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，图形化多重检验程序因其通用性和易于解释的特点而受到广泛关注。在现代研究中，常需进行在线错误控制，即在检验一个先验无界假设序列时，需保持诸如族系错误率（FWER）或错误发现率（FDR）等错误准则处于可控状态。尽管经典图形化程序可扩展至在线场景，但已有研究表明该方法功效较低，而自适应丢弃（ADDIS）程序等替代方案更受青睐。本文提出了具有FWER控制的ADDIS图形化程序及其针对FDR设置的扩展版本。这些图形化ADDIS程序将图形化程序良好的可解释性与ADDIS程序的高在线功效相结合。此外，它们还能适应局部依赖结构和异步检验设定，从而相较于当前最先进方法显著提升检验功效。因此，所提出的方法适用于广泛应用场景，包括创新型复合试验设计（如平台试验）和大规模检验设计（如市场研究中的A/B测试评估）。