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 commonly 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.