Restricted Mean Survival Time Explorer

Three ideas behind every RMST result

RMST gives an absolute summary of treatment benefit in units of time, and it does not require the proportional hazards assumption. That makes it an important alternative to the hazard ratio in survival analysis and health economic evaluation.

Area is average timeRMST(τ) = ∫₀^τ S(t) dtS(t) is the survival function; τ is the pre-specified restriction time.

Differences are absolute gainsΔRMST = RMST_A(τ) − RMST_B(τ)The average extra time survived within τ.

Ratios are relativeRMST ratio = RMST_A(τ) / RMST_B(τ)Both depend on the τ you choose.

Start with a survival scenario

Each scenario loads two illustrative survival curves. The data are fictional and chosen to show how RMST behaves; they are not clinical evidence.

Survival curves and the area up to τScenario: The published worked example

Restriction time, τ

Drag the slider, or drag across the chart. RMST only counts survival up to this time.

5.00 years

Shade on the chart

Area under A Area under B Difference between curves

RMST_A(τ)––

RMST_B(τ)––

ΔRMST = RMST_A − RMST_B––

RMST ratio, A / B–

Share of τ survived–

–

Read the concept page

How ΔRMST changes with τ

Different horizons give different values, so τ must be chosen and justified before results are read. This line recalculates ΔRMST for every τ in the scenario; the marker shows your current choice.

Show the calculation

What the explorer is showing

Summarised from the published HealthEconomics.wiki concept page.

Why restrict the mean?

True mean survival is the area under the whole survival curve, but that curve usually extends beyond the observed data and cannot be measured without extrapolation. Restricting to τ keeps the measure within the data: it is the average event-free time over that period, in the same units as survival.

Why use it instead of a hazard ratio?

ΔRMST is directly interpretable as a difference in average survival time and stays valid when hazards are non-proportional. The hazard ratio assumes proportional hazards and can mislead when the effect varies over time.

Try: the crossing-curves scenario at τ = 2 and τ = 8.

How it is estimated

Integrate the survival curve from 0 to τ. The curve may be a non-parametric Kaplan–Meier estimate or a fitted parametric or flexible parametric model, and the integral is usually computed numerically.

Where it is used: oncology, health technology assessment and economic modelling, especially when hazards are non-proportional or absolute survival gains are preferred.

The published worked example

Over a five-year restriction period, Kaplan–Meier integration gives RMST of 3.84 years for Treatment A and 3.26 years for Treatment B.

ΔRMST = 3.84 − 3.26 = 0.58 years, about seven months of extra average survival within the five years.

The core rule

RMST(τ) is the area under the survival curve up to τ. Compare treatments with ΔRMST or the RMST ratio, always at the same, pre-specified τ.

Doing this in Excel

The concept page lists these spreadsheet functions. Times are in column A, survival probabilities in column B, and τ in cell F1.

Function	Example formula	Use
SUMPRODUCT	`=SUMPRODUCT((A3:A100-A2:A99),(B2:B99+B3:B100)/2)`	Approximates the area under the survival curve using the trapezoidal rule.
SUM	`=SUM(C2:C100)`	Calculates cumulative survival time across intervals.
IF	`=IF(A2<=$F$1,B2,0)`	Restricts calculations to the specified follow-up time τ.
INDEX	`=INDEX(B2:B100,MATCH($F$1,A2:A100,1))`	Retrieves survival estimates at the restriction time.

“Show the calculation” above applies the same trapezoidal idea to the current curves. For a step-shaped Kaplan–Meier curve, the exact area is a sum of rectangles; applying the trapezoidal formula only to the points where the curve drops slightly understates it. The table shows both.

Limitations and safeguards

RMST depends on the chosen restriction time. Different horizons give different values, so the choice must be justified and its influence considered.
It summarises survival only up to τ, not the full lifetime. It does not capture longer-term differences, and lifetime estimates still need extrapolation.
Estimates near the end of follow-up, where few people remain at risk, are less reliable.
This explorer is an educational illustration. All curves are fictional; the worked-example curves were constructed to reproduce the published RMST values, not taken from a real trial. Results here are not evidence of clinical effectiveness and are not medical advice.
The tool shows point estimates only. Real analyses should report uncertainty, such as confidence intervals for ΔRMST, which this draft does not calculate.
Values are rounded to two decimal places in years. Differences and ratios are calculated before rounding, so they can differ by 0.01 from the difference of the rounded figures. Parametric curves are integrated numerically on a fine grid.

Source and references

Canonical source: Restricted Mean Survival Time, HealthEconomics.wiki (term code HE-EM-SM-073, content version 1.0.0). References below are reproduced from that page for reviewer checking.

Royston P, Parmar MKB. Restricted mean survival time: an alternative to the hazard ratio for the design and analysis of randomised trials with a time-to-event outcome. BMC Medical Research Methodology. 2013;13:152.
Uno H, Claggett B, Tian L, et al. Moving beyond the hazard ratio in quantifying the between-group difference in survival analysis. Journal of Clinical Oncology. 2014;32(22):2380–2385.
Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation. Oxford University Press; 2006.
NICE. Health Technology Evaluations: The Manual. National Institute for Health and Care Excellence; 2022.
Rutherford MJ, Lambert PC, Sweeting MJ, et al. NICE DSU Technical Support Document 21: Flexible methods for survival analysis. NICE Decision Support Unit; 2020.