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Currently, network-oriented analysis of fMRI data has become an important tool for understanding brain organization and brain networks. Among the range of network modeling methods, partial correlation has shown great promises in accurately detecting true brain network connections. However, the application of partial correlation in investigating brain connectivity, especially in large-scale brain networks, has been limited so far due to the technical challenges in its estimation. In this paper, we propose an efficient and reliable statistical method for estimating partial correlation in large-scale brain network modeling. Our method derives partial correlation based on the precision matrix estimated via Constrained L1-minimization Approach (CLIME), which is a recently developed statistical method that is more efficient and demonstrates better performance than the existing methods. To help select an appropriate tuning parameter for sparsity control in the network estimation, we propose a new  Dens -based selection method that provides a more informative and flexible tool to allow the users to select the tuning parameter based on the desired sparsity level. Another appealing feature of the  Dens -based method is that it is much faster than the existing methods, which provides an important advantage in neuroimaging applications. Simulation studies show that the  Dens -based method demonstrates comparable or better performance with respect to the existing methods in network estimation. We applied the proposed partial correlation method to investigate resting state functional connectivity using rs-fMRI data from the Philadelphia Neurodevelopmental Cohort (PNC) study. Our results show that partial correlation analysis removed considerable between-module marginal connections identified by full correlation analysis, suggesting these connections were likely caused by global effects or common connection to other nodes. Based on partial correlation, we find that the most significant direct connections are between homologous brain locations in the left and right hemisphere. When comparing partial correlation derived under different sparse tuning parameters, an important finding is that the sparse regularization has more shrinkage effects on negative functional connections than on positive connections, which supports previous findings that many of the negative brain connections are due to non-neurophysiological effects. An R package “DensParcorr” can be downloaded from CRAN for implementing the proposed statistical methods.

An Efficient and Reliable Statistical Method for Estimating Functional Connectivity in Large Scale Brain Networks Using Partial Correlation