Bayesian Estimation And Variable Selection For The Joint Model Of Longitudinal Proportional Data And Survival Data

In cancer clinical trials and biomedical follow-up studies,longitudinal data are collected for each individual at different points in time,and ultimately survival data for each individual is collected.In the early days,longitudinal data and survival data were analyzed separately,and the correlation between the two types of data was often ignored,leading to inefficient or biased results.Increasingly,it has been found that when there is a correlation between longitudinal data and survival data,joint modeling of these data will improve the efficiency of statistical inference.In the literature of the past,with the maximum likelihood method or longitudinal data and survival data of joint modeling common method is: Cox proportional risk model is used for event time modeling in the survival submodel,and linear mixed effects model is used for longitudinal data modeling in the vertical submodel.However,in order to be more flexible and practical,s However,in order to be more flexible and practical,a partial linear mixed effects model was used to model the longitudinal process,assuming that there was a nonlinear relationship between the longitudinal response and the observation time.This paper mainly considers the joint model of longitudinal proportional data and survival data.There are few literatures on longitudinal proportional data and survival data of joint modeling,and they all use maximum likelihood method based on frequency school to estimate the parameters.Therefore,similar to the method of maximum likelihood joint modeling of longitudinal data and survival data,this paper based on Bayesian method joint modeling of longitudinal proportional data and survival data,carries out parameter estimation and variable selection for the joint model at the same time.Based on the Bayesian method,the joint model of longitudinal proportional data and survival data is divided into two parts: longitudinal process and survival process.For the longitudinal component,the partial linear mixed model is used to logit transformed longitudinal responses,that is,the nonlinear relationship between the longitudinal responses and the observation time is considered.And the B-spline method is used to model the nonlinear function.For the survival component,assume Cox proportional hazards model for the survival times,and partial likelihood method was used to estimate parameters.Longitudinal process and survival process were linked by shared random effects.Based on the hybrid algorithm combining MH algorithm and Gibbs sampling,the Bayesian B-spline method and the Bayesian BLasso method,the unknown parameters,random effects and nonlinear functions in the proposed joint model were estimated by Bayesian estimation and variable selection simultaneously.