Abstract
Functional connectivity has become an increasingly important area of research in recent years. At a typical spatial resolution, approximately 300 million connections link each voxel in the brain with every other. This pattern of connectivity is known as the functional connectome. Connectivity is often compared between experimental groups and conditions. Standard methods used to control the type 1 error rate are likely to be insensitive when comparisons are carried out across the whole connectome, due to the huge number of statistical tests involved. To address this problem, two new cluster based methods – the cluster size statistic (CSS) and cluster mass statistic (CMS) – are introduced to control the family wise error rate across all connectivity values. These methods operate within a statistical framework similar to the cluster based methods used in conventional task based fMRI. Both methods are data driven, permutation based and require minimal statistical assumptions. Here, the performance of each procedure is evaluated in a receiver operator characteristic (ROC) analysis, utilising a simulated dataset. The relative sensitivity of each method is also tested on real data: BOLD (blood oxygen level dependent) fMRI scans were carried out on twelve subjects under normal conditions and during the hypercapnic state (induced through the inhalation of 6% CO2 in 21% O2 and 73%N2). Both CSS and CMS detected significant changes in connectivity between normal and hypercapnic states. A family wise error correction carried out at the individual connection level exhibited no significant changes in connectivity.
Highlights
Functional connectivity MRI has become a widely used method for investigating human brain networks in health and disease; its potential in cognitive neuroscience and clinical research has been demonstrated in a large number of neuroimaging studies [1,2].Investigating the functional connectivity between all grey matter voxels makes full use of the connectional information available in the data
Neither of these changes was significant at the p, 0.05 FWE corrected level when compared to the distribution of maximum/minimum t-statistics; the maximum and minimum tvalues corresponding to this level of significance are shown as solid lines
cluster size statistic (CSS) and cluster mass statistic (CMS) methods Both CSS and CMS detected changes in global connectivity between experimental conditions, while the element-wise comparison of connectivity matrices identified no significant changes when corrected for multiple comparisons (p,0.05 FWE corrected)
Summary
Investigating the functional connectivity between all grey matter voxels makes full use of the connectional information available in the data This approach results in a very large number of connectivity values, as illustrated by the following example: The total grey matter volume of the brain is approximately 675 ml [3]. Standard methods used to control the false positive rate (Type I error), such as the false detection rate (FDR) or the family wise error rate (FWER), perform well in the context of conventional task-related fMRI [4] These methods are likely to result in insufficient statistical power when applied to such a large number of multiple comparisons [5]
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