{
  "slug": "restricted-mean-survival-time",
  "term": "Restricted mean survival time",
  "aliases": [
    "RMST",
    "Restricted mean lifetime"
  ],
  "definition": "Restricted mean survival time is the expected event-free time accumulated from a defined time origin up to a specified finite horizon.",
  "note": "For nonnegative event time T and a fixed horizon tau > 0, RMST(tau) = E(min(T, tau)) = integral from 0 to tau of S(t) dt. The result has units of time and lies between zero and tau. It includes the contribution of devices surviving beyond tau; it is not the conditional mean among devices that fail before tau. [royston-parmar-2013]\n\nA Kaplan-Meier plug-in estimate integrates the right-continuous survival steps as rectangles, not by drawing sloping lines between events. The horizon must be supported by follow-up, and estimation still requires suitable censoring assumptions. An unfinished censored tail does not identify the unrestricted lifetime mean. [kaplan-meier-1958] RMST does not require proportional hazards, but this does not make it assumption-free. [royston-parmar-2013]\n\nComparisons must state a common horizon, event definition, population and time origin. Choose the primary horizon for relevance and feasible follow-up before examining which value favors a group; exploratory horizons should be identified as such. A difference in RMST is a time difference within that window, not a hazard ratio or evidence of a causal device advantage. [uno-2014-rmst]\n\nIn Hesela's existing six-fictional-device example, the Kaplan-Meier area through day 10 is 2 + 3*(5/6) + 3*(5/8) + 2*(5/16) = 7 days. Report the estimated survival at the horizon with the restricted mean: here S-hat(10) = 5/16, or 31.25%, following the reporting advice in Kaplan and Meier section 2.3. [kaplan-meier-1958] Only one device remains at risk just before day 10. This is an arithmetic illustration, not measured fleet reliability, a full mean lifetime, MTBF or the remaining lifetime of an already-aged drive. The paired Observatory analysis provides the original inputs, exact-fraction calculation and tests.",
  "related": [
    "kaplan-meier-estimator",
    "survival-function",
    "right-censoring",
    "informative-censoring",
    "mtbf"
  ],
  "citations": [
    {
      "id": "royston-parmar-2013",
      "title": "Royston and Parmar (2013): Restricted mean survival time, Methods, Definition of RMST, equation 1; BMC Medical Research Methodology 13:152",
      "url": "https://link.springer.com/article/10.1186/1471-2288-13-152",
      "accessed": "2026-11-05"
    },
    {
      "id": "uno-2014-rmst",
      "title": "Uno et al. (2014): Moving Beyond the Hazard Ratio in Quantifying the Between-Group Difference in Survival Analysis, JCO 32:2380-2385, pp. 2383-2384",
      "url": "https://med.stanford.edu/content/dam/sm/dbds/documents/biostats-workshop/2014-Uno-JCO.pdf",
      "accessed": "2026-11-05"
    },
    {
      "id": "kaplan-meier-1958",
      "title": "Kaplan and Meier (1958): Nonparametric Estimation from Incomplete Observations, sections 1.1, 1.4, 2.1 and 2.3, including limited-mean reporting on pp. 467-468",
      "url": "https://web.stanford.edu/~lutian/coursepdf/KMpaper.pdf",
      "accessed": "2026-11-05"
    }
  ],
  "status": "shipping",
  "advantages": [],
  "limitations": [],
  "supersedes": [],
  "supersededBy": [],
  "firstSeen": null,
  "lastSeen": null,
  "updated": "2026-11-05"
}