Semiparametric and nonparametric models for survival data

The Cox model usually assumes that the hazard rate is a product of an unspecified function of time common to all individuals and a known link function (usually exponential) of a linear combination of the covariates. It makes very restrictive assumptions that may not be realistic. If the assumptions are violated, misleading results can be obtained. In this dissertation, I have studied two flexible alternative models to the classical Cox model. We first consider the proportional hazards model with an unknown link function. We propose a method to estimate the link function and the regression parameters simultaneously. An iterative alternating optimization procedure is developed for efficient implementation. The proposed methods are illustrated using simulation and an application to two well-known medical data sets. In recent years, proportional odds model has been studied with great effect. It assumes that the odds ratio of two individuals is constant over time. However, this assumption needs to be justified in real data analysis. I will discuss a class of the time-varying coefficient linear cumulative-odds models which includes the proportional odds model as a special case. Estimation and inference procedure for this model are proposed. We illustrate our method by applying it to the node-positive primary breast cancer data