Bayesian Analysis For Semi-parametric Model Of Longitudinal Data With Non-Random Missing Mechanism

In many clinical trials and medical follow-up studies,longitudinal data collected by researchers often suffer from attrtion,which may lead to biased estimates of the model parameters.Hence,it is necessary to dispose of missing data to improve the quality of data analysis.In the process of processing missing data,longitudinal missing data are classified into two types,namely Intermittent missingness and Dropout for discussion and research,according to the different causes of longitudinal missing data.This paper assumes that the longitudinal response variables have a nonlinear relationship with the observed time points,and the random effects are modeled based on a semi-parametric approach,thus modeling the longitudinal data with a linear mixed-effects semi-parametric model and combining the model of missing data,a semi-parametric joint model of longitudinal data with non-random missing mechanism is established.This paper performs variable selection,bayesian estimation of the parameters of interest for this joint model and models comparison in a bayesian framework.Firstly,a longitudinal model is discussed based on the semi-parametric approach,and the prior distribution of random effects is modeled by a Centralization Dirichlet Process Mixture Model(CDPMM),which can availably capture the potential prior information of random effects and make the parameters estimation more robust; Secondly,the modeling methods of two major types of missing data,namely Intermittent missingness and Dropout,under the non-random missing mechanism are discussed and the transition probabilities model of Intermittent missingness and Dropout is established,by sharing random effects,the longitudinal semi-parametric model and the transition probabilities model are linked to form a joint semi-parametric model of longitudinal data with nonrandom missing mechanism; Then,bayesian estimates are made for the established joint semi-parametric model in a bayesian framework,for better analysis,the hybrid algorithm combining MH algorithm and Gibbs sampling is used,and the B-splines method is suggested to fit the smoothing function of observed time points of the longitudinal data,the BLasso method is applied to the variable selection of the parameters of interest to identify the important variables in the model,at the same time,the proposed model is compared with other competing models; Finally,the feasibility of the proposed model in this paper is verified by simulation studies and an example analysis of the ACTG-193 A study data for the joint semi-parametric model of longitudinal data with non-random missing mechanism.