The impact of adjusting for pure predictors of exposure, mediator, and outcome on the variance of natural direct and indirect effect estimators

Abstract

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.

An exact regression‐based approach for the estimation of natural direct and indirect effects with a binary outcome and a continuous mediator

“…Selection of the adjustment covariates is a crucial step to address causal questions from observational data. In a causal mediation context, Diop et al 40 recommended to adjust for pure predictors of the outcome, in addition to true confounders, to reduce the standard errors of the natural effects estimators. Moreover they suggested to avoid adjusting for pure predictors of the exposure since adjustment for such covariates tends to increase the standard errors of these estimators.…”

“…Moreover they suggested to avoid adjusting for pure predictors of the exposure since adjustment for such covariates tends to increase the standard errors of these estimators. Furthermore, considering that adjustment for pure predictors of the mediator was found to increase the standard error of the NDE estimators and could either increase or decrease the variance of the NIE estimators, Diop et al 40 advised to avoid adjusting for such predictors. We recommend for applying Diop et al 40 strategy when selecting the covariates to be adjusted for in the proposed exact approach.…”

“…Furthermore, considering that adjustment for pure predictors of the mediator was found to increase the standard error of the NDE estimators and could either increase or decrease the variance of the NIE estimators, Diop et al 40 advised to avoid adjusting for such predictors. We recommend for applying Diop et al 40 strategy when selecting the covariates to be adjusted for in the proposed exact approach. However, for large adjustment sets or when covariates types are not fully known, LASSO‐based methods (eg, outcome‐adaptive LASSO) 41 could be used to select covariates to control for confounding.…”

Prospective association of screen time with binge‐eating disorder among adolescents in the United States: The mediating role of depression

“…The prospective association between baseline screen time and the change in depression symptoms from baseline to year 1 was also examined. The model was not adjusted for the covariates, as doing so may increase the variance of the natural direct effect (NDE) estimator and may either elevate or diminish the variance of the natural indirect effect (NIE) estimator (Diop et al, 2021). Furthermore, the change in depression symptoms was examined as a mediator of the association between baseline screen time and year 2 BED.…”

A Comparison of Different Methods to Adjust Survival Curves for Confounders

“…Ignoring these would lead to systematically biased estimated of the coefficients, because of non-collapsibility (Aalen et al 2015;Martinussen and Vansteelandt 2013). It is also known that including predictors of the outcome in outcome models can result in smaller standard errors (Diop et al 2021). Comparing the goodness-of-fit of treatment assignment modelling based methods and outcome mechanism based methods in the CO & CT scenario could therefore be misleading.…”