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 statistical parametric maps (SPMs) used to detect multiple contrasts in a linear model for multivariate image data. These results complete the theoretical framework for all types of univariate and multivariate image data analyses. All previously known univariate and multivariate random field theory results now arise as special cases, making this a true unification of the currently available theory.
As an illustration, we apply these results to a deformation-based morphometry (DBM) analysis to identify brain regions where vector deformations in non-missile trauma patients are associated with multiple verbal memory scores. We also examine regions showing changes in anatomical effective connectivity between trauma patients and age- and sex-matched control subjects, and investigate anatomical connectivity patterns in cortical thickness.
In the DBM analysis of non-missile trauma data, trauma-minus-control average deformations are visualized along with Hotelling’s T² statistic for significant group differences (threshold t = 54.0, P = 0.05, corrected). A close-up view reveals outward anatomical displacement, possibly reflecting ventricular swelling or surrounding white matter atrophy. Regions of effective anatomical connectivity with a reference voxel are assessed using the maximum canonical correlation (threshold t = 0.746, P = 0.05, corrected), revealing both local and contralateral connectivity. Differences in connectivity between trauma and control groups are assessed using Roy’s maximum root (threshold t = 30.3, P = 0.05, corrected), indicating increased correlation in a small contralateral region in the trauma group.
This is joint work with Jonathan E. Taylor (Stanford University, Statistics), Francesco Tomaiuolo (IRCCS Fondazione Santa Lucia), and Jason Lerch (McGill University, Montreal Neurological Institute).