  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.
In this paper, we propose an improvement of their proposal that is conceptually
simpler, in the specific context of block-randomised trials with a fixed
allocation to the control arm. We show the modified method guarantees that
there will never be negative weights for blocks of data, and can also provide a
substantial power advantage in practice.
