The Wide Variety of Regression Models for Lifetime Data

Abstract

The dependence of lifetimes on covariates can be modelled in a regression format in various ways. In some fields, especially biostatistics, the most familiar approach is through the proportional hazards assumption. Less widely used is the proportional odds model and there are other “proportional” models in the literature, notably proportional reversed hazards and proportional mean residual life. Another approach, possessing the conceptual advantage of being based on a representation of the underlying process leading to the event (such as death or failure), is threshold regression in which (in the Inverse Gaussian case) two parameters of the underlying distribution are modelled. Burke and Mackenzie have also introduced a multi-parameter regression. I present and discuss these models, their differences and in what circumstances each is useful. Some theoretical relations are presented.