Comparative performance evaluation of data-driven causality measures applied to brain networks.

In this article, several well-known data-driven causality methods are revisited and comparatively evaluated. These are the Granger-Geweke Causality (GGC), the Partial Directed Coherence (PDC), the Directed Transfer Function (DTF) and the Direct Directed Transfer Function (dDTF). The robustness of the four causality measures against two degradation factors is quantitatively evaluated. These are: the presence of realistic biological/electronic noise at various SNR levels, as recorded on a MagnetoEncephalography (MEG) machine, and the presence of a weak node in the brain network where the causality analysis is applied. The causality measures are evaluated in terms of the relative estimation error and the compromise between true and fictitious causal density in the brain network. Both parametric and non-parametric causality analysis is performed. It is illustrated that the non-parametric method is a promising alternative to the more commonly applied MVAR-model based causality analysis. It is also demonstrated that, in the presence of both tested degradation factors, the DTF method is the most robust in terms of low estimation error, while the PDC in terms of low fictitious causal density. The dDTF provides lower fictitious causal density and higher spectral selectivity as compared to DTF, at high enough SNR. The GGC exhibits the worst compromise of performance. An application of the causality measures to a set of MEG resting-state experimental data is accordingly presented. It is demonstrated that significant contrast between the Eyes-Closed and Eyes-Open rest condition in the alpha frequency band allows to detect significant causality between the occipital cortex and the thalamus.