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

TL;DR

The paper introduces an anytime-valid logrank test that guarantees type-I error control under continuous monitoring, enabling sequential analysis and meta-analysis without fixed sample sizes, and extends to confidence intervals and other models.

Contribution

It presents a novel AV logrank test that maintains error control under optional stopping and continuation, with extensions to confidence intervals and broader survival analysis models.

Findings

Type-I error is controlled under optional stopping.

The test achieves similar rejection regions to O'Brien-Fleming but with potential for 100% power.

Expected sample size is competitive despite larger initial sample requirements.

Abstract

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.