The Theory of Response-Adaptive Randomization in Clinical Trials

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.