Abstract
Two methods dominate the regression analysis of time-to-event data: the accelerated failure time model and the proportional hazards model. Broadly speaking, these predominate in reliability modelling and biomedical applications, respectively. However, many other methods have been proposed, including proportional odds, proportional mean residual life and several other “proportional” models. This paper presents an overview of the field and the concept behind each of these ideas. Multi-parameter modelling is also discussed, in which (in contrast to, say, the proportional hazards model) more than one parameter of the lifetime distribution may depend on covariates. This includes first hitting time (or threshold) regression based on an underlying latent stochastic process. Many of the methods that have been proposed have seen little or no practical use. Lack of user-friendly software is certainly a factor in this. Diagnostic methods are also lacking for most methods.