Statistical Inference On Nonlinear Reproductive Dispersion Joint Models Of Longitudinal And Survival Data

In the research of medicine,life science,insurance and other fields,longitudinal and survival data are often collected simultaneously and are interrelated usually.If only one of them is analyzed separately,it is possible to get an unreliable conclusion.Therefore,in order to explore their mutual relationship and obtain effective statistical inference,many scholars establish the models that can handle simultaneously longitudinal and survival data,namely so-called joint models.At present,under the normality assumption of longitudinal responses,joint models have been widely studied.However,some data generated in practical problems do not satisfy normality assumption,at this time,if we still assume that the data follow a normal distribution,and implement modeling analysis to the data,we may obtain unreasonable or even wrong conclusions.For this reason,some scholars have studied the statistical inference problem on the joint models under the nonnormality assumption(such as partial t-distribution,finite mixed normal distribution,etc.).However,up to now,there have been no few studies on the joint models of longitudinal responses following the reproductive dispersion family.Thence,this paper studies the statistical inference on the nonlinear reproductive dispersion joint models of longitudinal and survival data has very crucial theoretical and realistic significance.This paper studies the nonlinear reproductive dispersion joint models of longitudinal and survival data:(1)Under the assumption that the longitudinal responses follow a reproductive dispersion family,we establish a nonlinear reproductive dispersion joint modeling of longitudinal and survival data;(2)Regarding random effects as missing data,using Bayesian penalty splines to approximate the unspecified nonparametric functions in the survival submodel,combining Gibbs sampling and MH algorithm,we propose a MCMC(Markov Chain Monte Carlo)method that can solves simultaneously unknown parameters and random effects in the considered joint models,based on the MCMC method,we obtain the joint Bayesian estimates of unknown parameters and random effects;(3)We investigate simulation studies of the nonlinear reproductive dispersion joint models,and use the considered joint models to analyze clinical trial data of PBC(Primary Biliary Cirrhosis);(4)We investigate Bayesian local influence analysis for the considered joint models in this paper.The results of simulation studies show that the Bayes method based on the MCMC algorithm is very effective in solving unknown parameters and nonparametric functions in the nonlinear reproductive dispersion joint models,and the Bayesian local influence diagnosis methods proposed for the joint models can identify inappropriate prior settings,influential longitudinal response points in the longitudinal process,and influential event times in the survival process.The results of analysis for PBC data show that the results of the joint models are significantly different from those of the survival model alone,and fitting the data with the nonlinear reproductive dispersion joint models can get better results.