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A Proportional Hazards Model for the Subdistribution of a Competing Risk
Jason P. Fine, Robert J. Gray. Journal of the American Statistical Association, 1999-06-01
Topic: Risk, prevention and care in population studies
With explanatory covariates, the standard analysis for competing risks data involves modeling the cause-specific hazard functions via a proportional hazards assumption. Unfortunately, the cause-specific hazard function does not have a direct interpretation in terms of survival probabilities for the particular failure type. In recent years many clinicians have begun using the cumulative incidence function, the marginal failure probabilities for a particular cause, which is intuitively appealing and more easily explained to the nonstatistician. The cumulative incidence is especially relevant in cost-effectiveness analyses in which the survival probabilities are needed to determine treatment utility. Previously, authors have considered methods for combining estimates of the cause-specific hazard functions under the proportional hazards formulation. However, these methods do not allow the analyst to directly assess the effect of a covariate on the marginal probability function. In this article we propose a novel semiparametric proportional hazards model for the subdistribution. Using the partial likelihood principle and weighting techniques, we derive estimation and inference procedures for the finite-dimensional regression parameter under a variety of censoring scenarios. We give a uniformly consistent estimator for the predicted cumulative incidence for an individual with certain covariates; confidence intervals and bands can be obtained analytically or with an easy-to-implement simulation technique. To contrast the two approaches, we analyze a dataset from a breast cancer clinical trial under both models.
Cite this study APA, Vancouver, BibTeX · download .bib or .ris
APA 7th
Fine, J. P., & Gray, R. J. (1999). A Proportional Hazards Model for the Subdistribution of a Competing Risk. Journal of the American Statistical Association. https://doi.org/10.1080/01621459.1999.10474144
Vancouver
Fine JP, Gray RJ. A Proportional Hazards Model for the Subdistribution of a Competing Risk. Journal of the American Statistical Association. 1999. doi:10.1080/01621459.1999.10474144.
BibTeX
@article{fine1999-cad7787c,
author = {Fine, Jason P. and Gray, Robert J.},
title = {{A Proportional Hazards Model for the Subdistribution of a Competing Risk}},
journal = {Journal of the American Statistical Association},
year = {1999},
doi = {10.1080/01621459.1999.10474144},
url = {https://doi.org/10.1080/01621459.1999.10474144}
}
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Why it matters
A statistics paper proposing a new proportional hazards model for competing risks data that directly assesses how a covariate affects the cumulative incidence of a particular type of failure. It is not about dementia; the worked example uses data from a breast cancer clinical trial.
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How this study scored 52/100
Published in a peer-reviewed journal. Scored zero for study design, sample size, effect reported, studied in people and randomized / blinded because the record does not state it. We have no data on strength of evidence and senior author's track record, so those were left out: it earned 47 of the 91 points we could judge it on, which is 52 out of 100.
| Component | Points | Why |
|---|---|---|
| Journal tier | 7 / 10 | Tier 3 — peer-reviewed journal (Journal of the American Statistical Association) |
| Journal's citation record | 4 / 4 | Journal of the American Statistical Association: journal h-index 634 (OpenAlex, 2026-10-29) |
| Study design | 0 / 12 | No study design recorded — scores zero, not guessed (not stated in the record — scored 0) |
| Strength of evidence | — / 5 | No evidence rating recorded — left out of this score |
| Peer-review validation | 10 / 10 | Peer-reviewed. Published as an article in a named peer-reviewed journal. |
| How recent | 1 / 5 | 1999 — older than 20 years, still counted |
| Sample size | 0 / 4 | Participant count not stated — scores zero (not stated in the record — scored 0) |
| Effect reported | 0 / 3 | No effect size reported — scores zero (not stated in the record — scored 0) |
| Studied in people | 0 / 3 | Not stated whether this was studied in people — scores zero (not stated in the record — scored 0) |
| Randomized / blinded | 0 / 2 | No randomization or blinding stated — scores zero (not stated in the record — scored 0) |
| Times cited | 7 / 7 | Cited 13,738 times (OpenAlex, 2026-10-10) |
| Citations per year | 5 / 5 | 473.7 citations a year over 29 year(s) since 1999 |
| Impact for its field and year | 4 / 6 | Cited 9.5× the average for papers of its field and year (OpenAlex FWCI) |
| Cited by studies here | 0 / 6 | No other study in this library cites it |
| Still being cited | 4 / 4 | Cited 2,535 times in 2024–2026 (2026 still in progress; OpenAlex) |
| Senior author's track record | — / 4 | Senior author's record not available — left out of this score |
| Institution's track record | 3 / 3 | Harvard University: institution h-index 3,235 (OpenAlex) |
| Multicenter collaboration | 1 / 3 | OpenAlex lists 3 institution(s) in 1 country |
| Indexed in PubMed | 1 / 2 | Not in PubMed, but has a DOI |
| Free to read | 0 / 2 | Behind a paywall — scores zero |
| Points | 47 / 91 | Scored on 18 of 20 parts. We have no data for the rest, so they are left out: 47 of the 91 points we could judge it on is 52 out of 100. |
| Total | 52 / 100 | — |
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