Appendix Table 1.

Approaches for using additive interaction to understand multiply marginalized groups

Approach/Measure	Expression	Interpretation	Focus	Conceptual Limitations
Joint disparityb	μ11−μ00	Excess outcome among the multiply marginalized group, as compared to the non-marginalized	---	---
Excess intersectional Disparity	μ11−μ10−μ01+μ00	Amount by which the joint disparity exceeds the sum of the referent disparitiesb	---	---
Ratio of excess intersectional disparity to joint disparity	μ11−μ10−μ01+μ00 /(μ11−μ00)	Proportion of joint disparity attributable to the intersection of race and SES	Contribution to joint disparity	---
Synergy Index (SI)	(μ11−μ00) /((μ10−μ00)+(μ01−μ00))	Ratio of observed joint disparity to the what one would expect the joint disparity to be if the excess intersectional disparity were zero	Change in joint disparity	---
Attributable Proportion (ratio of excess intersectional disparity to joint riskc)	(μ11−μ10−μ01+μ00) /μ11	Proportion of the joint riskd attributable to the intersection of race and SES	Contribution to joint riskd	Interpretation does not relate to joint disparity
Ratio of observed to expected relative joint effects (RJE)	μ11 /(μ10+μ01−μ00)	Ratio of the observed joint riskd to what one would expect the joint riskd to be if the excess intersectional disparity were zero	Change in joint riskd	Interpretation does not relate to joint disparity
Relative Excess Risk due to Interaction	(μ11−μ10−μ01+μ00) /μ00	The excess intersectional disparity scaled by the non-marginalized outcome	Presence of excess intersectional disparity	Interpretation does not relate to either joint disparity or joint riskd
Heterogeneity of effects	μ10−μ00 and μ11−μ01	The disparity for one category (race) within levels of another (SES)	Stratum-specific disparities, and presence of excess intersectional disparity	Adjusts away contribution of second status

^aMean outcome μ among blacks with low SES (μ₁₁), blacks with high SES (μ₁₀), whites with low SES (μ₀₁), whites with high SES (μ₀₀)

^bA referent disparity is the disparity for one social category at the refencence level of the other category. For example, the race disparity among those with high SES (referent race disparity), or the SES disparity among whites (referent SES disparity).

^cThe joint disparity decomposes into the sum of the excess intersectional disparity and the referent disparities

^dJoint risk = μ₁₁