Detecting mild traumatic brain injury with MEG scan data: One-vs-K-sample tests

Magnetoencephalography (MEG) scanner has been shown to be more accurate than other medical devices in detecting mild traumatic brain injury (mTBI). However, MEG scan data in certain spectrum ranges can be skewed, multimodal, and heterogeneous which can mislead the conventional case-control analysis that requires the data to be homogeneous and normally distributed within the control group. To meet this challenge, we propose a flexible one-vs-K-sample testing procedure for detecting brain injury for a single-case versus heterogeneous controls. The new procedure begins with source magnitude imaging using MEG scan data in frequency domain, followed by region-wise contrast tests for abnormality between the case and controls. The critical values for these tests are automatically determined by cross-validation. We adjust the testing results for heterogeneity effects by similarity analysis. An asymptotic theory is established for the proposed test statistic. By simulated and real data analyses in the context of neurotrauma, we show that the proposed test outperforms commonly used nonparametric methods in terms of overall accuracy and ability in accommodating data non-normality and subject-heterogeneity.