Unified univariate and multivariate random field theory applied to canonical correlation SPMs from DBM
Keith Worsley McGill University Mathematics and Statistics
We report new random field theory P-values for peaks of canonical correlation SPMs for detecting multiple contrasts in a linear model for multivariate image data. This completes results for all types of univariate and multivariate image data analysis. All other known univariate and multivariate random field theory results are now special cases, so these new results present a true unification of all currently known results. As an illustration, we use these results in a deformation based morphometry (DBM) analysis to look for regions of the brain where vector deformations of non-missile trauma patients are related to several verbal memory scores, to detect regions of changes in anatomical effective connectivity between the trauma patients and a group of age and sex matched controls, and to look for anatomical connectivity in cortical thickness.
Deformation based morphometry of non-missile trauma data. (a) Trauma minus control average deformations (arrows and color bar), sampled every 6mm, with Hotelling's T2 statistic for significant differences (threshold t=54.0, P=0.05, corrected). The reference voxel of maximum Hotelling's T2 is marked by the intersection of the three axes. (b) Closeup of (a) showing that the damage is an outward movement of the anatomy, either due to swelling of the ventricles or atrophy of the surrounding white matter. (c) Regions of effective anatomical connectivity with the reference voxel, assessed by the maximum canonical correlation (threshold t=0.746, P=0.05, corrected). The reference voxel is connected with its neighbours (due to smoothness) and with contralateral regions (due to symmetry). (d) Regions where the connectivity is different between trauma and control groups, assessed by Roy's maximum root (threshold t=30.3, P=0.05, corrected). The small region in the contralateral hemisphere is more correlated in the trauma group than the control group.
Joing work with Jonathan E. Taylor (Stanford University, Statistics), Francesco Tomaiuolo (IRCCS Fondazione Santa Lucia), and Jason Lerch (McGill University, Montreal Neurological Institute).