Competing Risks
When patients can experience an event that prevents the event you are studying, standard survival methods overestimate risk — and the fix depends on the question you are asking.
What it is
Kaplan-Meier assumes that patients censored at a given time are still at risk and would have had the same future hazard as those who remained. That assumption breaks when the reason for “censoring” is a competing event. A patient who dies of cardiac disease cannot subsequently die of their cancer; treating them as censored implicitly pretends they might have.
The consequence is one-directional and predictable: naive Kaplan-Meier on cause-specific death overestimates the cumulative incidence of that cause. The size of the bias grows with the frequency of competing events, which is why it bites hardest in older cohorts and in cancers with good prognosis.
Two correct approaches exist and they answer different questions.
- Cause-specific hazard models the rate of the event among those still event-free. This is the aetiological question: does this factor drive this mechanism?
- Fine-Gray subdistribution hazard models the cumulative incidence directly, keeping competing-event patients in the risk set in a specific weighted way. This is the prognostic question: what is this patient’s actual probability of this outcome?
They can disagree, and neither is wrong — they are answers to different questions. The usual recommendation is to report both and be explicit about which one supports each claim. For descriptive incidence, the cumulative incidence function replaces 1 minus Kaplan-Meier.
Why it matters for my work
jsurvival implements Fine-Gray and cause-specific models, and the chapter states the rule directly: when a non-trivial fraction of patients die of other causes, cause-specific or Fine-Gray is correct rather than naive KM on disease-specific death. The schema for this wiki also names this class of problem as one to flag on sight.
Practically, this applies to nearly every resection-outcome study in the group’s oncology portfolio, since pancreatic and gastric cohorts tend to be older with substantial non-cancer mortality.
How it connects
Survival Analysis Workflow — the practical pipeline in which the competing-risks decision sits, and where the choice needs recording.
jsurvival — the module that implements both estimators, so the correct analysis costs no extra work once the decision is made.
External Validation — competing-event frequency differs between populations, so a prognostic model built on one cohort’s competing-risk structure may transfer poorly.
Pancreas Cohorts — an older surgical population where non-cancer mortality is common enough that this decision changes the reported incidence.
Open questions
- Do the group’s existing survival analyses record whether competing risks were assessed? Not documented in the portal. [unverified] Worth auditing as a batch.
- Is there a house convention on reporting both cause-specific and subdistribution results, or is it decided per paper?