The general linear model (GLM) is a well established tool for analyzing
functional magnetic resonance imaging (fMRI) data. Most fMRI analyses via GLM
proceed in a massively univariate fashion where the same design matrix is used
for analyzing data from each voxel. A major limitation of this approach is the
locally varying nature of signals of interest as well as associated confounds.
This local variability results in a potentially large bias and uncontrolled
increase in variance for the contrast of interest. The main contributions of
this paper are two fold (1) We develop a statistical framework called SMART
that enables estimation of an optimal design matrix while explicitly
controlling the bias variance decomposition over a set of potential design
matrices and (2) We develop and validate a numerical algorithm for computing
optimal design matrices for general fMRI data sets. The implications of this
framework include the ability to match optimally the magnitude of underlying
signals to their true magnitudes while also matching the "null" signals to zero
size thereby optimizing both the sensitivity and specificity of signal
detection. By enabling the capture of multiple profiles of interest using a
single contrast (as opposed to an F-test) in a way that optimizes for both bias
and variance enables the passing of first level parameter estimates and their
variances to the higher level for group analysis which is not possible using
F-tests. We demonstrate the application of this approach to in vivo
pharmacological fMRI data capturing the acute response to a drug infusion, to
task-evoked, block design fMRI and to the estimation of a haemodynamic response
function (HRF) response in event-related fMRI. Our framework is quite general
and has potentially wide applicability to a variety of disciplines.Comment: 68 pages, 34 figure
