A note on response-adaptive randomization from a Bayesian prediction viewpoint

Starting from a Bayesian perspective, this paper proposes a novel response adaptive randomization rule based on the use of the predictive distribution. The intent is to design a randomized mechanism that favors the allocation of the next patient to the "best" treatment, considering the expected future outcomes obtained by combining accrued data with prior information. This predictive rule also stems from a decision-theoretic approach. The method is driven by patients' beneficial motivations, fully debated in this work, but also accounts for essential inferential purposes in clinical trials discussed within the framework of frequentist inference. Some asymptotic properties of the proposed rule are proved and also shown through numerical studies, which compare this method with other competing ones, as the notable Thompson rule for the special case of binary outcomes.