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.

翻译：我们提出了连续有效（AV）对数秩检验，该检验可在可选停止与可选继续条件下提供I类误差保证，无需指定最大样本量或停止规则即可进行序贯分析，并支持累积元分析的I类误差控制。该方法可扩展以定义连续有效置信区间。对数秩检验是基于近期发展的E-变量鞅检验的一个实例。我们在比例风险半参数设定下证明了该检验的I类误差保证，并展示了如何将其扩展至处理结、Cox回归及置信序列。通过对对数秩统计量进行高斯逼近，我们证明AV对数秩检验（其本身始终是精确的）具有与O'Brien-Fleming α消耗函数相似的拒绝域，但可通过可选继续实现100%的统计功效。虽然我们的研究设计方法需要更大的样本量，但通过可选停止，其*期望*样本量具有竞争力。