It is now well established that adjusting for pure predictors of the outcome, in addition to confounders, allows unbiased estimation of the total exposure effect on an outcome with generally reduced standard errors (SEs). However, no analogous results have been derived for mediation analysis. Considering the simplest linear regression setting and the ordinary least square estimator, we obtained theoretical results showing that adjusting for pure predictors of the outcome, in addition to confounders, allows unbiased estimation of the natural indirect effect (NIE) and the natural direct effect (NDE) on the difference scale with reduced SEs. Adjusting for pure predictors of the mediator increases the SE of the NDE's estimator, but may increase or decrease the variance of the NIE's estimator. Adjusting for pure predictors of the exposure increases the variance of estimators of the NIE and NDE. Simulation studies were used to confirm and extend these results to the case where the mediator or the outcome is binary. Additional simulations were conducted to explore scenarios featuring an exposure‐mediator interaction as well as the relative risk and odds ratio scales for the case of binary mediator and outcome. Both a regression approach and an inverse probability weighting approach were considered in the simulation study. A real‐data illustration employing data from the Canadian Study of Health and Aging is provided. This analysis is concerned with the mediating effect of vitamin D in the effect of physical activity on dementia and its results are overall consistent with the theoretical and empirical findings.

中文翻译：

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调整暴露，介体和结果的纯预测变量对自然直接和间接效应估算变量方差的影响

现已公认，除混杂因素外，对结果的纯预测指标进行调整还可以对总体暴露对结果的影响进行无偏估计，而标准误（SE）则通常会降低。但是，没有得到类似结果用于调解分析。考虑到最简单的线性回归设置和普通的最小二乘估计，我们获得的理论结果表明，除混杂因素外，对结果的纯预测变量进行调整还可以对自然间接效应（NIE）和自然直接效应（NDE）进行无偏估计），以减少SE。调整中介的纯预测变量会增加NDE估计量的SE，但可能会增加或减小NIE估计量的方差。调整暴露的纯预测变量会增加NIE和NDE的估算变量的方差。仿真研究被用于确认这些结果并将其扩展到调解人或结果为二元的情况。进行了其他模拟，以探索具有暴露-介体相互作用以及二元介体和结果的相对风险和优势比量表的场景。在模拟研究中考虑了回归方法和逆概率加权方法。提供了使用加拿大健康与老龄化研究数据的真实数据插图。该分析与维生素D在体育锻炼中对痴呆的介导作用有关，其结果总体上与理论和实验结果一致。