The Annals of Statistics

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

P. K. Andersen and R. D. Gill

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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.

Article information

Ann. Statist., Volume 10, Number 4 (1982), 1100-1120.

First available in Project Euclid: 12 April 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62F12: Asymptotic properties of estimators
Secondary: 62G05: Estimation 62M99: None of the above, but in this section 62P10: Applications to biology and medical sciences

Censoring intensity martingale survival analysis time dependent covariates


Andersen, P. K.; Gill, R. D. Cox's Regression Model for Counting Processes: A Large Sample Study. Ann. Statist. 10 (1982), no. 4, 1100--1120. doi:10.1214/aos/1176345976.

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