Considering the effect of correlation between the channels in multivariate detectors for evoked responses in the electroencephalogram

Abstract

Evoked potentials refer to the small responses in the electroencephalogram (EEG), resulting from repeated or continuous auditory, visual or other stimuli. The detection of these responses is most commonly based on visual inspection by experienced professionals. To overcome the inherent subjectivity, automated (usually statistical) methods can be used, which aim to find the statistical significance of some parameter(s) calculated from the recorded signals, based on the null-hypothesis of 'no stimulus response is present'. These tests need to rely on assumptions about the statistical distributions of the signals and their parameters which in many cases allows p-values to be calculated. For some convenient parameters, however, closed form mathematical solutions are intractable and simulations are often required to find p-values (or critical values). The use of multichannel recordings can increase the sensitivity of tests compared to single-channel EEG, permitting the detection of responses in shorter recordings. This can be achieved by simple extensions of originally single channel methods, such as magnitude-squared coherence, component synchrony measure or the spectral F-test. However, the correlation between EEG channels can lead to false-positive rates that are difficult to predict or control. In this paper we present a modified parametric bootstrap method that permits the accurate estimation of false positive rates (p-values and critical values) for multichannel extensions of univariate objective evoked response techniques, with concomitant increases in sensitivity over conventional single channel methods. Illustrative results with evoked potentials from repeated photic stimulation are provided, with multivariate magnitude-squared coherence demonstrating the most robust performance.