Table 2.

Illustration of the Decomposition of the Total Effect of a Binary Exposure on an Outcome, in the Presence of 2 Binary Mediators, Exposure-Mediators, and Mediator-Mediator Interactions

Component	Definition
CDE	(Y(100)) − Y(000))
${\mathrm{PNIE}}_{M_{\mathrm{1}}}$	(Y(010)) − Y(000)) [M1(1)) − M1(0)]a
${\mathrm{PNIE}}_{M_{\mathrm{2}}}$	(Y(001)) − Y(000)) [M2(1)) − M2(0)]b
${\mathrm{PNIE}}_{M_{\mathrm{1}}{M}_{\mathrm{2}}}$	(Y(011)) − Y(010)) − Y(001) + Y(000)) [M1(1)M2(1)) − M1(0)M2(0)]
$\mathrm{INT}re{f}_A{\cdot }_{M_{\mathrm{1}}}$	(Y(110)) − Y(100)) − Y(010) + Y(000)) [M1(0)]
$\mathrm{INT}re{f}_A{\cdot }_{M_{\mathrm{2}}}$	(Y(101)) − Y(100)) − Y(001) + Y(000)) [M2(0)]
$\mathrm{INT}re{f}_A{\cdot }_{M_{\mathrm{1}}}{\cdot }_{M_{\mathrm{2}}}$	(Y(111)) − Y(110)) − Y(101)) − Y(011) + Y(001) + Y(010) + Y(100)) − Y(000)) [M1(0)M2(0)]
$\mathrm{INT}me{d}_A{\cdot }_{M_{\mathrm{1}}}$	(Y(110)) − Y(100)) − Y(010) + Y(000)) [M1(1)) − M1(0)]
$\mathrm{INT}me{d}_A{\cdot }_{M_{\mathrm{2}}}$	(Y(101)) − Y(100)) − Y(001) + Y(000)) [M2(1)) − M2(0)]
$\mathrm{INT}me{d}_A{\cdot }_{M_{\mathrm{1}}}{\cdot }_{M_{\mathrm{2}}}$	(Y(111)) − Y(110)) − Y(101)) − Y(011) + Y(001) + Y(010) + Y(100)) − Y(000)) [M1(1)M2(1)) − M1(0)M2(0)]

Abbreviations: A, exposure of interest; CDE, controlled direct effect; INTref, defined reference interaction; INTmed, defined mediated interaction; M, possible mediator; PNIE, pure natural indirect effect; Y, outcome.

^aM₁(1) = I[M₁(1) = m₁], M₁(0) = I[M₁(0) = m₁].

^bM₂(1) = I[M₂(1) = m₂], M₂(0) = I[M₂(0) = m₂].