Introduction to the Analysis of Survival Data in the Presence of Competing Risks
Open accessAbstract
Competing risks occur frequently in the analysis of survival data. A competing risk is an event whose occurrence precludes the occurrence of the primary event of interest. In a study examining time to death attributable to cardiovascular causes, death attributable to noncardiovascular causes is a competing risk. When estimating the crude incidence of outcomes, analysts should use the cumulative incidence function, rather than the complement of the Kaplan-Meier survival function. The use of the Kaplan-Meier survival function results in estimates of incidence that are biased upward, regardless of whether the competing events are independent of one another. When fitting regression models in the presence of competing risks, researchers can choose from 2 different families of models: modeling the effect of covariates on the cause-specific hazard of the outcome or modeling the effect of covariates on the cumulative incidence function. The former allows one to estimate the effect of the covariates on the rate of occurrence of the outcome in those subjects who are currently event free. The latter allows one to estimate the effect of covariates on the absolute risk of the outcome over time. The former family of models may be better suited for addressing etiologic questions, whereas the latter model may be better suited for estimating a patient’s clinical prognosis. We illustrate the application of these methods by examining cause-specific mortality in patients hospitalized with heart failure. Statistical software code in both R and SAS is provided.
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We accounted for clustering by DA using a robust sandwich covariance matrix.
“We accounted for clustering by DA using a robust sandwich covariance matrix(30).”
From Social inequalities in COVID-19 death by area-level income in 11.2 million people in Ontario, Canada: patterns over time and the mediating role of vaccination. (2026) · cites this paper as [30]
The Statistical Software for Competing Risks Analyses section describes software for fitting survival models, but does not discuss robust sandwich covariance matrices or adjustment for clustering by DA. Searches for those methods and clustered-data variance estimation found no passage addressing them in our copy. (LLM, conf=0.75)
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- Authors
- Austin, P. C., Lee, D. S., & Fine, J. P.
- Affiliations
- University of North Carolina at Chapel Hill (US)
- University Health Network (CA)
- Corresponding author
- Austin, Peter C.
- Venue
- Circulation
- Published
- 2016-02-09
- Volume
- 133
- Issue
- 6
- Pages
- 601-609
- ISSN
- 0009-7322 (ISSN-L)
- 1524-4539
- PMC
- PMC4741409
- OpenAlex
- W2264767503
- Cited by
- 2,653
- References
- 3
- Citations by year
- 2026: 359 · 2025: 305 · 2024: 377 · 2023: 326 · 2022: 331 · 2021: 278 · 2020: 258 · 2019: 160 · 2018: 139 · 2017: 78 · 2016: 38 · 2014: 2
- FWCI
- 139.88
- Type
- journal article
- Language
- en
- Open access
- green
- www.ncbi.nlm.nih.gov
- Licence
- cc-by-nc-nd
- Locations
- Circulation (publishedVersion)
- PubMed Central (publishedVersion, cc-by-nc-nd)
- PubMed (publishedVersion)
- Carolina Digital Repository (University of North Carolina at Chapel Hill) (submittedVersion)
- UNC Libraries
- Funders
- Heart and Stroke Foundation of Canada
- Institute for Clinical Evaluative Sciences
- Ontario Ministry of Health and Long-Term Care
- Canadian Institutes of Health Research (86508, MOP86508)
- 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 Methods in Epidemiology
- Keywords
- competing risks, survival analysis, cumulative incidence function, cause-specific hazard, incidence estimation, heart failure mortality, cardiovascular mortality, absolute risk, prognostic model
- MeSH terms
- Aged, Aged, 80 and over, Cardiovascular Diseases, Female, Humans, Male, Risk Factors, Statistics as Topic, Models, Statistical, Survival Analysis, Databases, Factual, Kaplan-Meier Estimate
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