Table 3.

Illustration of the Empirical Analogues for the Components of the Total Effect Decomposition With 1 Binary Exposure and 2 Binary Mediators

Component	Empirical Analogues
CDE	(p(100) − p(000))a
${\mathrm{PNIE}}_{M_{\mathrm{1}}}$	(p(010) − p(000)) [P(M1 = 1|A = 1) − P(M1 = 1|A = 0)]
${\mathrm{PNIE}}_{M_{\mathrm{2}}}$	(p(001) − p(000)) [P(M2 = 1|A = 1) − P(M2 = 1|A = 0)]
${\mathrm{PNIE}}_{M_{\mathrm{1}}{M}_{\mathrm{2}}}$	(p(011) − p(010) − p(001) + p(000)) [P(M2 = 1, M2 = 1|A = 1) − P(M1 = 1, M2 = 1|A = 0)]
$\mathrm{INT}re{f}_A{\cdot }_{M_{\mathrm{1}}}$	(p(110) − p(100) − p(010) + p(000))P(M2 = 1|A = 0)
$\mathrm{INT}re{f}_A{\cdot }_{M_{\mathrm{2}}}$	(p(101) − p(100) − p(001) + p(000))P(M2 = 1|A = 0)
$\mathrm{INT}re{f}_A{\cdot }_{M_{\mathrm{1}}}{\cdot }_{M_{\mathrm{2}}}$	(p(111) − p(110) − p(101) + p(100) + p(011) − p(010) − p(001) + p(000))P(M1 = 1, M2 = 1|A = 0)
$\mathrm{INT}me{d}_A{\cdot }_{M_{\mathrm{1}}}$	(p(110) − p(100) − p(010) + p(000)) [P(M1 = 1|A = 1) − P(M1 = 1|A = 0)]
$\mathrm{INT}me{d}_A{\cdot }_{M_{\mathrm{2}}}$	(p(101) − p(100) − p(001) + p(000)) [P(M2 = 1|A = 1) − P(M2 = 1|A = 0)]
$\mathrm{INT}me{d}_A{\cdot }_{M_{\mathrm{1}}}{\cdot }_{M_{\mathrm{2}}}$	(p(111) − p(110) − p(101) + p(100) + p(011) − p(010) − p(001) + p(000))[P(M1 = 1, M2 = 1|A = 1) − P(M1 = 1, M2 = 1|A = 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.

^ap_am1m2 = E(Y|A = a; M₁ = m₁; M₂ = m₂).