Identifying Multiple Change Points In Joint Modeling Of Longitudinal And Survival Data

For the simple and flexible model form and good fitting effect, change-point regres-sion is a popular application of statisticians, which is widely used in finance, insurance, medicine and other fields. The number and position identification of change points is the core content in change-point regression, which determines the form and estimate method of change-point regression model. This study applies a maximum likelihood method to identify the locations of change points directly, which overcome inherent limitations of Bayesian inference and gets the number and position of change points on the timeline directly through likelihood ratio test. That is, for Bayesian methods, the prior distribution always affects the posterior distribution which may not avoid the influence of subjective factors.Joint inference is a statistical method which combines the longitudinal and survival data model basing on the potential mutual effects involved. It joints the two models through shared covariates and random effects and obtains unbiased estimations of parameters using all the information that influence the results. Joint inference study has a bright prospect and wide range of application thanks to the variety of forms and estimating methods of the two models. Joint inference achieves an excellent analysis re-sults through simple model structure and avoids the errors of two type models'separate parameter estimation that have interaction effects.Based on joint inference theoretical framework, this thesis studies the identification method of multiple change points in linear mixed effects (LME) model. Firstly, the thesis briefly describes the significance, background, domestic and foreign research status of longitudinal and survival data joint model and change-point regression and shows the structure of this thesis. Secondly, the research introduces LME model in longitudinal data analysis and its likelihood inference method, as well as accelerated failure time (AFT) model in survival analysis, where LME model is possibly the most widely used method in longitudinal studies and AFT model specifies that predictors act multiplicatively on the failure time or additively on the log failure time. Thirdly, the thesis proposes a joint model which combines a LME longitudinal response model with multiple change points and a mixed-effects AFT model with respect to shared covariates and random effects, uses a Likelihood Ratio Test (LRT) to find the optimal number of change points, and estimates all the parameters through the maximum likelihood method with Gauss-Hermite approximation to deal with the intractable integrals. Fourthly, the thesis verifies the reliability of the change points identification and parameter estimations method through four schemes of numerical simulation. Fifthly, the thesis elucidates the suitability of the method through simulation studies and two real data application about primary biliary cirrhosis (PBC) and heart valve surgery (HVS). Sixthly, we do the conclusion and prospect of this thesis.