Can online multiple testing be improved? This paper introduces a new principle for familywise error rate (FWER) control in online hypothesis testing, offering a uniform improvement over existing adaptive-discard (ADDIS) procedures. The new principle ensures that the probability of making at least one type I error remains under control while testing a potentially infinite sequence of hypotheses over time. This research provides a uniform improvement of the ADDIS principle, thereby enhancing all ADDIS procedures. The improved methods consistently reject at least as many hypotheses as ADDIS procedures, often rejecting more while maintaining FWER control. This means that the methods we propose reject as least as much hypotheses as ADDIS procedures and in some cases even more, while maintaining FWER control. The findings confirm that there is no other FWER controlling procedure that rejects any hypothesis. The new principle is applied to derive uniform improvements of the ADDIS-Spending and ADDIS-Graph, demonstrating its practical utility. This advancement enhances the power and reliability of online multiple testing, contributing to more robust statistical inference.
Published in Biometrical Journal, this paper addresses a core topic in biostatistics: controlling error rates in multiple hypothesis testing. Given the journal's focus on statistical methods in biological and medical research, the paper's uniform improvement of the ADDIS principle provides a valuable tool for researchers aiming to draw more reliable conclusions from complex datasets. It enhances the rigor of statistical inference in biomedical studies.