Efficient Response-Adaptive Randomization for Multi-arm Trials with Prioritized Composite Endpoints
The efficient randomized-adaptive design attains the minimal possible variance of the allocation proportion for any pre-specified target and has been extended from two to several treatment arms, but both versions target a single response. Confirmatory trials increasingly rely on several prioritized endpoints, typically efficacy followed by safety, that cannot be reduced to one summary without losing information. The efficient randomized-adaptive design is extended here to targets driven by the net treatment benefit of generalized pairwise comparisons, allowing any number of arms and endpoints of mixed type, including censored time-to-event outcomes. Strong consistency, a law of the iterated logarithm, and asymptotic normality of the allocation proportions are established by combining a sequential H\'ajek projection for the net benefit with the martingale technique used for the original design, and the design is shown to attain the semiparametric efficiency bound within the class of designs that track a smooth function of the net benefit. In simulations calibrated to a three-arm phase III melanoma trial, the proposed design concentrates allocation on the superior treatment more efficiently than designs driven by a single endpoint, while preserving type I error and power. A redesign of the trial illustrates the practical benefit, and the approach is discussed in relation to current regulatory thinking on adaptive designs for confirmatory trials.