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

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