Improving Risk Adjustment for Medicare Capitated Reimbursement Using Nonlinear Models

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Abstract
This article compares a linear risk-adjusted model of medical expenditures for Medicare patients with a model that explicitly account for skewness in distribution of expenditures. A model of expenditures and a model of the square root of expenditures, each expressed as linear combinations of risk adjusters, are estimated using data from the 1992 through 1994 Medicare Current Beneficiary Surveys. Five sets of risk adjusters are considered. Each combination of model and set of risk adjusters is tested for linearity, heteroscedasticity, in-sample fit (R2), forecast performance (forecast bias and forecast mean squared error), and overfitting the data. We analyze forecast performance (1)based on forecasts in same year used for estimation, and (2)based on forecasts in the year following that used for estimation. In the first analysis, the model using a square root transformation of expenditures as the dependent variable and the more parsimonious specification of risk adjusters performs best in terms of forecast squared error and overfitting. The untransformed model performs best in terms of forecast bias in each group based on severity of disability, with the exception of the severely disabled for whom the square root model is best. In the second analysis, the square root model performs better than the untransformed model in terms of forecast squared error, but neither model is statistically distinguishable from zero in terms of bias. Accounting for skewness in expenditures tends to improve precision but not necessarily bias, except among the severely disabled. Adjusting for health status improves risk adjustment.

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