Modelling long term survival with non-proportional hazards

In this work I consider models for survival data when the assumption of proportionality does not hold. The thesis consists of an Introduction, five papers, a Discussion and an Appendix. The Introduction presents technical information about the Cox model and introduces the ideas behind the extensions of the model proposed later on. In Chapter 2, reduced-rank methods for modelling non-proportional hazards are presented while Chapter 3 presents an algorithm for estimating Cox models with time varying effects of the covariates. The next Chapter deals with the gamma frailty (Burr) model and discusses alternative models with time dependent frailties. In Chapter 5 models with time varying effects of the covariates, frailty models and cure rate models are considered. The usefulness of each one of these models is discussed and their results are compared. The sixth Chapter of the thesis discusses ways of dealing with overdispersion when using generalized linear models. The Discussion is about future directions of the research presented in this thesis. Finally, there is an Appendix about the use of coxvc, a package written in R for fitting Cox models with time varying effects of the covariates.ZonMW project (ZON 912.02.015)UBL - phd migration 201