It is generally appreciated that a frequentist analysis of a group sequential trial must in order to avoid inflating type I error account for the fact that one or more interim analyses were performed. It is also to a lesser extent realised that it may be necessary to account for the ensuing estimation bias. A group sequential design is an instance of adaptive clinical trials where a study may change its design dynamically as a reaction to the observed data. There is a widespread perception that one may circumvent the statistical issues associated with the analysis of an adaptive clinical trial by performing the analysis under a Bayesian paradigm. The root of the argument is that the Bayesian posterior is perceived as unaltered by the data-driven adaptations. We examine this claim by analysing a simple trial with a single interim analysis. We approach the interpretation of the trial data under both a frequentist and Bayesian paradigm with a focus on estimation. The conventional result is that the interim analysis impacts the estimation procedure under the frequentist paradigm, but not under the Bayesian paradigm, which may be seen as expressing a "paradox" between the two paradigms. We argue that this result however relies heavily on what one would define as the universe of relevant trials defined by first samples of the parameters from a prior distribution and then the data from a sampling model given the parameters. In particular, in this set of trials, whether a connection exists between the parameter of interest and design parameters. We show how an alternative interpretation of the trial yields a Bayesian posterior mean that corrects for the interim analysis with a term that closely resembles the frequentist conditional bias. We conclude that the role of auxiliary trial parameters needs to be carefully considered when constructing a prior in an adaptive design.

翻译：学界普遍认识到，为避免膨胀Ⅰ类错误，对组序贯试验进行频率学派分析时，必须考虑已进行一次或多次期中分析的事实。在较小程度上，人们也意识到可能需要考虑由此产生的估计偏倚。组序贯设计是自适应临床试验的一个实例，其中研究可根据观测数据动态调整其设计方案。一种普遍看法是，通过在贝叶斯范式下进行分析，可以规避与自适应临床试验分析相关的统计问题。该观点的根源在于，贝叶斯后验被认为不受数据驱动调整的影响。我们通过分析一个仅包含单次期中分析的简单试验来检验这一主张。我们以估计为重点，从频率学派和贝叶斯学派两种范式解读试验数据。常规结论是：期中分析会影响频率学派范式下的估计过程，但不影响贝叶斯范式下的估计，这可能被视为两种范式间的“悖论”。然而，我们认为该结论在很大程度上取决于如何定义相关试验的总体——即首先从先验分布中抽取参数样本，再根据参数从抽样模型中生成数据所形成的试验集合。特别地，在该试验集合中，目标参数与设计参数之间是否存在关联。我们展示了另一种试验解读方式如何产生能校正期中分析的贝叶斯后验均值，其校正项与频率学派条件偏倚高度相似。我们得出结论：在自适应设计中构建先验分布时，必须审慎考虑辅助试验参数的作用。