Semiparametric analysis of multivariate longitudinal data

Abstract

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] Longitudinal studies are conducted widely in fields such as agriculture and life sciences, business and industry, demography and other social sciences, medicine and public health. In longitudinal studies, individuals are measured repeatedly over time and multivariate longitudinal data occur when subjects are measured repeatedly with regard to multiple response variables. Analysis of multivariate longitudinal data can be challenging since it requires accounting for not only correlations between repeated measures of the same subject but also correlations among different response variables. One special type of longitudinal study involves monitoring subjects continuously to record occurrences of events and thus generates so-called recurrent event data. In the first part of this dissertation, we will discuss analysis of a set of multivariate longitudinal data arising from a prospective study of alcohol and drug use in college freshmen. Several statistical models and estimation approaches are presented for joint analysis of conducting alcohol and drug use. In particular, a marginal means model is proposed that leaves the correlation between response outcomes arbitrary. In the second part, regression analysis of multivariate recurrent event data with time-varying covariate effects will be considered. For the problem, we present some marginal models for the underlying counting processes and develop estimating equation based inference approaches. The asymptotic properties of the proposed estimates are established and their finite sample properties are evaluated through simulation studies. Additionally, some procedures are presented for testing the time-dependence of covariate effects and the proposed methodology is applied to sets of univariate recurrent event data and bivariate recurrent event data. The third part of this dissertation will consider variable selection for univariate and multivariate recurrent event data in the context of regression analysis. For the problem, we adopt the idea behind the nonconcave penalized likelihood approach proposed in Fan and Li (2001) and develop a nonconcave penalized estimating function approach. The proposed approach selects variables and estimates regression coefficients simultaneously and an algorithm is presented for this process. We show that the proposed approach performs as well as the oracle procedure, yielding estimates as if the correct submodel were known. Simulation studies conducted for assessing the performance of the proposed approach suggest that it works well for practical situations. The methodology is illustrated using a set of bivariate recurrent event data.