . . . . . . . . . . . . . . . . 196 10.1.2 Bayesian power . . . . . . . . . . . . . . . . . 200 10.2 MultipleStage Design for SingleArm Trial . . . . . 201 10.2.1 Classical approach for twostage design . . . . . . . . . . . . . . . . . . . . . . 202 10.2.2 Bayesian approach . . . . . . . . . . . . . . . 203 10.3 Bayesian Optimal Adaptive Designs . . . . . . . . . . 205 10.4 Concluding Remarks . . . . . . . . . . . . . . . . . . . 209 11 Clinical Trial Simulation 211 11.1 Simulation Framework . . . . . . . . . . . . . . . . . 212 11.2 Early Phases Development . . . . . . . . . . . . . . . 213 11.2.1 Dose limiting toxicity (DLT) and maximum tolerated dose (MTD) . . . . . . . . . . . . . 214 11.2.2 Doselevel selection . . . . . . . . . . . . . . 21411.2.3 Sample size per dose level . . . . . . . . . . 215 11.2.4 Doseescalation design . . . . . . . . . . . . 215 11.3 Late Phases Development . . . . . . . . . . . . . . . . 215 11.3.1 Randomization rules . . . . . . . . . . . . . . 216 11.3.2 Early stopping rules . . . . . . . . . . . . . . 216 11.3.3 Rules for dropping losers . . . . . . . . . . . 216 11.3.4 Sample size adjustment . . . . . . . . . . . . 217 11.3.5 Response–adaptive randomization . . . . . 217 11.3.6 Utilityoffset model . . . . . . . . . . . . . . 218 11.3.7 Nullmodel versus model approach . . . . . 219 11.3.8 Alpha adjustment . . . . . . . . . . . . . . . 219 11.4 Software Application . . . . . . . . . . . . . . . . . . . 220 11.4.1 Overview of ExpDesign studio . . . . . . . . 220 11.4.2 How to design a trial with ExpDesign studio . . . . . . . . . . . . . . . 222 11.4.3 How to design a conventional trial . . . . . 222 11.4.4 How to design a group sequential trial . . . 223 11.4.5 How to design a multistage trial . . . . . . 224 11.4.6 How to design a doseescalation trial . . . . 225 11.4.7 How to design an adaptive trial . . . . . . . 227 11.5 Examples . . . . . . . . . . . . . . . . . . . . . . . . . 227 11.5.1 Early phases development . . . . . . . . . . 228 11.5.2 Late phases development . . . . . . . . . . . 230 11.6 Concluding Remarks . . . . . . . . . . . . . . . . . . . 235 12 Case Studies 239 12.1 Basic Considerations . . . . . . . . . . . . . . . . . . . 239 12.1.1 Dose and dose regimen . . . . . . . . . . . . 240 12.1.2 Study endpoints . . . . . . . . . . . . . . . . 240 12.1.3 Treatment duration . . . . . . . . . . . . . . 240 12.1.4 Logistical considerations . . . . . . . . . . . 241 12.1.5 Independent data monitoring committee . . . . . . . . . . . . . . . . . . . . 241 12.2 Adaptive Group Sequential Design . . . . . . . . . . 241 12.2.1 Group sequential design . . . . . . . . . . . 241 12.2.2 Adaptation . . . . . . . . . . . . . . . . . . . 242 12.2.3 Statistical methods . . . . . . . . . . . . . . 243 12.2.4 Case study — an example . . . . . . . . . . . 243 12.3 Adaptive DoseEscalation Design . . . . . . . . . . . 244 12.3.1 Traditional doseescalation design . . . . . . 244 12.3.2 Adaptation . . . . . . . . . . . . . . . . . . . 245 12.3.3 Statistical methods . . . . . . . . . . . . . . 245 12.3.4 Case study — an example . . . . . . . . . . . 24512.4 Adaptive Seamless Phase IIIII Design . . . . . . . . 247 12.4.1 Seamless phase IIIII design . . . . . . . . . 247 12.4.2 Adaptation . . . . . . . . . . . . . . . . . . . 248 12.4.3 Methods . . . . . . . . . . . . . . . . . . . . . 248 12.4.4 Case study — some examples . . . . . . . . 249 12.4.5 Issues and recommendations . . . . . . . . . 252

Boca Raton, FL 33487-2742

© 2007 by Taylor & Francis Group, LLC

Chapman & Hall/CRC is an imprint of Taylor & Francis Group, an Informa business

No claim to original U.S Government works

Printed in the United States of America on acid-free paper

10 9 8 7 6 5 4 3 2 1

International Standard Book Number-10: 1-58488-776-1 (Hardcover)

International Standard Book Number-13: 978-1-58488-776-8 (Hardcover)

This book contains information obtained from authentic and highly regarded sources Reprinted material is quoted with permission, and sources are indicated A wide variety of references are listed Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the conse- quences of their use

No part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers.

For permission to photocopy or use material electronically from this work, please access www copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc (CCC)

222 Rosewood Drive, Danvers, MA 01923, 978-750-8400 CCC is a not-for-profit organization that provides licenses and registration for a variety of users For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged.

Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and

are used only for identification and explanation without intent to infringe.

Library of Congress Cataloging-in-Publication Data

1 Clinical trials 2 Adaptive sampling (Statistics) 3 Experimental design 4

Clinical trials Statistical methods I Chang, Mark II Title.

The primary objectives of the Biostatistics Book Series are to provideuseful reference books for researchers and scientists in academia, in-dustry, and government, and also to offer textbooks for undergraduateand/or graduate courses in the area of biostatistics This book series willprovide comprehensive and unified presentations of statistical designsand analyses of important applications in biostatistics, such as those inbiopharmaceuticals A well-balanced summary will be given of currentand recently developed statistical methods and interpretations for bothstatisticians and researchers/scientists with minimal statistical knowl-edge who are engaged in the field of applied biostatistics The series iscommitted to providing easy-to-understand, state-of-the-art referencesand textbooks In each volume, statistical concepts and methodologieswill be illustrated through real-world examples.

On March 16, 2004, the FDA released a report addressing the recentslowdown in innovative medical therapies being submitted to the FDAfor approval, “Innovation/Stagnation: Challenge and Opportunity onthe Critical Path to New Medical Products.” The report describes the ur-gent need to modernize the medical product development process — theCritical Path — to make product development more predictable and lesscostly Through this initiative, the FDA took the lead in the development

of a national Critical Path Opportunities List, to bring concrete focus tothese tasks As a result, the FDA released a Critical Path Opportuni-ties List that outlines 76 initial projects to bridge the gap between thequick pace of new biomedical discoveries and the slower pace at whichthose discoveries are currently developed into therapies two years later.The Critical Path Opportunities List consists of six broad topic areas:(i) development of biomarkers, (ii) clinical trial designs, (iii) bioinformat-ics, (iv) manufacturing, (v) public health needs, and (iv) pediatrics Asindicated in the Critical Path Opportunities Report, biomarker develop-ment and streamlining clinical trials are the two most important areasfor improving medical product development Streamlining clinicaltrials calls for advancing innovative trial designs such as adaptive de-signs to improve innovation in clinical development These 76 initialprojects are the most pressing scientific and/or technical hurdles caus-ing major delays and other problems in the drug, device, and/or biologic

improving medical product development.

This volume provides useful approaches for implementation of tive design methods to clinical trials to pharmaceutical research anddevelopment It covers statistical methods for various adaptive designssuch as adaptive group sequential design, N-adjustable design, adap-tive dose-escalation design, adaptive seamless phase II/III trial design(drop-the-losers design), adaptive randomization design, biomarker-adaptive design, adaptive treatment-switching design, adaptive-hypotheses design, and any combinations of the above designs It will

adap-be adap-beneficial to biostatisticians, medical researchers, pharmaceuticalscientists, and reviewers in regulatory agencies who are engaged in theareas of pharmaceutical research and development

Shein-Chung Chow

In recent years, the use of adaptive design methods in clinical trialshas attracted much attention from clinical investigators and biostatis-ticians Adaptations (i.e., modifications or changes) made to the trialand/or statistical procedures of on-going clinical trials based on accrueddata have been in practice for years in clinical research and develop-ment In the past several decades, we have adopted statistical proce-dures in the literature and applied them directly to the design of clinicaltrials originally planned by ignoring the fact that adaptations, modifi-cations, and/or changes have been made to the trials As pointed out

by the United States Food and Drug Administration (FDA), these cedures, however, may not be motivated by best clinical trial practice.Consequently, they may not be the best tools to handle certain situa-tions Adaptive design methods in clinical research and developmentare attractive to clinical scientists and researchers due to the followingreasons First, they do reflect medical practice in the real world Second,they are ethical with respect to both efficacy and safety (toxicity) of thetest treatment under investigation Third, they are not only flexible butalso efficient in clinical development, especially for early phase clinicaldevelopment However, there are issues regarding the adjustments of

pro-treatment estimations and p-values In addition, it is also a concern

that the use of adaptive design methods in a clinical trial may have led

to a totally different trial that is unable to address the scientific/medicalquestions the trial is intended to answer

In practice, there existed no universal definition of adaptive designmethods in clinical research until recently, when The PharmaceuticalResearch and Manufacturers of America (PhRMA) gave a formal defini-tion Most literature focuses on adaptive randomization with respect tocovariate, treatment, and/or clinical response; adaptive group sequen-tial design for interim analysis; and sample size re-assessment In thisbook, our definition is broader Adaptive design methods include anyadaptations, modifications, or changes of trial and/or statistical proce-dures that are made during the conduct of the trials Although adaptivedesign methods are flexible and useful in clinical research, little or noregulatory guidances/guidelines are available The purpose of this book

is to provide a comprehensive and unified presentation of the principles

of on-going clinical trials In addition, this book is intended to give awell-balanced summary of current regulatory perspectives and recentlydeveloped statistical methods in this area It is our goal to provide a com-plete, comprehensive, and updated reference and textbook in the area

of adaptive design and analysis in clinical research and development.Chapter 1 provides an introduction to basic concepts regarding theuse of adaptive design methods in clinical trials and some statisticalconsiderations of adaptive design methods Chapter 2 focuses on theimpact on target patient populations as the result of protocol amend-ments Also included in this chapter is the generalization of statisticalinference, which is drawn based on data collected from the actual pa-tient population as the result of protocol amendments, to the originallyplanned target patient population Several adaptive randomization pro-cedures that are commonly employed in clinical trials are reviewed inChapter 3 Chapter 4 studies the use of adaptive design methods inthe case where hypotheses are modified during the conduct of clinicaltrials Chapter 5 provides an overall review of adaptive design methodsfor dose selection, especially in dose finding and dose response relation-ship studies in early clinical development Chapter 6 introduces thecommonly used adaptive group sequential design methods in clinicaltrials Blinded procedures for sample size re-estimation are given inChapter 7 Statistical tests for seamless phase II/III adaptive designsand statistical inference for switching from one treatment to anotheradaptively, and the corresponding practical issues that may arise arestudied in Chapter 8 and Chapter 9, respectively Bayesian approachesfor the use of adaptive design methods in clinical trials are outlined inChapter 10 Chapter 11 provides an introduction to the methodology ofclinical trial simulation for evaluation of the performance of the adap-tive design methods under various adaptive designs that are commonlyused in clinical development Case studies regarding the implementa-tion of adaptive group sequential design, adaptive dose-escalation de-sign, and adaptive seamless phase II/III trial design in clinical trialsare discussed in Chapter 12

From Taylor & Francis, we would like to thank David Grubbs and

Dr Sunil Nair for providing us the opportunity to work on this book

We would like to thank colleagues from the Department of Biostatisticsand Bioinformatics and Duke Clinical Research Institute (DCRI) ofDuke University School of Medicine and Millennium Pharmaceuticals,Inc., for their support during the preparation of this book We wish toexpress our gratitude to the following individuals for their encourage-ment and support: Roberts Califf, M.D and John Hamilton, M.D of

Gilbert, M.D of Millennium Pharmaceuticals, Inc.; Greg Campbell,Ph.D of the U.S Food and Drug Administration; and many friends fromacademia, the pharmaceutical industry, and regulatory agencies.Finally, the views expressed are those of the authors and not nec-essarily those of Duke University School of Medicine and MillenniumPharmaceuticals, Inc We are solely responsible for the contents anderrors of this edition Any comments and suggestions will be very muchappreciated.

Shein-Chung Chow, Ph.D Duke University School of Medicine, Durham, NC

Mark Chang, Ph.D Millennium Pharmaceuticals, Inc., Cambridge, MA

1 Introduction 1

1.1 What Is Adaptive Design? . 3

1.2 Regulatory Perspectives . 6

1.3 Target Patient Population . 8

1.4 Statistical Inference . 10

1.5 Practical Issues . 11

1.5.1 Moving target patient population . 12

1.5.2 Adaptive randomization . 13

1.5.3 Adaptive hypotheses . 14

1.5.4 Adaptive dose-escalation trials . 15

1.5.5 Adaptive group sequential design . 15

1.5.6 Adaptive sample size adjustment . 16

1.5.7 Adaptive seamless phase II/III design . 17

1.5.8 Adaptive treatment switching . 18

1.5.9 Bayesian and hybrid approaches . 18

1.5.10 Clinical trial simulation . 19

1.5.11 Case studies . 19

1.6 Aims and Scope of the Book . 20

2 Protocol Amendment 23 2.1 Actual Patient Population . 23

2.2 Estimation of Shift and Scale Parameters . 26

2.2.1 The case whereµ Actualis random andσ Actualis fixed . 28

2.3 Statistical Inference . 31

2.3.1 Test for equality . 33

2.3.2 Test for non-inferiority/superiority . 34

2.3.3 Test for equivalence . 34

2.4 Sample Size Adjustment . 35

2.4.1 Test for equality . 35

2.4.2 Test for non-inferiority/superiority . 36

2.4.3 Test for equivalence . 37

2.5 Statistical Inference with Covariate Adjustment . 38

2.5.1 Population and assumption . 38

2.6 Concluding Remarks . 43

3 Adaptive Randomization 47 3.1 Conventional Randomization . 48

3.2 Treatment-Adaptive Randomization . 52

3.3 Covariate-Adaptive Randomization . 55

3.4 Response-Adaptive Randomization . 58

3.5 Issues with Adaptive Randomization . 70

3.6 Summary . 73

4 Adaptive Hypotheses 75 4.1 Modifications of Hypotheses . 76

4.2 Switch from Superiority to Non-Inferiority . 78

4.3 Concluding Remarks . 87

5 Adaptive Dose-Escalation Trials 89 5.1 Introduction . 89

5.2 CRM in Phase I Oncology Study . 91

5.3 Hybrid Frequentist-Bayesian Adaptive Design . 93

5.4 Simulations . 100

5.5 Concluding Remarks . 104

6 Adaptive Group Sequential Design 107 6.1 Sequential Methods . 108

6.2 General Approach for Group Sequential Design . 112

6.3 Early Stopping Boundaries . 114

6.4 Alpha Spending Function . 122

6.5 Group Sequential Design Based on Independent p-Values . 123

6.6 Calculation of Stopping Boundaries . 125

6.7 Group Sequential Trial Monitoring . 128

6.8 Conditional Power . 133

6.9 Practical Issues . 135

7 Adaptive Sample Size Adjustment 137 7.1 Sample Size Re-estimation without Unblinding Data . 138

7.2 Cui–Hung–Wang’s Method . 140

7.3 Proschan–Hunsberger’s Method . 142

7.4 Muller–Schafer Method . 146

7.5 Bauer–K¨ohne Method . 146

7.7 Inverse-Normal Method . 157

7.8 Concluding Remarks . 158

8 Adaptive Seamless Phase II/III Designs 161 8.1 Why a Seamless Design Is Efficient . 161

8.2 Step-Wise Test and Adaptive Procedures . 162

8.3 Contrast Test and Naive p-Value . 163

8.4 Comparison of Seamless Designs . 165

8.5 Drop-the-Loser Adaptive Design . 167

8.6 Summary . 171

9 Adaptive Treatment Switching 173 9.1 Latent Event Times . 174

9.2 Proportional Hazard Model with Latent Hazard Rate . 177

9.2.1 Simulation results . 179

9.3 Mixed Exponential Model . 181

9.3.1 Biomarker-based survival model . 182

9.3.2 Effect of patient enrollment rate . 184

9.3.3 Hypothesis test and power analysis . 187

9.3.4 Application to trials with treatment switch . 189

9.4 Concluding Remarks . 193

10 Bayesian Approach 195 10.1 Basic Concepts of Bayesian Approach . 195

10.1.1 Bayes rule . 196

10.1.2 Bayesian power . 200

10.2 Multiple-Stage Design for Single-Arm Trial . 201

10.2.1 Classical approach for two-stage design . 202

10.2.2 Bayesian approach . 203

10.3 Bayesian Optimal Adaptive Designs . 205

10.4 Concluding Remarks . 209

11 Clinical Trial Simulation 211 11.1 Simulation Framework . 212

11.2 Early Phases Development . 213

11.2.1 Dose limiting toxicity (DLT) and maximum tolerated dose (MTD) . 214

11.2.2 Dose-level selection . 214

11.3 Late Phases Development . 215

11.3.1 Randomization rules . 216

11.3.2 Early stopping rules . 216

11.3.3 Rules for dropping losers . 216

11.3.4 Sample size adjustment . 217

11.3.5 Response–adaptive randomization . 217

11.3.6 Utility-offset model . 218

11.3.7 Null-model versus model approach . 219

11.3.8 Alpha adjustment . 219

11.4 Software Application . 220

11.4.1 Overview of ExpDesign studio . 220

11.4.2 How to design a trial with ExpDesign studio . 222

11.4.3 How to design a conventional trial . 222

11.4.4 How to design a group sequential trial . 223

11.4.5 How to design a multi-stage trial . 224

11.4.6 How to design a dose-escalation trial . 225

11.4.7 How to design an adaptive trial . 227

11.5 Examples . 227

11.5.1 Early phases development . 228

11.5.2 Late phases development . 230

11.6 Concluding Remarks . 235

12 Case Studies 239 12.1 Basic Considerations . 239

12.1.1 Dose and dose regimen . 240

12.1.2 Study endpoints . 240

12.1.3 Treatment duration . 240

12.1.4 Logistical considerations . 241

12.1.5 Independent data monitoring committee . 241

12.2 Adaptive Group Sequential Design . 241

12.2.1 Group sequential design . 241

12.2.2 Adaptation . 242

12.2.3 Statistical methods . 243

12.2.4 Case study — an example . 243

12.3 Adaptive Dose-Escalation Design . 244

12.3.1 Traditional dose-escalation design . 244

12.3.2 Adaptation . 245

12.3.3 Statistical methods . 245

12.3.4 Case study — an example . 245

12.4.2 Adaptation . 248

12.4.3 Methods . 248

12.4.4 Case study — some examples . 249

12.4.5 Issues and recommendations . 252

In clinical research, the ultimate goal of a clinical trial is to evaluatethe effect (e.g., efficacy and safety) of a test treatment as compared to acontrol (e.g., a placebo control, a standard therapy, or an active controlagent) To ensure the success of a clinical trial, a well-designed studyprotocol is essential A protocol is a plan that details how a clinical trial

is to be carried out and how the data are to be collected and analyzed

It is an extremely critical and the most important document in clinicaltrials, since it ensures the quality and integrity of the clinical investi-gation in terms of its planning, execution, conduct, and the analysis ofthe data of clinical trials During the conduct of a clinical trial, adher-ence to the protocol is crucial Any protocol deviations and/or violationsmay introduce bias and variation to the data collected from the trial.Consequently, the conclusion drawn based on the analysis results ofthe data may not be reliable and hence may be biased or misleading.For marketing approval of a new drug product, the United States Foodand Drug Administration (FDA) requires that at least two adequateand well-controlled clinical trials be conducted to provide substantialevidence regarding the effectiveness of the drug product under inves-tigation (FDA, 1988) However, under certain circumstances, the FDAModernization Act (FDAMA) of 1997 includes a provision (Section 115

of FDAMA) to allow data from a single adequate and well-controlledclinical trial to establish effectiveness for risk/benefit assessment ofdrug and biological candidates for approval The FDA indicates thatsubstantial evidence regarding the effectiveness and safety of the drugproduct under investigation can only be provided through the conduct

of adequate and well-controlled clinical studies According to the FDA

1988 guideline for Format and Content of the Clinical and Statistical Sections of New Drug Applications, an adequate and well-controlled

study is defined as a study that meets the characteristics of the ing: (i) objectives, (ii) methods of analysis, (iii) design, (iv) selection ofsubjects, (v) assignment of subjects, (vi) participants of studies, (vii) as-sessment of responses, and (viii) assessment of effect In the study pro-tocol, it is essential to clearly state the study objectives of the study.Specific hypotheses that reflect the study objectives should be provided

follow-in the study protocol The study design must be valid follow-in order to provide

a fair and unbiased assessment of the treatment effect as compared to

a control Target patient population should be defined through the clusion/exclusion criteria to assure the disease conditions under study.Randomization procedures must be employed to minimize potential biasand to ensure the comparability between treatment groups Criteria forassessment of the response should be pre-defined and reliable Appro-priate statistical methods should be employed for assessment of theeffect Procedures such as blinding for minimization of bias should beemployed to maintain the validity and integrity of the trial

in-In clinical trials, it is not uncommon to adjust trial and/or cal methods at the planning stage and during the conduct of clinicaltrials For example, at the planning stage of a clinical trial, as an alter-

statisti-native to the standard randomization procedure, an adaptive

random-ization procedure based on treatment response may be considered fortreatment allocation During the conduct of a clinical trial, some adapta-tions (i.e., modifications or changes) to trial and/or statistical proceduresmay be made based on accrued data Typical examples for adaptations

of trial and/or statistical procedures of on-going clinical trials include,but are not limited to, the modification of inclusion/exclusion criteria,the adjustment of study dose or regimen, the extension of treatmentduration, changes in study endpoints, and modification in study designsuch as group sequential design and/or multiple-stage flexible designs(Table 1.1) Adaptations to trial and/or statistical procedures of on-goingclinical trials will certainly have an immediate impact on the target pop-ulation and, consequently, statistical inference on treatment effect ofthe target patient population In practice, adaptations or modifications

to trial and/or statistical procedures of on-going clinical trials are essary, which not only reflect real medical practice on the actual patient

nec-Table 1.1 Types of Adaptation in Clinical Trials

Prospective (by design) Interim analysis

Stop trial early due to safety, futility/efficacySample size re-estimation, etc

On-going (ad hoc) Inclusion/exclusion criteria

Dose or dose regimenTreatment duration, etc

Retrospective∗ Study endpoint

Switch from superiority to non-inferiority, etc

∗Adaptation at the end of the study prior to database lock or unblinding.

population with the disease under study, but also increase the ity of success for identifying the clinical benefit of the treatment underinvestigation.

probabil-The remainder of this chapter is organized as follows In the nextsection, a definition regarding so-called adaptive design is given.Section 1.2 provides regulatory perspectives regarding the use of adap-tive design methods in clinical research and development Sections 1.3and 1.4 describe the impact of an adaptive design on the targetpatient population and statistical inference following adaptations oftrial and/or statistical procedures, respectively Practical issues thatare commonly encountered when applying adaptive design methods inclinical research and development are briefly outlined in Section 1.5.Section 1.6 presents the aims and scope of the book

1.1 What Is Adaptive Design

On March 16, 2006, the FDA released a Critical Path OpportunitiesList that outlines 76 initial projects to bridge the gap between the quickpace of new biomedical discoveries and the slower pace at which thosediscoveries are currently developed into therapies (See, e.g., http://www.fda.gov/oc/initiatives/criticalpath.) The Critical Path Opportunities Listconsists of six broad topic areas of (i) development of biomarkers, (ii) clin-ical trial designs, (iii) bioinformatics, (iv) manufacturing, (v) publichealth needs, and (iv) pediatrics As indicated in the Critical PathOpportunities Report, biomarker development and streamlining clini-cal trials are the two most important areas for improving medical prod-uct development The streamlining clinical trials call for advancing in-novative trial designs such as adaptive designs to improve innovation

in clinical development

In clinical investigation of treatment regimens, it is not uncommon

to consider adaptations (i.e., modifications or changes) in early phaseclinical trials before initiation of large-scale confirmatory phase III tri-als We will refer to the application of adaptations to clinical trials as

adaptive design methods in clinical trials The adaptive design

meth-ods are usually developed based on observed treatment effects To allowwider flexibility, adaptations in clinical investigation of treatment reg-imen may include changes of sample size, inclusion/exclusion criteria,study dose, study endpoints, and methods for analysis (Liu, Proschan,and Pledger, 2002) Along this line, the PhRMA Working Group de-

fines an adaptive design as a clinical study design that uses

accumu-lating data to decide on how to modify aspects of the study as it ues, without undermining the validity and integrity of the trial (Gallo

contin-et al., 2006) As indicated by the PhRMA Working Group, the tation is a design feature aimed to enhance the trial, not a remedy

adap-for inadequate planning In other words, changes should be made by design and not on an ad hoc basis By design changes, however, do not

reflect real clinical practice In addition, they do not allow flexibility

As a result, in this book we will refer to an adaptive design of a ical trial as a design that allows adaptations or modifications to someaspects (e.g., trial and/or statistical procedures) of the trial after its initi-ation without undermining the validity and integrity of the trial (Chow,Chang, and Pong, 2005) Adaptations or modifications of on-going clini-cal trials that are commonly made to trial procedures include eligibilitycriteria, study dose or regimen, treatment duration, study endpoints,laboratory testing procedures, diagnostic procedures, criteria for evalu-ability, assessment of clinical responses, deletion/addition of treatmentgroups, and safety parameters In practice, during the conduct of theclinical trial, statistical procedures including randomization procedure

clin-in treatment allocation, study objectives/hypotheses, sample size assessment, study design, data monitoring and interim analysis pro-cedure, statistical analysis plan, and/or methods for data analysis areoften adjusted in order to increase the probability of success of the trial

re-by controlling the pre-specified type I error Note that in many cases,

an adaptive design is also known as a flexible design (EMEA, 2002).

Adaptive design methods are very attractive to clinical researchersand/or sponsors due to their flexibility, especially when there are pri-ority changes for budget/resources and timeline constraints, scientific/statistical justifications for study validity and integrity, medical con-siderations for safety, regulatory concerns for review/approval, and/orbusiness strategies for go/no-go decisions However, there is little or

no information available in regulatory requirements as to what level

of flexibility in modifications of trial and/or statistical procedures ofon-going clinical trials would be acceptable It is a concern that theapplication of adaptive design methods may result in a totally differ-ent clinical trial that is unable to address the scientific/medical ques-tions/hypotheses the clinical trial is intended to answer In addition,

an adaptive design suffers from the following disadvantages First, itmay result in a major difference between the actual patient population

as the result of adaptations made to the trial and/or statistical dures and the (original) target patient population The actual patientpopulation under study could be a moving target depending upon thefrequency and extent of modifications (flexibility) made to study param-eters Second, statistical inferences such as confidence interval and/orp-values on the treatment effect of the test treatment under study maynot be reliable Consequently, the observed clinical results may not be

proce-reproducible In recent years, the use of adaptive design methods inclinical trials has attracted much attention from clinical scientists andbiostatisticians.

In practice, adaptation or modification made to the trial and/or tical procedures during the conduct of a clinical trial based on accrueddata is usually recommended by the investigator, the sponsor, or anindependent datamonitoring committee Although the adaptation ormodification is flexible and attractive, it may introduce bias and con-sequently has an impact on statistical inference on the assessment oftreatment effect for the target patient population under study The com-plexity could be substantial depending upon the adaptation employed.Basically, the adaptation employed can be classified into three cate-gories: prospective (by design) adaptation, concurrent (or on-going adhoc) adaptation (by protocol amendment), and retrospective adaptation(after the end of the conduct of the trial, before database lock and/or un-blinding) As it can be seen, the on-going ad hoc adaptation has higherflexibility, while prospective adaptation is less flexible Both types ofadaptation require careful planning It should be noted that statisticalmethods for certain kinds of adaptation may not be available in the lit-erature As a result, some studies with complicated adaptation may bemore successful than others

statis-Depending upon the types of adaptation or modification made, monly employed adaptive design methods in clinical trials include, butare not limited to: (i) an adaptive group sequential design, (ii) anN-adjustable design, (iii) an adaptive seamless phase II/III design, (iv) adrop-the-loser design, (v) an adaptive randomization design, (vi) anadaptive dose-escalation design, (vii) a biomarker-adaptive design,(viii) an adaptive treatment-switching design, (ix) an adaptive-hypotheses design, and (x) any combinations of the above An adaptivegroup sequential design is an adaptive design that allows for prema-turely terminating a trial due to safety, efficacy, or futility based on in-terim analysis results, while an N-adjustable design is referred to as anadaptive design that allows for sample size adjustment or re-estimationbased on the observed data at interim A seamless phase II/III adap-tive trial design refers to a program that addresses within a singletrial objectives that are normally achieved through separate trials inphases IIb and III (Inoue, Thall, and Berry, 2002; Gallo et al., 2006)

com-An adaptive seamless phase II/III design would combine two separatetrials (i.e., a phase IIb trial and a phase III trial) into one trial andwould use data from patients enrolled before and after the adapta-tion in the final analysis (Maca, et al., 2006) A drop-the-loser design

is a multiple-stage adaptive design that allows dropping the inferiortreatment groups Adaptive randomization design refers to a design

that allows modification of randomization schedules Adaptive escalation design is often used in early phase clinical development toidentify the maximum tolerable dose, which is usually considered theoptimal dose for later phase clinical trials Biomarker-adaptive design

dose-is a design that allows for adaptations based on the response of ers such as genomic markers Adaptive treatment-switching design is adesign that allows the investigator to switch a patient’s treatment from

biomark-an initial assignment to biomark-an alternative treatment if there is evidence oflack of efficacy or safety of the initial treatment Adaptive-hypothesesdesign refers to a design that allows change in hypotheses based oninterim analysis results Any combinations of the above adaptive de-signs are usually referred to as multiple adaptive designs In practice,depending upon the study objectives of clinical trials, a multiple adap-tive design with several adaptations may be employed at the same time

In this case, statistical inference is often difficult if not impossible to tain These adaptive designs will be discussed further in later chapters

ob-of this book

In recent years, the use of these adaptive designs has received much

attention For example, the Journal of Biopharmaceutical Statistics

(JBS) published a special issue (Volume 15, Number 4) on AdaptiveDesign in Clinical Research in 2005 (Pong and Luo, 2005) This specialissue covers many statistical issues related to the use of adaptive designmethods in clinical research (see e.g., Chang and Chow, 2005; Chow,Chang, and Pong, 2005; Chow and Shao, 2005; Hommel, Lindig, andFaldum, 2005; Hung et al., 2005; Jennison and Turnbull, 2005; Kelly,Stallard, and Todd, 2005; Kelly et al., 2005; Li, Shih, and Wang, 2005;Proschan, 2005; Proschan, Leifer, and Liu, 2005; Wang and Hung, 2005).The PhRMA Working Group also published an executive summary onadaptive designs in clinical drug development to facilitate wide usage ofadaptive designs in clinical drug development (Gallo et al., 2006) Thisbook is intended to address concerns and/or practical issues that mayarise when applying adaptive design methods in clinical trials

1.2 Regulatory Perspectives

As pointed out by the FDA, modification of the design of an ment based on accrued data has been in practice for hundreds, if notthousands, of years in medical research In the past, we have had atendency to adopt statistical procedures in the literature and applythem directly to the design of clinical trials (Lan, 2002) However, sincethese procedures were not motivated by clinical trial practice, they maynot be the best tools to handle certain situations The impact of any

experi-adaptations made to trial and/or statistical methods before, during, andafter the conduct of trial could be substantial.

The flexibility in design and analysis of clinical trials in early phases

of the drug development is very attractive to clinical researchers/scientists and the sponsors However, its use in late phase II or phase IIIclinical investigations has led to regulatory concerns regarding its limi-tation of interpretation and extrapolation from trial results As there is

an increasing need for flexibility in design and analysis of clinical trials,the European Agency for the Evaluation of Medicinal Products (EMEA)published a concept paper on points to consider on methodological is-sues in confirmatory clinical trials with flexible design and analysisplan (EMEA, 2002, 2006) The EMEA’s points to consider discuss pre-requisites and conditions under which the methods could be acceptable

in confirmatory phase III trials for regulatory decision making pal pre-requisite for all considerations is that methods under investi-gation can provide correct p-values, unbiased estimates, and confidenceintervals for the treatment comparison(s) in an actual clinical trial As

Princi-a result, the use of Princi-an Princi-adPrinci-aptive design not only rPrinci-aises the importPrinci-ance

of well-known problems of studies with interim analyses (e.g., lack of

a sufficient safety database after early termination and over-running),but also bears new challenges to clinical researchers

From a regulatory point of view, blinded review of the database at terim analyses is a key issue in adaptive design During these blindedreviews, often the statistical analysis plan is largely modified At thesame time, more study protocols are submitted, where little or no in-formation on statistical methods is provided and relevant decisions aredeferred to a statistical analysis or even the blinded review, which hasled to a serious regulatory concern regarding the validity and integrity

in-of the trial In addition, what is the resultant actual patient population

of the study after the adaptations of the trial procedures, especiallywhen the inclusion/exclusion criteria are made, is a challenge to theregulatory review and approval process A commonly asked question

is whether the adaptive design methods have resulted in a totally ferent trial with a totally different target patient population In thiscase, is the usual regulatory review and approval process still applica-ble? However, there is little or no information in regulatory guidances

dif-or guidelines regarding regulatdif-ory requirement dif-or perception as to thedegree of flexibility that would be accepted by the regulatory agencies

In practice, it is suggested that regulatory acceptance should be fied based on the validity of statistical inference of the target patientpopulation

justi-It should be noted that although adaptations of trial and/or tical procedures are often documented through protocol amendments,

statis-standard statistical methods may not be appropriate and may lead to valid inference/conclusion regarding the target patient population As aresult, it is recommended that appropriate adaptive statistical methods

in-be employed Although several adaptive design methods for obtainingvalid statistical inferences on treatment effects available in the liter-ature (see, e.g., Hommel, 2001; Liu, Proschan, and Pledger, 2002) areuseful, they should be performed in a completely objective manner Inpractice, however, it can be very difficult to reach this objectivity inclinical trials due to external inferences and different interests fromthe investigators and sponsors

As a result, it is strongly recommended that a guidance/guideline foradaptive design methods be developed by the regulatory authorities

to avoid every intentional or unintentional manipulation of the tive design methods in clinical trials The guidance/guideline shoulddescribe in detail not only the standards for use of adaptive designmethods in clinical trials, but also the level of modifications in an adap-tive design that is acceptable to the regulatory agencies In addition,any changes in the process of regulatory review/approval should also

adap-be clearly indicated in such a guidance/guideline It should adap-be noted thatthe adaptive design methods have been used in the review/approval pro-cess of regulatory submissions for years, though it may not have beenrecognized until recently

1.3 Target Patient Population

In clinical trials, patient populations with certain diseases under studyare usually described by the inclusion/exclusion criteria Patients whomeet all inclusion criteria and none of the exclusion criteria are quali-

fied for the study We will refer to this patient population as the target

patient population For a given study endpoint such as clinical response,time to disease progression, or survival in the therapeutic area of on-cology, we may denote the target patient population by (µ,σ), where µ

is the population mean of the study endpoint andσ denotes the

pop-ulation standard deviation of the study endpoint For a comparativeclinical trial comparing a test treatment and a control, the effect size ofthe test treatment adjusted for standard deviation is defined as

µ T − µ C

where µ T and µ C are the population means for the test treatmentand the control, respectively Based on the collected data, statisti-cal inference such as confidence interval and p-value on the effect

size of the test treatment can then be made for the target patientpopulation.

In practice, as indicated earlier, it is not uncommon to modify trialprocedures due to some medical and/or practical considerations dur-ing the conduct of the trial Trial procedures of a clinical trial arereferred to as operating procedures, testing procedures, and/or diag-nostic procedures that are to be employed in the clinical trial As aresult, trial procedures of a clinical trial include, but are not limited

to, the inclusion/exclusion criteria, the selection of study dose or imen, treatment duration, laboratory testing, diagnostic procedures,and criteria for evaluability In clinical trials, we refer to statisticalprocedures of a clinical trial as statistical procedures and/or statisticalmodels/methods that are employed at planning, execution, and con-duct of the trial as well as the analysis of the data Thus, statisticalprocedures of a clinical trial include power analysis for sample sizecalculation at planning stage, randomization procedure for treatmentallocation prior to treatment, modifications of hypotheses, change instudy endpoint, and sample size re-estimation at interim during theconduct of the trial As indicated in the FDA 1988 guideline and theInternational Conference on Harmonization (ICH) Good Clinical Prac-tices (GCP) guideline (FDA, 1988; ICH, 1996), a well-designed protocolshould detail how the clinical trial is to be carried out Any deviationsfrom the protocol and/or violations of the protocol will not only dis-tort the original patient population under study, but will also introducebias and variation to the data collected from the trial Consequently,conclusions drawn based on statistical inference obtained from theanalysis results of the data may not be applied to the original targetpatient population

reg-In clinical trials, the inclusion/exclusion criteria and study dose orregimen and/or treatment duration are often modified due to slowenrollment and/or safety concerns during the conduct of the trial Forexample, at screening, we may disqualify too many patients with strin-gent inclusion/exclusion criteria Consequently, the enrollments may betoo slow to meet the timeline of the study In this case, a typical approach

is to relax the inclusion/exclusion criteria to increase the enrollment

On the other hand, the investigators may wish to have the flexibility

to adjust the study dose or regimen to achieve optimal clinical benefit

of the test treatment during the trial The study dose may be reducedwhen there are significant toxicities and/or adverse experiences In ad-dition, the investigators may wish to extend the treatment duration

to (i) reach best therapeutic effect or (ii) achieve the anticipated eventrate based on accrued data during the conduct of trial These modifi-cations of trial procedures are commonly encountered in clinical trials

Modifications of trial procedures are usually accomplished through tocol amendments, which detail rationales for changes and the impact

pro-of the modifications

Any adaptations made to the trial and/or statistical procedures mayintroduce bias and/or variation to the data collected from the trial Con-sequently, it may result in a similar but slightly different target patient

population We will refer to such a patient population as the actual

pa-tient population under study As mentioned earlier, in practice, it is aconcern whether adaptations made to the trial and/or statistical proce-dures could lead to a totally different trial with a totally different targetpatient population In addition, it is of interest to determine whetherstatistical inference obtained based on clinical data collected from theactual patient population could be applied to the originally planned tar-get patient population These issues will be studied in the next chapter

1.4 Statistical Inference

As discussed in the previous section, modifications of trial procedureswill certainly introduce bias/variation to the data collected from thetrial The sources of these biases and variations can be classified into one

of the following four categories: (i) expected and controllable,(ii) expected but not controllable, (iii) unexpected but controllable, and(iv) unexpected and not controllable For example, additional bias/variation is expected but not controllable when there is a change instudy dose or regimen and/or treatment duration For changes in labo-ratory testing procedures and/or diagnostic procedures, bias/variation

is expected but controllable by (i) having experienced technicians to form the tests or (ii) conducting appropriate training for inexperiencedtechnicians Bias/variation due to patient non-compliance to trial pro-cedures is usually unexpected but is controllable by improving theprocedure for patients’ compliance Additional bias/variation due to un-expected and uncontrollable sources is usually referred to as the randomerror of the trial

per-In practice, appropriate statistical procedures should be employed toidentify and eliminate/control these sources of bias/variation wheneverpossible In addition, after the adaptations of the trial procedures, es-pecially the inclusion/exclusion criteria, the target patient populationhas been changed to the actual patient population under study In thiscase, how to generalize the conclusion drawn based on statistical infer-ence of the treatment effect derived from clinical data observed fromthe actual patient population to the original target patient population

is a challenge to clinical scientists It, however, should be noted that

although all modifications of trial procedures and/or statistical dures are documented through protocol amendments, it does not implythat the collected data are free of bias/variation Protocol amendmentsshould not only provide rationales for changes but also detail how thedata are to be collected and analyzed following the adaptations of trialand/or statistical procedures In practice, it is not uncommon to ob-serve the following inconsistencies following major adaptations of trialand/or statistical procedures of a clinical trial: (i) a right test for wronghypotheses, (ii) a wrong test for the right hypotheses, (iii) a wrong testfor wrong hypotheses, and (iv) the right test for the right hypotheses butinsufficient power Each of these inconsistencies will result in invalidstatistical inferences and conclusions regarding the treatment effectunder investigation.

proce-Flexibility in statistical procedures of a clinical trial is very attractive

to the investigator and/or sponsors However, it suffers the tage of invalid statistical inference and/or misleading conclusion if theimpact is not carefully managed Liu, Proschan, and Pledger (2002)provided a solid theoretical foundation for adaptive design methods inclinical development under which not only a general method for pointestimation, confidence interval, hypotheses testing, and overall p-valuecan be obtained, but also its validity can be rigorously established How-ever, they do not take into consideration the fact that the target patientpopulation has become a moving target patient population as the result

disadvan-of adaptations made to the trial and/or statistical procedures throughprotocol amendments This issue will be further discussed in the nextchapter

The ICH GCP guideline suggests that a thoughtful statisticalanalysis plan (SAP), which details statistical procedures (includingmodels/methods), should be employed for data collection and analysis.Any deviations from the SAP and violations of the SAP could decreasethe reliability of the analysis results, and consequently the conclusiondrawn from these analysis results may not be valid

In summary, the use of adaptive design methods in clinical trials mayhave an impact on the statistical inference on the target patient popula-tion under study Statistical inference obtained based on data collectedfrom the actual patient population as the result of modifications made

to the trial procedures and/or statistical procedures should be adjustedbefore it can be applied to the original target patient population

1.5 Practical Issues

As indicated earlier, the use of adaptive design methods in clinicaltrials has received much attention because it allows adaptations of

trial and/or statistical procedures of on-going clinical trials The bility for adaptations to study parameters is very attractive to clinicalscientists and sponsors However, from regulatory point of view, sev-eral questions have been raised First, what level of adaptations to thetrial and/or statistical procedures would be acceptable to the regulatoryauthorities? Second, what are the regulatory requirements and stan-dards for review and approval process of clinical data obtained fromadaptive clinical trials with different levels of adaptations to trial and/orstatistical procedures of on-going clinical trials? Third, has the clinicaltrial become a totally different clinical trial after the adaptations tothe trial and/or statistical procedures for addressing the study objec-tives of the originally planned clinical trial? These concerns are nec-essarily addressed by the regulatory authorities before the adaptivedesign methods can be widely accepted in clinical research and devel-opment.

flexi-In addition, from the scientific/statistical point of view, there are alsosome concerns regarding (i) whether the modifications to the trial pro-cedures have resulted in a similar but different target patient popu-lation, (ii) whether the modifications of hypotheses have distorted thestudy objectives of the trial, (iii) whether the flexibility in statistical pro-cedures has led to biased assessment of clinical benefit of the treatmentunder investigation In this section, practical issues associated with theabove questions that are commonly encountered in clinical trials whenapplying adaptive design methods of on-going clinical trials are brieflydescribed These issues include moving target patient population as theresult of protocol amendments, adaptive randomization, adaptive hy-potheses, adaptive dose-escalation trials, adaptive group sequential de-signs, adaptive sample size adjustment, adaptive seamless phase II/IIItrial design, dropping the losers adaptively, adaptive treatment switch-ing, Bayesian and hybrid approaches, clinical trial simulation, and casestudies

1.5.1 Moving target patient population

In clinical trials, it is important to define the patient population withthe disease under study This patient population is usually describedbased on eligibility criteria, i.e., the inclusion and exclusion criteria

This patient population is referred to as the target patient population.

As indicated in Chow and Liu (2003), a target patient population is ally roughly defined by the inclusion criteria and then fine-tuned by theexclusion criteria to minimize heterogeneity of the patient population.When adaptations are made to the trial and/or statistical procedures,

usu-especially the inclusion/exclusion criteria during the conduct of thetrial, the mean response of the primary study endpoint of the targetpatient population may be shifted with heterogeneity in variability As

a result, adaptations made to trial and/or statistical procedures couldlead to a similar but different patient population We will refer to this

resultant patient population as the actual patient population In

prac-tice, it is a concern that a major (or significant) adaptation could result

in a totally different patient population During the conduct of a clinicaltrial, if adaptations are made frequently, the target patient population

is in fact a moving target patient population (Chow, Chang, and Pong,

2005) As a result, it is difficult to draw an accurate and reliable cal inference on the moving target patient population Thus, in practice,

statisti-it is of interest to determine the impact of adaptive design methods onthe target patient population and consequently the corresponding sta-tistical inference and power analysis for sample size calculation Moredetails are given in the next chapter

1.5.2 Adaptive randomization

In clinical trials, randomization models such as the population model,the invoked population model, and the randomization model with themethod of complete randomization and permuted-block randomizationare commonly used to ensure a balanced allocation of patients to treat-ment within either a fixed total sample size or a pre-specified blocksize (Chow and Liu, 2003) The population model is referred to as theconcept that clinicians can draw conclusions for the target patient pop-ulation based on the selection of a representative sample drawn fromthe target patient population by some random procedure (Lehmann,1975; Lachin, 1988) The invoked population model is referred to asthe process of selecting investigators first and then selecting patients

at each selected investigator’s site As it can be seen, neither the lection of investigators nor the recruitment of patients at the selectedinvestigator’s site is random However, treatment assignment is ran-dom Thus, the invoked randomization model allows the analysis of theclinical data as if they were obtained under the assumption that thesample is randomly selected from a homogeneous patient population.Randomization model is referred to as the concept of randomization orpermutation tests based on the fact that the study site selection andpatient selection are not random, but the assignment of treatments topatients is random Randomization model/method is a critical compo-nent in clinical trials because statistical inference based on the datacollected from the trial relies on the probability distribution of the

se-sample, which in turn depends upon the randomization procedure ployed.

em-In practice, however, it is also of interest to adjust the probability ofassignment of patients to treatments during the study to increase theprobability of success of the clinical study This type of randomization

is called adaptive randomization because the probability of the ment to which a current patient is assigned is adjusted based on theassignment of previous patients The randomization codes based on themethod of adaptive randomization cannot be prepared before the studybegins This is because the randomization process is performed at thetime a patient is enrolled in the study, whereas adaptive randomizationrequires information on previously randomized patients In practice,the method of adaptive randomization is often applied with respect totreatment, covariate, or clinical response Therefore, the adaptive ran-domization is known as treatment-adaptive randomization, covariate-adaptive randomization, or response-adaptive randomization Adaptiverandomization procedures could have an impact on sample size requiredfor achieving a desired statistical power and consequently statistical in-ference on the test treatment under investigation More details regard-ing the adaptive randomization procedures described above and theirimpact on sample size calculation and statistical inference is given inChapter 3 of this book

treat-1.5.3 Adaptive hypotheses

Modifications of hypotheses during the conduct of a clinical trial monly occur due to the following reasons: (i) an investigational methodhas not yet been validated at the planning stage of the study, (ii) in-formation from other studies is necessary for planning the next stage

com-of the study, (iii) there is a need to include new doses, and (iv) mmendations from a pre-established data safety monitoring committee(Hommel, 2001) In clinical research, it is not uncommon to have morethan one set of hypotheses for an intended clinical trial These hypothe-ses may be classified as primary hypotheses and secondary hypothesesdepending upon whether they are the primary study objectives or sec-ondary study objectives In practice, a pre-specified overall type I errorrate is usually controlled for testing the primary hypotheses However,

reco-if the investigator is interested in controlling the overall type I error ratefor testing secondary hypotheses, then techniques for multiple testingare commonly employed Following the ideas of Bauer (1999), Kieser,Bauer, and Lehmacher (1999), and Bauer and Kieser (1999) for generalmultiple testing problems, Hommel (2001) applied the same techniques

to obtain more flexible strategies for adaptive modifications of ses based on accrued data at interim by changing the weights of hy-potheses, changing a prior order, or even including new hypotheses.The method proposed by Hommel (2001) enjoys the following advan-tages First, it is a very general method in the sense that any type ofmultiple testing problems can be applied Second, it is mathematicallycorrect Third, it is extremely flexible, which allows not only changes todesign, but also changes to the choice of hypotheses or weights for themduring the course of the study In addition, it also allows the addition

hypothe-of new hypotheses Modifications hypothe-of hypotheses can certainly have animpact on statistical inference for assessment of treatment effect Morediscussions are given in Chapter 4 of this book

1.5.4 Adaptive dose-escalation trials

In clinical research, the response in a dose response study could be a

biological response for safety or efficacy For example, in a dose-toxicitystudy, the goal is to determine the maximum tolerable dose (MTD) Onthe other hand, in a dose-efficacy response study, the primary objective

is usually to address one or more of the following questions: (i) Is thereany evidence of the drug effect? (ii) What is the nature of the dose-response? and (iii) What is the optimal dose? In practice, it is always aconcern as to how to evaluate dose–response relationship with limitedresources within a relatively tight time frame This concern led to a pro-posed design that allows less patients to be exposed to the toxicity andmore patients to be treated at potentially efficacious dose levels Such

a design also allows pharmaceutical companies to fully utilize their sources for development of more new drug products In Chapter 5, weprovide a brief background of dose escalation trials in oncology trials

re-We will review the continued reassessment method (CRM) proposed

by O’Quigley, Pepe, and Fisher (1990) in phase I oncology trials Wewill study the hybrid frequentist-Bayesian adaptive approach for bothefficacy and toxicity (Chang, Chow, and Pong, 2005) in detail

1.5.5 Adaptive group sequential design

In practice, flexible trials are usually referred to as trials that utilizeinterim monitoring based on group sequential and adaptive methodo-logy for (i) early stopping for clinical benefit or harm, (ii) early stoppingfor futility, (iii) sample size re-adjustment, and (iv) re-designing thestudy in midstream In practice, an adaptive group sequential design isvery popular due to the following two reasons First, clinical endpoint

is a moving target The sponsors and/or investigators may change theirminds regarding clinically meaningful effect size after the trial starts.Second, it is a common practice to request a small budget at the designand then seek supplemental funding for increasing the sample size afterseeing the interim data.

To protect the overall type I error rate in an adaptive design withrespect to adaptations in some design parameters, many authors haveproposed procedures using observed treatment effects This leads to thejustification for the commonly used two-stage adaptive design, in whichthe data from both stages are independent and the first data set is usedfor adaptation (see, e.g., Proschan and Hunsberger, 1995; Cui, Hung,and Wang, 1999; Liu and Chi, 2001) In recent years, the concept of two-stage adaptive design has led to the development of the adaptive groupsequential design The adaptive group sequential design is referred to

as a design that uses observed (or estimated) treatment differences atinterim analyses to modify the design and sample size adaptively (e.g.,Shen and Fisher, 1999; Cui, Hung, and Wang, 1999; Posch and Bauer,1999; Lehmacher and Wassmer, 1999)

In clinical research, it is desirable to speed up the trial and at thesame time reduce the cost of the trial The ultimate goal is to get theproducts to the marketplace sooner As a result, flexible methods foradaptive group sequential design and monitoring are the key factorsfor achieving this goal With the availability of new technology such aselectronic data capture, adaptive group sequential design in conjunctionwith the new technology will provide an integrated solution to the lo-gistical and statistical complexities of monitoring trials in flexible wayswithout biasing the final conclusions Further discussion regarding theapplication of adaptive group sequential designs in clinical trials can

be found in Chapter 6

1.5.6 Adaptive sample size adjustment

As indicated earlier, an adaptive design is very attractive to the sponsors

in early clinical development because it allows modifications of the trial

to meet specific needs during the trial within limited budget/resourcesand target timelines However, an adaptive design suffers from a loss ofpower to detect a clinically meaningful difference of the target patientpopulation under the actual patient population due to bias/variationthat has been introduced to the trial as the result of changes in studyparameters during the conduct of the trial To account for the expectedand/or unexpected bias/variation, statistical procedures for sample sizecalculation are necessarily adjusted for achieving the desired power

For example, if the study, regimen, and/or treatment duration havebeen adjusted during the conduct of the trial, not only the actual pa-tient population may be different from the target patient population,but also the baseline for the clinically meaningful difference to be de-tected may have been changed In this case, sample size required forachieving the desired power for correctly detecting a clinically mean-ingful difference based on clinical data collected from the actual patientpopulation definitely needs adjustment.

It should be noted that procedures for sample size calculation based

on power analysis of an adaptive design with respect to specific changes

in study parameters are very different from the standard methods.The procedures for sample size calculation could be very complicatedfor a multiple adaptive design (or a combined adaptive design) involv-ing more than one study parameter In practice, statistical tests for anull hypothesis of no treatment difference may not be tractable under

a multiple adaptive design Chapter 7 provides several methods foradaptive sample size adjustment which are useful for multiple adaptivedesigns

1.5.7 Adaptive seamless phase II/III design

A phase II clinical trial is often a dose-response study, where the goal is

to find the appropriate dose level for the phase III trials It is desirable

to combine phase II and III so that the data can be used more ciently and duration of the drug development can be reduced A seam-less phase II/III trial design refers to a program that addresses within asingle trial objective what is normally achieved through separate trials

effi-in phases IIb and III (Gallo et al., 2006) An adaptive seamless phaseII/III design is a seamless phase II/III trial design that would use datafrom patients enrolled before and after the adaptation in the final anal-ysis (Maca et al., 2006) Bauser and Kieser (1999) provide a two-stagemethod for this purpose, where the investigators can terminate the trialentirely or drop a subset of regimens for lack of efficacy after the firststage As pointed out by Sampson and Sill (2005), their procedure ishighly flexible, and the distributional assumptions are kept to a mini-mum This results in a usual design in a number of settings However,because of the generality of the method, it is difficult, if not impossi-ble, to construct confidence intervals Sampson and Sill (2005) derived

a uniformly most powerful conditionally unbiased test for normal point For other types of endpoints, no results match Sampson and Sill’sresults Thus, it is suggested that computer trial simulation be used insuch cases More information is provided in Chapter 8

end-1.5.8 Adaptive treatment switching

For evaluation of the efficacy and safety of a test treatment for sive diseases such as oncology and HIV, a parallel-group active-controlrandomized clinical trial is often conducted Under the parallel-groupactive-control randomized clinical trial, qualified patients are randomlyassigned to receive either an active control (a standard therapy or atreatment currently available in the marketplace) or a test treatmentunder investigation Patients are allowed to switch from one treatment

progres-to another, due progres-to ethical consideration, if there is lack of responses orthere is evidence of disease progression In practice, it is not uncommonthat up to 80% of patients may switch from one treatment to another.This certainly has an impact on the evaluation of the efficacy of the testtreatment Despite allowing a switch between two treatments, manyclinical studies are to compare the test treatment with the active-controlagent as if no patients had ever switched Sommer and Zeger (1991) re-ferred to the treatment effect among patients who complied with treat-ment as biological efficacy Branson and Whitehead (2002) widened theconcept of biological efficacy to encompass the treatment effect as ifall patients adhered to their original randomized treatments in clinicalstudies allowing treatment switch

The problem of treatment switching is commonly encountered in cer trials In cancer trials, most investigators would allow patients to getoff the current treatment and switch to another treatment (either thestudy treatment or a rescue treatment) when there is progressed dis-ease, due to ethical consideration However, treatment switching dur-ing the conduct of the trial has presented a challenge to clinical scien-tists (especially biostatisticians) regarding the analysis of some primarystudy endpoints such as median survival time Under certain assump-tions, Shao, Chang, and Chow (2005) proposed a method for estimation

can-of median survival time when treatment switching occurs during thecourse of the study Several methods for adaptive treatment switchingare reviewed in Chapter 9

1.5.9 Bayesian and hybrid approaches

Drug development is a sequence of drug decision-making processes,where decisions are made based on the constantly updated informa-tion The Bayesian approach naturally fits this mechanism However,

in the current regulatory setting, the Bayesian approach is not ready

as the criteria for approval of a drug Therefore, it is desirable to useBayesian approaches to optimize the trial and increase the probability

of success under current frequentist criterion for approval In the nearfuture, it is expected that drug approval criteria will become Bayesian.

In addition, full Bayesian is important because it can provide more formative information and optimal criteria for drug approval based onrisk-benefit ratio rather than subjectively (arbitrarily) setα = 0.05, as

in-frequentists did

1.5.10 Clinical trial simulation

It should be noted that for a given adaptive design, it is very likely thatadaptations will be made to more than one study parameter simulta-neously during the conduct of the clinical trial To assess the impact ofchanges in specific study parameters, a typical approach is to perform asensitivity analysis by fixing other study parameters In practice, the as-sessment of the overall impact of changes in each study parameter isalmost impossible due to possible confounding and/or masking effectsamong changes in study parameters As a result, it is suggested that aclinical trial simulation be conducted to examine the individual and/oroverall impact of changes in multiple study parameters In addition,the performance of a given adaptive design can be evaluated throughthe conduct of a clinical trial simulation in terms of its sensitivity,robustness, and/or empirical probability of reproducibility It, however,should be noted that a clinical trial simulation are conducted in such

a way that the simulated clinical data are able to reflect the real ation of the clinical trial after all of the modifications are made to thetrial procedures and/or statistical procedures In practice, it is then sug-gested that assumptions regarding the sources of bias/variation as theresults of modifications of the on-going trial be identified and be takeninto consideration when conducting the clinical trial simulation

situ-1.5.11 Case studies

As pointed out by Li (2006), the use of adaptive design methods vides a second chance to re-design the trial after seeing data inter-nally or externally at interim However, it may introduce so-called op-erational biases such as selection bias, method of evaluations, earlywithdrawal, modification of treatments, etc Consequently, the adap-tation employed may inflate type I error rate Li (2006) suggested acouple of principles when implementing adaptive designs in clinicaltrials: (i) adaptation should not alter trial conduct, and (ii) type I errorshould be preserved Following these principles, some studies with com-plicated adaptations may be more successful than others The successful

pro-experience for certain adaptive designs in clinical trials is important

to investigators in clinical research and development For illustrationpurposes, some successful case studies including the implementation of

an adaptive group sequential design (Cui, Hung, and Wang, 1999), anadaptive dose-escalation design (Chang and Chow, 2005), and adaptiveseamless phase II/III trial design (Maca et al., 2006) are provided in thelast chapter of this book

1.6 Aims and Scope of the Book

This is intended to be the first book entirely devoted to the use of tive design methods in clinical trials It covers all of the statistical is-sues that may occur at various stages of adaptive design and analysis

adap-of clinical trials It is our goal to provide a useful desk reference and thestate-of-the art examination of this area to scientists and researchersengaged in clinical research and development, those in governmentregulatory agencies who have to make decisions in the pharmaceuti-cal review and approval process, and biostatisticians who provide thestatistical support for clinical trials and related clinical investigation.More importantly, we would like to provide graduate students in theareas of clinical development and biostatistics an advanced textbook

in the use of adaptive design methods in clinical trials We hope thatthis book can serve as a bridge between the pharmaceutical industry,government regulatory agencies, and academia

The scope of this book covers statistical issues that are commonlyencountered when modifications of study procedures and/or statisticalprocedures are made during the course of the study In this chapter, thedefinition, regulatory requirement, target patient population, statisti-cal issues of adaptive design, and analysis for clinical trials have beendiscussed In the next chapter, the impact of modifications made to trialprocedures and/or statistical procedures on the target patient popula-tion, statistical inference, and power analysis for sample size calculation

as the result of protocol amendments are discussed In Chapter 3, ous adaptive randomization procedures for treatment allocation will bediscussed Chapter 4 covers adaptive design methods for modifications

vari-of hypotheses including the addition vari-of new hypotheses after the view of interim data Chapter 5 provides an overall review of adaptivedesign methods for dose selection, especially in dose-finding and dose-response relationship studies in early clinical development Chapter 6introduces the commonly used adaptive group sequential design in clin-ical trials Blinded procedures for sample size re-estimation are given inChapter 7 Statistical tests for adaptive seamless phase II/III designs,and statistical inference for switching from one treatment to another

re-adaptively and the corresponding practical issues that may arise arestudied in Chapter 8 and Chapter 9, respectively Bayesian and hy-brid approaches for the use of adaptive design methods in clinical trialsare outlined in Chapter 10 Chapter 11 provides an introduction to themethodology of clinical trial simulation for evaluation of the perfor-mance of the adaptive design methods under various adaptive designsthat are commonly used in clinical development Case studies regard-ing the implementation of adaptive group sequential design, adaptivedose-escalation design, and adaptive seamless phase II/III trial design

in clinical trials are discussed in Chapter 12

For each chapter, whenever possible, real examples from clinical als are included to demonstrate the use of adaptive design methods

tri-in cltri-inical trials tri-includtri-ing cltri-inical/statistical concepts, tri-interpretations,and their relationships and interactions Comparisons regarding therelative merits and disadvantages of the adaptive design methods inclinical research and development are discussed whenever deemed ap-propriate In addition, if applicable, topics for future research are pro-vided All computations in this book are performed using 8.20 of SAS.Other statistical packages such as S-plus can also be applied

Protocol Amendment

In clinical trials, it is not uncommon to modify the trial and/or tistical procedures of on-going trials due to scientific/statistical justi-fications, medical considerations, regulatory concerns, and/or businessinterest/decisions When modifications of trial and/or statistical proce-dures are made, a protocol amendment is necessarily filed to individualinstitutional review boards (IRBs) for review/approval before imple-mentation As discussed in the previous chapter, major (or significant)adaptation of trial and/or statistical procedures of a on-going clinicaltrial could alter the target patient population of the trial and conse-quently lead to a totally different clinical trial that is unable to answerthe scientific/medical questions the trial is intended to address In thischapter, we will examine the impact of protocol amendments on the tar-get patient population through the assessment of a shift parameter, ascale parameter, and a sensitivity index The impact of protocol amend-ments on power for detecting a clinically significant difference and thecorresponding statistical inference are also studied

sta-In the next section, a shift parameter, a scale parameter, and a sitivity index that provide useful measures of change in the targetpatient population as the result of protocol amendments are defined.Section 2.2 provides estimates of the shift and scale parameters of thetarget patient population and the sensitivity index both conditionallyand unconditionally, assuming that the resultant actual patient popula-tion after modifications is random The impact of protocol amendments

sen-on statistical inference and power analysis for sample size calculatisen-on

is discussed in Sections 2.3 and 2.4, respectively Section 2.5 providesstatistical inference for treatment effect when there are protocol amend-ments, assuming that changes in protocol are made based on one or afew covariates A brief concluding remark is given in the last section ofthis chapter

2.1 Actual Patient Population

As indicated earlier, in clinical trials it is not uncommon to modify trialand/or statistical procedures of on-going trials However, it should benoted that any adaptation made to the trial and/or statistical procedures