A comparison of urn designs for randomized clinical trials of K > 2 treatments.

Response-adaptive designs in clinical trials involve incorporating accruing information from patient responses to treatment into the randomization scheme in order to assign more patients to the treatment that has performed better in the trial up to that point. One probability model useful in generating an adaptive randomization scheme is an urn model. We will give a short overview of such adaptive models and compare four of them. We will be interested in how these four models minimize the number of treatment failures in a clinical trial with dichotomous response treatments. Comparison will be done via simulations for four treatments and exactly for three treatments for moderate sample sizes. We compare designs under the assumption that the results of treatments are known immediately, and we also allow some delay in response. Power is analyzed under various alternatives. Our results indicate that a birth and death urn with immigration is the best unless success probabilities are very small, in which case a randomized version of Polya's urn is preferred.