"Our analysis points to factors that may help explain disparities and guide policy. In particular, when we adjusted for both individual need and provider setting, we found that alcohol treatment disparities widened between whites and blacks and between whites and Native Americans. Blacks and Native Americans also were more likely to be treated in residential settings than were whites, suggesting that higher placement rates in residential treatment for these groups may actually help limit disparities and could compensate for other forms of disadvantage.

"Further adjustment for socioeconomic status narrowed the completion gap between whites and blacks and between whites and Hispanics for both alcohol and drug treatment. This change suggests that housing instability and lower employment are important barriers to treatment completion for blacks and Hispanics. Adjusting for socioeconomic status modestly increased the relative Asian American advantage, probably because if Asian Americans had the same educational attainment as whites, they would fare even better in treatment.

"Our findings linking lower socioeconomic status to worse treatment completion are important. Low socioeconomic status is a known risk factor for poor access to and quality of mental health treatment.30 Nonethless, some studies suggest that low socioeconomic status may, paradoxically, promote greater access to substance abuse treatment for minorities.31 Adjusting for socioeconomic status narrowed white-minority disparities for all groups except Native Americans in alcohol treatment. This finding warrants further investigation, since Native Americans in alcohol treatment were more likely than whites to be unemployed and to have less education."

Source

Brendan Saloner and Benjamin Lê Cook, "Blacks And Hispanics Are Less Likely Than Whites To Complete Addiction Treatment, Largely Due To Socioeconomic Factors," Health Affairs, 32, no.1 (2013):135-145 doi: 10.1377/hlthaff.2011.0983.