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

ABSTRACT: 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.

SUBMITTER: Kim J

PROVIDER: S-EPMC4432782 | biostudies-literature | 2015 May

REPOSITORIES: biostudies-literature

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

Kim Junghi J Wozniak Jeffrey R JR Mueller Bryon A BA Pan Wei W

Brain connectivity 20150225 4

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 anal ...[more]

PMID: 25492804

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Project description:Resting-state functional magnetic resonance imaging (rs-fMRI) and other technologies have been offering evidence and insights showing that altered brain functional networks are associated with neurological illnesses such as Alzheimer's disease. Exploring brain networks of clinical populations compared to those of controls would be a key inquiry to reveal underlying neurological processes related to such illnesses. For such a purpose, group-level inference is a necessary first step in order to establish whether there are any genuinely disrupted brain subnetworks. Such an analysis is also challenging due to the high dimensionality of the parameters in a network model and high noise levels in neuroimaging data. We are still in the early stage of method development as highlighted by Varoquaux and Craddock (2013) that "there is currently no unique solution, but a spectrum of related methods and analytical strategies" to learn and compare brain connectivity. In practice the important issue of how to choose several critical parameters in estimating a network, such as what association measure to use and what is the sparsity of the estimated network, has not been carefully addressed, largely because the answers are unknown yet. For example, even though the choice of tuning parameters in model estimation has been extensively discussed in the literature, as to be shown here, an optimal choice of a parameter for network estimation may not be optimal in the current context of hypothesis testing. Arbitrarily choosing or mis-specifying such parameters may lead to extremely low-powered tests. Here we develop highly adaptive tests to detect group differences in brain connectivity while accounting for unknown optimal choices of some tuning parameters. The proposed tests combine statistical evidence against a null hypothesis from multiple sources across a range of plausible tuning parameter values reflecting uncertainty with the unknown truth. These highly adaptive tests are not only easy to use, but also high-powered robustly across various scenarios. The usage and advantages of these novel tests are demonstrated on an Alzheimer's disease dataset and simulated data.

Project description:Structural and functional brain connectivity are increasingly used to identify and analyze group differences in studies of brain disease. This study presents methods to analyze uni- and bi-modal brain connectivity and evaluate their ability to identify differences. Novel visualizations of significantly different connections comparing multiple metrics are presented. On the global level, "bi-modal comparison plots" show the distribution of uni- and bi-modal group differences and the relationship between structure and function. Differences between brain lobes are visualized using "worm plots". Group differences in connections are examined with an existing visualization, the "connectogram". These visualizations were evaluated in two proof-of-concept studies: (1) middle-aged versus elderly subjects; and (2) patients with schizophrenia versus controls. Each included two measures derived from diffusion weighted images and two from functional magnetic resonance images. The structural measures were minimum cost path between two anatomical regions according to the "Statistical Analysis of Minimum cost path based Structural Connectivity" method and the average fractional anisotropy along the fiber. The functional measures were Pearson's correlation and partial correlation of mean regional time series. The relationship between structure and function was similar in both studies. Uni-modal group differences varied greatly between connectivity types. Group differences were identified in both studies globally, within brain lobes and between regions. In the aging study, minimum cost path was highly effective in identifying group differences on all levels; fractional anisotropy and mean correlation showed smaller differences on the brain lobe and regional levels. In the schizophrenia study, minimum cost path and fractional anisotropy showed differences on the global level and within brain lobes; mean correlation showed small differences on the lobe level. Only fractional anisotropy and mean correlation showed regional differences. The presented visualizations were helpful in comparing and evaluating connectivity measures on multiple levels in both studies.

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

Publications

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

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