Cited by 4,419Statistical Methods and InferenceProbability and Statistical ResearchStatistical Distribution Estimation and Applications

Cox’s regression model for counting processes: A large sample study

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Andersen, P. K., Gill, R. D.·1982·The Annals of Statistics

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.

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  • An additional pre-specified analysis, the Andersen-Gill model using a Cox proportional-hazard with the counting-process formulation, was performed to model the total events.

    “An additional pre-specified analysis, the Andersen-Gill model using a Cox proportional-hazard with the counting-process formulation, was performed to model the total events (50,51).”

    From Effects of Icosapent Ethyl on Total Ischemic Events (2019) · cites this paper as [50]

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Research works printed but not linked: 3

  1. BAILEy, K. R. (1979). The general maximum likelihood approach to the Cox regression model. Ph.D. dissertation, University of Chicago, Chicago, Illinois.
  2. DoLivo, F. G. (1974) Counting processes and integrated conditional rates: a martingale approach with application to detection theory. Ph.D. thesis, University of Michigan.
  3. RockAFELLAR, R. T. (1970). Convex analysis. Princeton University Press, Princeton.

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Authors
Andersen, P. K., & Gill, R. D.
Venue
The Annals of Statistics
Published
1982-12-01
Volume
10
Issue
4
Pages
1100-1120
ISSN
  • 0090-5364 (ISSN-L)
  • 2168-8966
OpenAlex
W1986705681
Cited by
4,419
References
26
Citations by year
2026: 174 · 2025: 189 · 2024: 217 · 2023: 180 · 2022: 207 · 2021: 244 · 2020: 228 · 2019: 197 · 2018: 219 · 2017: 162 · 2016: 181 · 2015: 181 · 2014: 189 · 2013: 163 · 2012: 148
FWCI
20.56
Type
journal article
Language
en
Open access
Locations
  • The Annals of Statistics (publishedVersion)
  • Project Euclid (Cornell University) (submittedVersion)
Topics
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
  • Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
Keywords
Cox regression model, counting processes, recurrent events, intensity process, censoring, time-varying covariates, martingale method, asymptotic properties, estimators

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