In a clinical trial, response-adaptive randomization (RAR) uses accumulating data to weigh the randomization of remaining patients in favour of the better performing treatment. The aim is to reduce the number of failures within the trial. However, many well-known RAR designs, in particular, the randomized play-the-winner-rule (RPWR), have a highly myopic structure which has sometimes led to unfortunate randomization sequences when used in practice.

This paper introduces random permuted blocks into two RAR designs, the RPWR and sequential maximum likelihood estimation, for trials with a binary endpoint. Allocation ratios within each block are restricted to be one of 1:1, 2:1 or 3:1, preventing unfortunate randomization sequences. Exact calculations are performed to determine error rates and expected number of failures across a range of trial scenarios. The results presented show that when compared with equal allocation, block RAR designs give similar reductions in the expected number of failures to their unmodified counterparts. The reductions are typically modest under the alternative hypothesis but become more impressive if the treatment effect exceeds the clinically relevant difference