Including Data Analytical Stability in Cluster-basedInference

In the statistical analysis of functional Magnetic Resonance Imaging (fMRI) brain data it remains a challenge to account for simultaneously testing activation in over 100.000 volume units or voxels. A popular method that reduces the dimensionality of this test problem is cluster-based inference. We propose a new testing procedure that allows to control the family-wise error (FWE) rate at the cluster level but improves cluster-based test decisions in two ways by (1) taking into account a measure for data analytical stability and (2) allowing a more voxel-based interpretation of the results. For each voxel, we define the re-selection rate conditional on a given FWE-corrected threshold and use this rate, which is a measure of stability, into the selection process. In our procedure, we set a more liberal and a more conservative FWE controlling threshold. Clusters that survive the liberal but not the conservative threshold are retained if sufficient evidence for voxelwise stability is available. Cluster that survive the conservative threshold are retained anyhow, and clusters that do not survive the liberal threshold are not further considered. Using the Human Connectome Project Data (Van Essen et al., 2012), we demonstrate how in a group analysis our method results not only in a higher number of selected voxels but also in a larger overlap between different test images. Additionally, we demonstrate the ability of our procedure to control the FWE, also in relatively small sample sizes.