We propose a method that combines the closed testing framework with the concept of safe anytime-valid inference (SAVI) to compute lower confidence bounds for the true discovery proportion in a multiple testing setting. The proposed procedure provides confidence bounds that are valid at every observation time point and that are simultaneous for all possible subsets of hypotheses. While the hypotheses are assumed to be fixed over time, the subsets of interest may vary. Anytime-valid simultaneous confidence bounds allow us to sequentially update the bounds over time and allow for optional stopping. This is a desirable property in practical applications such as neuroscience, where data acquisition is costly and time-consuming. We also present a computational shortcut which makes the application of the proposed procedure feasible when the number of hypotheses under consideration is large. We illustrate the performance of the proposed method in a simulation study and give some practical guidelines on the implementation of the proposed procedure.

翻译：我们提出一种将闭合检验框架与安全有效时序推断（SAVI）概念相结合的方法，用于在多假设检验场景下计算真发现比例的下置信界。该程序提供的置信界在每一个观测时间点均有效，且对所有可能的假设子集具有同时有效性。尽管假设随时间固定，但关注子集可能发生变化。同时有效的时序置信界允许我们随时间顺序更新置信界，并支持可选停止。这在数据采集成本高昂且耗时的实际应用（如神经科学）中是一个期望特性。我们还提出了一种计算捷径，使得当所考虑的假设数量较大时，该程序的应用成为可能。我们通过模拟研究展示了所提方法的性能，并给出了关于该程序实施的一些实用指南。