A Rejection Principle for Sequential Tests of Multiple Hypotheses Controlling Familywise Error Rates

TL;DR

This paper introduces a unifying rejection principle for sequential multiple hypothesis testing that ensures control of the familywise error rate, simplifies understanding of existing procedures, and derives new methods with practical applications.

Contribution

It extends fixed-sample FWER control methods to sequential testing, providing a unifying framework and new procedures with proven error control.

Findings

Established a rejection principle for sequential tests controlling FWER.

Simplified understanding of existing sequential multiple testing procedures.

Developed two new procedures with practical applications in biomedical data.

Abstract

We present a unifying approach to multiple testing procedures for sequential (or streaming) data by giving sufficient conditions for a sequential multiple testing procedure to control the familywise error rate (FWER), extending to the sequential domain the work of Goeman and Solari (2010) who accomplished this for fixed sample size procedures. Together we call these conditions the "rejection principle for sequential tests," which we then apply to some existing sequential multiple testing procedures to give simplified understanding of their FWER control. Next the principle is applied to derive two new sequential multiple testing procedures with provable FWER control, one for testing hypotheses in order and another for closed testing. Examples of these new procedures are given by applying them to a chromosome aberration data set and to finding the maximum safe dose of a treatment.