Power and sample size calculations for causal mediation analysis with a binary mediator in randomized trials

2026-08-31

AI Summary

本文解决了随机试验中二元中介变量的因果中介分析样本量不足的问题，通过开发NIE和NDE的分析功率和样本量公式来解决。

Abstract

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.

Problem

• causal mediation analysis
• binary mediator
• randomized trials
• natural indirect effect
• natural direct effect

Innovation

• ratio-of-mediator-probability weighting (RMPW)
• natural indirect effect (NIE)
• natural direct effect (NDE)
• power and sample size calculation
• binary mediator