Can Big Data Cure Risk Selection in Healthcare Capitation Program? A Game Theoretical Analysis

Problem definition: This paper analyzes a market design problem in Medicare Advantage (MA), the largest risk-adjusted capitation payment program in the U.S. healthcare market. Evidence exists that the current MA capitation payment program unintentionally incentivizes health plans to cherry pick profitable patient types, which is referred to as “risk selection”. However, the root causes of the risk selection are not comprehensively understood, which we study in this paper. Academic / Practical Relevance: The existing literature primarily attributes the observed risk selection in MA market to data limitations and low explanatory power (e.g. low R 2 ) of the current risk adjustment design. As a result, the current understanding and expectation are that risk selection would gradually disappear over time with increased availability of big data. However, if informationally imperfect risk adjustment is not the only cause of risk selection, big data would provide false assurance to key stakeholders, which we investigate in this paper. Given that risk-adjusted capitation payment models have been increasingly adopted by payers in the U.S., our study would be of primary interest to payers, providers and policy makers in the healthcare market. Results: This paper shows that big data alone cannot cure risk selection in the MA capitation program. In particular, we show that even if the current MA risk adjustment design became informationally perfect (e.g. R 2 = 1), health plans would still have incentives to conduct risk selection, as imperfect risk adjustment is not the only cause of risk selection in the MA market. More specifically, we show that incentives would continue to persist for risk selection in the age of big data through strategically subsidizing some subgroups of patients using capitation payments collected from other subgroups, which we call “risk selection induced by cross subsidization.” We further propose a simple mechanism to address this risk selection problem induced by cross subsidization in MA. Methodology: We construct a game-theoretical model to derive the MA capitation rates under informationally perfect risk adjustment, and show that these capitation rates cannot eliminate risk selection in MA. Managerial Implications: To eliminate risk selection, payers should modify their current capitation mechanisms to take into account the cross subsidization incentives, as proposed in this paper. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2022.1127 .