Abstract

A confirmatory randomized controlled trial can be severely underpowered if the variability and/or effect size estimated from a small-scale pilot study is not taken into account in the sample size calculation. This article reviews and summarizes four existing methods and proposes five new approaches, namely a tolerance probability (TP) based approach and four expected power (EP) based approaches. While the TP-based approach takes into account only sampling variability, the four EP-based approaches incorporate both sampling variability and effect size estimates from external pilot studies. Formulas for power and sample size determination of the proposed approaches are first derived for normally distributed response variables and then extended to binary and time-to-event outcome variables. Simulations are conducted to compare the performance of the proposed methods with two existing methods in terms of sample size inflation and total costs (assuming a fixed cost ratio per subject between external pilot and confirmatory trials). The proposed methods are illustrated in two examples, one with binary endpoint and another with time-to-event endpoint, in terms of study sample size and power. Finally, some recommendations are made based on the degree of uncertainty of sampling variance and effect size and the performance of the methods.

摘要

如果在样本量计算中未考虑根据小规模先导研究估算的变异性和/或效应量，则验证性随机对照试验的功能可能会严重不足。本文回顾并总结了四种现有方法，并提出了五种新方法，即基于容差概率（TP）的方法和四种基于预期功率（EP）的方法。尽管基于TP的方法仅考虑了采样变异性，但基于EP的四种方法却结合了采样变异性和外部先导研究的效应量估计值。首先为正态分布的响应变量导出用于确定所提出方法的功效和样本大小的公式，然后将其扩展为二进制和事件发生时间的结果变量。进行模拟以比较拟议方法与两种现有方法在样本数量膨胀和总成本（假设外部试验和验证性试验之间每个受试者的固定成本比率）方面的性能。根据研究样本的大小和功效，在两个示例中说明了所提出的方法，一个示例具有二进制终点，另一个具有事件发生时间终点。最后，根据抽样方差和影响大小的不确定性程度以及方法的性能提出了一些建议。在研究样本量和功效方面。最后，根据抽样方差和影响大小的不确定性程度以及方法的性能提出了一些建议。在研究样本量和功效方面。最后，根据抽样方差和影响大小的不确定性程度以及方法的性能提出了一些建议。