Measuring the coherence of intracranial electroencephalograms

Previous coherence studies of human intracranial electroencephalograms (EEGs) can be faulted on two methodological issues: (1) coherence estimates in a majority were formed from a very small number of independent sample spectra, and (2) the statistical significance of coherence estimates was either not reported or was poorly evaluated. Coherence estimator performance may be poor when a small number of independent sample spectra are employed, and the coupling of poor estimation and statistical testing can result in inaccuracy in the measurement of coherence. The performance characteristics of the coherence estimator and statistical testing of coherence estimates are described in this manuscript.

The bias, variance, probability density functions, and confidence intervals of the estimate of magnitude squared coherence (MSC); and power analysis for the test of zero MSC were developed from the exact analytic form of the probability density function of the estimate of MSC for Gaussian random processes. The coherence of a single epoch of background EEG, recorded from a patient with intractable seizures, was evaluated with different parameter values to aid in the exposition of the concepts developed here.

The statistical characteristics of WOSA coherence estimates are a function of a single estimator parameter, the number of independent sample spectra employed in the estimation. Bias and variance are high, confidence intervals may be large, and the probability of Type II errors is high if a small number of independent sample spectra are employed. A considerable improvement in measurement accuracy is possible with careful selection of estimator parameter values.

Coherence measurement accuracy can be improved over previous applications by attention to estimator performance and accurate statistical testing of coherence estimates.