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

Abstract

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.

KEYWORDS:

• Healthcare
• medical decision making
• cardiovascular disease
• resource allocation
• value-based insurance

Acknowledgements

We are grateful to the anonymous referees and the editors for their helpful comments and suggestions.

Funding

This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE1256260. Dr. Lavieri would like to acknowledge NSF CAREER (CMMI-1552545) for their funding support. Dr. Sussman was supported by the Department of Veterans Affairs CDA 13-021 and IIR 15-432.

Notes on contributors

Greggory J. Schell is a research scientist in data science at the Center for Naval Analyses. He holds a Bachelor’s in industrial engineering from the University of Pittsburgh, a Master’s in statistics and Ph.D. in industrial and operations engineering from the University of Michigan. His doctoral research focused on optimal sequential medical decision making for glaucoma and cardiovascular disease. His research has won the Medical Decision Making Lee Lusted Award, the INFORMS Doing Good with Good OR Award, and the IBM Research Service Science Best Student Paper Award. His primary research interests are in machine learning and optimization to derive data-driven policy recommendations to improve the Navy’s readiness across its manning, training, and equip functions.

Gian-Gabriel P. Garcia is a Ph.D. candidate in the Industrial and Operations Engineering Department at the University of Michigan. He holds a Bachelor’s degree in industrial engineering from the University of Pittsburgh and a Master’s degree in industrial and operations engineering from the University of Michigan. His primary research interest is in improving medical decision making through the development and analysis of models that incorporate optimization under uncertainty, stochastic modeling, game theory, and predictive modeling. His most recent work includes applications to concussion, glaucoma, and cardiovascular disease. Gian is the recipient of the National Science Foundation Graduate Research Fellowship, Rackham Merit Fellowship, and first prize at the INFORMS Minority Issues Forum Poster Competition. He has also received honorable mention for the Ford Foundation Pre-doctoral Fellowship.

Mariel S. Lavieri is an associate professor in the Industrial and Operations Engineering Department at the University of Michigan. She has Bachelor’s degrees in industrial and systems engineering and statistics and a minor in string bass performance from the University of Florida. She holds a Master’s and Ph.D. in management science from the University of British Columbia. In her work, she applies operations research to healthcare topics. In particular, she has developed dynamic programming, stochastic control, and continuous, partially observable state space models to guide screening, monitoring, and treatment decisions of chronic disease patients. She has also created models for health workforce and capacity planning. She is the recipient of the Willie Hobbs Moore Aspire, Advance, Achieve Mentoring Award, the National Science Foundation CAREER Award, the International Conference on Operations Research Young Participant with Most Practical Impact Award, and the Bonder Scholarship. She has also received the Pierskalla Best Paper Award, and an honorary mention in the George B. Dantzig Dissertation Award. She has guided work that won the Medical Decision Making Lee Lusted Award, the INFORMS Doing Good with Good OR Award, the IBM Research Service Science Best Student Paper Award and the Production and Operations Management Society College of Healthcare Operations Management Best Paper Award.

Jeremy B. Sussman is an assistant professor in internal medicine at the University of Michigan and a research scientist in the Center for Clinical Management Research at VA Ann Arbor Healthcare System, where he is also a primary care physician. He has a Bachelor’s degree in biology from Amherst College, an MD from the University of California, San Francisco, and Master’s degrees from the University of California, Berkeley, and the University of Michigan as part of the Robert Wood Johnson Clinical Scholars Program. He performed an internship and residency in internal medicine at Yale-New-Haven Hospital. His primary research interests are in improving the personal tailoring of medical decisions, particularly in cardiovascular disease and diabetes. His work uses risk prediction, decision analysis, and implementation science. He has been published in top medical journals, including JAMA Internal Medicine, Circulation, and BMJ.

Rodney A. Hayward is a Professor of Public Health and Internal Medicine at the University of Michigan and Co-Director of the Center for Practice Management and Outcomes Research at the Ann Arbor VA HSR&D. He received his training in health services research as a Robert Wood Johnson Clinical Scholar at UCLA and at the RAND Corporation, Santa Monica. His current and past work includes studies examining measurement of quality, costs and health status, environmental and educational factors affecting physician practice patterns, quality improvement, and physician decision making. His current work focuses on quality measurement and improvement for chronic diseases, such as diabetes, hypertension and heart disease.