 Solution

Causal mediation analysis decomposes the total causal effect of an exposure into a pathway operating through a mediator and a pathway not operating through that mediator. Let $M(x)$ be the potential mediator under exposure $x$, and let $Y(x,m)$ be the potential outcome under exposure $x$ with mediator set to $m$. One conventional decomposition usesfor the natural direct effect, andfor the natural indirect effect. In words, the direct effect changes exposure while holding the mediator at the value it would naturally have under no exposure; the indirect effect changes only that natural mediator value while holding exposure fixed at one.