Interpretable Sensitivity Analysis for the Baron–Kenny Approach to Mediation with Unmeasured Confounding

Mediation analysis assesses the extent to which the treatment affects the outcome through a mediator and the extent to which it operates through other pathways. As one of the most cited methods in empirical mediation analysis, the classic Baron–Kenny approach allows us to estimate the indirect and direct effects of the treatment on the outcome in linear structural equation models. However, when the treatment and the mediator are not randomized, the estimates of the direct and indirect effects from the Baron–Kenny approach may be biased due to unmeasured confounding among the treatment, mediator, and outcome. Building on Cinelli & Hazlett (2020), we provide a sharp and interpretable sensitivity analysis method for the Baron–Kenny approach to mediation in the presence of unmeasured confounding. We first generalize Cinelli & Hazlett (2020)’s sensitivity analysis method for linear regression to allow for heteroskedasticity and model misspecification. We then apply the general result to develop a sensitivity analysis method for the Baron–Kenny approach. Importantly, we express the sensitivity parameters in terms of the partial R^2s that correspond to the natural factorization of the joint distribution of the direct acyclic graph. Thus, they are interpretable as the proportions of variability explained by unmeasured confounding given the observed covariates. Moreover, we extend the method to deal with multiple mediators, based on a novel matrix version of the partial R^2. We prove that all our sensitivity bounds are attainable and thus sharp.