Showing papers by "William F. Rosenberger published in 2006"

The Theory of Response-Adaptive Randomization in Clinical Trials

Abstract: 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 Cramer-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.

Response‐Adaptive Randomization for Clinical Trials with Continuous Outcomes

Abstract: We provide an explicit asymptotic method to evaluate the performance of different response-adaptive randomization procedures in clinical trials with continuous outcomes. We use this method to investigate four different response-adaptive randomization procedures. Their performance, especially in power and treatment assignment skewing to the better treatment, is thoroughly evaluated theoretically. These results are then verified by simulation. Our analysis concludes that the doubly adaptive biased coin design procedure targeting optimal allocation is the best one for practical use. We also consider the effect of delay in responses and nonstandard responses, for example, Cauchy distributed response. We illustrate our procedure by redesigning a real clinical trial.

Sequential designs for logistic phase I clinical trials.

Abstract: Both parametric and nonparametric sequential designs and estimation methods are implemented in phase I clinical trials. In this article, we take a systematic approach, consisting of a start-up design, a follow-on design, a sequential dose-finding design, and an estimation method, to find an efficient estimate of the maximum tolerated dose under the assumption that the dose-response curve has a true underlying logistic distribution. In particular, for the problem of the nonexistence of the maximum likelihood estimates of the logistic parameters, a constraint on the probability of an undetermined maximum likelihood estimator (MLE) is incorporated into the parametric sequential designs. In addition, this approach can also be extended to incorporate ethical considerations, which prohibit an administered dose from exceeding the maximum acceptable dose. Comparison based on simulation studies between the systematic designs and nonparametric designs are described both for continuous dose spaces and discrete dose ...