Competing risks
What question does this help answer?
It decides how to estimate how often an outcome occurs, and the effect of covariates on it, when some patients die of something else first and therefore can never experience it.
When to use it
Whenever death from other causes, transplantation, or any event that removes the patient from risk can occur before the outcome of interest. In older or sicker populations that is most of the time, and the more competing events there are, the larger the error from ignoring them.
When not to use it
A competing-risks framework is unnecessary when no event can preclude the outcome, for example when the outcome is all-cause mortality, since nothing competes with dying.
How it works in plain language
Standard survival analysis treats a competing death as censoring, which assumes the patient could still have had the outcome later. They could not. The complement of a Kaplan-Meier curve therefore OVERSTATES cumulative incidence, and the cumulative incidence function should be used instead. For regression there are two distinct choices: a cause-specific hazard model, which describes the rate among those still event-free and suits questions about mechanism, and a Fine-Gray subdistribution hazard model, which relates covariates to the absolute probability over time and suits questions about prognosis. They answer different questions and their coefficients are not interchangeable.
What competing states look like
Why Mallard may recommend it
Mallard types competing events in the estimand, and recommends this framework when the plan records that a competing event is possible. The exhibits follow: a Kaplan-Meier curve is not offered where death competes.
Key assumptions and design requirements
- Competing events are identified and defined before the analysis, not discovered in the data.
- Incidence is reported with the cumulative incidence function, never one minus Kaplan-Meier.
- The choice between cause-specific and subdistribution hazards is stated WITH the question it answers.
- A subdistribution hazard ratio is interpreted as an effect on cumulative incidence, not as a rate among survivors.
- Both models are often worth reporting, since they answer complementary questions.
What to watch out for
The complement of a Kaplan-Meier curve OVERSTATES cumulative incidence when a competing event exists, because it treats the competing death as though the patient could still have the outcome later. Cause-specific and subdistribution hazard models answer different questions and their coefficients are widely misreported as interchangeable.
Clinical example
Question: Does a discharge intervention reduce readmission within a year among frail elderly patients? Design: Death before readmission is a competing event, so cumulative incidence of readmission is estimated with the cumulative incidence function, and covariate effects reported from a cause-specific or Fine-Gray model with the choice justified.
- Introduction to the Analysis of Survival Data in the Presence of Competing Risks (opens in a new tab) · Circulation · doi 10.1161/CIRCULATIONAHA.115.017719
- Practical recommendations for reporting Fine-Gray model analyses for competing risk data (opens in a new tab) · Stat Med · doi 10.1002/sim.7501