Clinical trials usually involve sequential patient entry. When designing a clinical trial, it is often desirable to include a provision for interim analyses of accumulating data with the potential for stopping the trial early. We review Bayesian sequential clinical trial designs based on posterior probabilities, posterior predictive probabilities, and decision-theoretic frameworks. A pertinent question is whether Bayesian sequential designs need to be adjusted for the planning of interim analyses. We answer this question from three perspectives: a frequentist-oriented perspective, a calibrated Bayesian perspective, and a subjective Bayesian perspective. We also provide new insights into the likelihood principle, which is commonly tied to statistical inference and decision making in sequential clinical trials. Some theoretical results are derived, and numerical studies are conducted to illustrate and assess these designs.

翻译：临床试验通常涉及患者的序贯入组。在设计临床试验时，通常希望纳入对累积数据进行中期分析的规定，以便有可能提前终止试验。本文综述了基于后验概率、后验预测概率以及决策理论框架的贝叶斯序贯临床试验设计。一个相关的问题是，贝叶斯序贯设计是否需要为中期分析的计划进行调整。我们从三个角度回答这一问题：频率学派导向视角、校准贝叶斯视角以及主观贝叶斯视角。我们还对似然原理提供了新的见解，该原理通常与序贯临床试验中的统计推断和决策相关联。文中推导了一些理论结果，并通过数值研究来阐释和评估这些设计。