Theory of Response-Adaptive Randomization in Clinical Trials

FEIFANG HU, PhD, is Associate Professor in the Department of Statistics at the University of Virginia. He is the recipient of numerous grants, honors, and awards. His research interests include biostatistics, applied probability and statistical inference, and resampling methods. He has authored over forty refereed articles. WILLIAM F. ROSENBERGER, PhD, is Professor and Chair of the Department of Applied and Engineering Statistics at George Mason University. He received the Association of American Publishers' Professional/Scholarly Publishing Award in 2002 for his coauthored work, Randomization in Clinical Trials: Theory And Practice (Wiley). A Fellow of the American Statistical Association, he has authored over fifty refereed articles and edited two monographs.

"The book provides a comprehensive overview of the theory of repsonse-adaptive radomization and is recommended to readers with an interest in this specialist area." (Statistics in Medicine, July 2008) "I can recommend this book for the intended target audience which will include industry statisticians with a special interest in this area." (Pharmaceutical Statisitcs, 2008)"…this ground-breaking text is certainly a useful guide and reference for the academic and industry statistician alike." (Journal of the American Statistical Association, December 2007)“This book is useful for graduate students in mathematics, statistics and biostatistics as well as researchers and industrial and academic biostatisticians.” (Zentralblatt MATH, 2007)"…a milestone in the literature on response-adaptive designs in clinical trials." (Biometrics, September 2007)

• Dedication. Preface.1. Introduction.1.1 Randomization in clinical trials.1.2 Response-adaptive randomization in a historical context.1.3 Outline of the book.1.4 References.2. Fundamental Questions of response-Adaptive Randomization.2.1 Optimal allocation.2.2 The realtionship between power and response-adaptive randomization.2.3 The relationship for K > 2 treatments.2.4 Asymptotically best procedures.2.5 References.3. Likelihood-based Inference.3.1 Data structure and Likelihood.3.2 Asymptotic properties of maximum likelihood estimators.3.4 Conclusion.3.5 References.4. Procedures Based on Urn Models.4.1 Generalized Friedman's urn.4.2 The class of ternary urn models.4.3 References.5. Procedures Based on Sequential Estimation.5.1 Examples.5.2 Properties of procedures based on sequential estimation for K = 2.5.3 Notation and conditions for the general framework.5.4 Asymptotic results and some examples.5.5 Proving the main theorems.5.6 References.6. Sample Size Calculation.6.1 Power of a randomization procedure.6.2 Three types of sample size.6.3 Examples.6.4 References.7. Additional Considerations.7.1 The effect of delayed response.7.2 Continuous responses.7.3 Multiple (K > 2) treatments.7.4 Accommodating heterogeneity.7.5 References.8. Implications for the Practice of Clinical Trials.8.1 Standards.8.2 Binary response.8.3 Continuous responses.8.4 The effect of delayed response.8.5 Conclusions.8.6 References.9. Incorporating Covariates.9.1 Introduction and examples.9.2 General framework and asymptotic results.9.3 Generalized linear models.9.4 Two treatments with binary responses.9.5 Conclusions.9.6 References.10. Conclusions and Open Problems.10.1 Conclusions.10.2 Open problems.10.3 References.Appendix A: Supporting Technical Material.A.1 Some matrix theory.A.2 Jordan decomposition.A.3 Matrix recursions.A.4 Martingales.A.5 Cramér-Wold device.A.6 Multivariate martingales.A.7 Multivariate Taylor's expansion.A.8 References.Appendix B: Proofs.B.1 Proofs theorems in Chapter 4.B.2 Proof of theorems in Chapter 5.B.3 Proof of theorems in Chapter 7.B.4 References.Author Index.Subject Index.