Granger Causality among Graphs and Application to Functional Brain Connectivity in Autism Spectrum Disorder.

Graphs/networks have become a powerful analytical approach for data modeling. Besides, with the advances in sensor technology, dynamic time-evolving data have become more common. In this context, one point of interest is a better understanding of the information flow within and between networks. Thus, we aim to infer Granger causality (G-causality) between networks' time series. In this case, the straightforward application of the well-established vector autoregressive model is not feasible. Consequently, we require a theoretical framework for modeling time-varying graphs. One possibility would be to consider a mathematical graph model with time-varying parameters (assumed to be random variables) that generates the network. Suppose we identify G-causality between the graph models' parameters. In that case, we could use it to define a G-causality between graphs. Here, we show that even if the model is unknown, the spectral radius is a reasonable estimate of some random graph model parameters. We illustrate our proposal's application to study the relationship between brain hemispheres of controls and children diagnosed with Autism Spectrum Disorder (ASD). We show that the G-causality intensity from the brain's right to the left hemisphere is different between ASD and controls.

Large miRNA survival analysis reveals a prognostic four-biomarker signature for triple negative breast cancer.

Triple negative breast cancer (TNBC) is currently the only major breast tumor subtype without effective targeted therapy and, as a consequence, usually presents a poor outcome. Due to its more aggressive phenotype, there is an urgent clinical need to identify novel biomarkers that discriminate individuals with poor prognosis. We hypothesize that miRNAs can be used to this end because they are involved in the initiation and progression of tumors by altering the expression of their target genes. To identify a prognostic biomarker in TNBC, we analyzed the miRNA expression of a cohort composed of 185 patients diagnosed with TNBC using penalized Cox regression models. We identified a four-biomarker signature based on miR-221, miR-1305, miR-4708, and RMDN2 expression levels that allowed for the subdivision of TNBC into high- or low-risk groups (Hazard Ratio - HR = 0.32; 95% Confidence Interval - CI = 0.11-0.91; p = 0.03) and are also statistically associated with survival outcome in subgroups of postmenopausal status (HR = 0.19; 95% CI = 0.04-0.90; p= 0.016), node negative status (HR = 0.12; 95% CI = 0.01-1.04; p = 0.026), and tumors larger than 2cm (HR = 0.21; 95% CI = 0.05-0.81; p = 0.021). This four-biomarker signature was significantly associated with TNBC as an independent prognostic factor for survival.

A comparative study of statistical methods used to identify dependencies between gene expression signals.

One major task in molecular biology is to understand the dependency among genes to model gene regulatory networks. Pearson's correlation is the most common method used to measure dependence between gene expression signals, but it works well only when data are linearly associated. For other types of association, such as non-linear or non-functional relationships, methods based on the concepts of rank correlation and information theory-based measures are more adequate than the Pearson's correlation, but are less used in applications, most probably because of a lack of clear guidelines for their use. This work seeks to summarize the main methods (Pearson's, Spearman's and Kendall's correlations; distance correlation; Hoeffding's D: measure; Heller-Heller-Gorfine measure; mutual information and maximal information coefficient) used to identify dependency between random variables, especially gene expression data, and also to evaluate the strengths and limitations of each method. Systematic Monte Carlo simulation analyses ranging from sample size, local dependence and linear/non-linear and also non-functional relationships are shown. Moreover, comparisons in actual gene expression data are carried out. Finally, we provide a suggestive list of methods that can be used for each type of data set.

Identification of segregated regions in the functional brain connectome of autistic patients by a combination of fuzzy spectral clustering and entropy analysis.

BACKGROUND: Several neuroimaging studies support the model of abnormal development of brain connectivity in patients with autism-spectrum disorders (ASD). In this study, we aimed to test the hypothesis of reduced functional network segregation in autistic patients compared with controls. METHODS: Functional MRI data from children acquired under a resting-state protocol (Autism Brain Imaging Data Exchange [ABIDE]) were submitted to both fuzzy spectral clustering (FSC) with entropy analysis and graph modularity analysis. RESULTS: We included data from 814 children in our analysis. We identified 5 regions of interest comprising the motor, temporal and occipitotemporal cortices with increased entropy (p < 0.05) in the clustering structure (i.e., more segregation in the controls). Moreover, we noticed a statistically reduced modularity (p < 0.001) in the autistic patients compared with the controls. Significantly reduced eigenvector centrality values (p < 0.05) in the patients were observed in the same regions that were identified in the FSC analysis. LIMITATIONS: There is considerable heterogeneity in the fMRI acquisition protocols among the sites that contributed to the ABIDE data set (e.g., scanner type, pulse sequence, duration of scan and resting-state protocol). Moreover, the sites differed in many variables related to sample characterization (e.g., age, IQ and ASD diagnostic criteria). Therefore, we cannot rule out the possibility that additional differences in functional network organization would be found in a more homogeneous data sample of individuals with ASD. CONCLUSION: Our results suggest that the organization of the whole-brain functional network in patients with ASD is different from that observed in controls, which implies a reduced modularity of the brain functional networks involved in sensorimotor, social, affective and cognitive processing.

RECK is not an independent prognostic marker for breast cancer.

BACKGROUND: The REversion-inducing Cysteine-rich protein with Kazal motif (RECK) is a well-known inhibitor of matrix metalloproteinases (MMPs) and cellular invasion. Although high expression levels of RECK have already been correlated with a better clinical outcome for several tumor types, its main function, as well as its potential prognostic value for breast cancer patients, remain unclear. METHODS: The RECK expression profile was investigated in a panel of human breast cell lines with distinct aggressiveness potential. RECK functional analysis was undertaken using RNA interference methodology. RECK protein levels were also analyzed in 1040 cases of breast cancer using immunohistochemistry and tissue microarrays (TMAs). The association between RECK expression and different clinico-pathological parameters, as well as the overall (OS) and disease-free (DFS) survival rates, were evaluated. RESULTS: Higher RECK protein expression levels were detected in more aggressive breast cancer cell lines (T4-2, MDA-MB-231 and Hs578T) than in non-invasive (MCF-7 and T47D) and non-tumorigenic (S1) cell lines. Indeed, silencing RECK in MDA-MB-231 cells resulted in elevated levels of pro-MMP-9 and increased invasion compared with scrambled (control) cells, without any effect on cell proliferation. Surprisingly, by RECK immunoreactivity analysis on TMAs, we found no association between RECK positivity and survival (OS and DFS) in breast cancer patients. Even considering the different tumor subtypes (luminal A, luminal B, Her2 type and basal-like) or lymph node status, RECK remained ineffective for predicting the disease outcome. Moreover, by multivariate Cox regression analysis, we found that RECK has no prognostic impact for OS and DFS, relative to standard clinical variables. CONCLUSIONS: Although it continues to serve as an invasion and MMP inhibitor in breast cancer, RECK expression analysis is not useful for prognosis of these patients.

XiP: a computational environment to create, extend and share workflows.

UNLABELLED: XiP (eXtensible integrative Pipeline) is a flexible, editable and modular environment with a user-friendly interface that does not require previous advanced programming skills to run, construct and edit workflows. XiP allows the construction of workflows by linking components written in both R and Java, the analysis of high-throughput data in grid engine systems and also the development of customized pipelines that can be encapsulated in a package and distributed. XiP already comes with several ready-to-use pipeline flows for the most common genomic and transcriptomic analysis and ∼300 computational components. AVAILABILITY: XiP is open source, freely available under the Lesser General Public License (LGPL) and can be downloaded from http://xip.hgc.jp.

A non-parametric statistical test to compare clusters with applications in functional magnetic resonance imaging data.

Statistical inference of functional magnetic resonance imaging (fMRI) data is an important tool in neuroscience investigation. One major hypothesis in neuroscience is that the presence or not of a psychiatric disorder can be explained by the differences in how neurons cluster in the brain. Therefore, it is of interest to verify whether the properties of the clusters change between groups of patients and controls. The usual method to show group differences in brain imaging is to carry out a voxel-wise univariate analysis for a difference between the mean group responses using an appropriate test and to assemble the resulting 'significantly different voxels' into clusters, testing again at cluster level. In this approach, of course, the primary voxel-level test is blind to any cluster structure. Direct assessments of differences between groups at the cluster level seem to be missing in brain imaging. For this reason, we introduce a novel non-parametric statistical test called analysis of cluster structure variability (ANOCVA), which statistically tests whether two or more populations are equally clustered. The proposed method allows us to compare the clustering structure of multiple groups simultaneously and also to identify features that contribute to the differential clustering. We illustrate the performance of ANOCVA through simulations and an application to an fMRI dataset composed of children with attention deficit hyperactivity disorder (ADHD) and controls. Results show that there are several differences in the clustering structure of the brain between them. Furthermore, we identify some brain regions previously not described to be involved in the ADHD pathophysiology, generating new hypotheses to be tested. The proposed method is general enough to be applied to other types of datasets, not limited to fMRI, where comparison of clustering structures is of interest.

Cavity approach for the approximation of spectral density of graphs with heterogeneous structures.

Graphs have become widely used to represent and study social, biological, and technological systems. Statistical methods to analyze empirical graphs were proposed based on the graph's spectral density. However, their running time is cubic in the number of vertices, precluding direct application to large instances. Thus, efficient algorithms to calculate the spectral density become necessary. For sparse graphs, the cavity method can efficiently approximate the spectral density of locally treelike undirected and directed graphs. However, it does not apply to most empirical graphs because they have heterogeneous structures. Thus, we propose methods for undirected and directed graphs with heterogeneous structures using a new vertex's neighborhood definition and the cavity approach. Our methods' time and space complexities are O(|E|h_{max}^{3}t) and O(|E|h_{max}^{2}t), respectively, where |E| is the number of edges, h_{max} is the size of the largest local neighborhood of a vertex, and t is the number of iterations required for convergence. We demonstrate the practical efficacy by estimating the spectral density of simulated and real-world undirected and directed graphs.

New insights in osteogenic differentiation revealed by mass spectrometric assessment of phosphorylated substrates in murine skin mesenchymal cells.

BACKGROUND: Bone fractures and loss represent significant costs for the public health system and often affect the patients quality of life, therefore, understanding the molecular basis for bone regeneration is essential. Cytokines, such as IL-6, IL-10 and TNFα, secreted by inflammatory cells at the lesion site, at the very beginning of the repair process, act as chemotactic factors for mesenchymal stem cells, which proliferate and differentiate into osteoblasts through the autocrine and paracrine action of bone morphogenetic proteins (BMPs), mainly BMP-2. Although it is known that BMP-2 binds to ActRI/BMPR and activates the SMAD 1/5/8 downstream effectors, little is known about the intracellular mechanisms participating in osteoblastic differentiation. We assessed differences in the phosphorylation status of different cellular proteins upon BMP-2 osteogenic induction of isolated murine skin mesenchymal stem cells using Triplex Stable Isotope Dimethyl Labeling coupled with LC/MS. RESULTS: From 150 µg of starting material, 2,264 proteins were identified and quantified at five different time points, 235 of which are differentially phosphorylated. Kinase motif analysis showed that several substrates display phosphorylation sites for Casein Kinase, p38, CDK and JNK. Gene ontology analysis showed an increase in biological processes related with signaling and differentiation at early time points after BMP2 induction. Moreover, proteins involved in cytoskeleton rearrangement, Wnt and Ras pathways were found to be differentially phosphorylated during all timepoints studied. CONCLUSIONS: Taken together, these data, allow new insights on the intracellular substrates which are phosphorylated early on during differentiation to BMP2-driven osteoblastic differentiation of skin-derived mesenchymal stem cells.

Measuring network's entropy in ADHD: a new approach to investigate neuropsychiatric disorders.

The application of graph analysis methods to the topological organization of brain connectivity has been a useful tool in the characterization of brain related disorders. However, the availability of tools, which enable researchers to investigate functional brain networks, is still a major challenge. Most of the studies evaluating brain images are based on centrality and segregation measurements of complex networks. In this study, we applied the concept of graph spectral entropy (GSE) to quantify the complexity in the organization of brain networks. In addition, to enhance interpretability, we also combined graph spectral clustering to investigate the topological organization of sub-network's modules. We illustrate the usefulness of the proposed approach by comparing brain networks between attention deficit hyperactivity disorder (ADHD) patients and the brain networks of typical developing (TD) controls. The main findings highlighted that GSE involving sub-networks comprising the areas mostly bilateral pre and post central cortex, superior temporal gyrus, and inferior frontal gyri were statistically different (p-value=0.002) between ADHD patients and TD controls. In the same conditions, the other conventional graph descriptors (betweenness centrality, clustering coefficient, and shortest path length) commonly used to identify connectivity abnormalities did not show statistical significant difference. We conclude that analysis of topological organization of brain sub-networks based on GSE can identify networks between brain regions previously unobserved to be in association with ADHD.

Spectral density-based clustering algorithms for complex networks.

Introduction: Clustering is usually the first exploratory analysis step in empirical data. When the data set comprises graphs, the most common approaches focus on clustering its vertices. In this work, we are interested in grouping networks with similar connectivity structures together instead of grouping vertices of the graph. We could apply this approach to functional brain networks (FBNs) for identifying subgroups of people presenting similar functional connectivity, such as studying a mental disorder. The main problem is that real-world networks present natural fluctuations, which we should consider. Methods: In this context, spectral density is an exciting feature because graphs generated by different models present distinct spectral densities, thus presenting different connectivity structures. We introduce two clustering methods: k-means for graphs of the same size and gCEM, a model-based approach for graphs of different sizes. We evaluated their performance in toy models. Finally, we applied them to FBNs of monkeys under anesthesia and a dataset of chemical compounds. Results: We show that our methods work well in both toy models and real-world data. They present good results for clustering graphs presenting different connectivity structures even when they present the same number of edges, vertices, and degree of centrality. Discussion: We recommend using k-means-based clustering for graphs when graphs present the same number of vertices and the gCEM method when graphs present a different number of vertices.

Predicting survival in metastatic non-small cell lung cancer patients with poor ECOG-PS: A single-arm prospective study.

BACKGROUND: Patients with advanced non-small cell lung cancer (NSCLC) are a heterogeneous population with short lifespan. We aimed to develop methods to better differentiate patients whose survival was >90 days. METHODS: We evaluated 83 characteristics of 106 treatment-naïve, stage IV NSCLC patients with Eastern Cooperative Oncology Group Performance Status (ECOG-PS) >1. Automated machine learning was used to select a model and optimize hyperparameters. 100-fold bootstrapping was performed for dimensionality reduction for a second ("lite") model. Performance was measured by C-statistic and accuracy metrics in an out-of-sample validation cohort. The "lite" model was validated on a second independent, prospective cohort (N = 42). Network analysis (NA) was performed to evaluate the differences in centrality and connectivity of features. RESULTS: The selected method was ExtraTrees Classifier, with C-statistic of 0.82 (p < 0.01) and accuracy of 0.81 (p = 0.01). The "lite" model had 16 variables and obtained C-statistic of 0.84 (p < 0.01) and accuracy of 0.75 (p = 0.039) in the first cohort, and C-statistic of 0.706 (p < 0.01) and accuracy of 0.714 (p < 0.01) in the second cohort. The networks of patients with lower survival were more interconnected. Features related to cachexia, inflammation, and quality of life had statistically different prestige scores in NA. CONCLUSIONS: Machine learning can assist in the prognostic evaluation of advanced NSCLC. The model generated with a reduced number of features showed high accessibility and reasonable metrics. Features related to quality of life, cachexia, and performance status had increased correlation and importance scores, suggesting that they play a role at later disease stages, in line with the biological rationale already described.

A model-based clustering algorithm with covariates adjustment and its application to lung cancer stratification.

Usually, the clustering process is the first step in several data analyses. Clustering allows identify patterns we did not note before and helps raise new hypotheses. However, one challenge when analyzing empirical data is the presence of covariates, which may mask the obtained clustering structure. For example, suppose we are interested in clustering a set of individuals into controls and cancer patients. A clustering algorithm could group subjects into young and elderly in this case. It may happen because the age at diagnosis is associated with cancer. Thus, we developed CEM-Co, a model-based clustering algorithm that removes/minimizes undesirable covariates' effects during the clustering process. We applied CEM-Co on a gene expression dataset composed of 129 stage I non-small cell lung cancer patients. As a result, we identified a subgroup with a poorer prognosis, while standard clustering algorithms failed.

Networks of Neurodevelopmental Traits, Socioenvironmental Factors, Emotional Dysregulation in Childhood, and Depressive Symptoms Across Development in Two U.K. Cohorts.

OBJECTIVE: Previous population-based studies have identified associations between childhood neurodevelopmental traits and depression in childhood, adolescence, and young adulthood. However, neurodevelopmental traits are highly correlated with each other, which could confound associations when traits are examined in isolation. The authors sought to identify unique associations between multiple neurodevelopmental traits in childhood and depressive symptoms across development, while taking into account co-occurring difficulties, in multivariate analyses. METHODS: Data from two U.K. population-based cohorts, the Twins Early Development Study (TEDS) (N=4,407 independent twins) and the Avon Longitudinal Study of Parents and Children (ALSPAC) (N=10,351), were independently analyzed. Bayesian Gaussian graphical models were estimated to investigate pairwise conditional associations between neurodevelopmental traits (autism and ADHD symptoms and general cognitive, learning, and communication abilities), socioenvironmental stressors (academic performance and peer relations), and emotional dysregulation in childhood (ages 7-11) and depressive symptoms across development (ages 12, 16, and 21). RESULTS: In both cohorts, bivariate correlations indicated several associations between neurodevelopmental traits and depressive symptoms across development. However, based on replicated findings across cohorts, these pairs of variables were mostly conditionally independent, and none were conditionally associated, after accounting for socioenvironmental stressors and emotional dysregulation. In turn, socioenvironmental stressors and emotional dysregulation were conditionally associated with both neurodevelopmental traits and depressive symptoms. Based on replicated findings across cohorts, neurodevelopmental traits in childhood could be associated only indirectly with depressive symptoms across development. CONCLUSIONS: This study indicates that associations between childhood neurodevelopmental traits and depressive symptoms across development could be explained by socioenvironmental stressors and emotional dysregulation. The present findings could inform future research aimed at the prevention of depression in youths with neurodevelopmental disorders.

Autoregulation of blood flow drives early hypotension in a rat model of systemic inflammation induced by bacterial lipopolysaccharide.

Uncontrolled vasodilation is known to account for hypotension in the advanced stages of sepsis and other systemic inflammatory conditions, but the mechanisms of hypotension in earlier stages of such conditions are not clear. By monitoring hemodynamics with the highest temporal resolution in unanesthetized rats, in combination with ex-vivo assessment of vascular function, we found that early development of hypotension following injection of bacterial lipopolysaccharide is brought about by a fall in vascular resistance when arterioles are still fully responsive to vasoactive agents. This approach further uncovered that the early development of hypotension stabilized blood flow. We thus hypothesized that prioritization of the local mechanisms of blood flow regulation (tissue autoregulation) over the brain-driven mechanisms of pressure regulation (baroreflex) underscored the early development of hypotension in this model. Consistent with this hypothesis, an assessment of squared coherence and partial-directed coherence revealed that, at the onset of hypotension, the flow-pressure relationship was strengthened at frequencies (<0.2 Hz) known to be associated with autoregulation. The autoregulatory escape to phenylephrine-induced vasoconstriction, another proxy of autoregulation, was also strengthened in this phase. The competitive demand that drives prioritization of flow over pressure regulation could be edema-associated hypovolemia, as this became detectable at the onset of hypotension. Accordingly, blood transfusion aimed at preventing hypovolemia brought the autoregulation proxies back to normal and prevented the fall in vascular resistance. This novel hypothesis opens a new avenue of investigation into the mechanisms that can drive hypotension in systemic inflammation.

Identifying regulational alterations in gene regulatory networks by state space representation of vector autoregressive models and variational annealing.

BACKGROUND: In the analysis of effects by cell treatment such as drug dosing, identifying changes on gene network structures between normal and treated cells is a key task. A possible way for identifying the changes is to compare structures of networks estimated from data on normal and treated cells separately. However, this approach usually fails to estimate accurate gene networks due to the limited length of time series data and measurement noise. Thus, approaches that identify changes on regulations by using time series data on both conditions in an efficient manner are demanded. METHODS: We propose a new statistical approach that is based on the state space representation of the vector autoregressive model and estimates gene networks on two different conditions in order to identify changes on regulations between the conditions. In the mathematical model of our approach, hidden binary variables are newly introduced to indicate the presence of regulations on each condition. The use of the hidden binary variables enables an efficient data usage; data on both conditions are used for commonly existing regulations, while for condition specific regulations corresponding data are only applied. Also, the similarity of networks on two conditions is automatically considered from the design of the potential function for the hidden binary variables. For the estimation of the hidden binary variables, we derive a new variational annealing method that searches the configuration of the binary variables maximizing the marginal likelihood. RESULTS: For the performance evaluation, we use time series data from two topologically similar synthetic networks, and confirm that our proposed approach estimates commonly existing regulations as well as changes on regulations with higher coverage and precision than other existing approaches in almost all the experimental settings. For a real data application, our proposed approach is applied to time series data from normal Human lung cells and Human lung cells treated by stimulating EGF-receptors and dosing an anticancer drug termed Gefitinib. In the treated lung cells, a cancer cell condition is simulated by the stimulation of EGF-receptors, but the effect would be counteracted due to the selective inhibition of EGF-receptors by Gefitinib. However, gene expression profiles are actually different between the conditions, and the genes related to the identified changes are considered as possible off-targets of Gefitinib. CONCLUSIONS: From the synthetically generated time series data, our proposed approach can identify changes on regulations more accurately than existing methods. By applying the proposed approach to the time series data on normal and treated Human lung cells, candidates of off-target genes of Gefitinib are found. According to the published clinical information, one of the genes can be related to a factor of interstitial pneumonia, which is known as a side effect of Gefitinib.

Systems biology model repository for macrophage pathway simulation.

SUMMARY: The Macrophage Pathway Knowledgebase (MACPAK) is a computational system that allows biomedical researchers to query and study the dynamic behaviors of macrophage molecular pathways. It integrates the knowledge of 230 reviews that were carefully checked by specialists for their accuracy and then converted to 230 dynamic mathematical pathway models. MACPAK comprises a total of 24 009 entities and 12 774 processes and is described in the Cell System Markup Language (CSML), an XML format that runs on the Cell Illustrator platform and can be visualized with a customized Cytoscape for further analysis. AVAILABILITY: MACPAK can be accessed via an interactive web site at http://macpak.csml.org. The CSML pathway models are available under the Creative Commons license.

Applications of graph theory to the analysis of fNIRS data in hyperscanning paradigms.

Hyperscanning is a promising tool for investigating the neurobiological underpinning of social interactions and affective bonds. Recently, graph theory measures, such as modularity, have been proposed for estimating the global synchronization between brains. This paper proposes the bootstrap modularity test as a way of determining whether a pair of brains is coactivated. This test is illustrated as a screening tool in an application to fNIRS data collected from the prefrontal cortex and temporoparietal junction of five dyads composed of a teacher and a preschooler while performing an interaction task. In this application, graph hub centrality measures identify that the dyad's synchronization is critically explained by the relation between teacher's language and number processing and the child's phonological processing. The analysis of these metrics may provide further insights into the neurobiological underpinnings of interaction, such as in educational contexts.

Genome-wide promoter methylation profiling in a cellular model of melanoma progression reveals markers of malignancy and metastasis that predict melanoma survival.

The epigenetic changes associated with melanoma progression to advanced and metastatic stages are still poorly understood. To shed light on the CpG methylation dynamics during melanoma development, we analyzed the methylome profiles of a four-stage cell line model of melanoma progression: non-tumorigenic melanocytes (melan-a), premalignant melanocytes (4C), non-metastatic melanoma cells (4C11-), and metastatic melanoma cells (4C11+). We identified 540 hypo- and 37 hypermethylated gene promoters that together characterized a malignancy signature, and 646 hypo- and 520 hypermethylated promoters that distinguished a metastasis signature. Differentially methylated genes from these signatures were correlated with overall survival using TCGA-SKCM methylation data. Moreover, multivariate Cox analyses with LASSO regularization identified panels of 33 and 31 CpGs, respectively, from the malignancy and metastasis signatures that predicted poor survival. We found a concordant relationship between DNA methylation and transcriptional levels for genes from the malignancy (Pyroxd2 and Ptgfrn) and metastasis (Arnt2, Igfbp4 and Ptprf) signatures, which were both also correlated with melanoma prognosis. Altogether, this study reveals novel CpGs methylation markers associated with malignancy and metastasis that collectively could improve the survival prediction of melanoma patients.

A fast and robust statistical test based on likelihood ratio with Bartlett correction to identify Granger causality between gene sets.

UNLABELLED: We propose a likelihood ratio test (LRT) with Bartlett correction in order to identify Granger causality between sets of time series gene expression data. The performance of the proposed test is compared to a previously published bootstrap-based approach. LRT is shown to be significantly faster and statistically powerful even within non-Normal distributions. An R package named gGranger containing an implementation for both Granger causality identification tests is also provided. AVAILABILITY: http://dnagarden.ims.u-tokyo.ac.jp/afujita/en/doku.php?id=ggranger.