Statistical Inference On Quantile Regression Joint Modeling Of Longitudinal And Survival Data With Missing Data

In survival analysis,people often need to deal with survival data and longitudinal data at the same time,and the common method to analyze such data is to establish models of survival data as well as longitudinal data respectively at the same time,which constitutes the well-known joint model.Up to now,many methods have been proposed to make statistical inference on the joint model,including frequency method and bayesian method.But most of these methods assume that the data are completely observed.However,in many practical situations,people often encounter the missing of response variables or covariates in longitudinal data models or survival data models.Therefore,under the assumption that the random errors follow normal distribution,some authors discuss the statistical inference problem of joint models with missing data.However,in many practical applications,random errors do not follow normal distribution,but may follow non-normal distribution or heavy-tailed distribution.And there are few studies on the non-normal joint model with missing data.Therefore,the statistical inference on the quantile regression joint modeling of longitudinal data and survival data with missing data studied in this paper has crucial theoretical and practical significance.This paper studies the quantile regression joint modeling of longitudinal and survival data with missing data:(1)we establish the quantile regression joint modeling of longutidinal and survival data,and discuss the parameter estimation of the quantile regression joint model based on the method of frequency;(2)Based on the MCMC method,we study the parameter estimation of the quantile regression joint modeling of longitudinal and survival data from the point of bayes;(3)we specifically consider the parameter estimation of the quantile regression joint modeling of longitudinal and survival data with missing data when the longitudinal response variables have ignorable missing data based on the multiple imputation method;(4)We do the simulation study firstly with the joint model we build before.What's more,a concrete example of AIDS data is also analyzed based on the joint model.The results of simulation show that the absolute value of the bias which come from the process of the parameter estimation of the quantile regression joint model using maximum likelihood estimation(MLE)are less than 0.03,in addition,the value of RMS and SD are very close,it means that the value of parameter estimation is very close to the true value.At the same time,the similar conclusion are drawn in the case that we do parameter estimation using the bayesian method.That is to say,both the method of frequency and the bayesian method can give the fruitful parameter estimation of quantile regression joint model.According to the analysis of AIDS data,we know that the quantile regression joint model based on the multiple imputation method when the longitudinal response variables have ignorable missing data can well deal with the missing data in longitudinal response variables under the inferior rate of missing,and the results of the parameter estimation of the quantile joint model turn out to be good.