A novel class of rank tests for high-dimensional data with an application to Alzheimer's disease

Abstract

Electroencephalography (EEG) signals are widely used in neuroscience research and biomedical applications, particularly for comparative analyses between two cohorts: patients and control subjects. In EEG research, multivariate two-sample tests remain underused, while multiple comparison procedures are often misapplied as a substitute, leading to inadequate error control. Moreover, existing rank-based tests rely solely on Euclidean distances and lack robustness to outliers. The objective of this work is to develop and evaluate a new class of rank-based tests for high-dimensional data that employ robust Mahalanobis interpoint distances, and to demonstrate their practical value in the analysis of EEG signals. This class includes a version based on the MRWCD (minimum regularized weighted covariance determinant) estimator, which enhances the robustness of the Mahalanobis distances by mitigating the influence of outliers. To illustrate the effectiveness of these tests, EEG data consisting of 1216 variables from 28 patients with Alzheimer’s disease and 146 healthy control individuals were analyzed. The results of multivariate tests reveal significant findings, which are also explored in the context of individual EEG channels and frequencies. Among the approaches tested, rank-based tests using the newly proposed interpoint distances, particularly in combination with the Cucconi test statistic, yield the strongest results. For the comparison between patients and controls, a p-value of 0.004 was obtained, which is below the significance level alpha=0.05, indicating a statistically significant difference.