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Estimates of marginal survival for dependent competing risks based on an assumed copula
Abstract
When time to death and time to censoring are associated one may be appreciably misled when the marginal survival functions are estimated using the product-limit estimators, which assume independent censoring. If no assumption about the relationship between the two times is made, the marginal survival functions are not identifiable. A natural function that defines the association between the two random variables is the copula. We show that if this function is known then the competing risks data are suflScient to identify the marginal survival functions and construct a suitable estimator. This estimator is consistent and reduces to the Kaplan-Meier estimator when death and censoring times are independent. This statistic can be used to provide bounds on the marginal survival functions based on a range of possible associations between the competing risks.
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Cites
The Jackknife, the Bootstrap and Other Resampling Plans
Efron, B. (1982) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9781611970319 · Cited by 8,120
Cited by
Understanding Relationships Using Copulas
Frees, E. W., & Valdez, E. A. (1998) · North American Actuarial Journal · doi:10.1080/10920277.1998.10595667 · Cited by 1,257
Frailty Models in Survival Analysis
Wienke, A. (2010) · Chapman & Hall/CRC eBooks · doi:10.1201/9781420073911 · Cited by 454
Metadata
- Authors
- ZHENG, M., & KLEIN, J. P.
- Venue
- Biometrika
- Publisher
- Oxford University Press (OUP)
- Published
- 1995-03-01
- Volume
- 82
- Issue
- 1
- Pages
- 127-138
- ISSN
- 0006-3444 (ISSN-L)
- 1464-3510
- OpenAlex
- W2001683154
- Cited by
- 325
- References
- 1
- FWCI
- 4.34
- Type
- journal article
- Language
- en
- Open access
- closed
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- ZHENG, M., & KLEIN, J. P. (1995). Estimates of marginal survival for dependent competing risks based on an assumed copula. Biometrika. https://doi.org/10.1093/biomet/82.1.127
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