Cox's Regression Model for Counting Processes: A Large Sample Study

TLDR

The Cox regression model for censored survival data assumes covariates have a proportional effect on the hazard function of an individual's lifetime distribution. We extend this model to allow covariate processes to have a proportional effect on the intensity of a multivariate counting process. This extension enables regression analysis of recurrent event intensities with time‑dependent covariates and complex censoring patterns. The resulting framework permits statistical regression of recurrent event intensities, yields asymptotically simple proofs via martingale techniques, and is illustrated with a practical example.

Abstract

The Cox regression model for censored survival data specifies that covariates have a proportional effect on the hazard function of the life-time distribution of an individual. In this paper we discuss how this model can be extended to a model where covariate processes have a proportional effect on the intensity process of a multivariate counting process. This permits a statistical regression analysis of the intensity of a recurrent event allowing for complicated censoring patterns and time dependent covariates. Furthermore, this formulation gives rise to proofs with very simple structure using martingale techniques for the asymptotic properties of the estimators from such a model. Finally an example of a statistical analysis is included.