A comparison of adaptive allocation rules for group-sequential binary response clinical trials

In clinical trials to compare two or more treatments with dichotomous responses, group-sequential designs may reduce the total number of patients involved in the trial and response-adaptive designs may result in fewer patients being assigned to the inferior treatments. In this paper, we combine group-sequential and response-adaptive designs, extending recent work on sample size re-estimation in trials to compare two treatments with normally distributed responses, to analogous binary response trials. We consider the use of two parameters of interest in the group-sequential design, the log odds ratio and the simple difference between the probabilities of success. In terms of the adaptive sampling rules, we study two urn models, the drop-the-loser rule and the randomized Pólya urn rule, and compare their properties with those of two sequential maximum likelihood estimation rules, which minimize the expected number of treatment failures. We investigate two ways in which adaptive urn designs can be used in conjunction with group-sequential designs. The first method updates the urn at each interim analysis and the second method continually updates the urn after each patient response, assuming immediate patient responses. Our simulation results show that the group-sequential design, which uses the drop-the-loser rule, applied fully sequentially, is the most effective method for reducing the expected number of treatment failures and the average sample number, whilst still maintaining the nominal error rates, over a range of success probabilities.