Asymptotic Behavior of a Randomization Test for a Response-Adaptive Design

Abstract

Response-adaptive designs allow the incorporation of ethical goals in the performance of a clinical trial, and they have been thoroughly studied assuming that treatment responses follow a population model. However, in some clinical trials, population models are not appropriate and randomization tests appear as a plausible alternative to make inference. Randomization-based tests can be devised but the calculation of their exact p-values when a response-adaptive design is used to allocate patients is either time consuming or not feasible for moderate to large sample sizes and so asymptotic results become helpful. Nevertheless, these asymptotic results are not available for response-adaptive designs with good properties. The Klein allocation rule is a response-adaptive design, with good ethical and inferential properties, that generalizes the classical Ehrenfest urn design by making the replacement policy dependent on the response of the last patient. The goal of this article is to study the asymptotic distribution of a test statistic under a randomization-based approach when patients are allocated by using the Klein allocation rule.