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

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). Together, we call these conditions a ‘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 finding the maximum safe dose of a treatment.