半变系数伽马脆弱模型惩罚部分似然估计  

Penalized partial likelihood estimation of semi-varying coefficient Gamma frailty models

作　　者：张中文 王晓光[1] 宋立新[1] ZHANG Zhongwen;WANG Xiaoguang;SONG Lixin(School of Mathematical Sciences,Dalian University of Technology,Dalian 116024,China;School of Public Health and Management,Binzhou Medical University,Yantai 264003,China)

机构地区：[1]大连理工大学数学科学学院,辽宁大连116024 [2]滨州医学院公共卫生与管理学院,山东烟台264003

出　　处：《大连理工大学学报》2018年第6期655-662,共8页Journal of Dalian University of Technology

基　　金：国家自然科学基金资助项目(11471065;11371077;81502891);全国统计科学研究项目(2018LY57);山东省统计科研重点课题资助项目(KT16244);山东省医药卫生科技发展计划资助项目(2016WS0009);山东省软科学研究计划项目(2018RKB14103)

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.

关 键 词：伽马脆弱模型 B-样条 变系数模型 惩罚部分似然估计 黄金搜索算法 

分 类 号：O212[理学—概率论与数理统计]