Competing risks occur when another event makes the occurrence of the event of interest permanently impossible. For example, if a patient dies before local tumor progression, this progression can no longer be observed in that patient. The Fine-Gray model describes the subdistribution hazard for this situation and allows for regression on the cumulative incidence of the target event while accounting for competing events.
What constitutes a competing risk
Not every additional event is a competing risk. An event only competes if it precludes the realization of the target event, not if it merely delays its observation temporarily. For the analysis, the target event, competing events, and administrative censoring must therefore be defined separately and coded uniquely in the raw data.
The clinical significance of this distinction is evident, for example, in the cumulative incidence of treatment-related toxicity when death occurs first. Those who remain toxicity-free until death do not have the same future chance of toxicity as an administratively censored participant. The decision as to which event counts as competing follows the medical question and not the convenience of a standard evaluation.
Subdistribution Hazard according to Fine and Gray
The Fine-Gray model relates the subdistribution hazard to the cumulative frequency of the target event. In this process, individuals with a competing event are not simply treated as if they had disappeared from observation without further information. The model estimates the influence of the treatment group or covariates on the temporal development of the cumulative incidence.
The resulting subdistribution hazard ratio is a relative model measure and not a direct difference in event probabilities. Its direction and magnitude are only understandable in conjunction with the cumulative incidence curves. A cause-specific Cox model answers a different question because it models the instantaneous rate of the target event among those still event-free and removes competing events from this risk set.
Distinction from Kaplan-Meier and Hazard Ratio
In the presence of competing risks, Kaplan-Meier overestimates the probability of the target event if the competing event is treated like ordinary censoring. This treatment implicitly assumes that censored individuals would continue to have the same chance of the target event. A prior death refutes exactly this assumption because it precludes the event.
The existing entries kaplan-meier-analysis, survival-analysis, hazard-ratio, and mortality cover the fundamentals of time-to-event analysis. Competing risks further require an explicit choice between cause-specific hazard and subdistribution hazard. Both analyses can be useful, but they are not interchangeable and must not be attributed the same clinical statement.
The choice can be aligned with the objective: if a therapy is intended to act on the biological rate of a specific event, the cause-specific hazard may be the focus. If the expected clinical burden of this event under the real death or competition rate is to be described, the cumulative incidence—and thus often the subdistribution perspective—is more appropriate. Both perspectives can show different treatment effects without contradicting each other.
An evaluation must also determine how events documented simultaneously or on the same day are prioritized. Without a deterministic sequence, it is impossible to decide which transition in the risk set occurred first. This rule belongs in the analysis programming and in the definition of data derivations.
Relevance for clinical trials
Study planning must capture whether deaths, transplants, or other definitive state changes prevent target observation. In data management, the cause and date of each first event should be verified, as an incorrect event sequence alters the risk sets. For the presentation of results, the number and type of competing events per group are just as essential as the estimated target incidence.
Full-service CROs like Mediconomics support the clinical operationalization of competing events, the definition of analyzable timelines, and the programming of cumulative incidence curves as well as Fine-Gray or cause-specific models. Statistical reporting can explain the chosen question—event probability or rate among event-free individuals—separately, thereby avoiding misinterpretation of the hazard ratios.
Frequently Asked Questions (FAQ)
Is death always a competing risk?
Only in relation to a target event that can no longer occur after death. For overall survival, on the other hand, death is the target event itself and not a competing risk. The classification is therefore always based on the specific endpoint.
Why are Kaplan-Meier curves not sufficient here?
They treat a competing event as censored and thus project a target event probability for individuals who can no longer experience the target event. In contrast, cumulative incidence curves distribute the observed first events among their actual causes.
Which hazard ratio should be reported?
That depends on the research question. A cause-specific model describes the rate among individuals without an event; a Fine-Gray model describes the relationship of covariates to the cumulative incidence. The protocol and analysis plan must justify the choice.
Regulatory References
- ICH E9(R1), Addendum on Estimands and Sensitivity Analysis – requires a precise variable and appropriate summary.
- EMA/CHMP/205/95 Rev.6, Guideline on the Clinical Evaluation of Anticancer Medicinal Products – covers time-to-event endpoints in oncology.
- EMA/CHMP/27994/2008/Rev.1, Appendix 1 on PFS and DFS – specifies event time, censoring, and evaluation requirements.
