Cox’s regression model for counting processes: A large sample study
Open accessAbstract
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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- Authors
- Andersen, P. K., & Gill, R. D.
- ORCID
- Gill, R. D.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical 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
- bronze
- doi.org
- 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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