Title: Statistical Analysis of Complex Data in Survival and Event History Analysis
Description: This thesis studies two aspects of the statistical analysis of complex data in survival and event history analysis. After a short introduction to survival and event history analysis in Chapter 1, we proposed a multivariate proportional intensity factor model for multivariate counting processes in Chapter 2. In an exploratory analysis on process data, a large number of possibly time-varying covariates maybe included. These covariates along with the high-dimensional counting processes often exhibit a low-dimensional structure that has meaningful interpretation. We explore such structure through specifying random coefficients in a low dimensional space through a factor model. For the estimation of the resulting model, we establish the asymptotic theory of the nonparametric maximum likelihood estimator (NPMLE). In particular, the NPMLE is consistent, asymptotically normal and asymptotically efficient with covariance matrix that can be consistently estimated by the inverse information matrix or the profile likelihood method under some suitable regularity conditions.

Furthermore, to obtain a parsimonious model and to improve interpretation of parameters therein, variable selection and estimation for both fixed and random effects are developed by penalized likelihood. We illustrate the method using simulation studies as well as a real data application from The Programme for the International Assessment of Adult Competencies (PIAAC). Chapter 3 concerns rare events and sparse covariates in event history analysis. In large-scale longitudinal observational databases, the majority of subjects may not experience a particular event of interest. Furthermore, the associated covariate processes could also be zero for most of the subjects at any time. We formulate such setting of rare events and sparse covariates under the proportional intensity model and establish the validity of using the partial likelihood estimator and the observed information matrix for inference under this framework.