Optimal coinsurance rates for a heterogeneous population under inequality and resource constraints

Although operations research has contributed heavily to the derivation of optimal treatment guidelines for chronic diseases, patient adherence to treatment plans is low and variable. One mechanism for improving patient adherence to guidelines is to tailor coinsurance rates for prescription medications to patient characteristics. We seek to find coinsurance rates that maximize the welfare of the heterogeneous patient population at risk for cardiovascular disease. We analyze the problem as a bilevel optimization model where the lower optimization problem has the structure of a Markov decision process that determines the optimal treatment plan for each patient class. The upper optimization problem is a nonlinear resource allocation problem with constraints on total expenditures and coinsurance inequality. We used dynamic programming with a penalty function for nonseparable constraint violations to derive the optimal coinsurance rates. We parameterized and solved this model by considering patients who are insured by Medicare and are prescribed medications for prevention of cardiovascular disease. We find that optimizing coinsurance rates can be a cost-effective intervention for improving patient adherence and health outcomes, particularly for those patients at high risk for cardiovascular disease.