# The Anytime-Valid Logrank Test: Error Control Under Continuous Monitoring with Unlimited Horizon

arXiv: https://arxiv.org/abs/2011.06931 · HTML: https://mlsanity.com/paper/2011.06931/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Nov 2020.

## Built on by (most cited first, 2 of 2)

- [Peeking with PEAK: Sequential, Nonparametric Composite Hypothesis Tests for Means of Multiple Data Streams](https://mlsanity.com/paper/2402.06122/) (2024)
- [Sequential Structure-Sensitive Residual Diagnostics for PDE Inverse Problems](https://mlsanity.com/paper/2607.02101/) (2026)

## Abstract (arXiv)

We introduce the anytime-valid (AV) logrank test, a version of the logrank test that provides type-I error guarantees under optional stopping and optional continuation. The test is sequential without the need to specify a maximum sample size or stopping rule, and allows for cumulative meta-analysis with type-I error control. The method can be extended to define anytime-valid confidence intervals. The logrank test is an instance of the martingale tests based on E-variables that have been recently developed. We demonstrate type-I error guarantees for the test in a semiparametric setting of proportional hazards and show how to extend it to ties, Cox' regression and confidence sequences. Using a Gaussian approximation on the logrank statistic, we show that the AV logrank test (which itself is always exact) has a similar rejection region to O'Brien-Fleming alpha-spending but with the potential to achieve 100% power by optional continuation. Although our approach to study design requires a larger sample size, the *expected* sample size is competitive by optional stopping.