Understanding Competing Risks, and Why They Change What a Survival Curve Means

A competing risk is any event that makes the outcome you are tracking impossible once it happens. If you are studying death from kidney disease and a patient dies of a heart attack first, that patient can never have the outcome you were counting, and treating them as if they still might is where the trouble begins. When competing events are common, a standard Kaplan-Meier estimate can overstate how many people will experience the event of interest, sometimes substantially. The correction is not exotic. Read the analysis for whether it reports a cumulative incidence function rather than one minus a Kaplan-Meier curve, and check that the cause-specific hazard and the subdistribution hazard are not being quietly swapped for each other. This is general education about reading evidence, not medical advice, and questions about your own care belong with a clinician who knows your history.

What makes an event a competing risk

Censoring and competing events look alike on a data sheet and behave very differently underneath. When someone is censored, we lose sight of them but assume their clock keeps ticking, that they could still have the event if only we could keep watching. A competing event is not a loss of information. It is information. The person can no longer have the outcome, because something mutually exclusive already closed that door.

Death from an unrelated cause is the clearest example, but competing risks are everywhere once you look. Study time to hip fracture, and death is a competing event. Track one type of cardiovascular death, and every other cause of death competes; follow time to kidney transplant, and dying on the waiting list competes. The pattern holds throughout: a person can experience only one of several mutually exclusive first events, and the occurrence of one removes them from the others.

The distinction matters most in the populations where these methods are used most, older patients and those with several conditions at once, because that is where competing mortality is high. In a young, healthy cohort followed briefly, competing death is rare and the issue is small. Push the follow-up to a decade in an elderly group and the competing event can dominate.

Why Kaplan-Meier can overstate the risk

The Kaplan-Meier estimator was built for a world with one event and honest censoring. It handles a competing event by censoring it, treating the person who died of the heart attack as if they had walked out of the study and might still return to have the kidney-disease death. That assumption is false. They are not coming back.

The estimator therefore keeps those people in the imagined at-risk pool and keeps attributing future risk to a group that partly no longer exists. So the curve drifts too high, and one minus that curve, read as the probability of the event, drifts too high in turn. As more competing events accumulate, the gap between the Kaplan-Meier number and the truth widens.

A useful sanity check falls straight out of this. Add up the one-minus-Kaplan-Meier estimates for every competing outcome in a study, each computed the naive way, and the total can exceed one hundred percent. Real probabilities of mutually exclusive events cannot do that. When the pieces sum past the whole, the method has broken.

Cause-specific hazard versus the cumulative incidence function

Two quantities answer two genuinely different questions, and most confusion comes from wanting one number to do both jobs.

The cause-specific hazard is the instantaneous rate of the event of interest among those still alive and event-free at that moment. It speaks to biology and mechanism, asking how fast this particular event is occurring among people still at risk right now. That makes it the right tool for asking whether a treatment acts on the pathway that produces the outcome. It treats competing events as censored, which suits a question about rate but not one about how many people will be affected.

The cumulative incidence function answers the question a patient usually has in mind. By a given time, what fraction of people like me will actually have had this event, in a world where the competing events are also happening. It builds in the reality that some people are removed by competing events before the outcome can occur, and it never lets the mutually exclusive pieces sum past one. For the real-world burden, this is the estimate to look for.

The trap is subtle. A factor can raise the cause-specific hazard of an event while lowering its cumulative incidence, because that same factor kills people faster through a competing route, so fewer survive long enough to reach the outcome. Both statements are true. They answer different questions, and reporting one while discussing the other is a common, honest-looking error.

The subdistribution hazard and where it fits

The Fine and Gray model works directly on the cumulative incidence scale through the subdistribution hazard, keeping people who had a competing event in a modified risk set so the coefficients line up with the incidence you actually observe. It is the natural companion to a cumulative incidence analysis. A cause-specific Cox model and a subdistribution model can point in opposite directions for the reason above, and neither is wrong. A careful paper reports both and says which question each answers.

How a careful reader spots a competing-risks problem

You do not need the raw data to catch most of these. A few questions do the work.

Ask what else could happen to these people before the outcome. If the population is old or sick and the follow-up is long, competing mortality is almost certainly non-trivial, and a survival analysis that never mentions it deserves a raised eyebrow.

Look at the exact words. A method described as one minus Kaplan-Meier, or a plain Kaplan-Meier curve presented as the probability of a specific non-death outcome in an elderly cohort, is the signature of the problem. Phrases like cumulative incidence function, Aalen-Johansen, or Fine and Gray are reassuring signs the authors saw the issue. Check whether the estimated probabilities are even plausible; if several competing outcomes sum past one hundred percent, or one looks too high for the population, the naive method is likely in play.

In our Diabetes Care meta-analysis, the discipline that protected the conclusions was refusing to let one summary number stand in for a more complicated reality, and competing risks are the same lesson in a different costume. Match the estimate to the question, sending rate questions to the cause-specific hazard and burden questions to cumulative incidence, and never let a tidy curve talk you out of asking what else was happening to the people it counted.