Multiple comparisons procedures for complex dependent data with application to study human brain complex network properties

We consider the problem of testing positively dependent multiple hypotheses, assuming that 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 a summary statistic that is associated with a subset p-value. Given the subset scores or equivalently the subsets p-values, a first screening is applied 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. We discuss as well the possible extensions of the proposed strategy. As an illustration, our method is applied on real data comparing topological differences between two groups of human brain networks.