Table 1.

Overview of the definitions and interpretations of the causal mediation effects

Effect	Definition	Interpretation
CDE	Yi(x, m) – Yi(x∗, m)	The direct effect of changing the individual’s exposure value from x to x*, while holding the mediator value constant at m.
PNDE	Yi(x, Mi(x∗)) − Yi(x∗, Mi(x∗))	The natural direct effect of changing the individual’s exposure value from x to x*, while holding the mediator for that individual constant at the value that would naturally be observed under exposure value x*.
TNDE	Yi(x, Mi(x)) − Yi(x∗, Mi(x))	The natural direct effect of changing the individual’s exposure value from x to x*, while holding the mediator for that individual constant at the value that would naturally be observed under exposure value x.
PNIE	Yi(x∗, Mi(x)) − Yi(x∗, Mi(x∗))	The natural indirect effect of changing the individual’s mediator value from M(x*) to M(x), while holding the individual’s exposure value constant at x*.
TNIE	Yi(x, Mi(x)) − Yi(x, Mi(x∗))	The natural indirect effect of changing the individual’s mediator value from M(x*) to M(x), while holding the individual’s exposure value constant at x.
TE	Yi(x, Mi(x)) − Yi(x∗, Mi(x∗))	The total effect of changing the individual’s exposure value from x to x*.

Abbreviations: CDE, controlled direct effect; PNDE, pure natural direct effect; TNDE, total natural direct effect; PNIE, pure natural indirect effect; TNIE, total natural indirect effect; TE, total effect