Abstract

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.

 抽象的

样本量推导是规划任何验证性试验的关键要素。所需的样本量通常是根据最大可接受的 I 类错误率和最小期望功率的约束得出的。功效取决于未知的真实效果，并且往往针对最小相关效果或可能的点替代进行计算。如果最小相关效应接近零，则前者可能会出现问题，因此需要过大的样本量，而后者则是可疑的，因为它没有考虑可能的替代效应的先验不确定性。对频率主义试验的样本量推导的贝叶斯观点可以调和关于替代效应的相对先验合理性的争论与基于效应量相关性的想法。关于如何在实践中实施这种“混合”方法，人们提出了许多建议。然而，文献中关键量的定义方式通常略有不同。从传统的完全频率论的样本量推导方法开始，我们对最常用的混合量得出了一致的定义，并强调了它们之间的联系，然后讨论和展示了它们在临床试验样本量推导中的用途。