Survival › Time-to-event

Restricted mean survival time (RMST)

Restricted mean survival time averages survival over a window [0, τ] and compares groups by difference or ratio, an alternative to the hazard ratio when proportional hazards fails.

What is Restricted mean survival time (RMST)?

RMST is the area under the survival curve from 0 to a chosen truncation τ — literally the expected time alive within the window. Unlike HR, which is a multiplicative effect on an unobservable hazard, RMST is on the time scale, so a 'difference of 3.5 months' is directly interpretable to patients.

RMST does not require proportional hazards. When K-M curves cross or the hazards diverge over time — situations where HR misleads — RMST gives an honest summary of the cumulative survival experience over the chosen window.

Pick τ before looking at the data. Common choices: the time horizon of clinical interest, the last event time where both arms still have substantial follow-up, or τ where Ŝ in each arm exceeds some minimum (say 10% to keep estimates stable).

When should I use Restricted mean survival time (RMST)?

  • Trial reporting where the time-scale effect is more interpretable than HR.
  • Non-proportional hazards (crossing K-M curves) where HR is misleading.
  • Clinical communication: 'gained 3.5 months of life over 5 years' beats HR for patients.

What data does it need?

Time + event + arm (binary) + optional τ (defaults to the smaller of the two arms' last event times).

What does it report?

RMST per arm with CI, between-arm difference + ratio with p-values.

What does it assume?

  • Independent observations.
  • Non-informative censoring within [0, τ].

How do I interpret the result?

Difference in RMST in months is on the time scale and is interpretable as 'patients in arm A gained X months over τ years follow-up'.

Ratio of RMST (e.g. 1.15) is a multiplicative summary of the relative life-years; useful for relative-effectiveness framings.

See also

References

  • Royston & Parmar (2013). Restricted mean survival time: an alternative to the hazard ratio for the design and analysis of randomized trials with a time-to-event outcome. BMC MRM 13.