  This paper provides robust estimators and efficient inference of causal
effects involving multiple interacting mediators. Most existing works either
impose a linear model assumption among the mediators or are restricted to
handle conditionally independent mediators given the exposure. To overcome
these limitations, we define causal and individual mediation effects in a
general setting, and employ a semiparametric framework to develop quadruply
robust estimators for these causal effects. We further establish the asymptotic
normality of the proposed estimators and prove their local semiparametric
efficiencies. The proposed method is empirically validated via simulated and
real datasets concerning psychiatric disorders in trauma survivors.
