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ideas through the ECMO trial, the CALGB~49907 breast cancer trial, and modern platform trials, and discuss the 2026 FDA draft guidance on Bayesian methodology.

翻译：本文从贝叶斯视角探讨临床试验设计中三个相互关联的方面：先验设定、序贯自适应分配与决策论优化。关于先验设定，我们认为临床试验中的治疗效果在已知先验条件下通常较小，这使得诸如Jeffreys先验等默认无信息先验不再适用；基于历史效应规模或LD50关系校准的先验既更符合实际又更具效率。在序贯设计方面，我们展示了Thompson（1933）的概率匹配准则如何与现代自适应随机化方法相关联，并阐释了基于充分统计量的逆向归纳法——遵循\citet{christen2003}与\citet{carlin1998}的研究——如何将看似难解的无限时域停止问题简化为有限表格形式。针对试验优化，我们回顾了\citet{thall2004}提出的基于效用的框架，该框架联合建模疗效与毒性，使得剂量探索设计能够最大化患者获益而非仅仅控制错误率。我们通过ECMO试验、CALGB~49907乳腺癌试验及现代平台试验阐释这些理念，并探讨FDA 2026年贝叶斯方法学草案指南。