Statistica Sinica 17(2007), 387-409

A GENERALIZED DROP-THE-LOSER URN FOR CLINICAL

TRIALS WITH DELAYED RESPONSES

Li-Xin Zhang$^1$, Wai Sum Chan$^2$, Siu Hung Cheung$^2$ and Feifang Hu$^3$

$^1$Zhejiang University, $^2$Chinese University of Hong Kong

and $^3$University of Virginia

Abstract: Urn models are 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 a clinical trial. 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 proportions.

Key words and phrases: Asymptotic normality, asymptotic power, clinical trial, delayed response, randomized play-the-winner rule, strong consistency.