Online control of the familywise error rate
This work addresses the need for robust statistical testing in biological research and other fields where data accumulates over time, offering a novel solution for online FWER control that improves upon existing methods.
The paper tackles the problem of controlling the familywise error rate (FWER) in an online setting where hypotheses are tested sequentially over time without prior knowledge of the future, ensuring no false discoveries with high probability. It introduces new adaptive online algorithms that achieve substantial gains in power, as demonstrated in experiments and formally proved in a Gaussian sequence model.
Biological research often involves testing a growing number of null hypotheses as new data is accumulated over time. We study the problem of online control of the familywise error rate (FWER), that is testing an apriori unbounded sequence of hypotheses (p-values) one by one over time without knowing the future, such that with high probability there are no false discoveries in the entire sequence. This paper unifies algorithmic concepts developed for offline (single batch) FWER control and online false discovery rate control to develop novel online FWER control methods. Though many offline FWER methods (e.g. Bonferroni, fallback procedures and Sidak's method) can trivially be extended to the online setting, our main contribution is the design of new, powerful, adaptive online algorithms that control the FWER when the p-values are independent or locally dependent in time. Our experiments demonstrate substantial gains in power, that are also formally proved in a Gaussian sequence model. Multiple testing, FWER control, online setting.