On a Holm-related MTP for rejecting at least hypotheses: general validity, optimality property, confidence regions, and applications.

This article concerns -value-based multiple testing procedures (MTPs) that can be used in a confirmatory clinical study under minimal assumptions in case the requirement for study-success is that at least out of primary/important hypotheses become rejected. Recently, a simple, generally valid Holm-type MTP was discussed that can be used for such a requirement for any from one to . It can only reject at least (or zero) hypotheses, but this increases the power to reject or more hypotheses compared to Holm's step-down MTP.

Note on a stepwise procedure for rejecting at least k out of m hypotheses: A simple Holm-type formulation and proof.

Mielke et al. (2021) proposed a stepwise multiple testing procedure (MTP) based on marginal p-values for rejecting at least k out of m null hypotheses. Briefly, the MTP cannot reject less than k hypotheses, but this property improves the power to reject k or more hypotheses relative to the stepdown MTP of Holm (1979).