title: A recycling framework for the construction of Bonferroni-based multiple tests.
abstract: In this paper we describe Bonferroni-based multiple testing procedures (MTPs) as strategies to split and recycle test mass. Here, 'test mass' refers to (parts of) the nominal level alpha at which the family-wise error rate is controlled. Briefly, test mass is split between different null hypotheses, and whenever a null hypothesis is rejected, the part of alpha allocated to it may be recycled to the testing of other hypotheses. These recycling MTPs are closed testing procedures based on raw p-values associated with testing the individual null hypotheses, and the class of such MTPs includes, for example, serial and parallel gatekeeping, fallback and Holm procedures. Graphical displays and a concise algebraic notation are provided for such MTPs. This recycling approach has pedagogical advantages and may facilitate the tailoring of MTPs for different purposes.
authors.affiliation: AstraZeneca R&D, SE-43183 Mölndal, Sweden. carl-fredrik.burman@astrazeneca.com
authors.forename: C-F
authors.initials: CF
authors.lastname: Burman
authors.forename: C
authors.initials: C
authors.lastname: Sonesson
authors.forename: O
authors.initials: O
authors.lastname: Guilbaud
mesh_terms: D000465:Algorithms; D015982:Bias; D001699:Biometry / Q000379:methods*; D002986:Clinical Trials as Topic; D005189:False Positive Reactions; D006801:Humans; D015233:Models, Statistical