  This work is motivated by a study of a population of multiple sclerosis (MS)
patients using dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI)
to identify active brain lesions. At each visit, a contrast agent is
administered intravenously to a subject and a series of images is acquired to
reveal the location and activity of MS lesions within the brain. Our goal is to
identify and quantify lesion enhancement location at the subject level and
lesion enhancement patterns at the population level. With this example, we aim
to address the difficult problem of transforming a qualitative scientific null
hypothesis, such as "this voxel does not enhance", to a well-defined and
numerically testable null hypothesis based on existing data. We call the
procedure "soft null hypothesis" testing as opposed to the standard "hard null
hypothesis" testing. This problem is fundamentally different from: 1) testing
when a quantitative null hypothesis is given; 2) clustering using a mixture
distribution; or 3) identifying a reasonable threshold with a parametric null
assumption. We analyze a total of 20 subjects scanned at 63 visits (~30Gb), the
largest population of such clinical brain images.
