In recent years, graphical multiple testing procedures have gained popularity due to their generality and ease of interpretation. In contemporary research, online error control is often required, where an error criterion, such as familywise error rate (FWER) or false discovery rate (FDR), shall remain under control while testing an a priori unbounded sequence of hypotheses. Although the classical graphical procedure can be extended to the online setting, previous work has shown that it leads to low power, and other approaches, such as Adaptive-Discard (ADDIS) procedures, are preferred instead. In this paper, we introduce an ADDIS-Graph with FWER control and its extension for the FDR setting. These graphical ADDIS procedures combine the good interpretability of graphical procedures with the high online power of ADDIS procedures. Moreover, they can be adapted to a local dependence structure and an asynchronous testing setup, leading to power improvements over the current state-of-art methods. Consequently, the proposed methods are useful for a wide range of applications, including innovative complex trial designs, such as platform trials, and large-scale test designs, such as in the evaluation of A/B tests for marketing research.

翻译：近些年来,图形多测试程序由于其普遍性和解释简便性而越来越受欢迎。在当代研究中,通常需要在线错误控制,因为错误标准,如家庭误差率(FWER)或虚假发现率(FDR)等,在测试一个先验的假设序列时仍应处于控制之下。虽然古典图形程序可以扩展到在线设置,但以往的工作表明,它导致权力低,而其他方法,如适应性磁盘(ADDDIS)程序,则取而代之。在本文中,我们引入了带有FWER控制及其FDR设置扩展的ADDDIS-Graph。这些图形ADDDDDIS程序将图形程序的良好可判读性与ADDDIS程序的高度在线能力相结合。此外,它们可以适应本地依赖性结构和不连续测试设置,导致对当前先进方法的动力改进。因此,拟议方法对广泛的应用十分有用,包括创新的复杂测试设计,如平台试验,以及大规模测试设计,如A/B研究测试。