Hu F., Rosenberger W.F. The Theory of Response-Adaptive Randomization in Clinical Trials

John Wiley & Sons, 2006. — 232 p. — ISBN: 0471653969, 978-0471653967.Presents a firm mathematical basis for the use of response-adaptive randomization procedures in practice.
The Theory of Response-Adaptive Randomization in Clinical Trials is the result of the authors' ten-year collaboration as well as their collaborations with other researchers in investigating the important questions regarding response-adaptive randomization in a rigorous mathematical framework. Response-adaptive allocation has a long history in biostatistics literature; however, largely due to the disastrous ECMO trial in the early 1980s, there is a general reluctance to use these procedures.
This timely book represents a mathematically rigorous subdiscipline of experimental design involving randomization and answers fundamental questions, including:
How does response-adaptive randomization affect power?
Can standard inferential tests be applied following response-adaptive randomization?
What is the effect of delayed response?
Which procedure is most appropriate and how can "most appropriate" be quantified?
How can heterogeneity of the patient population be incorporated?
Can response-adaptive randomization be performed with more than two treatments or with continuous responses?The answers to these questions communicate a thorough understanding of the asymptotic properties of each procedure discussed, including asymptotic normality, consistency, and asymptotic variance of the induced allocation. Topical coverage includes:The relationship between power and response-adaptive randomization.
The general result for determining asymptotically best procedures.
Procedures based on urn models.
Procedures based on sequential estimation.
Implications for the practice of clinical trials.Useful for graduate students in mathematics, statistics, and biostatistics as well as researchers and industrial and academic biostatisticians, this book offers a rigorous treatment of the subject in order to find the optimal procedure to use in practice.Randomization in clinical trials:
Complete randomization, Restricted randomization procedures, Response-adaptive randomization procedures,
Covariate-adaptive randomization procedures, Covariate-adjusted response-adaptive randomization procedures,
Response-adaptive randomization in a historical context
Outline of the book
Fundamental Questions of Response-Adaptive Randomization
Optimal allocation
The relationship between power andresponse-adaptive randomization
The relationship for K greater than 2 treatments
Asymptotically best procedures
Likelihood-Based Inference
Data structure and likelihood
Asymptotic properties of maximum likelihood estimators
The general result for determining asymptotically best procedures
Conclusions
Procedures Based on Urn Models
Generalized Friedman's urn:
Historical results on asymptotic properties, Assumptions and notation, Main asymptotic theorems
Some examples, Proving the main theoretical results
The class of ternary urn models:
Randomized Polya urn, Birth and death urn, Drop-the-loser rule, Generalized drop-the-loser rule,
Asymptotic properties of the GDL rule
Procedures Based on Sequential Estimation
Examples
Properties of procedures based on sequential estimation for K = 2
Notation and conditions for the general framework
Asymptotic results and some examples
Proving the main theorems
Sample Size Calculation
Power of a randomization procedure
Three types of sample size
Examples:
Restricted randomization, Response-adaptive randomization
Additional Considerations
The effects of delayed response
Continuous responses:
Asymptotic variance of the four procedures
Multiple (K greater than 2) treatments
Accommodating heterogeneity:
Heterogeneity based on time trends, Heterogeneity based on covariates, Statistical inference under heterogeneity
Implications for the Practice of Clinical Trials
Standards
Binary responses
Continuous responses
The efects of delayed response
Incorporating Covariates
Introduction and examples:
Covariate-adaptive randomization procedures, CARA Randomization Procedures
General framework and asymptotic results:
The procedure for K treatments, Main theoretical results
Generalized linear models
Two treatments with binary responses:
Power
Conclusions and Open Problems
Conclusions
Open problems
Appendix A: Supporting Technical Material
A.1 Some matrix theory
A.2 Jordan decomposition
A.3 Matrix recursions
A.4 Martingales:
Definition and properties of martingales, The martingale central limit theorem,
Gaussian approximations and the law of the iterated logarithm
A.5 Cramer-Wold device
A.6 Multivariate martingales
A.7 Multivariate Taylor's expansion
A.8 References
Appendix B: Proofs
B.1 Proofs of theorems in Chapter 4:
Proof of Theorems 4.1 - 4.3, Proof of Theorem 4.6
B.2 Proof of theorems in Chapter 5
B.3 Proof of theorems in Chapter 7
B.4 References