Patients-at-Risk (PaR): A new performance measure for response-adaptive trials

This article aims to remove the apparent conflict between statistical power and higher allocation to the better treatment, in a particular Ethical-optimal (Etoptimal) response-adaptive design for continuous responses. An existing criterion is extended to show that the Et-optimal design could be uniformly superior over the corresponding optimal design, in finite samples. Further, one of the reasons for why experimenters prefer the standard randomized control trial over a response-adaptive trial could be the high variability of patient allocations in the latter. Though there are many response-adaptive designs in the literature which promise higher allocation to the superior treatment, this is not always assured. Here we propose a new criterion, Patients-at-Risk, for evaluating response-adaptive designs, which partly addresses this problem. Under this new criterion, an algorithm based on the exploreexploit heuristic is shown to be superior to the Et-optimal design in this particular context, thus giving a win-win solution for both ethics and statistical power.