Table 1.

Mediation Estimand Definitions, Descriptions, and Assumptions

Estimand	Description	Identifying Assumptions in Addition to Positivity and Consistency
Controlled direct effect $E(Y_{a,m})-E(Y_{a^{*},m})$	Difference in the expected value of Y setting $A$ to $a$ versus $a^{*}$ and in both cases setting M to m	No unmeasured confounding between $A$ and $Y$$(A\perp Y_{a,m}|W)$. No unmeasured confounding between $M$ and $Y$$(M\perp Y_{a,m}|W,A)$.
Natural direct effect $E(Y_{a,M_{a^{*}}})-E(Y_{a^{*},M_{a^{*}}})$ Natural indirect effect $E(Y_{a,M_a})-E(Y_{a,M_{a^{*}}})$	Difference in the expected value of Y setting A to $a$ versus $a*$ and in both cases letting M be the value that it would naturally be under $a^{*}$ Difference in the expected value of Y in both cases setting A to $a$ and contrasting M under $a$ versus $a^{*}$	No unmeasured confounding between $A$ and $Y$$(A\perp Y_{a,m}|W)$. No unmeasured confounding between $M$ and $Y$$(M\perp Y_{a,m}|W,A)$. No unmeasured confounding of $A-M$$(A\perp M_a|W)$. No measured or unmeasured posttreatment confounding of the $M-Y$ relationship $(M_{a^{*}}\perp Y_{a,m}|W)$. $Y_a$ is equivalent to $Y_{a,M_a}$.
Stochastic direct effect $E(Y_{a,g_{M|a^{*},W}})-E(Y_{a^{*},g_{M|a^{*},W}})$ Stochastic indirect effect $E(Y_{a,g_{M|a,W}})-E(Y_{a,g_{M|a^{*},W}})$	Difference in the population average of Y setting A to $a$ versus $a^{*}$ and in both cases drawing the value of M from a distribution of M conditional on A = a* and the individual’s set of covariate values, W Difference in the population average of Y in both cases setting A to a and contrasting drawing the value of M from a distribution of M conditional on A = a versus A = a* and the individual’s set of covariate values, W	No unmeasured confounding between $A$ and $Y$$(A\perp Y_{a,m}|W)$. No unmeasured confounding between $M$ and $Y$$(M\perp Y_{a,m}|W,A)$. No unmeasured confounding of $A-M$$(A\perp M_a|W)$.

Abbreviations: A, treatment; M, mediator; W, covariates; Y, outcome.