Deriving difference between the Bayesian networks based patterns of the effective connectivity using permutation test in fMRI studies

Recently introduced in analyzing data from functional MRI (fMRI) and other neuroimaging techniques, Bayesian networks (BN) is a method to characterize effective connectivity patterns among multiple brain regions. So far, interests of using BN have been primarily on learning the connectivity pattern for each single group with well investigated computational algorithms. Examination of the connectivity pattern differences between groups, on the other hand, lacks rigorous statistical inference procedure. In this study, we propose using random permutation, a type of non-parametric statistical significance test in which a reference distribution is obtained by calculating all possible values of the test statistic under re-arrangements of the group labels on the observed data points, to infer whether the difference is significant. Two different approaches to perform the permutation test are introduced, compared to each other and both compared to the routinely used parametric t-test. Permutation approach 1 permutes the group labels first followed by learning BN pattern for each of the newly formed groups. Approach 2 learns BN pattern for each individual and connection parameters are then subjected to the group label permutations. Synthetic data generated under varying signal-to-noise ratios are used to investigate the performances of the proposed methods. Our results demonstrated that permutation approach 1 in detecting the effective connectivity pattern difference between two groups is superior to permutation approach 2 and to the common-sense two sample t-test.