Fitting parametric counting-processes by using log-linear models

Abstract

Counting processes constitute a means of describing how and when a series of events occurs to individuals. The risk or intensity of events, which may vary over time, can depend on any aspects of the previous history of the individual. Standard log-linear regression modelling techniques are used to choose from the explanatory variables those which are appropriate to describe this dependence on the past. Details are given on how to set up such repeated measurements of duration among events as log-linear models. Two examples show how the technique can be used, even for simple survival data, to choose between models of different complexity and highlight the importance of dependence on the past for repeated events such as infection due to chronic granulotomous disease in the study of the effect of gamma interferon treatment.