Randomization in Clinical Trials: Theory and Practice

by William F. Rosenberger, John M. Lachin

Overview

Winner of the 2002 Associaton of American Publishers Professional/Scholarly Publishing Division Award

The role of randomization techniques in clinical trials has become increasingly important. This comprehensive guide combines both the applied aspects of randomization in clinical trials with a probabilistic treatment of properties of randomization. Taking an unabashedly non-Bayesian and nonparametric approach to inference, the book focuses on the linear rank test under a randomization model, with added discussion on likelihood-based inference as it relates to sufficiency and ancillarity. Developments in stochastic processes and applied probability are also given where appropriate. Intuition is stressed over mathematics, but not without a clear development of the latter in the context of the former.

Providing a consolidated review of the field, the book includes relevant and practical discussions of:

• The benefits of randomization in terms of reduction of bias
• Randomization as a basis for inference
• Covariate-adaptive and response-adaptive randomization
• Current philosophies, controversies, and new developments

With ample problem sets, theoretical exercises, and short computer simulations using SAS, Randomization in Clinical Trials: Theory and Practice is equally useful as a standard textbook in biostatistics graduate programs as well as a reliable reference for biostatisticians in practice.

Product Details

ISBN-13:	9780471236269
Publisher:	Wiley
Publication date:	07/11/2002
Series:	Wiley Series in Probability and Statistics Series , #430
Edition description:	Older Edition
Pages:	288
Product dimensions:	6.50(w) x 9.60(h) x 0.90(d)

About the Author

WILLIAM F. ROSENBERGER is an associate professor (with tenure) of mathematics and statistics at The University of Maryland, Baltimore County. He is also an adjunct associate professor of epidemiology and preventive medicine at the University of Maryland School of Medicine. He serves as a biostatistical consultant on several clinical trials data and safety monitoring boards for the NIH, VA, and industry. He received his PhD in mathematical statistics from The George Washington University.

JOHN M. LACHIN III is presently Professor of Biostatistics and Epidemiology, and of Statistics, at The George Washington University. He holds a ScD in biostatistics from the University of Pittsburgh. He also serves as Director of the Graduate Program in Biostatistics and as Director of the Coordinating Center for two nationwide studies in diabetes.

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Table of 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
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's rule	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
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 [Sigma subscript T]	68
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
7.9	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, 1) 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
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
10.5	Urn models	179
10.5.1	The generalized Friedman's urn model	179
10.5.2	The randomized play-the-winner rule	180
10.5.3	Ternary urn models	183
10.6	Treatment effect mappings	184
10.7	Problems	185
10.8	References	186
11	Inference for Response-Adaptive Randomization	191
11.1	Introduction	191
11.2	Population-based inference	191
11.2.1	The likelihood	191
11.2.2	Sufficiency	193
11.2.3	Bias of the maximum likelihood estimators	193
11.2.4	Confidence interval procedures	195
11.3	Power	196
11.4	Randomization-based inference	199
11.5	Problems	201
11.6	References	201
12	Response-Adaptive Randomization in Practice	203
12.1	Basic assumptions	203
12.2	Bias, masking, and consent	204
12.3	Logistical issues	206
12.4	Selection of a procedure	206
12.5	Benefits of response-adaptive randomization	207
12.6	Some examples	209
12.6.1	The Extracorporeal Membrane Oxygenation trial	209
12.6.2	The fluoxetine trial	210
12.7	Conclusions	211
12.8	Problems	211
12.9	References	212
13	Some Useful Results in Large Sample Theory	215
13.1	Some useful central limit theorems	215
13.2	Martingales and sums of dependent random variables	217
13.3	Martingales and triangular arrays	219
13.4	Asymptotic normality of maximum likelihood estimators	220
13.4.1	The likelihood	221
13.4.2	Basic conditions for consistency and asymptotic normality	222
13.4.3	Alternative conditions	222
13.4.4	Conclusions	225
13.5	Problems	225
13.6	References	225
14	Large Sample Inference for Complete and Restricted Randomization	227
14.1	Introduction	227
14.2	Complete randomization	228
14.2.1	The unconditional test	228
14.2.2	The conditional test	229
14.2.3	Simulation results	230
14.3	Random allocation rule	231
14.4	Truncated binomial design	232
14.5	Efron's biased coin design	233
14.6	Wei's urn design	234
14.7	Wei, Smythe, and Smith's general allocation rules	238
14.7.1	The unconditional test for K > 2 treatments	238
14.7.2	The conditional test for two treatments	238
14.8	Conclusions	240
14.9	Problems	240
14.10	References	241
15	Large Sample Inference for Response-Adaptive Randomization	243
15.1	Introduction	243
15.2	Maximum likelihood estimation	243
15.2.1	Asymptotic normality of the maximum likelihood estimator: Urn models	243
15.2.2	Delayed response	244
15.2.3	Likelihood ratio test for K treatments	245
15.2.4	Asymptotic properties of sequential maximum likelihood procedures	245
15.3	Large sample linear rank tests	247
15.4	Problems	249
15.5	References	249
	Author Index	251
	Subject Index	255

What People are Saying About This

From the Publisher

"…excellent for learning on how to use randomization ideas…" (Journal of Statistical Computation & Simulation, May 2004)

"This book is one of the first to devote a substantial part of its content to the theory and practice of the techniques of response-adaptive design in the context of randomized clinical trials." (Apria Healthcare)

"...should be very useful in graduate courses...a valuable reference work..." (Short Book Reviews, 2004)

"All medical statisticians involved in clinical trials should read this book...." (Controlled Clinical Trials)

“..combines the applied aspects of randomization in clinical trials with a probabilistic treatment of properties of randomization...” (Quarterly of Applied Mathematics, Vol. LXI, No. 2, June 2003)