关键词: 线性混合效应模型, 多项式混合效应模型, 健康保险, 医疗费用

Abstract: Prediction of medical expenses is the precondition and basis for health insurance premium ratemaking. Linear mixed-effects models are often used to fit multi-year medical cost data, but for longitudinal data with nonlinear relationship between response variable and covariate variables, the linear mixed-effects models have certain limitations. In this paper, based on the medical cost data with non-linear relationships, the linear mixed-effects models are extended to establish polynomial mixed-effects models, and the models are applied to a set of actual medical expense data for empirical research. The result shows that the polynomial mixed-effects models can fit medical expense better than linear mixed-effects models. The method proposed in the paper is valuable for practical medical expense management and health insurance ratemaking.

Key words: Linear Mixed-effects Model, Polynomial Mixed-effects Model, Health Insurance, Medical Expense