The DOI matches its Crossref record; 25 of the 26 references it cites were found in a registry or an index.
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 (50,51).”
From Effects of Icosapent Ethyl on Total Ischemic Events (2019) · cites this paper as [50]
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Cites
Convergence of Probability Measures
Billingsley, P. (1999) · Wiley series in probability and statistics · doi:10.1002/9780470316962 · Cited by 14,153
Linear Statistical Inference and its Applications
Rao, C. R. (1973) · Wiley series in probability and statistics · doi:10.1002/9780470316436 · Cited by 10,474
Covariance Analysis of Censored Survival Data
Breslow, N. E. (1974) · Biometrics · doi:10.2307/2529620 · Cited by 1,778
Nonparametric Inference for a Family of Counting Processes
Aalen, O. O. (1978) · The Annals of Statistics · doi:10.1214/aos/1176344247 · Cited by 1,505
Milner, R. (1976) · Cited by 742
Censoring and Stochastic Integrals
Gill, R. D. (1980) · Statistica Neerlandica · doi:10.1111/j.1467-9574.1980.tb00692.x · Cited by 660
Self-citationA Large Sample Study of Cox's Regression Model
Tsiatis, A. A. (1981) · The Annals of Statistics · doi:10.1214/aos/1176345335 · Cited by 482
A Model for Nonparametric Regression Analysis of Counting Processes
Aalen, O. O. (1980) · Lecture notes in statistics · doi:10.1007/978-1-4615-7397-5_1 · Cited by 383
Central limit theorems for local martingales
Rebolledo, R. (1980) · Probability Theory and Related Fields · doi:10.1007/bf00587353 · Cited by 254
Testing Goodness of Fit of Cox's Regression and Life Model
Andersen, P. K. (1982) · Biometrics · doi:10.2307/2530289 · Cited by 242
Self-citation
Research works printed but not linked: 3
- BAILEy, K. R. (1979). The general maximum likelihood approach to the Cox regression model. Ph.D. dissertation, University of Chicago, Chicago, Illinois.
- DoLivo, F. G. (1974) Counting processes and integrated conditional rates: a martingale approach with application to detection theory. Ph.D. thesis, University of Michigan.
- RockAFELLAR, R. T. (1970). Convex analysis. Princeton University Press, Princeton.
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The Robust Inference for the Cox Proportional Hazards Model
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Metadata
- 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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