半变系数伽马脆弱模型惩罚部分似然估计
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摘要
为了更好地分析对数风险函数与协变量之间复杂的非线性关系,提出一种半变系数伽马脆弱模型并给出其估计方法.首先,应用B-样条将半变系数伽马脆弱模型近似转化为线性伽马脆弱模型,然后运用惩罚部分似然法估计转化后模型的线性参数,随后采用近似轮廓似然法并运用黄金搜索算法估计随机效应的参数;在通过迭代获得转化后的线性系数以及随机效应参数的估计以后,运用B-样条得到变系数函数的估计.经蒙特卡罗模拟研究发现,该方法可以给出协变量的线性参数以及变系数函数较为精准、稳定的估计,是分析协变量对于风险率影响的有效方法.最后,应用所提出的方法分析了NCCTG肺癌数据.
To analyze more complex nonlinear relationships between the logarithmic risk function and covariants,a set of semi-varying coefficient Gamma frailty models and their estimation method are proposed.Firstly,the semi-varying coefficient Gamma frailty models are approximatively transformed to linear Gamma frailty models using B-spline.Secondly,the linear parameters of transformed models are estimated by the penalized partial likelihood.Thirdly,the profile likelihood method is adopted to estimate the parameter of random effect using the golden section search method.After the estimations of linear parameters and random effect parameters are gotten from the iterative algorithm,the estimations of varying coefficient functions can be obtained taking advantage of B-spline.The finite sample performance of the proposed method is assessed by Monte Carlo simulation studies,the method can give fully precise and stabilized estimation of the linear parameters and varying coefficient function,and can be used to analyze the influence of the covariants on hazard rates.At last,the proposed method is demonstrated by the analysis of NCCTG lung cancer data.
To analyze more complex nonlinear relationships between the logarithmic risk function and covariants,a set of semi-varying coefficient Gamma frailty models and their estimation method are proposed.Firstly,the semi-varying coefficient Gamma frailty models are approximatively transformed to linear Gamma frailty models using B-spline.Secondly,the linear parameters of transformed models are estimated by the penalized partial likelihood.Thirdly,the profile likelihood method is adopted to estimate the parameter of random effect using the golden section search method.After the estimations of linear parameters and random effect parameters are gotten from the iterative algorithm,the estimations of varying coefficient functions can be obtained taking advantage of B-spline.The finite sample performance of the proposed method is assessed by Monte Carlo simulation studies,the method can give fully precise and stabilized estimation of the linear parameters and varying coefficient function,and can be used to analyze the influence of the covariants on hazard rates.At last,the proposed method is demonstrated by the analysis of NCCTG lung cancer data.
引文
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[3] ZHANG Z,SONG L,WANG X,et al.Estimation ofmultivariatefrailtymodelswithvarying coefficients[J].Communication in Statistics-Theory and Methods,2018(2):1-12.
[4] THERNEAUTM, GRAMBSCHPM,PANKRATZ V S.Penalized survival models and frailty[J].Journal of Computational&Graphical Statistics,2003,12(1):156-175.
[5] GRAMBSCH P M. Modeling Survival Data:Extending the Cox Model[M]. New York:Springer-Verlag,2000.
[6] DUCHATEAU L, JANSSEN P. The Frailty Model[M].New York:Springer,2008:199-233.
[7] RIPATTI S, PALMGREN J. Estimation of multivariate frailty models using penalized partial likelihood[J].Biometrics,2000,56(4):1016-1022.
[8] YU Zhangsheng,LIU Lei,BRAVATA D M,et al.A semiparametric recurrent events model with time-varying coefficients[J].Statistics in Medicine,2013,32(6):1016-1026.
[9] LOPRINZI C L,LAURIE J A,WIEAND H S,et al.Prospective evaluation of prognostic variables from patient-completed questionnaires[J].Journal of Clinical Oncology:Official Journal of the American Society of Clinical Oncology,1994,12(3):601-607.
[10]WANGXiaoguang, SHIXinyong. Robust estimation for survival partially linear single-index models[J]. Computational Statistics&Data Analysis,2014,80(4):140-152.