Randomization in Clinical Trials: Theory and Practice (Wiley Series in Probability and Statistics)

286 Pages·2002·13.52 MB·English

by  William F. Rosenberger

Randomization in
Clinical Trials
This page intentionally left blank
Randomization in
Clinical Trials
Theory and Practice
WILLIAM F. ROSENBERGER
University of Maryland, Baltimore County
JOHN M. LACHIN
The George Washington University
WILEY-
INTERSCIENCE
A JOHN WILEY & SONS, INC., PUBLICATION
This text is printed on acid-free paper. ©
Copyright © 2002 by John Wiley & Sons, Inc., New York. All rights reserved.
Published simultaneously in Canada.
No part of this publication may be reproduced, stored in a retrieval system or transmitted in any
form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise,
except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without
either the prior written permission of the Publisher, or authorization through payment of the
appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA
01923, [phone], fax [phone]. Requests to the Publisher for permission should be
addressed to the Permissions Department, John Wiley & Sons, Inc., 605 Third Avenue, New York,
NY 10158-0012, [phone], fax [phone], E-Mail: PERMREQ @ WILEY.COM.
For ordering and customer service, call 1-800-CALL WILEY.
Library of Congress Cataloging-in-Publication Data is available.
ISBN 0-471-23626-8
Printed in the United States of America
10 9 8 7 6 5 4 3 21
Contents
Preface xiii
1 Randomization and the Clinical Trial 1
1.1 Introduction 1
1.2 Causation and association 2
1.3 Randomized clinical trials 6
1.4 Ethics of randomization 9
1.5 Problems 12
1.6 References 13
2 Issues in the Design of Clinical Trials 15
2.1 Introduction 15
2.2 Study outcomes 15
2.3 Sources of bias 18
2.3.1 Standardization and masking 18
2.3.2 Statistical analysis philosophy 20
2.3.3 Losses to follow-up and noncompliance 21
2.3.4 Covariates 21
2.4 Experimental design 22
2.5 Recruitment and follow-up 23
V
vi CONTENTS
2.6 Determining the number of randomized subjects 25
2.6.1 Development of the main formula 25
2.6.2 Example 27
2.6.3 Survival trials 28
2.6.4 Adjustment for noncompliance 30
2.6.5 Additional considerations 31
2.7 Problems 31
2.8 References 33
3 Randomization for Balancing Treatment Assignments 35
3.1 Introduction 35
3.2 The balancing properties of complete randomization 36
3.3 Random allocation rule 37
3.4 Truncated binomial design 39
3.5 Permuted block designs 41
3.6 Efron's biased coin design 43
3.7 Wei's urn design 45
3.8 Generalized biased coin designs 47
3.9 Comparison of balancing properties 48
3.10 K > 2 treatments 48
3.11 Restricted randomization for unbalanced allocation 50
3.12 Problems 51
3.13 References 51
4 Balancing on Known Covariates 53
4.1 Introduction 53
4.2 Stratified randomization 54
4.3 Treatment imbalances in stratified trials 56
4.4 Covariate-adaptive randomization 57
4.4.1 Zelen'srule 57
4.4.2 The Pocock-Simon procedure 58
4.4.3 Wei's marginal urn design 59
4.5 Optimal design based on a linear model 59
4.6 Conclusions 61
4.7 Problems 62
4.8 References 62
CONTENTS vii
5 The Effects of Unobserved Covariates 65
5.1 Introduction 65
5.2 A bound on the probability of a covariate imbalance 66
5.3 Accidental bias 67
5.4 Maximum eigenvalue of S 68
T
5.5 Accidental bias for the biased coin designs 69
5.6 Simulation results 70
5.7 Conclusions 72
5.8 Problems 72
5.9 References 73
6 Selection Bias 75
6.1 Introduction 75
6.2 The Blackwell-Hodges model 76
6.3 Selection bias for the random allocation rule 79
6.4 Selection bias for the truncated binomial design 79
6.5 Selection bias in a permuted block design 81
6.5.1 Permuted blocks using the random allocation
rule 81
6.5.2 Variable block design 82
6.5.3 Permuted blocks with truncated binomial
randomization 83
6.5.4 Conclusions 83
6.6 Selection bias for Efron's biased coin design 84
6.7 Wei's urn design 85
6.8 Generalized biased coin designs 85
6.9 Controlling selection bias in practice 87
6.10 Problems 87
6.11 References 88
7 Randomization as a Basis for Inference 89
7.1 Introduction 89
7.2 The population model 89
7.3 The randomization model 92
7.4 Permutation tests 95
7.5 Linear rank tests 96
7.6 Variance of the linear rank test 99
7.7 Optimal rank scores 101
7.8 Construction of exact permutation tests 103
viii CONTENTS
1.9 Large sample permutation tests 104
7.10 Group sequential monitoring 106
7.11 Problems 109
7.12 References 110
7.13 Appendix A: DCCT Data 112
7.14 Appendix B: SAS Code for Conditional U/D(0,l)
Linear Rank Test 113
8 Inference for Stratified, Blocked, and
Covariate-Adjusted Analyses 117
8.1 Introduction 117
8.2 Stratified analysis 118
8.2.1 The Mantel-Haenszel procedure 118
8.2.2 Linear rank test 120
8.2.3 Small strata 124
8.3 Stratified versus unstratified tests with stratified
randomization 124
8.4 Efficiency of stratified randomization in a stratified
analysis 126
8.5 Post-hoc stratified and subgroup analyses 130
8.5.1 Complete randomization 131
8.5.2 Random allocation rule 134
8.5.3 Permuted block randomization with a random
allocation rule 134
8.5.4 Wei's urn design 135
8.5.5 Pre-and post-stratified analyses 136
8.6 Analyses with missing data 138
8.7 Covariate-adjusted analyses 139
8.8 Example 1: The Neonatal Inhaled Nitric Oxide Study 141
8.8.1 A Blocked Randomization and Analysis 141
8.8.2 A Post-Stratified Blocked Analysis 142
8.8.3 Covariate-Adjusted Blocked Analysis 143
8.9 Example 2: The Diabetes Control and Complications
Trial 144
8.9.1 A Stratified Urn Randomization and Analysis 144
8.9.2 Urn Analysis with Missing Data 145
8.9.3 Covariate-Adjusted Urn Analysis 145
8.10 Conclusions 146
8.11 Problems 147
CONTENTS ix
8.12 References 147
9 Randomization in Practice 149
9.1 Introduction 149
9.2 Stratification 150
9.3 Characteristics of randomization procedures 151
9.3.1 Consideration of selection bias 151
9.3.2 Implications for analysis 153
9.4 Choice of randomization procedure 153
9.4.1 Complete randomization 154
9.4.2 Forced-balance designs 154
9.4.3 Permuted block design 154
9.4.4 Biased coin-type designs 155
9.5 Generation and checking of sequences 155
9.6 Implementation 158
9.6.1 Packaging and labeling 158
9.6.2 The actual randomization 160
9.7 Special situations 161
9.8 Some examples 164
9.8.1 The Optic Neuritis Treatment Trial 164
9.8.2 Vesnarinone in congestive heart failure 164
9.8.3 The Diabetes Control and Complications Trial 164
9.8.4 Captopril in diabetic nephropathy 165
9.8.5 The Diabetes Prevention Program 165
9.8.6 Adjuvant chemotherapy for locally invasive
bladder cancer 166
9.9 Problems 166
9.10 References 167
10 Response-Adaptive Randomization 169
10.1 Introduction 169
10.2 Historical notes 170
10.2.1 Roots in bandit problems 170
10.2.2 Roots in sequential stopping problems 171
10.2.3 Roots in randomization 172
10.3 Optimal allocation 173
10.4 Response-adaptive randomization to target R* 176
10.4.1 Sequential maximum likelihood procedure 176
10.4.2 Doubly-adaptive biased coin design 178