Kunzmann Kevin, Grayling Michael J, Lee Kim May, Robertson David S, Rufibach Kaspar, Wason James M S
MRC Biostatistics Unit, University of Cambridge, Cambridge, UK.
Population Health Sciences Institute, Newcastle University, Newcastle upon Tyne, UK.
Am Stat. 2021;75(4):424-432. doi: 10.1080/00031305.2021.1901782. Epub 2021 Apr 22.
Sample size derivation is a crucial element of planning any confirmatory trial. The required sample size is typically derived based on constraints on the maximal acceptable Type I error rate and minimal desired power. Power depends on the unknown true effect and tends to be calculated either for the smallest relevant effect 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, while the latter is dubious since it does not account for the a priori uncertainty about the likely alternative effect. A Bayesian perspective on sample size derivation for a frequentist trial can reconcile arguments about the relative a priori plausibility of alternative effects 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. However, key quantities are often defined in subtly different ways in the literature. Starting from the traditional 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 sample size derivation for clinical trials.
样本量推导是规划任何确证性试验的关键要素。所需样本量通常基于对最大可接受的I型错误率和最小期望检验效能的限制来推导。检验效能取决于未知的真实效应，并且倾向于针对最小的相关效应或一个可能的点备择假设来计算。如果最小的相关效应接近零假设，那么前者可能会有问题，因为这需要过大的样本量；而后者则值得怀疑，因为它没有考虑到关于可能的备择效应的先验不确定性。对于频率学派试验的样本量推导，贝叶斯观点可以将关于备择效应的相对先验似然性的争论与基于效应大小相关性的观点协调起来。关于如何在实践中实施这种“混合”方法，已经提出了许多建议。然而，关键量在文献中常常以微妙不同的方式定义。从传统的完全频率学派的样本量推导方法出发，我们为最常用的混合量推导一致的定义，并突出它们之间的联系，然后讨论并展示它们在临床试验样本量推导中的应用。
