Causal mediation analysis

Causal mediation analysis decomposes a total causal effect into effects transmitted through a designated mediator and effects operating through other pathways. Identification generally requires assumptions about exposure-outcome, exposure-mediator, and mediator-outcome confounding.

For binary exposure $A$, the total causal effect on an additive scale is $\mathbb{E}[Y(1)-Y(0)]$. With mediator potential outcome $M(a)$ and nested outcome $Y(a,m)$, consistency gives $Y(a)=Y(a,M(a))$.

One natural direct effect iswhich changes exposure while holding the mediator at its natural value under no exposure.

One natural indirect effect iswhich changes the mediator between its two natural values while holding exposure fixed.

Mediator-outcome confounding occurs when a common cause of the mediator and outcome is not adequately controlled. If exposure itself affects such a common cause, ordinary adjustment can fail to identify natural direct and indirect effects.