Some Bayesian Perspectives on Clinical Trials

Abstract: We provide a Bayesian perspective on three interconnected aspects of clinical trial design: prior specification, sequential adaptive allocation, and decision-theoretic optimization. For prior specification, we argue that treatment effects in clinical trials are known a priori to be small, rendering default noninformative priors such as Jeffreys' prior inappropriate; priors calibrated to historical effect sizes or LD50 relationships are both more honest and more efficient. For sequential design, we show how Thompson's (1933) probability-matching rule connects to modern adaptive randomization, and how backward induction on sufficient statistics -- following \citet{christen2003} and \citet{carlin1998} -- reduces the seemingly intractable infinite-horizon stopping problem to a finite table. For trial optimization, we review the utility-based framework of \citet{thall2004} that jointly models efficacy and toxicity, enabling dose-finding designs that maximize patient benefit rather than merely controlling error rates. We illustrate these ideas through the ECMO trial, the CALGB~49907 breast cancer trial, and modern platform trials, and discuss the 2026 FDA draft guidance on Bayesian methodology.