A New Approach to Partial Conjunction Analysis in Neuroimaging

Abstract: The problem of identifying the brain regions activated through a particular cognitive task is pivotal in neuroimaging. This problem becomes even more complex if we have several cognitive tasks or several subjects. In this paper, we view this problem as a partial conjunction (PC) hypotheses testing problem, i.e., we are testing whether a specific brain region is activated in at least $\gamma$ (for some pre-fixed $\gamma$) subjects. We propose the application of a recent advance in the simultaneous statistical inference literature to activation localization in neuroimaging. We apply the recently proposed CoFilter method to neuroimaging data to discover brain regions activated in at least $\gamma$ subjects. Our proposal has two distinct advantages. First, it alleviates the conservativeness displayed by the traditional multiple testing procedures in testing PC hypotheses by eliminating many of the conservative PC $p$-values. Second, it is especially suitable for several high-dimensional studies, each of which examines a large number of null hypotheses. We also compare the performance of our proposal with existing methods for testing PC hypotheses through extensive simulation studies on neuroimaging data and a real dataset.