Bayesian Inference For The Joint Model Of Non-ignorable Missing And Skewed Distribution

Longitudinal data is a common data form in many fields such as medicine and psychology.Joint modeling is a common method to analyze longitudinal data.In this thesis,we break through the conventional empirical models and propose a new joint modeling method,which takes the nonlinear mixed effects model whose measurement error follows a skewed distribution as the covariate model and the generalized semi-parametric linear mixed effects model with a wider application range.Based on the joint model,Bayesian method is used to estimate the parameters.However,in the real data,there are some problems such as skewness,left deletion and non-ignorable missing values.In this thesis,we discuss the following two models:(1)The joint model which considers the left censored problem in the covariable;(2)The joint model considering the nonignorable missing problem of both covariate and response variables.For the first part of the thesis,considering that the data has data skewness,left-censoring and discretization problems at the same time,the nonlinear mixed effect model,generalized semi-parametric linear mixed effect model and left center-out model is used for joint modeling,and the parameters of the joint model are estimated by Bayesian method.Firstly,two skewness distributions,ST distribution and SN distribution,are considered for the error term of the nonlinear mixed effects model.Then R software is used to select the appropriate generalized semi-parameter linear mixed effect model and nonlinear mixed effect model according to the AIC/BIC values.Secondly,the left-censoring problem is considered and combined with the left censoring model.Finally,Bayesian estimation,Naive Bayesian estimation and two-step Bayesian estimation methods are used in Win BUGS software to estimate the parameters respectively.According to the estimated parameters,the observed-fit value curve of virus loading volume is drawn,and the skewness distribution of more fitted data is elected from ST distribution and SN distribution according to the predicted deviation EPD value.The skewness distribution is used for example analysis and simulation research.For the second part of the thesis,consindering the non-ignorable missing questions based on the first part.On the basis of the nonlinear mixed effects model,the generalized semi-parametric linear mixed effects model and the left censor model,a survival model to describe the non-ignorable missing problem is introduced for joint modeling.Using Win BUGS software,Bayesian estimation,Naive Bayesian estimation and two-step Bayesian estimation methods to estimate the parameters respectively.According to the estimated parameters,the observed-fit value curve of virus loading volume is drawn,and the skewness distribution of more fitted data is selected from ST distribution and SN distribution according to the predicted deviation EPD value.The skewness distribution is used for example analysis and simulation research.