Variable Selection In Semiparametric Additive Cox Model

The research of random events is done by different research in many fields,such as Medicine, Biology,Actuarial Science,Reliability Engineering,Public Health,Economics and other fields as well as Demographic,which analyzes the regularity of the events' happening time.A lot of models have been proposed,and the most important one is the Cox proportional hazards model which is proposed by Cox(1972).The model is a semiparametric method,which allows containing censored data,meanwhile analyzes the effect of many factors on the living time,and it plays a particular role in survival analysis.Before analyzing the survival data,all the covariates of influencing the living time should be selected in order to determine which ones should be introduced into the model.If some insignificant covariates are introduced,they will not only increase the computation,but also reduce the model parameter estimation and the prediction accuracy as well.In this paper,we will estimate the parameters and select covariates for the semiparametric additive Cox model.Firstly,the model can be obtained by using the cubic spline function and the stepwise method which is to estimate coefficients,since the relationship between the continuous covariates and the response variable is unknown and non-linear.Secondly,the method of GLM path-following algorithm which is proposed by Park and Hastie(2006) can be used to estimate the coefficients for the semiparametric additive Cox model and select covariates.Finally,the approach is illustrated by real data examples to verify the flexibility and effectiveness.