A statistical test to identify differences in clustering structures

TL;DR

This paper introduces ANOCVA, a novel statistical test for comparing clustering structures across groups in brain imaging data, revealing differences and new insights in ADHD-related brain organization.

Contribution

The paper presents a new statistical method, ANOCVA, for directly testing differences in clustering structures between groups in fMRI data, addressing limitations of voxel-wise analysis.

Findings

ANOCVA detects significant clustering differences between ADHD and control groups.

The method identifies new brain regions with differential clustering not previously reported.

Results support the hypothesis of altered brain clustering in ADHD.

Abstract

Statistical inference on functional magnetic resonance imaging (fMRI) data is an important task in brain imaging. One major hypothesis is that the presence or not of a psychiatric disorder can be explained by the differential clustering of neurons in the brain. In view of this fact, it is clearly of interest to address the question of whether the properties of the clusters have changed between groups of patients and controls. The normal method of approaching group differences in brain imaging is to carry out a voxel-wise univariate analysis for a difference between the mean group responses using an appropriate test (e.g. a t-test) and to assemble the resulting "significantly different voxels" into clusters, testing again at cluster level. In this approach of course, the primary voxel-level test is blind to any cluster structure. Direct assessments of differences between groups (or reproducibility within groups) at the cluster level have been rare in brain imaging. For this reason, we introduce a novel statistical test called ANOCVA - ANalysis Of Cluster structure Variability, which statistically tests whether two or more populations are equally clustered using specific features. The proposed method allows us to compare the clustering structure of multiple groups simultaneously, and also to identify features that contribute to the differential clustering. We illustrate the performance of ANOCVA through simulations and an application to an fMRI data set composed of children with ADHD and controls. Results show that there are several differences in the brain's clustering structure between them, corroborating the hypothesis in the literature. Furthermore, we identified some brain regions previously not described, generating new hypothesis to be tested empirically.