Statistical hypothesis tests typically use prespecified sample sizes, yet data often arrive sequentially. Interim analyses invalidate classical error guarantees, while existing sequential methods require rigid testing preschedules or incur substantial losses in statistical power. We introduce a simple procedure that transforms any fixed-sample hypothesis test into an anytime-valid test while ensuring Type-I error control and near-optimal power with substantial sample savings when the null hypothesis is false. At each step, the procedure predicts the probability that a classical test would reject the null hypothesis at its fixed-sample size, treating future observations as missing data under the null hypothesis. Thresholding this probability yields an anytime-valid stopping rule. In areas such as clinical trials, stopping early and safely can ensure that subjects receive the best treatments and accelerate the development of effective therapies.

翻译：统计假设检验通常使用预先设定的样本量，但数据往往以序列形式到达。期中分析会破坏经典误差保证，而现有的序贯方法要么需要严格的预设检验计划，要么导致统计功效大幅损失。我们提出一种简单方法，可将任意固定样本假设检验转化为任意时间有效检验，在保证第一类错误控制的同时，当原假设为假时能以显著的样本节约获得接近最优的检验功效。该方法在每一步预测经典检验在其固定样本量下拒绝原假设的概率，并将未来观测值视为原假设下的缺失数据进行处理。对该概率设定阈值即可得到任意时间有效的停止规则。在临床试验等领域，提前且安全地停止试验既能确保受试者获得最佳治疗方案，又能加速有效疗法的研发进程。