Optimality, variability, power: Evaluating response-adaptive randomization procedures for treatment comparisons

We provide a theoretical template for the comparison of response-adaptive randomization procedures for clinical trials. Using a Taylor expansion of the noncentrality parameter of the usual chi-squared test for binary responses, we show explicitly the relationship among the target allocation proportion, the bias of the randomization procedure from that target, and the variability induced by the randomization procedure. We also generalize this relationship for more than two treatments under various multivariate alternatives. This formulation allows us to directly evaluate and compare different response-adaptive randomization procedures and different target allocations in terms of power and expected treatment failure rate without relying on simulation. For K = 2 treatments, we compare four response-adaptive randomization procedures and three target allocations based on multiple objective optimality criteria. We conclude that the drop-the-loser rule and the doubly adaptive biased coin design are clearly superior to sequential maximum likelihood estimation or the randomized play-the-winner rule in terms of decreased variability, but the latter is preferable because it can target any desired allocation. We discuss how the template developed in this article is useful in the design and evaluation of clinical trials using response-adaptive randomization.