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A novel sparse partial correlation method for simultaneous estimation of functional networks in group comparisons

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Xiaoyun Liang
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The conventional way to estimate functional networks is primarily based on Pearson correlation along with classic Fisher Z test. In general, networks are usually calculated at the individual-level and subsequently aggregated to obtain group-level networks. However, such estimated networks are inevitably affected by the inherent large inter-subject variability. A joint graphical model with Stability Selection (JGMSS) method was recently shown to effectively reduce inter-subject variability, mainly caused by confounding variations, by simultaneously estimating individual-level networks from a group. However, its benefits might be compromised when two groups are being compared, given that JGMSS is blinded to other groups when it is applied to estimate networks from a given group. We propose a novel method for robustly estimating networks from two groups by using group-fused multiple graphical-lasso combined with stability selection, named GMGLASS. Specifically, by simultaneously estimating similar within-group networks and between-group difference, it is possible to address inter-subject variability of estimated individual networks inherently related with existing methods such as Fisher Z test, and issues related to JGMSS ignoring between-group information in group comparisons. To evaluate the performance of GMGLASS in terms of a few key network metrics, as well as to compare with JGMSS and Fisher Z test, they are applied to both simulated and in vivo data. As a method aiming for group comparison studies, our study involves two groups for each case, i.e., normal control and patient groups; for in vivo data, we focus on a group of patients with right mesial temporal lobe epilepsy.
Xiaoyun Liang
added 2 research items
Synopsis We propose a novel approach, Graphical-LAsso with Stability-Selection (GM-GLASS), by employing sparse group penalties for simultaneously estimating networks from healthy control and patient groups. Simulations demonstrate that both GM-GLASS and JGMSS outperform Fisher Z-transform. Our in vivo results further show that GM-GLASS yields highest contrast of network metrics between groups, demonstrating the superiority of GM-GLASS in detecting signi᥼cance group diᦴerences over JGMSS and Fisher Z-transform. Overall, by controlling confounding variations between subjects, and therefore enhancing the statistical power, our simulated and in vivo results demonstrate that GM-GLASS provides a robust approach for conducting group comparison studies. Purpose Functional networks at group-level can be used to gain insight into complex brain function, including in group comparison studies. Joint graphical model with stability selection () was shown to greatly control confounding variations when computing group-level connectomic networks [1]. However, deals with one single group at a time. Recently, a fused graphical-lasso model () was proposed to robustly estimate group-level graphs from multiple groups simultaneously [2,3]. We aim to simultaneously estimate individual-and group-level networks from 2 groups using. We propose a novel approach, Group-fused-Multiple-Graphical-LAsso with Stability-Selection (), by employing sparse group penalties for simultaneously estimating connectivity matrices from within 2 contrast groups, e.g. normal control (NC) and patient (PT) group, while controlling for confounding variations. Methods can be described as follows (see Fig. 1 for ‱㌵owchart): datasets, for groups (㤱〮rst from group , last from group), : matrix, : number of time-points, : number of regions (nodes). The empirical covariance-matrix for is: , and the maximum-likelihood estimate of is [2,3]: , , with the constraint that all are positive-de㤱〮nite; the fused regularization [2,3] is reformulated as: with : nonnegative regularization-parameters, and , and. With stability selection [4], the data are subsampled many times and all positive-correlations that occur in a large fraction of the resulting selection sets are selected. The combination patterns (i.e. the order of subjects) in the second part of are shu㔰〼ed for each resampling to avoid bias. For a given ,. For a cut-o吠㸸 and a set of regularization parameters, the set of stable positive-correlations are as follows:. Simulation: Simulations were conducted according to [6]. A structural-connectivity matrix [5] was employed to simulate data for NCs (see [6]); by randomly deleting (adding) existing (new) edges, patient data were then simulated, with and. Ten datasets were generated (i.e. 'subjects') for each group. To perform stability selection, observations were randomly subsampled 1 2,3 1,4 1,4 1 2 3 4 ,