论文标题

贝叶斯关于验证性试验样本量推导的观点的评论

A review of Bayesian perspectives on sample size derivation for confirmatory trials

论文作者

Kunzmann, Kevin, Grayling, Michael J., Lee, Kim May, Robertson, David S., Rufibach, Kaspar, Wason, James M. S.

论文摘要

样本量推导是任何确认试验计划阶段的关键要素。样本量通常是基于对最大可接受类型错误率和最小所需功率的最大可接受类型的限制来得出的。在这里,功率取决于未知的真实效果大小。实际上,功率通常是针对最小的相关效应大小或可能的替代方案计算的。如果最小相关效应接近零,则前者可能会出现问题,因此需要过多的样本量。后者是可疑的,因为它没有说明有关替代效应大小的先验不确定性。对经常试验的样本量推导的贝叶斯观点自然出现,是一种调和有关相对替代效应大小的先验合理性与基于效应大小相关性的思想的先验合理性的方式。文献中已经提出了有关如何在实践中实施这种“混合”方法的许多建议。但是,在文献中,通常以微妙的方式定义了诸如保证,成功或预期功率之类的关键数量。从传统和完全频繁的样本量推导的方法开始,我们在讨论并证明其在样本量导出临床试验的背景下,为最常用的“混合”数量和突出显示了一致的定义,并突出显示了连接。

Sample size derivation is a crucial element of the planning phase of any confirmatory trial. A sample size is typically derived based on constraints on the maximal acceptable type I error rate and a minimal desired power. Here, power depends on the unknown true effect size. In practice, power is typically calculated either for the smallest relevant effect size or a likely point alternative. The former might be problematic if the minimal relevant effect is close to the null, thus requiring an excessively large sample size. The latter is dubious since it does not account for the a priori uncertainty about the likely alternative effect size. A Bayesian perspective on the sample size derivation for a frequentist trial naturally emerges as a way of reconciling arguments about the relative a priori plausibility of alternative effect sizes with ideas based on the relevance of effect sizes. Many suggestions as to how such `hybrid' approaches could be implemented in practice have been put forward in the literature. However, key quantities such as assurance, probability of success, or expected power are often defined in subtly different ways in the literature. Starting from the traditional and entirely frequentist approach to sample size derivation, we derive consistent definitions for the most commonly used `hybrid' quantities and highlight connections, before discussing and demonstrating their use in the context of sample size derivation for clinical trials.

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