2015, Schildknecht, Konstantin, Olek, Sven, Dickhaus, Thorsten

Epigenetic research leads to complex data structures. Since parametric model assumptions for the distribution of epigenetic data are hard to verify we introduce in the present work a nonparametric statistical framework for two-group comparisons. Furthermore, epigenetic analyses are often performed at various genetic loci simultaneously. Hence, in order to be able to draw valid conclusions for specific loci, an appropriate multiple testing correction is necessary. Finally, with technologies available for the simultaneous assessment of many interrelated biological parameters (such as gene arrays), statistical approaches also need to deal with a possibly unknown dependency structure in the data. Our statistical approach to the nonparametric comparison of two samples with independent multivariate observables is based on recently developed multivariate multiple permutation tests. We adapt their theory in order to cope with families of hypotheses regarding relative effects. Our results indicate that the multivariate multiple permutation test keeps the pre-assigned type I error level for the global null hypothesis. In combination with the closure principle, the family-wise error rate for the simultaneous test of the corresponding locus/parameter-specific null hypotheses can be controlled. In applications we demonstrate that group differences in epigenetic data can be detected reliably with our methodology.

2021, Neumann, André, Peitek, Norman, Brechmann, André, Tabelow, Karsten, Dickhaus, Thorsten

We are considering the statistical analysis of functional magnetic resonance imaging (fMRI) data. As demonstrated in previous work, grouping voxels into regions (of interest) and carrying out a multiple test for signal detection on the basis of these regions typically leads to a higher sensitivity when compared with voxel-wise multiple testing approaches. In the case of a multi-subject study, we propose to define the regions for each subject separately based on their individual brain anatomy, represented, e.g., by so-called Aparc labels. The aggregation of the subject-specific evidence for the presence of signals in the different regions is then performed by means of a combination function for p-values. We apply the proposed methodology to real fMRI data and demonstrate that our approach can perform comparably to a two-stage approach for which two independent experiments are needed, one for defining the regions and one for actual signal detection.