The generalized shrinkage estimator for the analysis of functional connectivity of brain signals

We develop a new statistical method for estimating functional connectivity between neurophysiological signals represented by a multivariate time series. We use partial coherence as the measure of functional connectivity. Partial coherence identifies the frequency bands that drive the direct linear association between any pair of channels. To estimate partial coherence, one would first need an estimate of the spectral density matrix of the multivariate time series. Parametric estimators of the spectral density matrix provide good frequency resolution but could be sensitive when the parametric model is misspecified. Smoothing-based nonparametric estimators are robust to model misspecification and are consistent but may have poor frequency resolution. In this work, we develop the generalized shrinkage estimator, which is a weighted average of a parametric estimator and a nonparametric estimator. The optimal weights are frequency-specific and derived under the quadratic risk criterion so that the estimator, either the parametric estimator or the nonparametric estimator, that performs better at a particular frequency receives heavier weight. We validate the proposed estimator in a simulation study and apply it on electroencephalogram recordings from a visual-motor experiment.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS396 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

A graphical vector autoregressive modelling approach to the analysis of electronic diary data

<p>Abstract</p> <p>Background</p> <p>In recent years, electronic diaries are increasingly used in medical research and practice to investigate patients' processes and fluctuations in symptoms over time. To model dynamic dependence structures and feedback mechanisms between symptom-relevant variables, a multivariate time series method has to be applied.</p> <p>Methods</p> <p>We propose to analyse the temporal interrelationships among the variables by a structural modelling approach based on graphical vector autoregressive (VAR) models. We give a comprehensive description of the underlying concepts and explain how the dependence structure can be recovered from electronic diary data by a search over suitable constrained (graphical) VAR models.</p> <p>Results</p> <p>The graphical VAR approach is applied to the electronic diary data of 35 obese patients with and without binge eating disorder (BED). The dynamic relationships for the two subgroups between eating behaviour, depression, anxiety and eating control are visualized in two path diagrams. Results show that the two subgroups of obese patients with and without BED are distinguishable by the temporal patterns which influence their respective eating behaviours.</p> <p>Conclusion</p> <p>The use of the graphical VAR approach for the analysis of electronic diary data leads to a deeper insight into patient's dynamics and dependence structures. An increasing use of this modelling approach could lead to a better understanding of complex psychological and physiological mechanisms in different areas of medical care and research.</p

Functional Connectivity Analysis of FMRI Time-Series Data

The term ``functional connectivity' is used to denote correlations in activation among spatially-distinct brain regions, either in a resting state or when processing external stimuli. Functional connectivity has been extensively evaluated with several functional neuroimaging methods, particularly PET and fMRI. Yet these relationships have been quantified using very different measures and the extent to which they index the same constructs is unclear. We have implemented a variety of these functional connectivity measures in a new freely-available MATLAB toolbox. These measures are categorized into two groups: whole time-series and trial-based approaches. We evaluate these measures via simulations with different patterns of functional connectivity and provide recommendations for their use. We also apply these measures to a previously published fMRI dataset in which activity in dorsal anterior cingulate cortex (dACC) and dorsolateral prefrontal cortex (DLPFC) was evaluated in 32 healthy subjects during a digit sorting task. Though all implemented measures demonstrate functional connectivity between dACC and DLPFC activity during event-related tasks, different participants appeared to display qualitatively different relationships.We also propose a new methodology for exploring functional connectivity in slow event-related designs, where stimuli are presented at a sufficient separation to examine the dynamic responses in brain regions. Our methodology simultaneously determines the level of smoothing to obtain the underlying noise-free BOLD response and the functional connectivity among several regions. Smoothing is accomplished through an empirical basis via functional principal components analysis. The coefficients of the basis are assumed to be correlated across regions, and the nature and strength of functional connectivity is derived from this correlation matrix. The model is implemented within a Bayesian framework by specifying priors on the parameters and using a Markov Chain Monte Carlo (MCMC) Gibbs sampling algorithm. We demonstrate this new approach on a sample of clinically depressed subjects and healthy controls in examining relationships among three brain regions implicated in depression and emotion during emotional information processing. The results show that depressed subjects display decreased coupling between left amygdala and DLPFC compared to healthy subjects and this may potentially be due to inefficient functioning in mediating connectivity from the rostral portion Brodmann's area24 (BA24)