  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.

Methodology