Fine-Gray Competing Risks Model
Fine-Gray Proportional Subdistribution Hazards Model · Also known as: competing risks regression, subdistribution hazard model, Fine-Gray model, Fine-Gray Competing Risks Modeli
The Fine-Gray model is a semiparametric regression method for survival data in which two or more mutually exclusive event types compete to occur first. Proposed by Fine and Gray in 1999, it models the subdistribution hazard of each event type directly, allowing covariates to be linked to the cumulative incidence function (CIF) — the quantity that actually answers 'what is the probability of experiencing event type k by time t?'. It corrects the well-known shortcoming of standard Cox regression, which ignores competing events and thereby overestimates cause-specific probabilities.
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When to use it
Use the Fine-Gray model when (1) the study outcome is a time-to-event variable, (2) two or more mutually exclusive event types are possible and at least one type prevents the others from occurring, and (3) the scientific question concerns the absolute probability of experiencing the event of interest in the real world — as opposed to a hypothetical cause-specific rate. Four assumptions must hold: data are in time-to-event format with clearly labelled event types; the censoring mechanism is non-informative (independent of both the event of interest and the competing events); the subdistribution hazard is proportional across covariate levels (verify with Schoenfeld residuals on the subdistribution); and the minimum effective sample is approximately 50 events for the event of interest. When the assumption of proportional subdistribution hazards is violated, consider flexible parametric extensions. When no covariates are needed, the Aalen-Johansen estimator alone suffices for CIF estimation.
Strengths & limitations
- Directly models the cumulative incidence function, the clinically relevant probability of event occurrence in the presence of competing risks.
- Avoids the systematic overestimation of event probability that arises when competing events are treated as simple censoring in standard Kaplan-Meier or Cox analysis.
- Produces interpretable subdistribution hazard ratios that link covariates to observable event probabilities.
- Semiparametric: no distributional assumption is imposed on survival time, giving flexibility comparable to the Cox model.
- Requires the proportional subdistribution hazards assumption, which must be tested and may not hold in practice.
- The subdistribution hazard ratio is harder to interpret mechanistically than the cause-specific hazard ratio, because it blends the direct effect on the event of interest with indirect effects on competing events.
- Demands a minimum of roughly 50 observed events for the event of interest; smaller counts yield unstable estimates.
- Not natively available in SPSS; implementation relies on R (cmprsk, tidycmprsk) or Python (lifelines, scikit-survival).
Frequently asked
When should I use the Fine-Gray model instead of cause-specific Cox regression?
Use the Fine-Gray model when your scientific question is about the absolute probability of event type k occurring by a given time — i.e., the cumulative incidence function. Use cause-specific Cox regression when you want to understand the biological or mechanistic process governing each event type separately, or when you need to model what would happen if competing events were hypothetically eliminated. The two approaches are complementary and ideally both are reported.
What is the subdistribution hazard ratio, and does a higher SHR always mean higher risk?
The SHR is the ratio of instantaneous subdistribution hazards comparing two covariate levels. An SHR > 1 means the CIF rises faster — i.e., the cumulative incidence of the event of interest is higher in the exposed group. However, a covariate can have an SHR > 1 (increases CIF) while simultaneously having a cause-specific hazard ratio < 1, if it strongly reduces the competing event. Always interpret SHRs alongside CIF curves.
How do I test the proportional subdistribution hazards assumption?
Plot scaled Schoenfeld residuals against time for each covariate in the subdistribution model: a flat, roughly horizontal pattern supports proportionality. You can also add a time-by-covariate interaction term to the model; a significant interaction indicates the assumption is violated. In that case, consider a stratified Fine-Gray model or a flexible parametric alternative.
Is the minimum sample size of 50 per event type a hard rule?
It is a practical guideline, not a fixed threshold. Simulation studies suggest that reliable estimation of subdistribution hazard ratios requires at least 10 events per predictor variable (EPV rule), and typically at least 50 total events for the event of interest to achieve adequate power and stable baseline CIF estimates. With fewer events, wide confidence intervals and convergence problems are common.
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 ↗
- Austin, P.C. et al. (2016). Introduction to the Analysis of Survival Data in the Presence of Competing Risks. Circulation, 133(6), 601–609. DOI: 10.1161/CIRCULATIONAHA.115.017719 ↗
How to cite this page
ScholarGate. (2026, June 1). Fine-Gray Proportional Subdistribution Hazards Model. ScholarGate. https://scholargate.app/en/statistics/fine-gray-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.
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- Time-Dependent Cox RegressionSurvival↔ compare