hesela.devRestricted mean survival time
Restricted mean survival time is the expected event-free time accumulated from a defined time origin up to a specified finite horizon.
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. [1]
A 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. [3] RMST does not require proportional hazards, but this does not make it assumption-free. [1]
Comparisons 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. [2]
In 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. [3] 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.
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Citations
- Royston and Parmar (2013): Restricted mean survival time, Methods, Definition of RMST, equation 1; BMC Medical Research Methodology 13:152
- 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
- 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