William F. Rosenberger, PhD, is University Professor and Chairman of the Department of Statistics at George Mason University.  He is a Fellow of the American Statistical Association and the Institute of Mathematical Statistics, and author of over 80 refereed journal articles and The Theory of Response-Adaptive Randomization in Clinical Trials, also published by Wiley.John M. Lachin, ScD, is Research Professor in the Department of Epidemiology and Biostatistics as well as the Department of Statistics at The George Washington University.  He is a fellow of the American Statistical Association and the Society for Clinical Trials and is actively involved in coordinating center activities for clinical trials of diabetes. He is the author of Biostatistical Methods: The Assessment of Relative Risks, Second Edition, also published by Wiley.

"Featuring a unique combination of the applied aspects of randomization in clinical trials with a nonparametric approach to inference, the book is the go-to guide for biostatisticians and pharmaceutical industry statisticians." (Zentralblatt MATH 2016)

• Preface xi1 Randomization and the Clinical Trial 11.1 Introduction 11.2 Causation and Association 21.3 Randomized Clinical Trials 61.4 Ethics of Randomization 91.5 Problems 121.6 References 132 Issues in the Design of Clinical Trials 152.1 Introduction 152.2 Study Outcomes 152.3 Sources of Bias 182.3.1 Selection and ascertainment bias 192.3.2 Statistical analysis philosophy 202.3.3 Losses to follow-up and noncompliance 212.3.4 Covariates 212.4 Experimental Design 232.5 Recruitment and Follow-Up 252.6 Determining the Number of Randomized Subjects 262.6.1 Development of the main formula 272.6.2 Example 292.6.3 Survival trials 292.6.4 Adjustment for noncompliance 322.6.5 Additional considerations 322.7 Problems 332.8 References 343 Randomization for Balancing Treatment Assignments 373.1 Introduction 373.2 Complete Randomization 383.3 Forced Balance Procedures 403.3.1 Random allocation rule 403.3.2 Truncated binomial design 423.3.3 Hadamard randomization 443.3.4 Maximal procedure 463.4 Forced Balance Randomization Within Blocks 463.4.1 Permuted block design 463.4.2 Random block design 473.5 Efron’s Biased Coin Design 483.6 Other Biased Coin Designs and Generalizations 513.7 Wei’s Urn Design 523.8 Other urn Models and Generalizations 543.9 Comparison of Balancing Properties 553.10 Restricted Randomization for Unbalanced Allocation 583.11 K > 2 Treatments 613.12 Problems 623.13 References 643.14 Appendix 664 The Effects of Unobserved Covariates 674.1 Introduction 674.2 A Bound on the Probability of a Covariate Imbalance 684.3 Simulation Results 704.4 Accidental Bias 714.5 Maximum Eigenvalue of 𝚺T 734.6 Accidental Bias for Biased Coin Designs 744.7 Chronological Bias 754.8 Problems 764.9 References 764.10 Appendix 775 Selection Bias 795.1 Introduction 795.2 The Blackwell–Hodges Model 815.3 Predictability of a Randomization Sequence 835.4 Selection Bias for the Random Allocation Rule and Truncated Binomial Design 845.5 Selection Bias in a Permuted Block Design 875.5.1 Permuted blocks using the random allocation rule 875.5.2 Permuted blocks with truncated binomial randomization 875.5.3 Random block design 875.5.4 Conclusions 895.6 Selection Bias for Other Restricted Randomization Procedures 905.6.1 Efron’s biased coin design 905.6.2 Wei’s urn design 905.6.3 Smith’s design 915.7 Simulation Results 915.8 Controlling and Testing for Selection Bias in Practice 935.9 Problems 945.10 References 945.11 Appendix 956 Randomization as a Basis for Inference 976.1 Introduction 976.2 The Population Model 976.3 The Randomization Model 1006.4 Randomization Tests 1036.5 Linear Rank Tests 1056.6 Variance of the Linear Rank Test 1086.7 Optimal Rank Scores 1106.8 Exact and Large-Sample Randomization Tests 1116.8.1 Computation of exact tests 1126.8.2 Large sample randomization tests 1136.9 Monte Carlo Re-Randomization Tests 1156.9.1 Unconditional tests 1156.9.2 Example 1166.9.3 Conditional tests 1176.10 Preservation of Error Rates 1186.11 Regression Modeling 1206.12 Analyses with Missing Data 1216.13 Sample Size Considerations for Random Sample Fractions 1226.14 Group Sequential Monitoring 1236.14.1 Establishing a stopping boundary 1246.14.2 Information fraction 1256.15 Problems 1266.16 References 1276.17 Appendix A 1296.18 Appendix B 1317 Stratification 1337.1 Introduction 1337.2 Stratified Randomization 1347.3 Is Stratification Necessary? 1357.4 Treatment Imbalances in Stratified Trials 1367.5 Stratified Analysis Using Randomization Tests 1387.6 Efficiency of Stratified Randomization in a Stratified Analysis 1407.7 Conclusions 1447.8 Problems 1447.9 References 1458 Restricted Randomization in Practice 1478.1 Introduction 1478.2 Stratification 1488.3 Characteristics of Randomization Procedures 1498.3.1 Consideration of selection bias 1498.3.2 Implications for analysis 1518.4 Selecting a Randomization Procedure 1518.4.1 Choosing parameter values 1528.4.2 Comparing procedures 1538.4.3 Conclusions 1568.5 Generation of Sequences 1568.6 Implementation 1578.6.1 Packaging and labeling 1588.6.2 The actual randomization 1598.7 Special Situations 1608.8 Some Examples 1638.8.1 The optic neuritis treatment trial 1638.8.2 Vesnarinone in congestive heart failure 1638.8.3 The diabetes control and complications trial 1638.8.4 Captopril in diabetic nephropathy 1648.8.5 The diabetes prevention program 1648.8.6 Scleral buckling versus primary vitrectomy in retinal detachment (The SPR Study) 1648.9 Problems 1658.10 References 1669 Covariate-Adaptive Randomization 1699.1 Early Work 1699.1.1 Zelen’s rule 1709.1.2 The Pocock–Simon procedure 1709.1.3 Example: Adjuvant chemotherapy for locally invasive bladder cancer 1719.1.4 Wei’s marginal urn design 1719.1.5 Is marginal balance sufficient? 1719.1.6 Is randomization necessary? 1729.2 More Recent Covariate-Adaptive Randomization Procedures 1739.2.1 Balancing within strata 1739.2.2 Balancing with respect to continuous covariates 1749.3 Optimal Design Based on a Linear Model 1759.4 The Trade-Off Among Balance, Efficiency, and Ethics 1779.5 Inference for Covariate-Adaptive Randomization 1799.5.1 Model-based inference 1799.5.2 Randomization-based inference 1809.6 Conclusions 1819.7 Problems 1829.8 References 18510 Response-Adaptive Randomization 18910.1 Introduction 18910.2 Historical Notes 19010.2.1 Roots in bandit problems 19010.2.2 Roots in sequential stopping problems 19110.2.3 Roots in randomization 19210.3 Optimal Allocation 19310.4 Response-Adaptive Randomization to Target R∗ 19610.4.1 Sequential maximum likelihood procedure 19610.4.2 Doubly adaptive biased coin design 19810.4.3 Example 20010.4.4 Efficient randomized-adaptive design 20110.5 Urn Models 20110.5.1 The generalized Friedman’s urn model 20110.5.2 The randomized play-the-winner rule 20210.5.3 Designs to target any allocation 20510.5.4 Ternary urn models 20610.5.5 Klein urn 20710.6 Treatment Effect Mappings 20710.7 Covariate-Adjusted Response-Adaptive Randomization 20810.8 Problems 20910.9 References 21110.10 Appendix 21411 Inference for Response-Adaptive Randomization 21711.1 Introduction 21711.2 Population-Based Inference 21711.2.1 The likelihood 21711.2.2 Sufficiency 22011.2.3 Bias of the maximum likelihood estimators 22011.2.4 Confidence interval procedures 22211.3 Power 22311.3.1 The relationship between power and the variability of the design 22311.3.2 Asymptotically best procedures 22511.3.3 Response-adaptive randomization and sequential monitoring 22611.4 Randomization-Based Inference 22611.5 Problems 22811.6 References 22812 Response-Adaptive Randomization in Practice 23112.1 Basic Assumptions 23112.2 Bias, Masking, and Consent 23212.3 Logistical Issues 23312.4 Selection of A Procedure 23412.5 Benefits of Response-Adaptive Randomization 23612.6 Some Examples 23712.6.1 The extracorporeal membrane oxygenation trial 23712.6.2 The fluoxetine trial 23812.7 Conclusions 23912.8 Problems 24012.9 References 240Author Index 243Subject Index 249

William F. Rosenberger, PhD, is University Professor and Chairman of the Department of Statistics at George Mason University.  He is a Fellow of the American Statistical Association and the Institute of Mathematical Statistics, and author of over 80 refereed journal articles and The Theory of Response-Adaptive Randomization in Clinical Trials, also published by Wiley.John M. Lachin, ScD, is Research Professor in the Department of Epidemiology and Biostatistics as well as the Department of Statistics at The George Washington University.  He is a fellow of the American Statistical Association and the Society for Clinical Trials and is actively involved in coordinating center activities for clinical trials of diabetes. He is the author of Biostatistical Methods: The Assessment of Relative Risks, Second Edition, also published by Wiley.

"Featuring a unique combination of the applied aspects of randomization in clinical trials with a nonparametric approach to inference, the book is the go-to guide for biostatisticians and pharmaceutical industry statisticians." (Zentralblatt MATH 2016)

• Preface xi1 Randomization and the Clinical Trial 11.1 Introduction 11.2 Causation and Association 21.3 Randomized Clinical Trials 61.4 Ethics of Randomization 91.5 Problems 121.6 References 132 Issues in the Design of Clinical Trials 152.1 Introduction 152.2 Study Outcomes 152.3 Sources of Bias 182.3.1 Selection and ascertainment bias 192.3.2 Statistical analysis philosophy 202.3.3 Losses to follow-up and noncompliance 212.3.4 Covariates 212.4 Experimental Design 232.5 Recruitment and Follow-Up 252.6 Determining the Number of Randomized Subjects 262.6.1 Development of the main formula 272.6.2 Example 292.6.3 Survival trials 292.6.4 Adjustment for noncompliance 322.6.5 Additional considerations 322.7 Problems 332.8 References 343 Randomization for Balancing Treatment Assignments 373.1 Introduction 373.2 Complete Randomization 383.3 Forced Balance Procedures 403.3.1 Random allocation rule 403.3.2 Truncated binomial design 423.3.3 Hadamard randomization 443.3.4 Maximal procedure 463.4 Forced Balance Randomization Within Blocks 463.4.1 Permuted block design 463.4.2 Random block design 473.5 Efron’s Biased Coin Design 483.6 Other Biased Coin Designs and Generalizations 513.7 Wei’s Urn Design 523.8 Other urn Models and Generalizations 543.9 Comparison of Balancing Properties 553.10 Restricted Randomization for Unbalanced Allocation 583.11 K > 2 Treatments 613.12 Problems 623.13 References 643.14 Appendix 664 The Effects of Unobserved Covariates 674.1 Introduction 674.2 A Bound on the Probability of a Covariate Imbalance 684.3 Simulation Results 704.4 Accidental Bias 714.5 Maximum Eigenvalue of 𝚺T 734.6 Accidental Bias for Biased Coin Designs 744.7 Chronological Bias 754.8 Problems 764.9 References 764.10 Appendix 775 Selection Bias 795.1 Introduction 795.2 The Blackwell–Hodges Model 815.3 Predictability of a Randomization Sequence 835.4 Selection Bias for the Random Allocation Rule and Truncated Binomial Design 845.5 Selection Bias in a Permuted Block Design 875.5.1 Permuted blocks using the random allocation rule 875.5.2 Permuted blocks with truncated binomial randomization 875.5.3 Random block design 875.5.4 Conclusions 895.6 Selection Bias for Other Restricted Randomization Procedures 905.6.1 Efron’s biased coin design 905.6.2 Wei’s urn design 905.6.3 Smith’s design 915.7 Simulation Results 915.8 Controlling and Testing for Selection Bias in Practice 935.9 Problems 945.10 References 945.11 Appendix 956 Randomization as a Basis for Inference 976.1 Introduction 976.2 The Population Model 976.3 The Randomization Model 1006.4 Randomization Tests 1036.5 Linear Rank Tests 1056.6 Variance of the Linear Rank Test 1086.7 Optimal Rank Scores 1106.8 Exact and Large-Sample Randomization Tests 1116.8.1 Computation of exact tests 1126.8.2 Large sample randomization tests 1136.9 Monte Carlo Re-Randomization Tests 1156.9.1 Unconditional tests 1156.9.2 Example 1166.9.3 Conditional tests 1176.10 Preservation of Error Rates 1186.11 Regression Modeling 1206.12 Analyses with Missing Data 1216.13 Sample Size Considerations for Random Sample Fractions 1226.14 Group Sequential Monitoring 1236.14.1 Establishing a stopping boundary 1246.14.2 Information fraction 1256.15 Problems 1266.16 References 1276.17 Appendix A 1296.18 Appendix B 1317 Stratification 1337.1 Introduction 1337.2 Stratified Randomization 1347.3 Is Stratification Necessary? 1357.4 Treatment Imbalances in Stratified Trials 1367.5 Stratified Analysis Using Randomization Tests 1387.6 Efficiency of Stratified Randomization in a Stratified Analysis 1407.7 Conclusions 1447.8 Problems 1447.9 References 1458 Restricted Randomization in Practice 1478.1 Introduction 1478.2 Stratification 1488.3 Characteristics of Randomization Procedures 1498.3.1 Consideration of selection bias 1498.3.2 Implications for analysis 1518.4 Selecting a Randomization Procedure 1518.4.1 Choosing parameter values 1528.4.2 Comparing procedures 1538.4.3 Conclusions 1568.5 Generation of Sequences 1568.6 Implementation 1578.6.1 Packaging and labeling 1588.6.2 The actual randomization 1598.7 Special Situations 1608.8 Some Examples 1638.8.1 The optic neuritis treatment trial 1638.8.2 Vesnarinone in congestive heart failure 1638.8.3 The diabetes control and complications trial 1638.8.4 Captopril in diabetic nephropathy 1648.8.5 The diabetes prevention program 1648.8.6 Scleral buckling versus primary vitrectomy in retinal detachment (The SPR Study) 1648.9 Problems 1658.10 References 1669 Covariate-Adaptive Randomization 1699.1 Early Work 1699.1.1 Zelen’s rule 1709.1.2 The Pocock–Simon procedure 1709.1.3 Example: Adjuvant chemotherapy for locally invasive bladder cancer 1719.1.4 Wei’s marginal urn design 1719.1.5 Is marginal balance sufficient? 1719.1.6 Is randomization necessary? 1729.2 More Recent Covariate-Adaptive Randomization Procedures 1739.2.1 Balancing within strata 1739.2.2 Balancing with respect to continuous covariates 1749.3 Optimal Design Based on a Linear Model 1759.4 The Trade-Off Among Balance, Efficiency, and Ethics 1779.5 Inference for Covariate-Adaptive Randomization 1799.5.1 Model-based inference 1799.5.2 Randomization-based inference 1809.6 Conclusions 1819.7 Problems 1829.8 References 18510 Response-Adaptive Randomization 18910.1 Introduction 18910.2 Historical Notes 19010.2.1 Roots in bandit problems 19010.2.2 Roots in sequential stopping problems 19110.2.3 Roots in randomization 19210.3 Optimal Allocation 19310.4 Response-Adaptive Randomization to Target R∗ 19610.4.1 Sequential maximum likelihood procedure 19610.4.2 Doubly adaptive biased coin design 19810.4.3 Example 20010.4.4 Efficient randomized-adaptive design 20110.5 Urn Models 20110.5.1 The generalized Friedman’s urn model 20110.5.2 The randomized play-the-winner rule 20210.5.3 Designs to target any allocation 20510.5.4 Ternary urn models 20610.5.5 Klein urn 20710.6 Treatment Effect Mappings 20710.7 Covariate-Adjusted Response-Adaptive Randomization 20810.8 Problems 20910.9 References 21110.10 Appendix 21411 Inference for Response-Adaptive Randomization 21711.1 Introduction 21711.2 Population-Based Inference 21711.2.1 The likelihood 21711.2.2 Sufficiency 22011.2.3 Bias of the maximum likelihood estimators 22011.2.4 Confidence interval procedures 22211.3 Power 22311.3.1 The relationship between power and the variability of the design 22311.3.2 Asymptotically best procedures 22511.3.3 Response-adaptive randomization and sequential monitoring 22611.4 Randomization-Based Inference 22611.5 Problems 22811.6 References 22812 Response-Adaptive Randomization in Practice 23112.1 Basic Assumptions 23112.2 Bias, Masking, and Consent 23212.3 Logistical Issues 23312.4 Selection of A Procedure 23412.5 Benefits of Response-Adaptive Randomization 23612.6 Some Examples 23712.6.1 The extracorporeal membrane oxygenation trial 23712.6.2 The fluoxetine trial 23812.7 Conclusions 23912.8 Problems 24012.9 References 240Author Index 243Subject Index 249