Cox比例风险模型的桥估计

Bridge estimator for Cox’s proportional hazard model

在经济领域和生物科学领域的研究中,经常会遇到包括有变量指标多、样本量大的数据集.一般来说,在一个复杂模型中如果包括有很多微不足道的变量,统计结果往往很难解释.因此,为了减少这种误差,在没有先验的专业知识情况下,研究变量的选择方法非常重要.Cox比例风险模型是生存分析中重要的模型之一.本文将桥估计的变量选择方法应用于Cox比例风险模型中,该方法使用的惩罚函数是p∑j=1|βj|γ.用桥估计方法估计未知参数和变量选择,在一定条件下,讨论了基于惩罚部分似然的桥估计方法在Cox比例风险模型中的Oracle性质,即:相合性和渐近正态性.

Many variable and large numbers of observation is used in Economics and Bioscience.In general,a complicated model including many insignificant variables may result in less predictive power,and it may often be difficult to interpret the results.In the absence of prior knowledge,the study of variable selection is fundamental in order to reduce model bias.One of the popular models used in the study of survival analysis is the Cox’s proportional hazard model.We propose a unified variable selection and procedure with bridge estimator in Cox’s proportional hazard model.The new method is based on a penalized log partial likelihood with bridge penalty p∑j=1｜βj｜γ on regression coefficients.Under reasonable conditions the consistency of the bridge estimator can be achieved.Furthermore,it can select the nonzero coefficients with a probability converging to 1and the estimators of nonzero coefficients have the asymptotic normality,namely the oracle property.