{
  "slug": "cumulative-incidence-function",
  "term": "Cumulative incidence function",
  "aliases": [
    "CIF"
  ],
  "definition": "A cumulative incidence function gives the probability that a specified event type occurs by a given time before any competing event.",
  "note": "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. [therneau-competing]\n\nCensoring: 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. [therneau-competing]",
  "related": [
    "competing-risks",
    "cause-specific-hazard",
    "kaplan-meier-estimator",
    "survival-function"
  ],
  "citations": [
    {
      "id": "therneau-competing",
      "title": "Therneau, Crowson and Atkinson: Multi-state models and competing risks (2026), section 2.1",
      "url": "https://stat.ethz.ch/R-manual/R-patched/library/survival/doc/compete.pdf",
      "accessed": "2026-10-16"
    },
    {
      "id": "sksurv-competing",
      "title": "scikit-survival 0.28.0: Analysis of Competing Risks",
      "url": "https://scikit-survival.readthedocs.io/en/v0.28.0/user_guide/competing-risks.html",
      "accessed": "2026-10-16"
    }
  ],
  "status": "shipping",
  "advantages": [],
  "limitations": [],
  "supersedes": [],
  "supersededBy": [],
  "firstSeen": null,
  "lastSeen": null,
  "updated": "2026-10-16",
  "provenance": [
    "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."
  ]
}