Establishing correlations of scalp field maps with other experimental variables using covariance analysis and resampling methods.

TL;DR: Covariance mapping combined with bootstrapping methods has high statistical power and yields unique and directly interpretable results in EEG/MEG scalp data analysis.

About: This article is published in Clinical Neurophysiology.The article was published on 2008-06-01 and is currently open access. It has received 45 citations till now. The article focuses on the topics: Covariance & Resampling.

Summary

1. Introduction

• Technical improvements have made it possible that in EEG/MEG and ERP/ERF experiments, the number of sensors on the scalp could be substantially increased.
• In many studies, the statistical approaches chosen to analyze multi-channel scalp field data do not take the relations between sensors properly into account and disregard the physical basis of the signals to be analyzed.
• The additional information obtained with higher spatial sampling is thus often poorly exploited by the statistics applied.
• In terms of statistics of EEG/MEG and ERP/ERF data, this implies that the basic entity for analysis should be the scalp electric field.
• By repeating this randomization many times, one can therefore obtain a good estimate of the distribution of the total map difference under the null hypothesis.

2. Methods

• Bold symbols denote a column vector or matrix and non-bold symbols, a scalar magnitude.
• When inter-subject covariance is modeled, 1980) .
• In the Fisher transformed distribution of r * , the so-called studentized bootstrap confidence intervals are constructed from the bootstrap replicates (see Davison and Hinkley, 1997 for details).
• The TANOVA is thus similar to the ANOVA in the sense that it used categorical independent variables, while the present method is similar to the ANCOVA by using one continuous independent variable.

3. Simulations

• The random map was multiplied by the random external variable to obtain simulated data that are compatible with the model outlined in formula (4).
• Using these noisy random simulated data and the random external variable, the p-value was computed for each simulation run.
• For each step of the SNR ratio, 500 simulations were computed, each with 500 randomization runs.
• The graphs of the mean p-values and the mean r 2 -values against the SNR are shown in Fig. 1 .
• The figure indicates that with 12 subjects and 19 channels of EEG, significant (p < .05) effects can be detected at SNRs above about 10%.

4. Example

• Seventy-four channel ERPs were collected in 10 English-speaking exchange students to Switzerland while reading single-German words.
• The ERPs were collected after the students had spent about 3 months in Switzerland and had already acquired some proficiency in German.
• The study was approved by the Canton of Bern's ethical committee.
• The topography of the map series was correlated to a combined score of both language tests.
• The covariance map at the most significant time point (448 ms post stimulus) is shown, together with a distributed inverse solution of that map (Fig. 2 ).

5. Discussion

• The presented methodology provides an extension of the currently available methods for multi-channel randomization statistics of EEG and MEG topographies.
• By limiting the number of external variables to one, no rotation of the covariance matrix is necessary, and the resulting covariance map remains directly interpretable in terms of intracerebral sources associated with the external variable.
• By basing the analysis on a vector of scalp potentials that is scaled for each subject (Eq. 5), it is furthermore assumed that across subjects a common vector of scalp potentials corresponds to the same distribution and orientation of current density.
• Since ERP averaging has produced an abundant mass of meaningful results and often served as the basis for the computation of convincing inverse solutions, the authors think that practically, this assumption is very plausible.

Figures

Fig. 4. Mean covariance matrix of the noise across subjects estimated from the data shown in Fig. 3. Ninety seven percent of the variance of the matrix is on the diagonal, indicating little covariance of noise across subjects.

Fig. 3. Covariance map (upper-left graph, seen from above, with isopotential contour lines) of the data used in Fig. 2 at the moment with minimal p-value (448 ms post stimulus), and LORETA inverse solution of the covariance map. The LORETA solution was computed in 2394 cortical voxels (7 7 7 mm) of the digitized brain atlas of the Montreal Neurological Institute (MNI). The crosshair line indicates the point of maximal current source density, which was at Talairach coordinates x = 52, y = 67, z = 8, close to left BA 37, 19 and 39.

Fig. 1. Results of the simulations with 19 and 64 channel EEG data and 12 and 50 subjects. (a) The vertical axis indicates the obtained p-value as a function of the SNR, plotted on the horizontal axis. Bold lines indicate p-values below .05. (b) Mean r2-values as function of the SNR. The sensitivity of the method clearly improves with more electrodes on the scalp and an increasing number of subjects.

Fig. 2. Moment by moment TANCOVA results obtained when correlating 74 channel visual, German-language evoked ERP data with German proficiency scores. The data were obtained in an ongoing study investigating American students learning German. The significance (vertical, upper graph) and the correlation coefficient with its 95% studentized confidence interval (vertical, lower graph) are shown as function of time (horizontal axis). There was a significant effect of language proficiency between 400 and 500 ms and around 900 ms post-stimulus. Note that during periods of non-significance, the confidence interval of r often includes zero, which is closely related to the null hypothesis we tested, namely that there may be no relation. Regarding the width of the confidence interval, the simulations shown in Fig. 1 indicate that one may be able to reject the null-hypothesis while the estimation of the covariance map (and thus the correct r-value) might contain considerable noise and thus be quite uncertain.

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Establishing correlations of scalp field maps with other experimental variables using covariance analysis and resampling methods" ?

The authors introduce a procedure to identify spatially extended scalp fields that correlate with some external, continuous measure ( reaction-time, performance, clinical status ) and to test their significance. The authors formally deduce that the channel-wise covariance of some experimental variable with scalp field data directly represents intracerebral sources associated with that variable. The authors furthermore show how the significance of such a representation can be tested with resampling techniques. The introduced methodology overcomes some of the ‘ traditional ’ statistical problems in EEG/MEG scalp data analysis. In a sample analysis of real data, the authors found that foreign-language evoked ERP data were significantly associated with foreign-language proficiency. 

Q2. How many channels were collected in the study?

Seventy-four channel ERPs were collected in 10 English-speaking exchange students to Switzerland while reading single-German words. 

Q3. What is the amplitude of the estimated covariance map b?

The amplitudes of the estimated covariance map b depend on the variance of V, on the variance of X, and on the strength of the relation between V and X. 

Q4. What is the common method of establishing the statistical significance of difference maps?

In order to establish the statistical significance of such difference maps, one can either use the standard multivariate statistical approaches such as MANOVA (Vasey and Thayer, 1987). 

Q5. What is the effect of increasing the number of subjects or electrodes?

Increasing the number of subjects or electrodes improves the sensitivity of the method, and effects can be detected at lower SNRs.