Probability waves: Adaptive cluster-based correction by convolution of p-value series from mass univariate analysis.

BACKGROUND: Methods for p-value correction are criticized for either increasing Type II error or improperly reducing Type I error in large exploratory data analysis. This text considers patterns in probability vectors resulting from mass univariate analysis to correct p-values, where clusters of significant p-values may indicate true H0 rejection. NEW METHOD: We used ERP experimental data from control and ADHD boys to test the method. The Log10 of p-vector was convolved with a Gaussian window whose length was set as the shortest lag above which autocorrelation of each ERP wave may be assumed to have vanished. We realized Monte-Carlo simulations (MC) to (1) evaluate confidence intervals of rejected and non-rejected areas of our data, (2) to evaluate differences between corrected and uncorrected p-vectors or simulated ones in terms of distribution of significant p-values, and (3) to empirically verify the type-I error rate (comparing 10,000 pairs of mixed samples whit control and ADHD subjects). RESULTS: The differences between simulation or raw p-vector and corrected p-vectors were, respectively, minimal and maximal for window length set by autocorrelation in p-vector convolution. COMPARISON WITH EXISTING METHODS: Our method was less conservative while FDR methods rejected basically all significant p-values.The MC simulations presented 2.78 ± 4.83% of difference (20 channels) from corrected p-vector, while difference from raw p-vector was 596 ± 5.00% (p = 0.0003). CONCLUSION: As a cluster-based correction, the present new method seems to be biological and statistically suitable to correct p-values in mass univariate analysis of ERP waves, which adopts adaptive parameters to correction.

Multivariate evoked response detection based on the spectral F-test.

BACKGROUND: Objective response detection techniques, such as magnitude square coherence, component synchrony measure, and the spectral F-test, have been used to automate the detection of evoked responses. The performance of these detectors depends on both the signal-to-noise ratio (SNR) and the length of the electroencephalogram (EEG) signal. NEW METHOD: Recently, multivariate detectors were developed to increase the detection rate even in the case of a low signal-to-noise ratio or of short data records originated from EEG signals. In this context, an extension to the multivariate case of the spectral F-test detector is proposed. RESULTS: The performance of this technique is assessed using Monte Carlo. As an example, EEG data from 12 subjects during photic stimulation is used to demonstrate the usefulness of the proposed detector. COMPARISON WITH EXISTING METHOD(S): The multivariate method showed detection rates consistently higher than those ones when only one signal was used. CONCLUSIONS: It is shown that the response detection in EEG signals with the multivariate technique was statistically significant if two or more EEG derivations were used.

Multiple Coherence vs Multiple Component Synchrony Measure for somatosensory evoked response detection.

This work aims at comparing the performance of two Multivariate Objective Response Detection (MORD) techniques in the frequency domain, the Multiple Coherence (MC) and the Multiple Component Synchrony Measure (MCSM), for tibial nerve somatosensory evoked potential (SEP) detection. Electroencephalographic (EEG) signals during somatosensory stimulation were collected from forty adult volunteers using the 10-20 International System. The stimulation was carried out throughout current pulses (200 µs width) applied to the right posterior tibial nerve (motor threshold intensity level) at the rate of 5 Hz. The response detection was based on rejecting the null hypothesis of response absence (M = 100 and M = 800 epochs and significance level α = 0.05). The MORD techniques were applied to the pairs of derivations [Cz][Fz] and [C3][C4]. The MC outperforms the MCSM, regardless the pair of derivations or the number of epochs used for the estimates calculation. Hence, the MC should be used, if two derivations are available for SEP recording.

A multiple coherence-based detector for evoked responses in the EEG during sensory stimulation.

The sampling distribution of the multiple coherence estimate between a periodic signal and a set of filtered versions of evoked responses embedded in additive noise signals is derived for the zero-coherence case. For a fixed number of signals used in the estimation, the probability density function varies with the number of data segments. Analytical expressions for both bias and variance of the estimate were derived and together with the critical values constitute the statistical apparatus for the detector based on this multiple coherence estimate. An illustration of the technique as applied to detect evoked responses in the Electroencephalogram during sensory stimulation is also provided.

Evaluating the event-related synchronization and desynchronization by means of a statistical frequency test.

In the present work, a commonly used index for evaluating the Event-Related Synchronization and Desynchronization (ERS/ERD) in the EEG was expressed as a function of the Spectral F-Test (SFT), which is a statistical test for assessing if two sample spectra are from populations with identical theoretical spectra. The sampling distribution of SFT has been derived, allowing hence ERS/ERD to be evaluated under a statistical basis. An example of the technique was also provided in the EEG signals from 10 normal subjects during intermittent photic stimulation.

Evaluating the relationship of non-phase locked activities in the electroencephalogram during intermittent stimulation: a partial coherence-based approach.

Partial coherence estimate between two signals removing the contribution of a periodic, deterministic one is proposed for measuring the coherence between two ongoing eletroencephalografic (EEG) activities collected at distinct cortical regions under sensory stimulation. The estimator expression was derived and shown to be independent of the stimulating signal. Simulations were used for obtaining the critical values for this coherence estimate. The technique was also evaluated throughout simulations and next applied to the EEG from 12 subjects under intermittent photic stimulation at 4 and 6 Hz. In both simulation and EEG data, major differences between partial and simple coherences occurred at the stimulation frequency and harmonics, except for those falling within the alpha band. These findings suggest that the technique is highly selective in removing the contribution of the periodic source. They also indicate high coherence values of the ongoing EEG within the alpha band.

A coherence-based technique for separating phase-locked from non-phase-locked power spectrum estimates during intermittent stimulation.

In addition to evoked responses, which are phase-locked to the stimuli, the stimulation may also change the ongoing EEG in a time-locked manner. This change has been investigated in event-related synchronization/desynchronization (ERS/ERD) studies by comparing the spectra before and during stimulation or alternatively by using the intertrial variance method (IVM). In the present work, a technique based on the coherence estimate (kappa(y)(2)(f)) between the stimulation signal and the EEG is proposed for separating the ongoing EEG activity spectrum from that of the evoked responses. Furthermore, a statistical criterion is applied to reduce spurious spectral peaks. The performance of this procedure was assessed through simulation and illustrated with EEG during photic stimulation. For simulated data (signal-to-noise-ratio of 0.995 within 10-12.5 Hz) kappa(y)(2)(f) led to a non-phase-locked spectrum estimate with an average normalized error of 12.4%, which is reduced to only 0.2% after applying the statistical criterion. The methodology proposed is asymptotically equivalent to the IVM but it does not require previous filtering the EEG data. Kappa(y)(2)(f) together with the statistical correction criterion allows investigating the entrainment within a narrow-band range, particularly in frequencies close to that of the alpha peak. Hence it is useful in ERS/ERD studies. Moreover, it can be also used for characterizing frequencies within the gamma band.

Evaluating the entrainment of the alpha rhythm during stroboscopic flash stimulation by means of coherence analysis.

Two major conflicting hypotheses propose that alpha rhythm activity should be either the output of a linear filter having a white noise as input or reflect the output of a nonlinear oscillator. External stimulation can be employed to test for nonlinearity in alpha genesis, since an entrainment of such rhythmic activity (shift in the alpha peak) could only be explained by nonlinear relationships. Flash photic stimulation has been used to investigate such entrainment. Nevertheless, only entrainments due to the second harmonic of the stimulation could be suitably measured. Aiming at overcoming this limitation, a coherence-based technique is proposed for evaluating the strength of responses due to rhythmic stimulation. It was applied to the occipital EEG derivations of 12 normal subjects during stroboscopic stimulation. Entrainment of alpha rhythm by the second harmonic of the stimulation occurred in 75% of the subjects, whilst no spectral shifts were observed for the remained that exhibited broadband alpha peak at rest. However, stimulating with fundamental frequency close to that peak led to entrainment in all subjects. These differences in the degree of synchronization due to stimulation at the first and second harmonics should reflect complex nonlinear mechanisms in alpha genesis.

A matrix-based algorithm for estimating multiple coherence of a periodic signal and its application to the multichannel EEG during sensory stimulation.

The coherence between the stimulation signal and the electroencephalogram (EEG) has been used in the detection of evoked responses. The detector's performance, however, depends on both the signal-to-noise ratio (SNR) of the responses and the number of data segments (M) used in coherence estimation. In practical situations, when a given SNR occurs, detection can only be improved by increasing M and hence the total data length. This is particularly relevant when monitoring is the objective. In the present study, we propose a matrix-based algorithm for estimating the multiple coherence of the stimulation signal taking into account a set of N EEG channels as a way of increasing the detection rate for a fixed value of M. Monte Carlo simulations suggest that thresholds for such multivariate detector are the same as those for multiple coherence of Gaussian signals and that using more than six signals is not advisable for improving the detection rate with M = 10. The results with EEG from 12 normal subjects during photic stimulation at 10 Hz showed a maximum detection for N greater than 2 in 58% of the subjects with M = 10, and hence suggest that the proposed multivariate detector is valuable in evoked responses applications.

Multi-channel evoked response detection using only phase information.

The phase consistency of contiguous segments of the electroencephalogram (EEG) has been used in the detection of evoked responses to rhythmic stimulation. One of such techniques is the component synchrony measure (CSM), which is often used since the threshold for the detection task is easily obtained based on the estimates of asymptotic sample distribution. In this work we investigated the appropriateness of such thresholds for practical number of segments (M). The performance of CSM was next evaluated by Monte Carlo simulations with different signal-to-noise ratios (SNR) and values of M, and the results, compared with those for the magnitude-squared coherence. A way of improving the detection with CSM was also proposed, by suggesting the estimation taking into account the mean phase angle of a set of N signals. This multivariate detector was evaluated in simulations and an illustration of the technique was also given with the EEG of 14 subjects during photic stimulation. In simulated signals with equal SNR, the detection rate with this multivariate measure increased with N. The application to EEG data lead to similar results in 70% of the subjects, which suggests that improvements might be expected when more signals are available to detect evoked responses in EEG.

Improving the detection of evoked responses to periodic stimulation by using multiple coherence--application to EEG during photic stimulation.

The coherence between the stimulation signal and the electroencephalogram (EEG) has been used in the detection of evoked responses. However the detector's performance depends on both the signal-to-noise ratio (SNR) of the responses and the number of data segments (M) used in coherence estimation. In this work, a technique for detecting evoked responses was developed based on the extension to the multivariate case of this coherence. Thus, instead of using the EEG collected at a unique region, the estimation is proposed using two EEG derivations. As for the univariate case, this multiple coherence is independent of the stimulation signal. In addition, considering equal SNR in both signals, the detection rate with this multiple coherence is always greater than that one using only one signal. This was verified in Monte Carlo simulations, which also showed that a superior performance is still expected in practical situations, when a smaller SNR is found in the second signal. The results with EEG from 12 normal subjects during photic stimulation confirm this better performance. Since the proposed technique allows a higher detection rate without the need of increasing M, it permits evoked responses to be detected faster, which is very useful during monitored surgeries.