Specialty › Power (hypothesis tests)

Log-rank (survival)

Log-rank power analysis uses Schoenfeld's formula to solve for the number of events, the detectable hazard ratio or the power, given α and the allocation ratio.

What is Log-rank (survival)?

Time-to-event sample-size is driven by *events*, not patients. The Schoenfeld formula: required events ≈ (z_{1−α/2} + z_{power})² / [(allocation·(1 − allocation)) · log²(HR)]. Patients needed = events / expected event probability over the follow-up window.

Choose HR as the smallest clinically meaningful detect-worthy hazard ratio. HR = 0.7 (30% reduction) is a typical 'meaningful' threshold for clinical trials. Smaller HRs to detect require more events quadratically.

When should I use Log-rank (survival)?

  • Planning sample size for a time-to-event trial.
  • Confirming a study is adequately powered for the planned HR.

What data does it need?

Solve for events / HR / power given α + arm allocation + event probability.

What does it report?

Required events / patients per arm / achieved power.

Formula

events = (z_{1−α/2} + z_{power})² / [allocation·(1 − allocation) · log²(HR)]

How do I interpret the result?

If event accrual is slow, lengthen follow-up rather than enroll more patients — events are what matter.

See also

References

  • Schoenfeld (1981). The asymptotic properties of nonparametric tests for comparing survival distributions. Biometrika 68(1).