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

• Published in: Statistics in medicine Vol. 34; no. 9; pp. 1511 - 1526
• Main Author: Marozzi, Marco
• Format: Journal Article
• Language: English
• Published: England Blackwell Publishing Ltd 30.04.2015; Wiley Subscription Services, Inc
• Subjects: Adult; Biometry - methods; Cardiology; Cardiovascular Diseases - diagnosis; Cardiovascular Diseases - physiopathology; Case-Control Studies; combined tests; Data Interpretation, Statistical; Humans; hypothesis testing; Magnetic Resonance Imaging; Male; Medical imaging; Middle Aged; Molecular biology; Multivariate Analysis; nonparametric tests; Probability distribution; Proteomics; Sample Size; Smoking - adverse effects; combined tests; magnetic resonance imaging; hypothesis testing; nonparametric tests
• ISSN: 0277-6715; 1097-0258; 1097-0258
• DOI: 10.1002/sim.6418

A class of multivariate tests for case‐control studies with high‐dimensional low sample size data and with complex dependence structure, which are common in medical imaging and molecular biology, is proposed. The tests can be applied when the number of variables is much larger than the number of subjects and when the underlying population distributions are heavy‐tailed or skewed. As a motivating application, we consider a case‐control study where phase‐contrast cinematic cardiovascular magnetic resonance imaging has been used to compare many cardiovascular characteristics of young healthy smokers and young healthy non‐smokers. The tests are based on the combination of tests on interpoint distances. It is theoretically proved that the tests are exact, unbiased and consistent. It is shown that the tests are very powerful under normal, heavy‐tailed and skewed distributions. The tests can also be applied to case‐control studies with high‐dimensional low sample size data from other medical imaging techniques (like computed tomography or X‐ray radiography), chemometrics and microarray data (proteomics and transcriptomics). Copyright © 2015 John Wiley & Sons, Ltd.