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arXiv · 2011.06931

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

J. ter Schure·M. F. Perez-Ortiz·A. Ly·P. Grunwald
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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.

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J. ter Schure, M. F. Perez-Ortiz, A. Ly, P. Grunwald. 2020-11-13. The Anytime-Valid Logrank Test: Error Control Under Continuous Monitoring with Unlimited Horizon. https://arxiv.org/abs/2011.06931

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