Multivariate multidistance tests for\ud high-dimensional low sample size\ud case-control studies

A class of multivariate tests for case-control studies with high-dimensional low sample size data and with complex\ud dependence structure, which are common in medical imaging and molecular biology, is proposed. The tests can\ud be applied when the number of variables is much larger than the number of subjects and when the underlying\ud population distributions are heavy-tailed or skewed. As a motivating application, we consider a case-control study\ud where phase-contrast cinematic cardiovascular magnetic resonance imaging has been used to compare many\ud cardiovascular characteristics of young healthy smokers and young healthy non-smokers. The tests are based on\ud the combination of tests on interpoint distances. It is theoretically proved that the tests are exact, unbiased and\ud consistent. It is shown that the tests are very powerful under normal, heavy-tailed and skewed distributions. The\ud tests can also be applied to case-control studies with high-dimensional low sample size data from other medical\ud imaging techniques (like computed tomography or X-ray radiography), chemometrics and microarray data\ud (proteomics and transcriptomics)