hesela.devCumulative incidence function
A cumulative incidence function gives the probability that a specified event type occurs by a given time before any competing event.
Probability: F_k(t) = P(T <= t, J = k), where T is the first-event time and J its type; it is dimensionless and is not conditional on remaining event-free at t. The Aalen-Johansen estimator includes all competing exits. A failure-only Kaplan-Meier complement generally overestimates this probability. [1]
Censoring: Without early censoring, the estimate reduces to the fraction entering that state. With earlier loss to follow-up, it uses the changing risk sets instead; dividing observed failures by the starting cohort is not generally equivalent. Population interpretation still requires appropriate censoring assumptions. [1]
Relations
- related
- competing-risks, cause-specific-hazard, kaplan-meier-estimator, survival-function
Citations
Further reading
Sources & caveats
- The scikit-survival tutorial is retained as further reading; the mathematical definition follows the survival vignette. The linked Hesela examples are synthetic, not fleet estimates.