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Mediation Analysis with Multiple Mediators under Unmeasured Mediator-Outcome Confounding

It is often of interest in the health and social sciences to investigate the joint mediation effects of multiple post-exposure mediating variables. Identification of such joint mediation effects generally require no unmeasured confounding of the outcome with respect to the whole set of mediators. As the number of mediators under consideration grows, this key assumption is likely to be violated as it is often infeasible to intervene on any of the mediators. In this paper, we develop a simple two-step method of moments estimation procedure to assess mediation with multiple mediators simultaneously in the presence of potential unmeasured mediator-outcome confounding. Our identification result leverages heterogeneity of the exposure effect on each mediator in the population, which is plausible under a variety of empirical settings. The proposed estimators are illustrated through both simulations and an application to evaluate the mediating effects of post-traumatic stress disorder symptoms in the association between self-efficacy and fatigue among health care workers during the COVID-19 outbreak.