title: Modeling and detecting potentially ruinous streaks in health expenditures.
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.
authors.affiliation: Department of Biostatistics, University of Washington, F-600 Health Sciences Building Campus Mail Stop, Seattle, WA 98195-7232, USA.
authors.forename: Joseph S
authors.initials: JS
authors.lastname: Koopmeiners
authors.forename: Bryan E
authors.initials: BE
authors.lastname: Dowd
authors.forename: Bradley P
authors.initials: BP
authors.lastname: Carlin
mesh_terms: D001499:Bayes Theorem; D005102:Health Expenditures / Q000706:statistics & numerical data*; D006801:Humans; D015271:Insurance Pools / Q000639:trends*; D007348:Insurance, Health / Q000191:economics* / Q000706:statistics & numerical data; D017059:Models, Econometric; D020414:Risk Sharing, Financial / Q000379:methods*