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

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 作者 单位 E-mail 张中文 大连理工大学数学科学学院 zhangzhongwen994@163.com 王晓光 大连理工大学数学科学学院 wangxg@dlut.edu.cn 宋立新 大连理工大学数学科学学院

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，本文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。 经数值模拟研究发现，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、稳定地估计， 是分析协变量对于风险率影响的有效方法。 最后，应用本文提出的方法分析了NCCTG肺癌数据。

To analyze more complex relationships between the survival time and covariants, a set of semi-varying coefficients Gamma Frailty models are proposed in this paper.Firstly, the semi-varying coefficients Gamma Frailty models are approximatively transformed to be linear Gamma Frailty models using B-spline.Secondly, the linear parameters 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 were gotten from the iterative algorithm, the estimations of varying coefficent 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 methods are fully precise and stabilized, and can be used to analyze the influence of the covariants on hazard rats. At last, the proposed methods are demonstrated by the analysis of NCCTG data.
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