2020/11/13 by Judith ter Schure, M. F. Perez-Ortiz, ter Schure, J. +5 · 2 citations
Decision Sciences · Mathematics · #Advanced Statistical Process Monitoring #FOS: Computer and information sciences #FOS: Mathematics #Forecasting Techniques and Applications #Methodology (stat.ME) #Statistical Methods in Clinical Trials #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2011.06931
openalex publication_date 2020/11/13 · openalex created_date 2023/05/03 · openalex updated_date 2026/07/28
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.