Soft Null Hypotheses: A Case Study of Image Enhancement Detection in Brain Lesions

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 are acquired to reveal the location and activity of MS lesions within the brain. Our goal is to identify the enhancing lesion locations at the subject level and lesion enhancement patterns at the population level. We analyze a total of 20 subjects scanned at 63 visits (∼30Gb), the largest population of such clinical brain images. After addressing the computational challenges, we propose possible solutions to 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 the existing data. We call such procedure "soft null" hypothesis testing as opposed to the standard "hard null" hypothesis testing. This problem is fundamentally different from: (1) finding testing statistics when a quantitative null hypothesis is given; (2) clustering using a mixture distribution; or (3) setting a reasonable threshold with a parametric null assumption. Supplementary materials are available online.