RMST — Restricted Mean Survival Time (area under S(t) to τ)

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Advanced & specialized

Independently verified. Every statistic this test reports has been re-derived against an independent reference — never the library the pipeline itself calls — the rendered output was read back in a browser, and the result is locked with a committed regression suite.

Run this test straight away on a free built-in teaching dataset — no data of your own needed — or bring your own. Either opens the guided workspace: variable setup, assumption diagnostics, results with effect sizes and confidence intervals, figures, and APA-ready reporting.

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Area under the Kaplan-Meier curve from 0 to a pre-specified restriction time τ — interpreted as 'expected event-free time within the τ-year window'.

The engine reports per-group RMST(τ), RMST difference + ratio between groups with 95% CIs (Greenwood plug-in delta method + bootstrap validation), and KM curves with the τ marker. The reviewer-friendly alternative to the hazard ratio when proportional hazards fails — RMST is interpretable WITHOUT requiring PH or any specific hazard pattern.

Worked example

How much longer, on average, do patients survive up to 3 years?

Restricted mean survival time — the average event-free time up to a 36-month horizon — is compared between two arms; an assumption-light alternative to the hazard ratio.

Result

The new arm gained about 5.2 more event-free months (RMST 29.0 vs 23.8 months; difference = 5.2).

How you'd report it (APA)

The restricted mean survival time was 5.2 months longer in the new arm (29.0 vs 23.8 months).

Try it yourself: Load this ready-made sample and follow the run above.

When to use it

  • Two-group RMST when PH is violated or not assumed
    Immunotherapy vs chemotherapy for stage-IV cancer: KM curves cross at 18 months (chemo better early, immunotherapy better late), so HR is meaningless.
  • Single-group RMST estimate
    Cancer registry: 3-year RMST for newly-diagnosed Stage-III patients = 28.3 months (95% CI 27.1, 29.5) — cleaner summary than median survival when ~40% are still alive at 3 years.

When NOT to — use instead

Hypotheses

H₀: RMST_1(τ) − RMST_0(τ) = 0 — restricted mean survival is equal across groups.
Hₐ: RMST_1(τ) ≠ RMST_0(τ).

Parameter tested: RMST_g(τ) per group; RMST difference + ratio with 95% CI.

Assumptions (and what to do if they fail)

The chosen restriction time τ is within the observed follow-up window of EVERY group — no extrapolation.high

Check: Compare τ against per-group max times.

If violated: τ beyond the observed support forces the KM estimator to extrapolate flat — biasing the area estimate.

Censoring is INDEPENDENT of the event hazard — censored subjects would have had the same survival function as those still at risk.high

Check: Per-group censoring rates within 30 pct pts.

If violated: Informative censoring biases the area under Ŝ(t).

At least 10 events per group within the τ window.medium

Check: Per-group events ≥ 10.

If violated: Too few events make Greenwood SE unstable; bootstrap CI is safer.

Ready to run a RMST — Restricted Mean Survival Time (area under S(t) to τ) on your own data?

Guided setup, automatic assumption checks, effect sizes, figures and an APA write-up.

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