Testing group differences in brain functional connectivity: using correlations or partial correlations?

Area of Science:

• Neuroimaging
• Network Neuroscience
• Statistical Inference

Background:

• Resting-state functional magnetic resonance imaging (rs-fMRI) reveals brain functional connectivity.
• Altered functional connectivity is observed in disorders like Alzheimer's disease.
• Group-level functional network analysis lacks robust statistical inference methods.

Purpose of the Study:

• To investigate the performance of correlations versus partial correlations for testing group differences in brain connectivity.
• To assess the influence of sparsity and network topology on statistical power.
• To provide guidance on selecting appropriate statistical measures for functional connectivity group comparisons.

Main Methods:

• Comparative analysis of correlation and partial correlation statistics for pairwise associations in functional connectivity networks.
• Evaluation of statistical power under varying sparsity levels and topological structures of connectivity matrices.
• Investigation of the impact of regularization on covariance and precision matrices.

Main Results:

• Testing group differences in networks differs significantly from network estimation.
• High regularization can increase statistical power, but optimal regularization on precision matrices may paradoxically reduce power.
• The choice between correlation and partial correlation critically depends on the sparsity of covariance versus precision matrices.

Conclusions:

• If precision matrices are sparse, correlations generally provide more powerful and stable results than partial correlations.
• If covariance matrices are sparse (and precision matrices are not), partial correlations may be superior.
• These findings have significant implications for designing future studies on functional connectivity group differences.