ABSTRACT
This chapter begins with a description of a number of possible distributions for survival times, including the exponential, Weibull, log-logistic and Gompertz distributions. Methods for assessing the suitability of possible models are described, and there is a detailed description of how they can be fitted using the method of maximum likelihood. Techniques for comparing alternative models are also summarised. The accelerated failure time family of models, an alternative to proportional hazards models, is presented. This family includes many parametric models and underpins most computer software for fitting parametric models to survival data. Particular accelerated failure time models are described and illustrated using a number of examples. The use of a time ratio or acceleration factor to summarise the impact of an explanatory variable on survival is also considered. Another general class of models, the proportional odds model, is introduced and the log-logistic proportional odds model illustrated. The chapter also includes a section on modelling cure rates.
