高维附加信息下的商业医疗保险费用评估模型和方法
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摘要
医疗保险费用的评估是商业医疗费用管理中的重要环节,附加信息在医疗费用的远期预测中具有重要作用。但是,如果费用数据中含有高维的附加信息,传统的方法就不再适用。因此,本文提出一个新模型来拟合含有大范围附件信息的医疗费用,并用两步法估计医疗费用数据。首先,用充分降维方法将高维协变量降为低维,得到中心降维子空间的基方向和结构维数后,再利用局部回归方法去估计医疗费用曲线,最后通过模拟和实例分析来评价该模型和方法的可行性。
Model of medical cost is very important for the insurers,and the cost data might include some high-dimension covariates,which may be useful to predict the future cost.However,the existing statistical methods may not be effective.Hence,in this paper,a cost model is proposed to model the data with high-dimension covariates,and the two-step method is applied to get the estimation.The first step to obtain the central dimension reduction subspace and the structural dimension,and then,local regression method is employed to get an estimate of the completely unknown regression curve.Some simulations and a real data analysis are given as well to assess the proposed model and methods in this paper.
Model of medical cost is very important for the insurers,and the cost data might include some high-dimension covariates,which may be useful to predict the future cost.However,the existing statistical methods may not be effective.Hence,in this paper,a cost model is proposed to model the data with high-dimension covariates,and the two-step method is applied to get the estimation.The first step to obtain the central dimension reduction subspace and the structural dimension,and then,local regression method is employed to get an estimate of the completely unknown regression curve.Some simulations and a real data analysis are given as well to assess the proposed model and methods in this paper.
引文
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[2]Mullahy,J..Much Ado about Two:Reconsidering Retransformation and Two-part Model in Health Econometrics[J].Journal ofHealth Economics,1998,Vol(17):247-281.
[3]Manning,W.G.and Mullahy,J..Estimating Log Models:to Transform or Not to Transform?[J].Journal of Health Economics,2001,Vol(20):461-494.
[4]Ettner,S.L.,Frank,R.G.,McGuire,T.G.,Newhouse,J.P.and Notman,E.H.Risk Adjustment of Mental Health andSubstance Abuse Payments[J].Inquiry,1998,Vol(35):223-239.
[5]D.Y.Lin.Linear Regression Analysis of Censored Medical Costs.Biostatistics[J].Biostatistics,2001,Vol(1):35-47.
[6]D.Y.Lin.Regression Analysis of Incomplete Medical Cost Data[J].Statistics in Medicine,2003,Vol(22):1181-1200.
[7]Nixon,R.M.,Thompson,S.G..Parametric Modeling of Cost Data in Medical Studies[J].Statistics in Medicine,2004,Vol(23):1311-1331.
[8]Zhou,X.H..Estimation of the Log-normal Mean[J].Statistics in Medicine,1998,Vol(17):2251-2264.
[9]Briggs,A.,Nixon,R.,Dixon,S..Parametric Modeling of Cost Data:Some Simulation Evidence[J].Health Economics,2005,Vol(14):421-428.
[10]Lin,D.Y.,Feuer,E.J.,Etzioni,R.,Wax,Y..Estimating Medical Costs from Incomplete Follow-up Data[J].Biometrics,1997,Vol(53):419-434.
[11]Mihaylova,B.;Briggs,A.;O'Hagan,A.and Thompson S.G.Review of Statistical Methods for Analyzing Healthcare Resourceand Costs[J].Health Economics.2011,Vol(20):897-916.
[12]K.C.Li.Sliced Inverse Regression for Dimension Reduction(with discussion)[J].Journal of the American Statistical Association,1991,Vol(86):316-327.
[13]Wenbin Lu,Lexin Li.Sufficient Dimension Reduction for Censored Regressions[J].Biometrics.2011,Vol(67):513-523.
[14]Zhu,L.X.,Miao,B.,and Peng,H.On Sliced Inverse Regression with Large Dimensional Covariates[J].Journal of the Ameri-can Statistical Association,2006,Vol(101):630-643.
[15]仇春涓,陈滔.商业医疗保险损失分析:基于广义线性模型的实证研究[J].应用概率统计,2012,(28):389-399.