Regression analysis of longitudinal covariates with censored and longitudinal outcome

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] Longitudinal data contain repeated measurements of variables on the same experimental subject. It is often of interest to analyze the relationship between these variables. Typically, there is one or several longitudinal covariates and a response variable that can be either longitudinal or time to an event. Regression models can be employed to analyze these relationships. Ideally, longitudinal variables should be continuously monitored and their complete trajectories along the time are observed. Practically, however, this is unrealistic, either economically or methodologically. Often one only obtains so called sparse longitudinal data, where variables are intermittently observed at relatively sparse time points within the period of study. Such sparse longitudinal data give rise to an issue for the analysis of the response of time to an event, where survival analysis is typically implemented, e.g. the Cox model or additive hazards model. In both models, the values of covariates of all subjects at risk are needed in order to calculate the partial likelihood. But in the case of sparse longitudinal data, the availability of these observations may not be satis fied. Moreover, if the response variable is also longitudinal, it is possible that the response and covariates are not observed altogether, or at least not close to each other enough to be considered as observed simultaneously. Although a wealth of studies have been dedicated to longitudinal data analysis, very few of them have seriously considered and rigorously studied the situation aforementioned. In this dissertation, we discuss the regression analysis of longitudinal cavities with censored and longitudinal outcome. To be specific, Chapter 2 targets the additive hazards models with sparse longitudinal covariates, Chapter 3 studies the partially linear models with longitudinal covariates and response observed at mismatched time points, also known as asynchronous longitudinal data, and Chapter 4 explores longitudinal data with more complex structures with linear models. Kernel weighting technique is the key idea to all the stated researches. Estimators are derived based on kernel weighting technique and their asymptotical properties were rigorously examined, along with simulation studies for their fi nite sample performance, and illustrations using real data sets.