The Analysis For Joint Model Of Longitudinal And Failure Time Data With Interval Censoring

The joint model of longitudinal data and time-to-event data are usually employed to study the association between the longitudinal data and survival data.In the past 30 years,the joint model has made many breakthroughs in various fields and it has become a valuable tool in the analysis of follow-up data,which is widely used in clinical trials and epidemiological studies.A common assumption for the survival sub-model in previous articles is that the failure time is right censored.In practice,however,the failure time of interest T can not be observed exactly but only known to occur in a time interval(L,R],it is the so called interval censored data,right-censored data is a special case of interval-censored data（R=∞）.Therefore,it is of practical significance to study the estimation and variable selection for joint model of longitudinal data and interval-censored failure time data.This dissertation discusses some topics of the joint model:the estimation of parameters,variable selection and time-varying coefficients joint model.The dissertation mainly does the following aspects of work:1.The proposed joint model of longitudinal data and interval-censored failure time data,comprises a linear mixed-effects model for the longitudinal sub-model and a Cox proportional hazard（PH）models for the survival sub-model,which incorporates the underlying longitudinal biomarkers and survival process as time-dependent covariates.A MCEM algorithm is proposed based on poisson potential variables and random effects to estimate the parameters in the joint model.In E-step,the Gibbs sampler algorithm is presented for sampling observations from the conditional distribution to estimate random effects and Poisson latent variables.In M-step,the parameters which have closed expression can be directly solved,while the parameters which don’t are solved by one-step Newton-Raphson iterative.Numerical simulations and real data analysis from the AIDS clinical trial data verify the practical application value of the proposed model.2.Based on the joint analysis of longitudinal data and interval-censored failure time data,simultaneous variable selection and estimation the joint model in the framework of divergent by using the Broken Adaptive Ridge Regression（BAR）penalty function.We present the BAR penalized procedure that has both the oracle property and group effect.It approximates the L0-penalized regression using an iteratively reweighted L2-penalized algorithm and has the advantages of simultaneous parameter estimation,variable selection and clustering.Also the BAR iterative algorithm is fast and converges to a unique global optimal solution.At the same time compare it to the traditional penalty functions LASSO,ALASSO,MCP,SCAD,SELO and SICA,and the simulation results show that the BAR penalty function is superior to other penalty functions.3.Analysis model selection of the joint model of longitudinal data and interval-censored failure time data with time-varying coefficients.This model is an extensions of the classical joint model.It is flexibility and interpretability.Consider the B-spline function to estimate the unknown coefficient functions and simultaneous variable selection and estimation by using the BAR,group ALASSO penalty function.To make sure that the Q function always goes down,we propose a modified MCEM algorithm based on poisson potential variables and random effects to estimate the maximum likelihood of the parameters in the joint model.In E-step,the Gibbs sampler algorithm is presented for sampling observations from the conditional distribution to estimate random effects and Poisson latent variables.In M-step,approximation the Q function by using modified local quadratic approximation algorithm for minimizing penalized convex loss functions.The proposed algorithm iteratively solves penalized local quadratic approximations of the loss function,and then modifies the solution whenever it fails to decrease the original penalized loss function（Lee et al.2016）.And simulation results verify the effectiveness of the proposed method.