Assessing Sensitivity to Unmeasured Confounders in Causal Mediation Analysis with Multiple Mediators and Clustered Data

Music City Center 

Mediation analysis is an important part of social science research, which helps examine the extent to which the effect of a treatment on an outcome operates through mediators of interest (VanderWeele, 2015). A key assumption for identifying causal mediation effects, such as the interventional indirect effects (Vansteelandt & Daniel, 2017), is the absence of unmeasured pretreatment confounders of the mediator-outcome relation. This assumption is difficult to satisfy even in randomized controlled trials.

Various sensitivity analysis methods have been developed to assess the impact of unmeasured confounders on mediation results (Ding & Vanderweele, 2016; Hong et al., 2018; Imai et al., 2010; Park & Esterling, 2021; Rubinstein et al., 2023; Tchetgen Tchetgen & Shpitser, 2012; VanderWeele, 2010; Zhang & Ding, 2023). A majority of existing sensitivity analysis methods focus on a single mediator and non-clustered data. Mediation analyses in social science, however, often involve multiple mediators and require accounting for clustered data (e.g., students clustered in schools), yet sensitivity analysis methods for this setting remain scarce (Qin et al., 2021). Furthermore, the use of parametric models for causal effect estimation has become increasingly concerning (Ogburn & Shpitser, 2021), and recent years have seen growing use of machine learning methods in estimation of causal effects (Kennedy, 2024; van der Laan & Rose, 2018). Despite this, tools for assessing sensitivity to unmeasured confounders in mediation analyses using machine learning based estimators are lacking.

This study presents a sensitivity analysis method for causal mediation analysis with multiple mediators and clustered data, incorporating nonparametric estimation based on doubly robust machine learning methods (Benkeser & Ran, 2021; Chernozhukov et al., 2018, 2024; Liu et al., 2024; Rubinstein et al., 2023). Under the assumption of no interference, we examine the influence of unmeasured pretreatment confounders in the mediator-outcome relationship on inferences of interventional indirect effects. Using data from the Educational Longitudinal Study (ELS; Ingels et al., 2007), we illustrate our sensitivity analysis approach in assessing the interventional indirect effects of extracurricular activity participation (treatment) on student academic achievement (outcome) via two mediators related to student educational aspirations and beliefs. We hope this study adds to researchers' toolbox for quantifying the sensitivity of causal mediation analysis results to unmeasured confounders.



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causal mediation analysis

unmeasured confounding

sensitivity analysis

doubly robust machine learning methods

social and behavioral sciences