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

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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

DOI 10.1214/aos/1176345976

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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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Self-citation
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Self-citation

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Research works printed but not linked: 3

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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
DOI: 10.1214/aos/1176345976
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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Cox’s regression model for counting processes: A large sample study

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