Proportional Hazards Model for Right Censored Survival Data with Longitudinal Covariates

Abstract

The proportional hazards model is one of the most widely used tools in analyzing survival data. In medical and epidemiological studies, the interrelationship between time-to-event variable and longitudinal covariates is often the primary research interest. Thus, joint modeling of survival data and longitudinal data has received very much attention in statistical literature, but it's a considerably difficult problem due to censoring on the survival time and that the longitudinal covariate process is in fact a completely unknown and not completely observed stochastic process. Up to now, all existing works made parametric or semi-parametric assumptions on the longitudinal covariate process, and resulting inferences critically depends on validity of these not justifiable assumptions. This dissertation does not make any parametric or semi-parametric assumptions on the longitudinal covariate process. We use the empirical likelihood method to derive the maximum likelihood estimator (MLE) for the proportional hazards model based on right censored survival data with longitudinal covariates. Computation algorithm is developed here and our simulation studies show that our MLE performs very well.