中文摘要：

医疗费用预测是健康保险费率厘定的前提和基础。对于多年期的医疗费用数据，通常使用线性混合效应模型对其进行拟合，但线性混合效应模型对非线性关系的纵向数据建模具有一定的局限性。本文对线性混合效应模型进行扩展，根据医疗费用数据中变量之间的非线性关系，建立了多项式混合效应模型，并将其应用于一组医疗费用数据进行实证研究。结果表明，多项式混合效应模型对住院医疗费用的拟合效果显著优于通常使用的线性混合模型，在医疗费用管理和健康保险的费率厘定中具有重要的应用价值。

英文摘要：

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.