Detrended Partial Cross Correlation for Brain Connectivity Analysis
Brain connectivity analysis is a critical component of ongoing human connectome projects to decipher the healthy and diseased brain. Recent work has highlighted the power-law (multi-time scale) properties of brain signals; however, there remains a lack of methods to specifically quantify short-vs. long-time range brain connections. In this paper, using detrended partial cross-correlation analysis (DPCCA), we propose a novel functional connectivity measure to delineate brain interactions at multiple time scales, while controlling for covariates. We use a rich simulated fMRI dataset to validate the proposed method, and apply it to a real fMRI dataset in a cocaine dependence prediction task. We show that, compared to extant methods, the DPCCA-based approach not only distinguishes short and long memory functional connectivity but also improves feature extraction and enhances classification accuracy. Together, this paper contributes broadly to new computational methodologies in understanding neural information processing.
The paper proposes a partialized version of DCCA, and applies it to synthetic and real fMRI data. While the contribution is incremental (this is a straight analogy to Whittaker's 1990 estimator of partial correlation), the results are at least on par with existing methods, and offer very interesting additional insights into connectivity across time scales. It also brings methods from statistical physics into neuroimaging, where they have been used (for DFA see e.g. e.g. Shen et al Clin Neurophysiol 2003 (EEG),  Mutch et al PLoS one 2012 (fMRI)), but not often for connectivity analysis. There are a few technical issues to address.
# Section 2.2.1
ROIs are derived from task fMRI on the whole dataset. This is problematic for the cocaine dependence prediction task (section 4.4) because it happens outside the cross-validation fold. The GLM should be re-trained within each fold using only training data, to compute ROIS which would then be applied to constructuct both training and testing graphs. Doing it outside the fold gives an unfair advantage and artificially boosts performance. Given the relatively large (by neuroimaging standards) sample size, this should not be too dramatic but it needs to be acknowledged in the text.
This is of course causes no problem in comparisons between connectivity methods since they all use the same ROIs.
# Section 3.1
Equation 1: in the denominator, should `C_{a,b} be C_{a,a}`, and likewise for `C_{b,b}` ?
Is there a guarantee that \rho in equation 2 is always invertible ?
# Section 3.2.2, 3.2.3
Why use the max over all time scales rather than some other statistic of the absolute value ? Figure 3 illustrates why the authors chose this, but this choice of an extreme statistic probably comes with a bias towards false positives. In this respect it is not clear why the authors say on lines 177-178 that DPCCA has low TPR?
Also, step 17 in algorithm 1 does not correct for multiple comparisons, using an uncorrected p-value while where are many hypothesis tests, which also contributes to false positives. This is not necessarily an issue but, together with the max operator of line 5, it is unclear how to assign proper p-values to each edge after algorithm 1, if that were desireable.
The null model chosen works for multi-subject studies only. It yields a very different (much lower) degree distribution. Is this a concern?
# Section 4.1
DCCA max is actually also located correctly at 10 s (fig 3e)
# Section 4.2
Please move hypothesis test results about DPCCA+CCA > ICOV from conclusion to this section. Given table 1 and large std it is not obvious at all that DPCCA+CCA is better, so having the test result here will be more convincing.
# Section 4.4.
As mentioned in my remarks on 2.2.1, ROIs are computed out-of-fold, which gives a small unfair edge to all methods, but does not affect comparison between methods computing connectivity on the same ROIs.
Using AUC is not recommended for comparing different classifiers (Hand, Machine Learning 77, 2009, but also Hanczar et al., Bioinformatics 26, 2010). Please show balanced accuracy as well. 
# Section 5
In table 3 it looks as if all methods (except Corr) do about the same, but the authors state in lines 241-242 that DPCCA+PCA works best. Given large std I don't think that the difference with, say ICOV or ParCorr is significant. Please provide a hypothesis test here.