## Abstract

### Purpose

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.

### Methods

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.

This is a preview of subscription content, access via your institution.

## References

Braveman P (2014) What are health disparities and health equity? We need to be clear. Public health reports 129(Suppl 2):5–8

**(Washington, D.C.: 1974)**Jackson PB, Williams DR (2006) The intersection of race, gender, and SES. In: Schulz Mullings (ed) Gender, race, class, & health: intersectional approaches. Jossey-Bass, San Francisco

Ostlin P, Schrecker T, Sadana R et al (2011) Priorities for research on equity and health: towards an equity-focused health research agenda. PLoS Med 8(11):e1001115

Bowleg L (2012) The problem with the phrase women and minorities: intersectionality-an important theoretical framework for public health. Am J Public Health 102(7):1267–1273

Collins P (2015) Intersectionality’s Definitional Dilemnas. Annu Rev Sociol 41:1–20

Crenshaw K (1989) Demarginalizing the intersection of race and sex: a black feminist critique of antidiscrimination doctrine, feminist theory and antiracist politics. Univ Chic Leg Forum 1989(1), article 8. http://chicagounbound.uchicago.edu/uclf/vol1989/iss1/8. Accessed 9 Aug 2016

Crenshaw K (1994) Mapping the margins: intersectionality, identity, politics, and violence against women of color. In: Finneman M, Mykitiuk R (eds) The public nature of private violence. Routledge, New York, pp 93–118

Williams DR, Mohammed SA, Leavell J, Collins C (2010) Race, socioeconomic status, and health: complexities, ongoing challenges, and research opportunities. Ann N Y Acad Sci 1186:69–101

Cole ER (2009) Intersectionality and research in psychology. The American psychologist. 64(3):170–180

Combahee River Collective (1995) Combahee river collective statement. In: Guy-Sheftall B (ed) Words of fire: an anthology of African American feminist thought. New York Press, New York, pp 232–240

**(original work published 1977)**Bauer GR (2014) Incorporating intersectionality theory into population health research methodology: challenges and the potential to advance health equity. Soc Sci Med (1982) 110:10–17

Williams DR, Kontos EZ, Viswanath K et al (2012) Integrating multiple social statuses in health disparities research: the case of lung cancer. Health Serv Res 47(3 Pt 2):1255–1277

Veenstra G (2013) Race, gender, class, sexuality (RGCS) and hypertension. Soc Sci Med (1982) 89:16–24

Agenor M, Krieger N, Austin SB, Haneuse S, Gottlieb BR (2014) At the intersection of sexual orientation, race/ethnicity, and cervical cancer screening: assessing Pap test use disparities by sex of sexual partners among black, Latina, and white US women. Soc Sci Med (1982) 116:110–118

Rothman KJ (1986) Modern epidemiology. Little Brown, Boston

Gebrekristos HT, Howe CJ (2015) Ratio of observed and expected joint effects. Epidemiology 26(1):e3–4

**(Cambridge, Mass.)**Agerbo E (2005) Effect of psychiatric illness and labour market status on suicide: a healthy worker effect? J Epidemiol Community Health 59(7):598–602

Harper S, Charters TJ, Strumpf EC, Galea S, Nandi A (2015) Economic downturns and suicide mortality in the USA, 1980–2010: observational study. Int J Epidemiol 44(3):956–966

Bailey ZD, Okechukwu C, Kawachi I, Williams DR (2015) Incarceration and current tobacco smoking among black and Caribbean black Americans in the National Survey of American Life. Am J Public Health p e1–e8

Reskin B (2012) The race discrimination system. Annu Rev Sociol 38:17–35

Williams DR, Mohammed SA (2013) Racism and health I: pathways and scientific evidence. Am Behav Sci 57:1152

Wilson W (2010) Structural and cultural forces that contribute to racial inequality. More than just race: being black and poor in the inner city, W.W. Nortion & Company, Inc., New York

Bureau of Labor Statistics, US Department of Labor (2013) National Longitudinal Survey of Youth 1997 cohort, 1997–2011, (rounds 1–15). In: National Opinion Research Center, the University of Chicago, Center for Human Resource Research, The Ohio State University, Columbus

Fryer R (2010) Inequality in the 21st Century: the declining significance of discrimination. Handb Labor Econ 4:855–971

VanderWeele TJ, Tchetgen Tchetgen EJ (2014) Attributing effects to interactions. Epidemiology 25(5):711–722

**(Cambridge, Mass.)**VanderWeele TJ, Tchetgen Tchetgen EJ (2015) Alternative decompositions for attributing effects to interactions. Epidemiology 26(3):e32–34

**(Cambridge, Mass.)**Orfield G, Frankenberg E, Garces L (2008) Statement of American social scientists of research on school desegregation to the US Supreme Court in Parents v. Seattle School District and Meredith v. Jefferson County. Urban Rev 40(1):96–136

Pager D, Western B, Bonikowski B (2009) Discrimination in a low-wage labor market: a field experiment. Am Sociol Rev 74:777–799

Luksyte A, Waite E, Avery D, Rumela R (2013) Held to a different standard: racial differences in the impact of lateness on advancement opportunity. J Occup Organ Psychol 86(2):142–165

Western B, Muller C (2013) Mass incarceration, macrosociology, and the poor. ANNALS Am Acad Political Soc Sci 647:166–189

Alexander M (2012) The new Jim Crow: mass incarceration in the age of colorblindness. Perseus Distribution, New York

Neckerman K, Kirschenman J (1991) Hiring strategies, racial bias, and inner-city workers. Soc Probl 38:433–437

Pager D (2003) The mark of a criminal record. Am J Sociol 108(5):937–975

Hahm HC, Cook BL, Ault-Brutus A, Alegria M (2015) Intersection of race-ethnicity and gender in depression care: screening, access, and minimally adequate treatment. Psychiatr Serv 66(3):258–264

**(Washington, D.C.)**Carliner H, Collins PY, Cabassa LJ, McNallen A, Joestl SS, Lewis-Fernandez R (2014) Prevalence of cardiovascular risk factors among racial and ethnic minorities with schizophrenia spectrum and bipolar disorders: a critical literature review. Compr Psychiatry 55(2):233–247

VanderWeele TJ, Robinson WR (2014) On the causal interpretation of race in regressions adjusting for confounding and mediating variables. Epidemiology 25(4):473–484

**(Cambridge, Mass.)**Auchinbaugh A, Gardecki RM (2007) Attrition in the National longitudinal survey of youth 1997. Tech Rep 1–18. https://fcsm.sites.usa.gov/files/2014/05/2007FCSM_Aughinbaugh-V-C.pdf. Accessed 9 Aug 2016

Cook BL, McGuire TG, Zaslavsky AM (2012) Measuring racial/ethnic disparities in health care: methods and practical issues. Health Serv Res 47(3 Pt 2):1232–1254

Vanderweele TJ, Vansteelandt S, Robins JM (2010) Marginal structural models for sufficient cause interactions. Am J Epidemiol 171(4):506–514

Hosmer DW, Lemeshow S (1992) Confidence interval estimation of interaction. Epidemiology 3(5):452–456

**(Cambridge, Mass.)**VanderWeele TJ, Knol MJ (2014) A tutorial on interaction. Epidemiol Methods 3(1):33–72

## Acknowledgments

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.

## Author information

### Authors and Affiliations

### Corresponding author

## Ethics declarations

### Conflict of interest

The authors have no conflicts of interest to report.

## Appendix

### Appendix

### 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 [25]. 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, α_{1} + α_{2} + α_{3} equals the joint disparity in unemployment μ_{11} − μ_{00} comparing black men with low SES to white men with high SES; α_{1} equals μ_{10} − μ_{00} the racial disparity in unemployment among high SES persons, α_{2} equals μ_{01} − μ_{00-} the SES disparity among whites; and α_{3} equals the excess intersectional disparity μ_{11} − μ_{10} − μ_{01} + μ_{00}. In our underlying model α_{1} is the referent race disparity, α_{2} is the referent SES disparity, α_{3} is the excess intersectional disparity. These can be reported as proportions, in relation to the joint disparity, i.e., α_{1}/(α_{1} + α_{2} + α_{3}), α_{2}/(α_{1} + α_{2} + α_{3}), and α_{3}/(α_{1} + α_{2} + α_{3}). Standard errors can be obtained for these measures and the corresponding proportions [25].

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 μ_{11} − μ_{00} comparing black men with low SES to white men with high SES; *η*
_{1} equals μ_{10} − μ_{00} the racial disparity in unemployment among high SES persons, i.e., the referent race disparity; *η*
_{2} equals μ_{01} − μ_{00-} the SES disparity among whites, i.e., the referent SES disparity; and *η*
_{3} equals the excess intersectional disparity μ_{11} − μ_{10} − μ_{01} + μ_{00}. 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 [39]).

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(β_{1}) − 1)/(exp(β_{1} + β_{2} + β_{3}) − 1) equals (μ_{10} − μ_{00})/(μ_{11} − μ_{00}) the ratio of the referent race disparity to the joint disparity. The quantity (exp(β_{2}) − 1)/(exp(β_{1} + β_{2} + β_{3}) − 1) equals (μ_{01} − μ_{00})/(μ_{11} − μ_{00}) the ratio of the referent SES disparity to the joint disparity. The quantity (exp(β_{1} + β_{2} + β_{3}) − exp(β_{1}) − exp(β_{2}) + 1)/(exp(β_{1} + β_{2} + β_{3}) − 1) is equal to (μ_{11} − μ_{10} − μ_{01} + μ_{00})/(μ_{11} − μ_{00}) 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 (α_{1} + α_{2} + α_{3})/(α_{1} + α_{2}), the ratio of observed vs. expected joint effects on the relative scale (RJE) as (α_{0} + α_{1} + α_{2} + α_{3})/(α_{0} + α_{1} + α_{2}), the attributable proportion (AP) as α_{3}/(α_{0} + α_{1} + α_{2} + α_{3}), and the relative excess risk due to interaction (RERI) as α_{3}/α_{0}. 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(β_{1} + β_{2} + β_{3}) − 1)/((exp(β_{1}) − 1) + (exp(β_{2}) − 1)), RJE as (exp(β_{1} + β_{2} + β_{3}))/(exp(β_{1}) + exp(β_{2}) − 1), AP as (exp(β_{1} + β_{2} + β_{3}) − exp(β_{1}) − exp(β_{2}) + 1)/exp(β_{1} + β_{2} + β_{3}), and RERI as (exp(β_{1} + β_{2} + β_{3}) − exp(β_{1}) − exp(β_{2}) + 1). Standard errors can be obtained for these measures through the non-parametric bootstrap or multivariate delta method [25]. 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 [39]. 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.

## Rights and permissions

## About this article

### Cite this article

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

Received:

Accepted:

Published:

Issue Date:

DOI: https://doi.org/10.1007/s00127-016-1276-6

### Keywords

- Disparities
- Intersectionality
- Interaction
- Decomposition
- Relative excess risk for interaction
- Synergy index
- Attributable proportion
- Ratio of observed to expected joint effects
- Joint disparity
- Excess intersectional disparity
- Heterogeneity of effects