Survival analysis with incomplete observation or insufficient follow-up

Abstract

In the first part of the thesis, we address the issue of missing covariates in survival analysis. One approach to handle missing data is the likelihood-based approach, where the incomplete variables are modeled. Although likelihood-based approaches are theoretically appealing, they often become computationally inefficient or even infeasible when dealing with a large number of missing variables. We consider the Cox regression model with Gaussian covariates that are missing at random. We develop an expectation-maximization (EM) algorithm for nonparametric maximum likelihood estimation, utilizing a transformation technique in the E-step that involves only one-dimensional integration. This innovation enhances the scalability of our methods with respect to the dimensionality of the missing variables. We demonstrate the feasibility and advantages of the proposed methods over existing methods via large-scale simulation studies and apply the proposed methods to a cancer genomic study. In the second part of the thesis, we address the issue of insufficient follow-up in survival analysis with a cure fraction. For some events of interest, not all subjects are susceptible; these non-susceptible subjects are referred to as being cured. When follow-up time is insufficient, the survival model may not be identifiable, and, in particular, the cure probability may not be consistently estimated. We focus on the promotion time cure model and develop a two-step approach for estimation. In the first step, we perform nonparametric maximum likelihood estimation. In the second step, we utilize extreme value theory and the tail behavior of the estimated hazard function to extrapolate the cure probability. We demonstrate the feasibility and advantages of the proposed methods using large-scale simulation studies.