Reducing Overdose Deaths and Mitigating County Disparities: Optimal Allocation of Substance Use Treatment Centers

Problem definition : Substance use disorder (SUD) is a pressing health concern in the United States, and connecting communities with treatment is a growing public health imperative. We study the optimal allocation of substance use treatment centers across counties within U.S. states over a multiyear time horizon. We use a three-part objective function that minimizes (i) statewide overdose deaths, (ii) mismatch between counties’ treatment center access and overdose death rates (inequity), and (iii) mismatch between counties’ treatment center access and population (inequality). We also consider the temporal interdependence of counties’ treatment center allocations and their death-rate-based equity targets. Methodology/results : We use a predict-then-optimize approach based on data from more than 2,500 U.S. counties between 1999 and 2016. We first estimate SUD treatment centers’ causal impact on county-level overdose death rates, using mental health parity laws as an instrument. We then use these estimates in a nonlinear program that reallocates states’ observed levels of SUD treatment funding. Results suggest that this approach can meaningfully reduce statewide overdose deaths and between-county disparities in treatment access. Managerial implications : Prioritizing death rate reductions over equity/equality results in more resources being directed to high-population counties, where treatment centers are most effective. Prioritizing equity/equality in treatment access results in more resources being directed to underserved, low-population counties. We also find that states differ in their Pareto-optimal trade-offs between death rates and inequity/inequality.