The perils of global signal regression for group comparisons: a case study of Autism Spectrum Disorders

Abstract

We have previously argued from a theoretical basis that the standard practice of regression of the Global Signal from the fMRI time series in functional connectivity studies is ill advised, particularly when comparing groups of participants. Here, we demonstrate in resting-state data from participants with an Autism Spectrum Disorder and matched controls that these concerns are also well founded in real data. Using the prior theoretical work to formulate predictions, we show: (1) rather than simply altering the mean or range of correlation values amongst pairs of brain regions, Global Signal Regression systematically alters the rank ordering of values in addition to introducing negative values, (2) it leads to a reversal in the direction of group correlation differences relative to other preprocessing approaches, with a higher incidence of both long-range and local correlation differences that favor the Autism Spectrum Disorder group, (3) the strongest group differences under other preprocessing approaches are the ones most altered by Global Signal Regression, and (4) locations showing group differences no longer agree with those showing correlations with behavioral symptoms within the Autism Spectrum Disorder group. The correlation matrices of both participant groups under Global Signal Regression were well predicted by our previous mathematical analyses, demonstrating that there is nothing mysterious about these results. Finally, when independent physiological nuisance measures are lacking, we provide a simple alternative approach for assessing and lessening the influence of global correlations on group comparisons that replicates our previous findings. While this alternative performs less well for symptom correlations than our favored preprocessing approach that includes removal of independent physiological measures, it is preferable to the use of Global Signal Regression, which prevents unequivocal conclusions about the direction or location of group differences.

Keywords: GCOR; artifact; functional connectivity; global correlation; resting-state fMRI; typically developing.

Figure 1

Distortion of simulated group differences in correlation by GS regression. Adapted from Figure 4 in Saad et al. (2012), patterns of correlation are shown for two simulated groups of participants, Group A and B (N = 30 in each). Pre-GS regression (left panels), both groups have three patches of simulated voxels (counter-clockwise from lower left: patches 1, 2, and 3) that have average within-patch correlations of 0.5 (see color bar to the right). Group B also has a correlation across patches 1 and 2, with all other inter-patch correlations in both groups set to be approximately 0. The presence of the across-patch correlation in Group B leads to an overall larger level of global correlation (GCOR values shown to left in green). After GS regression (middle panels), negative correlations are introduced among many of the patches and a larger amount of global variation is removed from patches 1 and 2 in Group B. Significant group correlation differences (right panel) are then found at all locations instead of at the one appropriate location (correlation between, not within, patches 1 and 2). The appropriate group differences are most distorted (Δ) by GS regression in and between patches 1 and 2, the locations involved in the largest true differences.

Figure 2

Sampling the group brain mask with 1880 ROIs. The original group brain mask from Gotts et al. (2012) (voxels shared in >85% of participants in both ASD and TD groups; shown in green) was sampled by choosing every fourth voxel from the original voxel grid (in X, Y, Z directions in Talairach coordinates). Each chosen voxel (red voxels) served as the center for a 6-mm radius sphere, totaling 1880 ROIs. The original group brain mask excluded voxels in white matter, the ventricles, and the sagittal sinus.

Figure 3

ROIs showing the largest group differences (TD > ASD) in Gotts et al. (2012). ROIs 1–27 are shown using a distinct color for each ROI, ranging from cool colors (blue = 1) up to hot colors (red = 27).

Figure 4

GCOR method of removing global correlations. (top panel) The x-axis shows the global level of Pearson correlation (GCOR) for each of the 29 TD participants, calculated among all possible voxel combinations in a whole brain mask and then transformed with Fisher's z. The y-axis shows the Fisher's z-transformed correlation value between two example ROIs for each participant, with frequency histograms across participants shown to the left of the y-axis. The blue dots are the original values of GCOR and ROI-ROI correlation for each participant under the Basic preprocessing model. Covariate removal is illustrated here for a single-group of participants, but appropriate removal for group comparisons is more complicated, carried out using Analysis of Covariance (ANCOVA), which is implemented in AFNI with the program 3dttest++ for two-level grouping variables. For a single group, the best-fit regression line (dashed red) is used to adjust y-values as a function of the distance from the median x-value (dashed blue vertical line). The adjusted values are shown relative to the blue dots using black vertical lines, with the new values at the endpoints. The adjusted values have a reduced standard deviation on the y-axis relative to the original distribution (see histogram of solid black bars on the left). (bottom panel) Frequency histograms of GCOR values are shown for TD (black) and ASD (red) participants. Distributions are overlapping and skewed for both groups, which motivated the choice of median rather than mean for re-centering.

Figure 5

Effect of preprocessing model on ROI-ROI correlations and group differences. Correlation matrices for the TD and ASD groups and the corresponding group comparisons are shown for each of the four preprocessing models using 1880 ROIs sampled from the group brain mask. Results for the “Basic” model (Motion+Ventricles+Local WM) are shown in the upper left, the Basic+GCOR model in the upper right, the Basic+GS regression model in the lower left, and the full ANATICOR model in the lower right. The upper two plots of each model show the average ROI-ROI correlation matrices for the TD and ASD groups (see corresponding colorbars for scale), the lower left plot of each model shows the unthresholded t-values, and the lower right plot of each model shows the t-values thresholded at p < 0.05 (uncorrected). ROIs are ordered by scanner coordinates (ranked by Inferior-Superior, then by Anterior-Posterior, then by Right-Left).

Figure 6

Effect of preprocessing model on the distributions of group differences. (A) Full distributions of t-values (TD-ASD) over all unique combinations of the 1880 ROIs (N = 1766260) under all four preprocessing models. (B) (top panel) Ratio of positive to negative t-values that survive the threshold t-value, shown as a function of the threshold on the x-axis (ranging from p < 0.05 to p < 0.0005, uncorrected). (bottom panel) Percentage of tests that yield significant negative t-values (i.e., favoring the ASD group) as a function of threshold t-value and preprocessing model. These values serve as the denominator in the ratios of the top panel. (C) Mean t-value across all 1880 ROI for each ROI as the seed (i.e., averaging across the rows of the full, unthresholded t-matrix of each model), rank-ordered from small to large by the mean t-values in the Basic model. These curves demonstrate that the largest alterations to the group comparisons by GS regression are for ROIs that elicit the largest average t-values under the +GCOR and ANATICOR models.

Figure 7

Mathematical prediction of correlation matrices under GS regression. The left two panels show the group average ROI-ROI correlation matrices for the TD and ASD groups under the +GS preprocessing model (shown also in Figure 5). The middle two panels show the matrices predicted by the equations developed by Saad et al. (2013) when applied to the time series data under the Basic preprocessing model (for equations used, see section Mathematical prediction of GS correlation matrices). Scatterplots of the agreement between the left and middle panels are shown in the rightmost panels, with Pearson and Spearman rank correlations shown to quantify the level of agreement. The predictions are accurate despite only estimating the distortions under GS regression from 1880 ROIs sampled in the group brain mask (excluding nuisance tissue signals such as white matter, ventricles, and sinuses).

Figure 8

Group comparisons of whole-brain connectedness for the +GS and +GCOR preprocessing models. Whole-brain connectedness (i.e., the average correlation of each voxel time series with the rest of the voxels in the brain mask) was compared separately for the +GS regression and the +GCOR models. The +GS regression model, shown in the left plots, led to a larger number of locations with ASD connectedness values larger than TD values, as well as the absence of TD > ASD effects in locations found previously using ANATICOR. In contrast, the +GCOR method of removing global correlations, shown in the right plots, largely replicated the results found with ANATICOR (compare to ROIs in Figure 3 from the same sagittal and axial views). See text for full description.

Figure 9

Effect of preprocessing model on group comparisons of local correlation. Group t-tests of local correlation (TD-ASD) under the four preprocessing models are shown for regions in Gotts et al. (2012) that exhibited greater long-range correlations for TD participants (ROIs 1-27; see Figure 3). Dashed red (TD > ASD) and blue horizontal lines (ASD > TD) mark the p < 0.05 significance level for individual tests. On average, the +GS model yielded more negative t-values (favoring the ASD participants) relative to the other three models.

Figure 10

Effect of preprocessing model on the agreement of group differences and social symptom correlations within the ASD group. Group t-tests are shown for the four preprocessing models in the top row using ROIs 1–27 (Figure 3) (see colorbar for scale of t-values to the right). Partial correlations of SRS total score with ROI-ROI correlation level within the ASD group, removing shared variation with Age and full scale IQ, are shown in the bottom row (see colorbar for scale of partial r-values to the right). Only the ANATICOR model produced significant correspondence between the group differences and behavioral correlations solely within the ASD group (see text for details). The +GS model also failed to exhibit strong group differences using these ROIs, consistent with the results of Figure 6C.

Figure 11

Effect of preprocessing model on the agreement of group differences and ASD social symptom correlations using whole-brain connectedness. Whole-brain connectedness was compared between groups for each of the four preprocessing models (top row; see colorbar to right for scale and direction of effects). Whole-brain connectedness for the ASD participants was also correlated with SRS total score, partialling Age and IQ, for the four models (bottom row; see colorbar to the right for scale and direction of effects). While select locations overlapped between the two effects for the Basic and +GCOR models, the best correspondence was still obtained under the ANATICOR model. The two effects were robust individually under the +GS model, but they exhibited little spatial overlap with each other and only minor overlap with the effects under the other models (e.g., TD > ASD in the ventromedial prefrontal cortex). Only the +GS model exhibited prominent reversed effects (ASD > TD) for the group comparisons (see also Figure 8).