On the finite-sample and asymptotic error control of a randomization-probability test for response-adaptive clinical trials

It is now commonly known that using response-adaptive designs for data collection offers great potential in terms of optimizing expected outcomes, but poses multiple challenges for inferential goals. In many settings, such as phase-II or confirmatory clinical trials, a main barrier to their practical use is the lack of type-I error guarantees and/or power efficiency, especially in finite samples. This work addresses this gap. Specifically, focusing on a novel test statistic defined on the randomization probabilities of the (randomized) adaptive design, we derive its finite-sample and asymptotic guarantees. Further theoretical properties are evaluated for Thompson sampling, a Bayesian response-adaptive design that is com- monly used both in clinical applications and beyond (eg, recommendation systems or mobile health). The frequentist error control advantages of the proposed approach—also able to preserve expected outcome optimalities—are illustrated in a real-world phase-II oncology trial and in simulation experiments.