Local Estimation Method And Application For Nonparametric And Semiparametric Regression Models With Longitudinal Data

Longitudinal data are common in social, economic, biomedicine, epidemiology and other fields of natural and social science. Regression analysis is commonly used to study the relationship between a response variable and a vector of covariates. Specifically, in recent years nonparametric and semiparametric regression models have attracted a great deal of attention due to their flexibility and power to uncover hidden relationship between the response and covariates. Hence, we focus on local estimation method for nonparametric and semiparametric regression models with longitudinal data. The main works are as follows:(1) Varying-coefficient models are very useful for longitudinal data analysis. In Chap-ter 2, we discuss varying-coefficient models for longitudinal data. We develop a new estimation procedure, incorporating the within-subject correlation, to estimate the corre-lation structure and regression function simultaneously, based on Cholesky decomposition and profile least squares techniques. Asymptotic normality for the proposed estimators of varying-coefficient functions are established. Extensive simulations and real data ap-plication are employed to confirm the efficiency of proposed estimations.(2) Single index models are natural extensions of linear models and overcome the so-called "curse of dimensionality". They are very useful for longitudinal data analysis. In Chapter 3, we develop a new efficient estimation procedure for single index models with longitudinal data, based on Cholesky decomposition and local linear smoothing method. Asymptotic normality for the proposed estimators of both the parametric and nonpara- metric parts are established. Monte Carlo simulation studies and real data analysis show that the proposed estimations has stable and excellent performance.(3) Vascular access for hemodialysis is of paramount importance. Although stud-ies have found that central venous catheter is often associated with poor outcomes and switching to arteriovenous fistula is beneficial, it has not been fully elucidated how the effect of switching of access on outcomes changes over time and whether the effect de-pends on switching time. Analysis of the longitudinal data needs to account for changes over multiple time indices. In Chapter 4 we propose a flexible model that jointly models the change over treatment time, the trend over calendar time, the change associated with treatment switching and time-varying effects of covariates. The effect of switching may depend on both the time of switching and time since switching. All unknown functions are modeled nonparametrically using local linear smoothers and estimated using a back-fitting procedure. Large sample properties are studied. Simulation studies show excellent finite-sample performance. Our methods are applied to investigate the effect of vascular access change on albumin in dialysis patients. It is concluded that the benefit of switching from central venous catheter to arteriovenous fistula depends on the time of switching, the sooner the better.(4) Vascular access complications have been the major cause of excessive morbid-ity and mortality in the dialysis population. They also account for a large portion of hospitalisation for dialysis patients and are a main contributor to the high dialysis care cost. In Chapter 5 we investigate whether switching from a central venous catheter to an arteriovenous fistula sooner is associated with smaller hospitalisation rate. We propose a flexible generalised treatment switching effect model. We model all unknown functions nonparametrically using local linear smoothers and estimate them using weighted local quasi-likelihood. We show that the proposed estimators have the desirable large-sample properties and excellent performance in simulations. Application of the proposed method to a real data set indicates that hospitalisation rate is smaller when patients switch from a central venous catheter to an arteriovenous fistula sooner. The proposed methods are general which are applicable to other situations with treatment switching.The achievements and methodologies in our study enrich the estimation theory of nonparametric and semiparametric regression models with longitudinal data, which also help to analyse the complicated and volatile problems in many application fields, such as economics and biometrics.