Posttreatment Confounding in Causal Mediation Studies: A Cutting-Edge Problem and a Novel Solution via Sensitivity Analysis

Abstract

In causal mediation studies that decompose an average treatment effect into indirect and direct effects, examples of posttreatment confounding are abundant. In the presence of treatment-by-mediator interactions, past research has generally considered it infeasible to adjust for a posttreatment confounder of the mediatoroutcome relationship due to incomplete information: for any given individual, a posttreatment confounder is observed under the actual treatment condition while missing under the counterfactual treatment condition. This paper proposes a new sensitivity analysis strategy for handling posttreatment confounding and incorporates it into weighting-based causal mediation analysis. The key is to obtain the conditional distribution of the posttreatment confounder under the counterfactual treatment as a function of not only pretreatment covariates but also its counterpart under the actual treatment. The sensitivity analysis then generates a bound for the natural indirect effect and that for the natural direct effect over a plausible range of the conditional correlation between the posttreatment confounder under the actual and that under the counterfactual conditions. Implemented through either imputation or integration, the strategy is suitable for binary as well as continuous measures of posttreatment confounders. Simulation results demonstrate major strengths and potential limitations of this new solution. A reanalysis of the National Evaluation of Welfare-to-Work Strategies (NEWWS) Riverside data reveals that the initial analytic results are sensitive to omitted posttreatment confounding.

Application of 4-way decomposition to the analysis of placental-fetal biomarkers as intermediary variables between maternal body mass index and birthweight

“…It will allow one to (1) test for conditional associations of an unmeasured pre-exposure confounder with the exposure, mediator, and outcome, (2) simulate the confounder from its conditional distribution, and (3) assess its influence by comparing the five effect estimates before and after adjusting for it in the analysis. In this study, we assume no post-exposure confounding of the mediatoroutcome relationship as there are still few sensitivity analysis methods for assessing the influencing of post-exposure confounding (39)(40)(41)(42).…”

Practical challenges in mediation analysis: a guide for applied researchers

“…The partial indirect effect consists only of the pathway that goes through the mediator but not through the post-treatment confounder, whereas the total indirect effect consists of all pathways that go through M. Similarly, the partial direct effect consists only of the path between the exposure and the outcome that does not involve either the mediator or the post-treatment confounder, whereas the total direct effect consists of all pathways that do not go through M. It is essential to appropriately account for post-treatment confounding, as treating a post-treatment confounder like a baseline confounder (e.g., using regression adjustment) will result in biased estimates of the direct effect. See (Coffman and Zhong 2012;De Stavola et al 2015;Hong et al 2022;Miles et al 2020;Moerkerke et al 2015;Valente et al 2017) for more discussion.…”