Multichannel Detection of Evoked Responses Using Critical Values Corrected by a Parametric Bootstrap: Frequency-domain Cholesky Correction

Multivariate Objective Response Detection (MORD) techniques aim to detect evoked responses in multichannel electroencephalographic (EEG) recordings. They provide enhanced statistical power, allowing the detection of small signals in shorter or noisy recordings. However, the correlation between the signals in multichannel recordings can lead to false positive rates greater than the nominal significance level of the tests. To address this, we propose a parametric bootstrap approach that adjusts the critical values based on the correlation between EEG channels in the time domain, a method called time-domain Cholesky correction (TDCC). In that first approach, we assumed that correlation (or, more precisely, coherence) is constant across all frequency bands. However, this is unlikely to hold true, as signal-to-noise ratios (where the signal is the evoked response and noise all other signal components) may vary across frequencies. Thus, in the current work, we propose an alternative parametric bootstrap method for estimating the critical values of MORD techniques based on the correlation in the frequency domain (FDCC, frequency-domain Cholesky-corrected critical values). The proposed methods are evaluated using simulated data and an auditory steady-state response (ASSR) database in the 40 Hz range. The proposed method controlled the false positive rate well, with increased sensitivity compared to single-channel methods. When compared to TDCC, FDCC achieved similar performance but with the advantage of being, on average, 27 times faster in terms of computational time required to estimate the critical values.