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：近年来，图形多重检验程序因其通用性和易于解释的特点而广受欢迎。在当代研究中，通常需要在线错误控制，即在检验先验无界假设序列时，需将族系错误率或错误发现率等错误准则控制在预设范围内。尽管经典图形程序可扩展至在线场景，但先前研究表明该方法效能较低，而自适应丢弃（ADDIS）程序等其他方法更受青睐。本文提出具有族系错误率控制的ADDIS图及其在错误发现率场景下的扩展。这些图形化ADDIS程序融合了图形程序良好的可解释性与ADDIS程序的高在线效能。此外，它们可适配局部依赖结构与异步检验框架，从而在效能上优于现有先进方法。因此，所提出的方法适用于广泛的应用场景，包括平台试验等创新型复杂试验设计，以及市场调研中A/B测试评估等大规模检验设计。