Two step multiple comparisons procedures for positively dependent data with application to detecting differences in human brain network topologies

We consider the problem of testing positively dependent multiple hypotheses assuming that a prior information about the dependence structure is available. We propose two-step multiple comparisons procedures that exploit the prior information of the dependence structure, without relying on strong assumptions. In the first step, we group the tests into subsets where tests are supposed to be positively dependent and in each of which we compute the standardized mean of the test scores. Given the subset mean scores or equivalently the subsets p-values, we apply a first screening at a predefined threshold, which results in two types of subsets. Based on this typing, the original single test p-values are modified such that they can be used in conjunction with any multiple comparison procedure. We show by means of different simulation that power is gained with the proposed two-step methods, and compare it with traditional multiple comparison procedures. As an illustration, our method is applied on real data comparing topological differences between two groups of human brain networks.