A Variable Selection Problem For Joint Model Of Longitudinal And Survival Data

In medical research,the joint model of linear mixed effects model and Cox propotional hazard model is one of the commonly used model. However, with the increasing of the number of observed variables,variable selection problems of model have become increasingly prominent.The traditional variable selection method such as AIC criterion, BIC criterion, stepwise regression method exists inadequencies. And pennalized methods make up for the inadequcies of traditional method,which are widely used. The variable selection of joint model is a challenging feild.Until2015, He attempted to use the penalized likelihood method to select variables of the joint model.In this paper, based on the idea of He, a variable selection problem of one kind of joint models is studied. First, we estimate parameters of three models by maximum likelihood estimation,respectively. Then variables are selected by P-value. Finally, parameters of three models are estimated by LASSO penalized likelihood estimation and SCAD penalized likelihood estimation,respectively. Comparision p-value method with penalized likelihood estimation,we can conclude that:(1) Penalized likelihood methods can select variable coefficients tested significantly and make the smaller absolute value of coefficiedts are automatically compress into 0. Thus simultaneous variable selection and estimations of variable coefficients for joint models of longutudinal and survival outcomes can be achieve. In this paper, according to comparision,LASSO method is bertter than SCAD merhod.(2) In the case of large variables and random effects’ dimension,the efficiency of penalized likelihood estimation is higher than P-value method.,as well as AIC criterion and BIC criterion,. In analysis of data contained more variables, penalized likelihood methods have obvious advantage.(3) penalized likelihood approach can derive more concise model.