Robustness and sensitivity of hotelling´s T2-based permutation tests for selection of 3D morphological markers

Multivariate statistics are a powerful tool to analyze morphological changes in three-dimensional brain structures. The Hotelling´s T² (HT²) statistic has previously been used to this purpose. HT² is a parametric test which assumes normal distribution of the data: when this does not hold, as often happens for shape analysis, the test can still be used as basis for nonparametric permutation tests (PT). In their approximate version, PT are nondeterministic, being affected by the randomly pooled subset of permutations. In this study, we investigate the sensitivity and robustness of HT²-based PT, with respect to nondeterministic effects, both on simulated data and a medical application: the detection of hippocampal morphological changes to accurately predict conversion to Alzheimer´s disease. The sensitivity of PT increases significantly with larger sample size, while is less dependent on the number of permutations. Moreover, PT provides statistically consistent classification performances: 80% accuracy in predicting conversion to Alzheimer´s disease.