TY - JOUR
T1 - Testing Group Differences in Brain Functional Connectivity
T2 - Using Correlations or Partial Correlations?
AU - Kim, Junghi
AU - Wozniak, Jeffrey R
AU - Mueller, Bryon A
AU - Pan, Wei
N1 - Publisher Copyright:
© Mary Ann Liebert, Inc. 2015.
PY - 2015/5/1
Y1 - 2015/5/1
N2 - Resting-state functional magnetic resonance imaging allows one to study brain functional connectivity, partly motivated by evidence that patients with complex disorders, such as Alzheimer's disease, may have altered functional brain connectivity patterns as compared with healthy subjects. A functional connectivity network describes statistical associations of the neural activities among distinct and distant brain regions. Recently, there is a major interest in group-level functional network analysis; however, there is a relative lack of studies on statistical inference, such as significance testing for group comparisons. In particular, it is still debatable which statistic should be used to measure pairwise associations as the connectivity weights. Many functional connectivity studies have used either (full or marginal) correlations or partial correlations for pairwise associations. This article investigates the performance of using either correlations or partial correlations for testing group differences in brain connectivity, and how sparsity levels and topological structures of the connectivity would influence statistical power to detect group differences. Our results suggest that, in general, testing group differences in networks deviates from estimating networks. For example, high regularization in both covariance matrices and precision matrices may lead to higher statistical power; in particular, optimally selected regularization (e.g., by cross-validation or even at the true sparsity level) on the precision matrices with small estimation errors may have low power. Most importantly, and perhaps surprisingly, using either correlations or partial correlations may give very different testing results, depending on which of the covariance matrices and the precision matrices are sparse. Specifically, if the precision matrices are sparse, presumably and arguably a reasonable assumption, then using correlations often yields much higher powered and more stable testing results than using partial correlations; the conclusion is reversed if the covariance matrices, not the precision matrices, are sparse. These results may have useful implications to future studies on testing functional connectivity differences.
AB - Resting-state functional magnetic resonance imaging allows one to study brain functional connectivity, partly motivated by evidence that patients with complex disorders, such as Alzheimer's disease, may have altered functional brain connectivity patterns as compared with healthy subjects. A functional connectivity network describes statistical associations of the neural activities among distinct and distant brain regions. Recently, there is a major interest in group-level functional network analysis; however, there is a relative lack of studies on statistical inference, such as significance testing for group comparisons. In particular, it is still debatable which statistic should be used to measure pairwise associations as the connectivity weights. Many functional connectivity studies have used either (full or marginal) correlations or partial correlations for pairwise associations. This article investigates the performance of using either correlations or partial correlations for testing group differences in brain connectivity, and how sparsity levels and topological structures of the connectivity would influence statistical power to detect group differences. Our results suggest that, in general, testing group differences in networks deviates from estimating networks. For example, high regularization in both covariance matrices and precision matrices may lead to higher statistical power; in particular, optimally selected regularization (e.g., by cross-validation or even at the true sparsity level) on the precision matrices with small estimation errors may have low power. Most importantly, and perhaps surprisingly, using either correlations or partial correlations may give very different testing results, depending on which of the covariance matrices and the precision matrices are sparse. Specifically, if the precision matrices are sparse, presumably and arguably a reasonable assumption, then using correlations often yields much higher powered and more stable testing results than using partial correlations; the conclusion is reversed if the covariance matrices, not the precision matrices, are sparse. These results may have useful implications to future studies on testing functional connectivity differences.
KW - brain networks
KW - correlation
KW - neuroimaging
KW - partial correlation
KW - rs-fMRI
KW - statistical power
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U2 - 10.1089/brain.2014.0319
DO - 10.1089/brain.2014.0319
M3 - Article
C2 - 25492804
AN - SCOPUS:84945955874
SN - 2158-0014
VL - 5
SP - 214
EP - 231
JO - Brain connectivity
JF - Brain connectivity
IS - 4
ER -