Survival

Event-driven sizing for time-to-event endpoints.

3.1 · Log-rank sample size (Schoenfeld)

Total number of EVENTS required to detect a hazard ratio with the log-rank test, and the corresponding number of subjects.

Hazard ratio HR

≠ 1; < 1 favors group 1

Allocation proportion to group 1 (proportion)

Significance level α

two-sided

Power (1−β)

Overall probability of observing the event (proportion)

in (0, 1]

Required events E	247
Total subjects N	309

Formula

Events E = (z₁₋α/₂ + z₁₋β)² / [p(1−p)·(ln HR)²]; subjects N = ⌈E / Pr(event)⌉

Reference

Schoenfeld, D.A. (1983) Biometrics 39:499–503.

Assumptions & notes

Label the hazard ratio clearly: HR < 1 means fewer events in group 1 (numerator) than group 2.
Accrual and follow-up modeling are out of scope for v1 — the overall event probability is user-supplied.

Note

Accrual/follow-up modeling is out of scope for v1 — event probability is user-supplied.

Exploratory / educational use only — not validated for regulatory submissions. See footer.

3.2 · Median survival CI — planned, not in v1

The Brookmeyer & Crowley (1982, Biometrics) method inverts the Kaplan–Meier confidence interval to get a CI for median survival. It requires the full Kaplan–Meier curve as input, which is out of scope for a summary-statistic calculator in v1.

Recorded as a future enhancement.