Mental health disparities exist across several dimensions of social inequality, including race/ethnicity, socioeconomic status and gender. Most investigations of health disparities focus on one dimension. Recent calls by researchers argue for studying persons who are marginalized in multiple ways, often from the perspective of intersectionality, a theoretical framework applied to qualitative studies in law, sociology, and psychology. Quantitative adaptations are emerging but there is little guidance as to what measures or methods are helpful.
Here, we consider the concept of a joint disparity and its composition, show that this approach can illuminate how outcomes are patterned for social groups that are marginalized across multiple axes of social inequality, and compare the insights gained with that of other measures of additive interaction. We apply these methods to a cohort of young men from the National Longitudinal Survey of Youth, examining disparities for black men with low early life SES vs. white men with high early life SES across several outcomes that predict mental health, including unemployment, wages, and incarceration.
Results and conclusions
We report striking disparities in each outcome, but show that the contribution of race, SES, and their intersection varies.
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John W. Jackson was funded by the Alonzo Smythe Yerby Fellowship, Tyler J. VanderWeele was funded by the National Institutes of health Grant ES017876, and David R. Williams was funded by the National Institutes of Health Grant 5PC0CA148596-05. The funding sources had no bearing on any aspect of this work.
Conflict of interest
The authors have no conflicts of interest to report.
Decomposing the joint disparity: estimation via regression models
The main text proposes a decomposition of a joint disparity into component disparities. Mathematically, it is equivalent to estimators for decomposing a joint effect of two exposures into main effects and their causal interaction, when the joint effect can be identified from observational data . Because the joint disparity is a descriptive measure, the decomposition can be computed from observed data without assumptions. To help interpretation, though, it may be useful to adjust for variables that proceed both dimensions (e.g., confounding variables, such as age). To obtain adjusted joint disparity measures for continuous outcomes one can fit standard linear regression for the outcome Y (e.g., unemployment) among men:
Where, conditional on age, α1 + α2 + α3 equals the joint disparity in unemployment μ11 − μ00 comparing black men with low SES to white men with high SES; α1 equals μ10 − μ00 the racial disparity in unemployment among high SES persons, α2 equals μ01 − μ00- the SES disparity among whites; and α3 equals the excess intersectional disparity μ11 − μ10 − μ01 + μ00. In our underlying model α1 is the referent race disparity, α2 is the referent SES disparity, α3 is the excess intersectional disparity. These can be reported as proportions, in relation to the joint disparity, i.e., α1/(α1 + α2 + α3), α2/(α1 + α2 + α3), and α3/(α1 + α2 + α3). Standard errors can be obtained for these measures and the corresponding proportions .
We argue that disparity measures on the additive scale will be much more useful for public health planning purposes because they can be used to describe absolute gains in population health were that disparity fully addressed. Sometimes it is difficult to estimate such measures for binary outcomes using additive regression models. But the joint disparity and also each component can be estimated using a saturated weighted linear regression model, where the weights are the inverse probability of jointly belonging to particular race/ethnic and SES categories. To do this, one first estimates two logistic regression models, one predicting childhood SES group conditional on age alone, and the other predicting race conditional on childhood SES and age:
Taking the predicted values from these models, one then develops a stabilized weight SW for each person according to their race and SES group membership:
with these, one then fits a saturated weighted linear regression model for the outcome given race, SES, and their product:
Here η 1 + η 2 + η 3 equals the joint disparity in unemployment μ11 − μ00 comparing black men with low SES to white men with high SES; η 1 equals μ10 − μ00 the racial disparity in unemployment among high SES persons, i.e., the referent race disparity; η 2 equals μ01 − μ00- the SES disparity among whites, i.e., the referent SES disparity; and η 3 equals the excess intersectional disparity μ11 − μ10 − μ01 + μ00. The estimates obtained from this approach differ from the previous model-based estimates, in that they are with respect to the entire population and not just those who share the same age group. Robust standard errors can be obtained for statistical inference (we refer the reader elsewhere for details ).
Another option is to estimate the proportion of the joint disparity due to each component disparity via multiplicative regression models. For example, if the binary outcome Y (e.g., unemployment) were rare in each stratum one could fit the logistic regression model among men:
where, conditional on age, (exp(β1) − 1)/(exp(β1 + β2 + β3) − 1) equals (μ10 − μ00)/(μ11 − μ00) the ratio of the referent race disparity to the joint disparity. The quantity (exp(β2) − 1)/(exp(β1 + β2 + β3) − 1) equals (μ01 − μ00)/(μ11 − μ00) the ratio of the referent SES disparity to the joint disparity. The quantity (exp(β1 + β2 + β3) − exp(β1) − exp(β2) + 1)/(exp(β1 + β2 + β3) − 1) is equal to (μ11 − μ10 − μ01 + μ00)/(μ11 − μ00) the ratio of the excess intersectional disparity to the joint disparity. When the outcome is not rare in one or more strata (i.e., >10 %) the model can be fit using a log-link, and standard errors for either model can be obtained using the multivariate delta method [40, 41] or the non-parametric bootstrap.
Estimating other measures of additive interaction
Each of the model-based strategies described in the previous section can be used to estimate other measures of additive interaction. Suppose, we fit a conditional linear regression model for unemployment given age (e.g., model 1). Using the parameters from this model, we could estimate the synergy index (SI) as (α1 + α2 + α3)/(α1 + α2), the ratio of observed vs. expected joint effects on the relative scale (RJE) as (α0 + α1 + α2 + α3)/(α0 + α1 + α2), the attributable proportion (AP) as α3/(α0 + α1 + α2 + α3), and the relative excess risk due to interaction (RERI) as α3/α0. If, instead we fit a saturated marginal structural model (e.g., model 4), then the same expressions can be used (replacing α with η) but now the measures would pertain to the entire population as opposed to a particular age group. Last, suppose we fit a conditional logistic regression model given age (e.g., model 5). We could use the parameters of this model to estimate the SI as (exp(β1 + β2 + β3) − 1)/((exp(β1) − 1) + (exp(β2) − 1)), RJE as (exp(β1 + β2 + β3))/(exp(β1) + exp(β2) − 1), AP as (exp(β1 + β2 + β3) − exp(β1) − exp(β2) + 1)/exp(β1 + β2 + β3), and RERI as (exp(β1 + β2 + β3) − exp(β1) − exp(β2) + 1). Standard errors can be obtained for these measures through the non-parametric bootstrap or multivariate delta method . Table 4 summarizes these methods' merits and limitations for understanding multiply marginalized groups.
Statistical analyses for NLSY examples
We estimated age-standardized means jointly stratified by race and SES, and also age-standardized differences comparing each strata to white men with high SES using inverse probability weighting . Robust standard errors for the differences were obtained using the sandwich variance estimator for generalized estimating equations. Standard errors for the decomposition method described in the main text were estimated using unweighted generalized linear models adjusted for age, with the identity link and multivariate delta method for log-wages, and logit link for unemployment and incarceration. When incarceration and unemployment rates were over 10 % for any stratum, we instead used the log-link and calculated standard errors using the non-parametric bootstrap with 5000 samples.
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Jackson, J.W., Williams, D.R. & VanderWeele, T.J. Disparities at the intersection of marginalized groups. Soc Psychiatry Psychiatr Epidemiol 51, 1349–1359 (2016). https://doi.org/10.1007/s00127-016-1276-6
- Relative excess risk for interaction
- Synergy index
- Attributable proportion
- Ratio of observed to expected joint effects
- Joint disparity
- Excess intersectional disparity
- Heterogeneity of effects