ADDIS-Graphs for Online Error Control With Application to Platform Trials

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. The existing online literature mainly considered large-scale studies and constructed powerful but rigid algorithms for these. However, smaller studies, such as platform trials, require high flexibility and easy interpretability to take study objectives into account and facilitate the communication. Another challenge in platform trials is that due to the shared control arm some of the $p$-values are dependent and significance levels need to be prespecified before the decisions for all the past treatments are available. We propose adaptive-discarding-Graphs (ADDIS-Graphs) with FWER control that due to their graphical structure perfectly adapt to such settings and provably uniformly improve the state-of-the-art method. We introduce several extensions of these ADDIS-Graphs, including the incorporation of information about the joint distribution of the $p$-values and a version for FDR control.