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

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).

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