Online multiple hypothesis testing

TL;DR

This paper reviews the development of online multiple hypothesis testing methods that control error rates like FDR in sequential data analysis, highlighting key theories, applications, and recent methodological advances.

Contribution

It provides a comprehensive review of online error control methods, including theory, simulations, and extensions, for sequential hypothesis testing in large-scale data analysis.

Findings

Comparison of different online testing algorithms through simulations

Overview of recent methodological extensions in online error control

Application examples demonstrating practical utility

Abstract

Modern data analysis frequently involves large-scale hypothesis testing, which naturally gives rise to the problem of maintaining control of a suitable type I error rate, such as the false discovery rate (FDR). In many biomedical and technological applications, an additional complexity is that hypotheses are tested in an online manner, one-by-one over time. However, traditional procedures that control the FDR, such as the Benjamini-Hochberg procedure, assume that all p-values are available to be tested at a single time point. To address these challenges, a new field of methodology has developed over the past 15 years showing how to control error rates for online multiple hypothesis testing. In this framework, hypotheses arrive in a stream, and at each time point the analyst decides whether to reject the current hypothesis based both on the evidence against it, and on the previous rejection decisions. In this paper, we present a comprehensive exposition of the literature on online error rate control, with a review of key theory as well as a focus on applied examples. We also provide simulation results comparing different online testing algorithms and an up-to-date overview of the many methodological extensions that have been proposed.