Online control of the familywise error rate

TL;DR

This paper develops new adaptive online algorithms for controlling the familywise error rate in sequential hypothesis testing, unifying offline and online methods, with proven power gains in independent or locally dependent p-value sequences.

Contribution

It introduces novel, powerful online FWER control algorithms that extend offline methods and are effective under independence or local dependence of p-values.

Findings

Significant power improvements demonstrated in experiments.

Formal proofs of control in Gaussian models.

Unified framework for offline and online FWER control.

Abstract

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.