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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Gisev, N., Bharat, C., Larney, S., Dobbins, T., Weatherburn, D., Hickman, M., Farrell, M., & Degenhardt, L. J. (2019) · The Lancet Public Health · doi:10.1016/s2468-2667(19)30060-x · Cited by 49
Longitudinal adherence to maternal antiretroviral therapy and infant Nevirapine prophylaxis from 6 weeks to 18 months postpartum amongst a cohort of mothers and infants in South Africa
Larsen, A., Magasana, V., Dinh, T., Ngandu, N. K., Lombard, C. J., Cheyip, M., Ayalew, K., Chirinda, W., Kindra, G., Jackson, D. J., et al. (2019) · BMC Infectious Diseases · doi:10.1186/s12879-019-4341-4 · Cited by 52
Protection From Natural Immunity Against Enteric Infections and Etiology-Specific Diarrhea in a Longitudinal Birth Cohort
McQuade, E. T. R., Liu, J., Kang, G., Kosek, M. N., Lima, A. Â. M., Bessong, P. O., Samie, A., Haque, R., Mduma, E. R., Shrestha, S. K., et al. (2020) · The Journal of Infectious Diseases · doi:10.1093/infdis/jiaa031 · Cited by 45
“To model these effects, we used the Andersen and Gill extension of the Cox model for recurrent events [21] with a counting process formulation.”
Method
Analytic strategies for recurrent events in epidemiologic studies
Stürmer‎, T., Glynn, R. J., Kliebsch, U., & Brenner, H. (2000) · Journal of Clinical Epidemiology · doi:10.1016/s0895-4356(99)00137-7 · Cited by 46
A Modification of the Redistribution to the Right Algorithm Using Disease Markers
Malani, H. M. (1995) · Biometrika · doi:10.1093/biomet/82.3.515 · Cited by 49
A Generalized Moments Specification Test of the Proportional Hazards Model
Horowitz, J. L., & Neumann, G. R. (1992) · Journal of the American Statistical Association · doi:10.1080/01621459.1992.10475197 · Cited by 49
Statistical survival analysis of male larynx‐cancer patients ‐ a case study
Kardaun, O. (1983) · Statistica Neerlandica · doi:10.1111/j.1467-9574.1983.tb00806.x · Cited by 49
Temporal process regression
Fine, J. P., Yan, J., & Kosorok, M. R. (2004) · Biometrika · doi:10.1093/biomet/91.3.683 · Cited by 49
An Exact Corrected Log‐Likelihood Function for Cox's Proportional Hazards Model under Measurement Error and Some Extensions
Augustin, T. (2004) · Scandinavian Journal of Statistics · doi:10.1111/j.1467-9469.2004.00371.x · Cited by 49
Robustness of Survival Estimates from Radio-Telemetry Studies with Uncertain Relocation of Individuals
Bunck, C. M., Chen, C.-L., & Pollock, K. H. (1995) · Journal of Wildlife Management · doi:10.2307/3801958 · Cited by 49
Hearing and justice: The link between hearing impairment in early childhood and youth offending in Aboriginal children living in remote communities of the Northern Territory, Australia
He, V. Y., Su, J., Guthridge, S. L., Malvaso, C., Howard, D., Williams, T., & Leach, A. J. (2019) · Health & Justice · doi:10.1186/s40352-019-0097-6 · Cited by 48
“In the multivariable analysis, the Cox proportional hazard method was used to examine the association between HI and the youth offending (defined by first offence) (Andersen and Gill 1982).”
Method
Early primary care physician contact and health service utilisation in a large sample of recently released ex-prisoners in Australia: prospective cohort study
Young, J. T., Arnold-Reed, D. E., Preen, D. B., Bulsara, M. K., Lennox, N., & Kinner, S. A. (2015) · BMJ Open · doi:10.1136/bmjopen-2015-008021 · Cited by 48
Major adverse cardiac events in elderly patients with coronary artery disease undergoing noncardiac surgery: A multicenter prospective study in China
Xu, L., Yu, C., Jiang, J., Zheng, H., Yao, S., Pei, L., Li, S., Xue, F., & Huang, Y. (2015) · Archives of Gerontology and Geriatrics · doi:10.1016/j.archger.2015.07.006 · Cited by 48
Explorative data analysis of MCL reveals gene expression networks implicated in survival and prognosis supported by explorative CGH analysis
Blenk, S., Engelmann, J. C., Pinkert, S., Weniger, M., Schultz, J., Rosenwald, A., Müller‐Hermelink, H. K., Müller, T., & Dandekar, T. (2008) · BMC Cancer · doi:10.1186/1471-2407-8-106 · Cited by 48
Migration cues and timing in leatherback sea turtles
Sherrill-Mix, S. A., James, M. C., & Myers, R. A. (2007) · Behavioral Ecology · doi:10.1093/beheco/arm104 · Cited by 48
Clinical trial design principles and endpoint definitions for transcatheter mitral valve repair and replacement: part 1: clinical trial design principles
Stone, G. W., Vahanian, A. S., Adams, D. H., Abraham, W. T., BORER, J. S., Bax, J. J., Schöfer, J., Cutlip, D. E., Krucoff, M. W., Blackstone, E. H., et al. (2015) · European Heart Journal · doi:10.1093/eurheartj/ehv281 · Cited by 52
Prognostic Value of Long-Term Blood Pressure Changes in Patients with Chronic Heart Failure
Schmid, F. A., Schlager, O., Keller, P., Seifert, B., Huang, R., Fröhlich, G., Lüscher, T. F., Ruschitzka, F. T., & Enseleit, F. (2017) · European Journal of Heart Failure · doi:10.1002/ejhf.805 · Cited by 48
Epidemiology of viral acute lower respiratory infections in a community-based cohort of rural north Indian children
Krishnan, A., Kumar, R., Broor, S., Gopal, G., Saha, S. S., Amarchand, R., Choudekar, A., Purakayastha, D. R., Whitaker, B., Pandey, B. G., et al. (2019) · Journal of Global Health · doi:10.7189/jogh.09.010433 · Cited by 48
Survival benefit of multidisciplinary care in amyotrophic lateral sclerosis in Spain: association with noninvasive mechanical ventilation
Paipa, A., Povedano, M., Barceló, M. A., Domínguez, R., Sáez, M., Turón‐Sans, J., Prats, E., Farrero, E., Virgili, M. N., Matos, J. M., et al. (2019) · Journal of Multidisciplinary Healthcare · doi:10.2147/jmdh.s205313 · Cited by 48
Association of Blood Donor Sex and Prior Pregnancy With Mortality Among Red Blood Cell Transfusion Recipients
Edgren, G., Murphy, E. L., Brambilla, D. J., Westlake, M., Rostgaard, K., Lee, C., Cable, R. G., Triulzi, D. J., Bruhn, R. L., Lezin, E. S., et al. (2019) · JAMA · doi:10.1001/jama.2019.7084 · Cited by 48
Pregnancy and risk of COVID‐19: a Norwegian registry‐linkage study
Magnus, M. C., Oakley, L., Gjessing, H. K., Stephansson, O., Engjom, H. M., Macsali, F., Júlíusson, P. B., Andersen, A.-M. N., & Håberg, S. (2021) · BJOG An International Journal of Obstetrics & Gynaecology · doi:10.1111/1471-0528.16969 · Cited by 47

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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