A Generalized Urn Model in Clinical Trials

Urn models are very popular and useful for adaptive designs in clinical studies. Among various urn models, the drop-the-loser rule is an efficient adaptive treatment allocation scheme, recently proposed for comparing different treatments in clinical trials. This rule is superior to other randomization schemes in terms of variability and power. In this paper, the drop-the-loser rule is generalized to cope with more popular and practical circumstances including (1) delayed responses when test results cannot be obtained immediately, (2) continuous responses, and (3) a pre-specified target of allocation proportion. In addition, our proposed procedure has several favorable asymptotic properties such as strong consistency and asymptotic normality of the allocation proportion. When the outcomes are dichotomous with identical average allocation proportions as the Wei and Durham (1978), the variabilities of our treatment assignment rule are asymptotic minimum and the rule tends to assign more patients to the better treatment.