Exact group‐sequential designs for clinical trials with randomized play‐the‐winner allocation

The use of both sequential designs and adaptive treatment allocation are effective in reducing the number of patients receiving an inferior treatment in a clinical trial. In large samples, when the asymptotic normality of test statistics can be utilized, a standard sequential design can be combined with adaptive allocation. In small samples the planned error rate constraints may not be satisfied if normality is assumed. We address this problem by constructing sequential stopping rules with specified properties by consideration of the exact distribution of test statistics under a particular adaptive allocation scheme, the randomized play-the-winner rule. Using this approach, compared to traditional equal allocation trials, trials with adaptive allocation are shown to require a larger total sample size to achieve a given power. More interestingly, the expected number patients allocated to the inferior treatment may also be larger for the adaptive allocation designs depending on the true success rates.