The effect of normalization of Partial Directed Coherence on the statistical assessment of connectivity patterns: A simulation study

Partial Directed Coherence (PDC) is a spectral multivariate estimator for effective connectivity, relying on the concept of Granger causality. Even if its original definition derived directly from information theory, two modifies were introduced in order to provide better physiological interpretations of the estimated networks: i) normalization of the estimator according to rows, ii) squared transformation. In the present paper we investigated the effect of PDC normalization on the performances achieved by applying the statistical validation process on investigated connectivity patterns under different conditions of Signal to Noise ratio (SNR) and amount of data available for the analysis. Results of the statistical analysis revealed an effect of PDC normalization only on the percentages of type I and type II errors occurred by using Shuffling procedure for the assessment of connectivity patterns. No effects of the PDC formulation resulted on the performances achieved during the validation process executed instead by means of Asymptotic Statistic approach. Moreover, the percentages of both false positives and false negatives committed by Asymptotic Statistic are always lower than those achieved by Shuffling procedure for each type of normalization.

[1]  Y. Benjamini,et al.  Controlling the false discovery rate: a practical and powerful approach to multiple testing , 1995 .

[2]  Koichi Sameshima,et al.  Using partial directed coherence to describe neuronal ensemble interactions , 1999, Journal of Neuroscience Methods.

[3]  M. Kaminski,et al.  Granger causality and information flow in multivariate processes. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Laura Astolfi,et al.  Assessing cortical functional connectivity by partial directed coherence: simulations and application to real data , 2006, IEEE Transactions on Biomedical Engineering.

[5]  C. Granger.  Investigating causal relations by econometric models and cross-spectral methods , 1969 .

[6]  Mingzhou Ding,et al.  Evaluating causal relations in neural systems: Granger causality, directed transfer function and statistical assessment of significance , 2001, Biological Cybernetics.

[7]  Katarzyna J. Blinowska,et al.  A new method of the description of the information flow in the brain structures , 1991, Biological Cybernetics.

[8]  Schneider Gt,et al.  Partial coherence estimates of brain rhythms. , 1983 .

[9]  G. A. Miller,et al.  Comparison of different cortical connectivity estimators for high‐resolution EEG recordings , 2007, Human brain mapping.

[10]  Michael Eichler,et al.  Abstract Journal of Neuroscience Methods xxx (2005) xxx–xxx Testing for directed influences among neural signals using partial directed coherence , 2005 .

[11]  K. Sameshima,et al.  Connectivity Inference between Neural Structures via Partial Directed Coherence , 2007 .

[12]  Laura Astolfi,et al.  Testing the asymptotic statistic for the assessment of the significance of partial directed coherence connectivity patterns , 2011, 2011 Annual International Conference of the IEEE Engineering in Medicine and Biology Society.