Compound optimal allocation for individual and collective ethics in binary clinical trials

In recent years, several authors have investigated response-adaptive allocation rules for comparative clinical trials, in order to favour, at each stage of the trial, the treatment that appears to be best. In this paper, we define admissible allocations, namely treatment assignments that cannot be simultaneously improved upon with respect to both a specific design criterion, reflecting the inferential properties of the experiment, and the proportion of patients assigned to the best treatment or treatments; we survey existing designs from this viewpoint. We also suggest combining information and ethical considerations by taking a suitable weighted mean of two corresponding standardized criteria, with weights that depend on the actual treatment effects. This compound criterion leads to a locally optimal allocation that can be targeted by some response-adaptive randomization rule. The paper mainly deals with the case of two treatments, but the suggested methodology is shown to extend to more than two.