Competing Risks Survival Analysis
Also known as: Rekabet Eden Riskler Analizi, cumulative incidence function, CIF analysis, cause-specific survival analysis
Competing risks analysis, formalized by Fine and Gray in 1999, is a survival analysis framework for settings where a subject can experience one of several mutually exclusive event types. The key quantity is the cumulative incidence function (CIF), which estimates the probability of a specific event occurring by time t in the presence of the other competing events.
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When to use it
Use competing risks analysis when subjects are at risk for two or more mutually exclusive event types and you want to estimate the absolute probability of each. The method requires time-to-event data with a cause indicator, non-informative censoring, and — for the Fine-Gray regression step — the proportional subdistribution hazards assumption. A minimum of 100 observations is recommended to allow stable estimation of separate CIFs. When covariates must be adjusted for and the proportional subdistribution hazards assumption holds, the Fine-Gray model is the appropriate tool; when only a descriptive CIF is needed without regression, the non-parametric Aalen-Johansen estimator suffices.
Strengths & limitations
- Provides the cumulative incidence function, which is the clinically and epidemiologically meaningful probability of the event of interest in the presence of competing causes.
- Avoids the upward bias of Kaplan-Meier when competing events are treated as ordinary censoring.
- The Fine-Gray regression framework allows covariate adjustment while preserving the direct link between model parameters and the CIF.
- Requires a sample of at least 100 observations; with fewer, subdistribution hazard estimates become unreliable.
- The proportional subdistribution hazards assumption must be verified; when it fails, the Fine-Gray coefficients become time-varying and their summary interpretation breaks down.
- Cause of failure must be recorded and clearly classified; misclassified or ambiguous causes invalidate the analysis.
Frequently asked
Why can I not just use Kaplan-Meier and censor competing events?
The Kaplan-Meier estimator treats censored subjects as if they retain the same event risk as uncensored subjects. Subjects who die from a competing cause can no longer experience the event of interest, so censoring them at the competing event time introduces informative censoring and inflates the estimated cumulative incidence. The CIF from competing risks analysis correctly accounts for this by including the probability of the competing event in the denominator.
What is the difference between the cause-specific hazard and the subdistribution hazard?
The cause-specific hazard for event k is estimated from the subset of subjects still event-free; it governs the instantaneous rate of the event among those who have not yet experienced any event. The subdistribution hazard keeps failed-from-competing-cause subjects in an enlarged risk set, and is mathematically linked to the CIF for cause k. Regression on cause-specific hazards answers which covariates speed or slow the underlying biological process; regression on subdistribution hazards answers which covariates affect the absolute probability of the event of interest.
How do I test whether two groups have different CIFs?
The Gray test (an extension of the log-rank test for competing risks settings) compares the cumulative incidence functions across groups. It is the appropriate omnibus test when competing events are present, and supersedes the standard log-rank test in this context.
When is the Fine-Gray model preferred over cause-specific Cox regression?
If the scientific question is about the absolute risk of the event of interest — for example, what is the 5-year probability of cancer-specific death given a covariate profile — the Fine-Gray model is preferred because its regression coefficients map directly to the CIF. If the question is about the biological hazard mechanism (which factors independently accelerate the event process), cause-specific Cox regression is more interpretable.
Sources
- Fine, J.P. & Gray, R.J. (1999). A Proportional Hazards Model for the Subdistribution of a Competing Risk. Journal of the American Statistical Association, 94(446), 496–509. DOI: 10.1080/01621459.1999.10474144 ↗
How to cite this page
ScholarGate. (2026, June 1). Competing Risks Survival Analysis. ScholarGate. https://scholargate.app/en/survival/competing-risks
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Bayesian Survival AnalysisBayesian↔ compare
- Fine-Gray Competing Risks ModelStatistics↔ compare
- Kaplan-MeierSurvival↔ compare
- Log-Rank TestSurvival↔ compare
- Nelson-Aalen EstimatorSurvival↔ compare