Table 2

Interpretation of parametersa,b

Parameter (label)EffectAlgebraEstimate with proper controlsEstimate with improper (CVD) controls
RRc of E in GEffect of E specific to GR(E+,G−)/R(E−,G−)αα/A
RR of E in G+Effect of E specific to G+R(E+,G+)/R(E−,G+)αγ(αγ)/(AC)
RR of E adjusting for GdSummary effect of E over Gαα/A
RR of G in EEffect of G specific to ER(E−,G+)/R(E−,G−)ββ/B
RR of G in E+Effect of G specific to E+R(E+,G+)/R(E+,G−)βγ(βγ)/(BC)
RR of G adjusting for EdSummary effect of G over Eββ/B
Additive interactionRatio of difference between stratum-specific risk differences and R(E−,G−){[R(E+,G+) − R(E−,G+)] − [R(E+,G−) − R(E−,G−)]}/R(E −,G−) = {[R(E+,G+) − R(E+,G−)] − [R(E−,G+) − R(E−,G−)]}/R(E−,G−)1 − α − β + αβγ1 − β/B − α/A − + αβγ/ABC
Multiplicative interactionRatio of stratum-specific RRs[R(E+,G+)/R(E−,G+)]/[R(E+,G−)/R(E−,G−)] = [R(E+,G+)/R(E+,G−)]/[R(E−,G+)/R(E−,G−)]αγ/α = βγ/β = γ[(αγ)/(AC)]/[α/A] = [(βγ)/(BC)]/[β/B] = γ/C
• a R(E+,G+), the absolute risk of disease in those exposed to E and to G; R(E+,G−), R(E−,G+) and R(E−,G−) are defined analogously.

• b The arguments in bold-face type are used to emphasize the contrast being made and do not change the interpretation.

• c RR, is the relative risk (odds ratio) for the specified level of environmental agent E and genetic variant G relative to those unexposed to E and G.

• d If there is no G-E interaction for lung cancer or for CVD, i.e., γ = C = 1.