Modeling and detecting potentially ruinous streaks in health expenditures
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Modeling and detecting potentially ruinous streaks in health expenditures Joseph S. Koopmeiners · Bryan E. Dowd · Bradley P. Carlin
Received: 12 December 2006 / Accepted: 7 February 2007 / Published online: 10 March 2007 © Springer Science+Business Media, LLC 2007
Abstract The mean of a distribution of medical expenditures in an insured population can be affected significantly by the occurrence of a few high cost cases. This fact leads some organizations that hold the primary risk for the population (e.g., health plans or self-insured employers) to seek reinsurance arrangements that spread the risk of high cost cases across a broader pool. Recently, the private reinsurance market has experienced some difficulties, attributable to information asymmetries between primary risk holders and reinsurers. The disproportionate effect of a few high cost cases also has generated interest in the development of “risk-adjustment” systems that attempt to reduce the difference in health plans’ unreimbursed costs either to endogenous management decisions or random chance. We discuss these issues in light of a well-known statistical result regarding the probability of “streaks” in random data. We illustrate problems that can arise and suggest methods to distinguish random streaks from systematic trends. Keywords Risk · Reinsurance · Risk-adjustment · Autocorrelation · Bayesian methods JEL Classifications I11 · C11
J. S. Koopmeiners Department of Biostatistics, University of Washington, F-600 Health Sciences Building Campus Mail Stop 357232, Seattle WA 98195-7232, USA B. E. Dowd Division of Health Services Research, Policy and Administration, School of Public Health, University of Minnesota, Minneapolis, MN 55455-0392, USA B. P. Carlin (B) Division of Biostatistics, MMC 303, School of Public Health, University of Minnesota, Minneapolis, MN 55455-0392, USA e-mail: [email protected]
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Introduction Traits, streaks, and trends in health care expenditure data The importance of high cost cases in health care expenditures is well-documented. In the non-elderly, privately insured population in 2002, one percent of the population accounted for 21% of expenditures, while 10% of the population accounted for 60% of expenditures (Yu & Ezzati-Rice, 2005). In the fee-for-service Medicare program, five percent of all beneficiaries accounted for forty-three percent of total spending and twenty-five percent accounted for 85% percent of total spending in 2001 (CBO, 2005). The occurrence of high cost claims can have an important effect on markets for health insurance, whether those claims occur randomly across health plans in a market or tend to be concentrated in a subset of plans over time. Both health plans and employers or other “sponsors” such as the Medicare program that offer health plans to groups of consumers are concerned about the distribution of high cost cases among competing plans. The health plan’s interest is self-preservation and the sponsor’s interest is in maintaining a healthy degree and type of comp
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