{
  "slug": "kaplan-meier-estimator",
  "term": "Kaplan-Meier estimator",
  "aliases": [
    "Product-limit estimator",
    "Kaplan-Meier estimate"
  ],
  "definition": "The Kaplan-Meier estimator is a nonparametric estimator of the survival function that multiplies conditional survival estimates at observed event times while accounting for right-censored observations.",
  "note": "At each distinct failure time, multiply by 1 - d_i/n_i, where d_i counts failures and n_i counts devices at risk just beforehand. Censoring removes devices from later risk sets without causing a failure step. [nist-km] Interpretation requires appropriate censoring assumptions; nonparametric does not mean assumption-free. [kaplan-meier-1958] For delayed entry, devices contribute to risk sets only after their observed entry ages. Adjusted risk sets can support population survival estimation under suitable truncation assumptions, but do not reconstruct individual unobserved failures or identify survival before ages supported by the cohort. [schisterman-2013] Report numbers at risk, uncertainty and the supported time range, not an extrapolated lifetime guarantee. For tied recorded failure and censoring times, the usual failure-before-censoring convention includes the censored unit in that event-time risk set. If the last observation is censored, the tail need not fall to zero; it is not a lifetime extrapolation. [kaplan-meier-1958]",
  "related": [
    "survival-function",
    "right-censoring",
    "left-truncation",
    "informative-censoring",
    "hazard-rate"
  ],
  "citations": [
    {
      "id": "nist-km",
      "title": "NIST e-Handbook 8.2.1.5: Empirical model fitting, Kaplan-Meier approach",
      "url": "https://www.itl.nist.gov/div898/handbook/apr/section2/apr215.htm",
      "accessed": "2026-10-13"
    },
    {
      "id": "kaplan-meier-1958",
      "title": "Kaplan and Meier (1958): Nonparametric Estimation from Incomplete Observations, sections 1.1, 1.4 and 2.1",
      "url": "https://web.stanford.edu/~lutian/coursepdf/KMpaper.pdf",
      "accessed": "2026-10-13"
    },
    {
      "id": "schisterman-2013",
      "title": "Schisterman et al. (2013): Accuracy Loss Due to Selection Bias in Cohort Studies with Left Truncation, Discussion",
      "url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC6151356/",
      "accessed": "2026-10-13"
    }
  ],
  "status": "shipping",
  "advantages": [],
  "limitations": [],
  "supersedes": [],
  "supersededBy": [],
  "firstSeen": null,
  "lastSeen": null,
  "updated": "2026-10-13"
}