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Title: Interpretable sensitivity analysis for the Baron-Kenny approach to mediation with unmeasured confounding Authors:  Peng Ding - University of California, Berkeley (United States) [presenting]
Abstract: Mediation analysis assesses the extent to which the treatment affects the outcome indirectly through a mediator and the extent to which it operates directly through other pathways. As the most popular method in empirical mediation analysis, the BaronKenny approach estimates the indirect and direct effects of the treatment on the outcome based on linear structural equation models. However, when the treatment and the mediator are not randomized, the estimates may be biased due to unmeasured confounding among the treatment, mediator, and outcome. Building on previous work, we propose a sharp and interpretable sensitivity analysis method for the BaronKenny approach to mediation in the presence of unmeasured confounding. We first generalize their 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. To facilitate interpretation, we must express the sensitivity parameters in terms of the partial R2s that correspond to the natural factorization of the joint distribution of the direct acyclic graph. They measure 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 R2 and a general form of the omitted variable bias formula.