Familywise error rate control for block response-adaptive randomization

Response-adaptive randomization allows the probabilities of allocating patients to treatments in a clinical trial to change based on the previously observed response data, in order to achieve different experimental goals. One concern over the use of such designs in practice, particularly from a regulatory viewpoint, is controlling the type I error rate. To address this, Robertson and Wason (Biometrics, 2019) proposed methodology that guarantees familywise error rate control for a large class of response-adaptive designs by re-weighting the usual $z$-test statistic. In this article, we propose an improvement of their method that is conceptually simpler, in the context where patients are allocated to the experimental treatment arms in a trial in blocks (i.e. groups) using response-adaptive randomization. We show the modified method guarantees that there will never be negative weights for the contribution of each block of data to the adjusted test statistics, and can also provide a substantial power advantage in practice.