A multiclass multivariate group comparison test: Application to drug safety

Hypothesis tests are used to compare and show the efficiency of drugs. However, usual tests do not perform properly whenever the number of variables is greater than, or of the same order of magnitude as, the number of observations. In this paper, we propose an alternative to usual multiclass multivariate group comparison tests such as MANOVA or Wilcoxon tests. We present a pattern recognition approach to compare drugs in high dimensional spaces. Our test is based on the classification probability of error of a classifier. The decision statistics is obtained using the leave one out procedure. The statistics power density function has been experimentally shown independent from the data distribution under the null hypothesis, that allows to determine the threshold, or the p-values, of our test. This test has been applied on clinical data registered to ensure the safety side and tolerability of drugs tested.