随机试验中含二分类中介变量的因果中介分析的效力与样本量计算
Power and sample size calculations for causal mediation analysis with a binary mediator in randomized trials
- Yau Mathematical Sciences Center, Tsinghua University（丘成桐数学科学中心，清华大学）
- Yanqi Lake Beijing Institute of Mathematical Sciences and Applications（北京国际数学研究中心）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文针对随机试验中含二分类中介变量的因果中介分析，开发了NIE和NDE的解析效力与样本量公式，经模拟验证其样本量匹配基准、效力达标且I类错误符合要求，还通过ACTG175实例展示了试点数据的校准方法。
AI中文摘要：
中介分析在随机试验中越来越多地被应用，但足以检测总处理效应的样本量可能会使自然间接效应（NIE）或自然直接效应（NDE）的效力严重不足。随机化并未延伸至中介变量，因此估计精度取决于条件中介变量分布和中介变量-结局关联，而这两者均未纳入总效应计算。在线性结构方程模型之外的规划工作大多基于完全指定的数据生成机制下的模拟，而该机制在设计阶段通常无法获得。本文针对含二分类中介变量、连续或二分类结局的情况，开发了NIE和NDE的解析效力与样本量公式。在标准识别假设下，我们聚焦于无需结局模型即可进行效应估计的中介概率比加权（RMPW）估计量，将RMPW估计量的“理想”方差分解为中介概率比变异性、结局变异性及其关联的分量，其中NIE还包含额外的共享臂协方差项。在probit潜指数中介变量和工作结局模型下，这些分量由少量可解释的设计输入决定，而非由协变量、中介变量和结局的完整联合分布决定。模拟结果表明，解析样本量与基于模拟的基准值高度匹配，可达到目标效力，并将I类错误维持在名义水平附近。通过ACTG175实例展示了如何利用试点数据校准这些输入参数。
英文摘要：
Mediation analyses are increasingly conducted in randomized trials, but a sample size adequate for the total treatment effect may leave the natural indirect effect (NIE) or natural direct effect (NDE) substantially underpowered. Randomization does not extend to the mediator, so precision depends on the conditional mediator distribution and the mediator-outcome association, neither of which enters a total-effect calculation. Planning outside linear structural equation models is largely based on simulation under a fully specified data-generating mechanism rarely available at the design stage. This paper develops analytic power and sample size formulas for the NIE and NDE with a binary mediator and a continuous or binary outcome. Under standard identification assumptions, we focus on the ratio-of-mediator-probability weighting (RMPW) estimator that does not require an outcome model for effect estimation. We decompose the oracle variances of the RMPW estimators into components capturing mediator-probability-ratio variability, outcome variation, and their association, with an additional shared-arm covariance term for the NIE. Under a probit latent-index mediator and a working outcome model, these components are determined by a small number of interpretable design inputs rather than by the full joint distribution of covariates, mediator, and outcome. Simulations show that the analytic sample sizes closely match simulation-based benchmarks, attain the target power, and maintain type I error near the nominal level. An ACTG175 illustration shows how pilot data can calibrate the inputs.
