  An increasingly important goal of psychiatry is the use of brain imaging data
to develop predictive models. Here we present two contributions to statistical
methodology for this purpose. First, we propose and compare a set of
wavelet-domain procedures for fitting generalized linear models with scalar
responses and image predictors: sparse variants of principal component
regression and of partial least squares, and the elastic net. Second, we
consider assessing the contribution of image predictors over and above
available scalar predictors, in particular, via permutation tests and an
extension of the idea of confounding to the case of functional or image
predictors. Using the proposed methods, we assess whether maps of a spontaneous
brain activity measure, derived from functional magnetic resonance imaging, can
meaningfully predict presence or absence of attention deficit/hyperactivity
disorder (ADHD). Our results shed light on the role of confounding in the
surprising outcome of the recent ADHD-200 Global Competition, which challenged
researchers to develop algorithms for automated image-based diagnosis of the
disorder.
