An Urn Model for Odds-Ratio-Based Response-Adaptive Phase III Clinical Trials for Two or More Treatments

Abstract

Adaptive data-dependent allocation designs are used in phase III clinical trials having two or more competing treatments with sequential entrance of patients, in order to allocate a larger number of patients to the better treatment. The odds ratio is a popular concept for biomedical practitioners; hence, odds-ratio-based adaptive designs could be very useful in practice. Rosenberger et al. (2001) introduced an odds-ratio-based two-treatment response-adaptive design; however, they did not study the properties in details. In this article, we describe these designs by means of urn models and provide limiting results for them. Some properties of the design are also studied numerically. We compare the performance of the proposed design with some possible competitors with respect to a few criteria. A real dataset is used to illustrate the applicability of the proposed design. Thus, we provide a base for using odds-ratio-based response-adaptive designs in practice. We extend our design for covariates and also for more than two treatments. In particular, we study the three-treatment design in this article.

Key Words:

• Adaptive designs
• Limiting allocation probability
• Odds ratio estimates
• Play-the-winner rule
• Treatment effect mapping

ACKNOWLEDGMENTS

The authors thank two anonymous referees for their careful reading and constructive suggestions, which led to some improvement over an earlier version of the article. The authors thank Peter Green for many helpful comments.