Fitting Parametric Counting Processes by Using Log-Linear Models

TLDR

Counting processes model the timing and occurrence of events, with risk or intensity varying over time and depending on an individual’s prior history. The authors employ standard log‑linear regression to select explanatory variables and set up repeated‑measurement duration models for events. Two examples demonstrate the method’s utility for simple survival data, enabling model selection of varying complexity and underscoring the role of past dependence in repeated events such as infection in chronic granulotomous disease under gamma‑interferon treatment.

Abstract

SUMMARY 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.