Hu / Rosenberger The Theory of Response-Adaptive Randomization in Clinical Trials

1. Auflage 2006
ISBN: 978-0-470-05587-8
Verlag: John Wiley & Sons
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 232 Seiten, E-Book

Reihe: Wiley Series in Probability and Statistics

Presents a firm mathematical basis for the use ofresponse-adaptive randomization procedures in practice
The Theory of Response-Adaptive Randomization in ClinicalTrials is the result of the authors' ten-year collaboration aswell as their collaborations with other researchers ininvestigating the important questions regarding response-adaptiverandomization in a rigorous mathematical framework.Response-adaptive allocation has a long history in biostatisticsliterature; however, largely due to the disastrous ECMO trial inthe early 1980s, there is a general reluctance to use theseprocedures.
This timely book represents a mathematically rigoroussubdiscipline of experimental design involving randomization andanswers fundamental questions, including:
* How does response-adaptive randomization affect power?
* Can standard inferential tests be applied followingresponse-adaptive randomization?
* What is the effect of delayed response?
* Which procedure is most appropriate and how can "mostappropriate" be quantified?
* How can heterogeneity of the patient population beincorporated?
* Can response-adaptive randomization be performed with more thantwo treatments or with continuous responses?
The answers to these questions communicate a thoroughunderstanding of the asymptotic properties of each procedurediscussed, including asymptotic normality, consistency, andasymptotic variance of the induced allocation. Topical coverageincludes:
* The relationship between power and response-adaptiverandomization
* The general result for determining asymptotically bestprocedures
* Procedures based on urn models
* Procedures based on sequential estimation
* Implications for the practice of clinical trials
Useful for graduate students in mathematics, statistics, andbiostatistics as well as researchers and industrial and academicbiostatisticians, this book offers a rigorous treatment of thesubject in order to find the optimal procedure to use inpractice.

Autoren/Hrsg.

Hu, Feifang

Rosenberger, William F.

Inhaltsverzeichnis

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-AdaptiveRandomization.
2.1 Optimal allocation.
2.2 The realtionship between power and response-adaptiverandomization.
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 forK = 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.

Über Autor(innen)

FEIFANG HU, PhD, is Associate Professor in the Department ofStatistics at the University of Virginia. He is the recipient ofnumerous grants, honors, and awards. His research interests includebiostatistics, applied probability and statistical inference, andresampling methods. He has authored over forty refereed articles.
WILLIAM F. ROSENBERGER, PhD, is Professor and Chair ofthe Department of Applied and Engineering Statistics at GeorgeMason University. He received the Association of AmericanPublishers' Professional/Scholarly Publishing Award in 2002 for hiscoauthored work, Randomization in Clinical Trials: Theory AndPractice (Wiley). A Fellow of the American Statistical Association,he has authored over fifty refereed articles and edited twomonographs.