Multivariate spatially oriented data sets are prevalent in the environmental and physical sciences. Scientists seek to jointly model multiple variables, each indexed by a spatial location, to capture any underlying spatial association for each variable and associations among the different dependent variables. Multivariate latent spatial process models have proved effective in driving statistical inference and rendering better predictive inference at arbitrary locations for the spatial process. High‐dimensional multivariate spatial data, which are the theme of this article, refer to data sets where the number of spatial locations and the number of spatially dependent variables is very large. The field has witnessed substantial developments in scalable models for univariate spatial processes, but such methods for multivariate spatial processes, especially when the number of outcomes are moderately large, are limited in comparison. Here, we extend scalable modeling strategies for a single process to multivariate processes. We pursue Bayesian inference, which is attractive for full uncertainty quantification of the latent spatial process. Our approach exploits distribution theory for the matrix‐normal distribution, which we use to construct scalable versions of a hierarchical linear model of coregionalization (LMC) and spatial factor models that deliver inference over a high‐dimensional parameter space including the latent spatial process. We illustrate the computational and inferential benefits of our algorithms over competing methods using simulation studies and an analysis of a massive vegetation index data set.
Brain connectivity analysis is now at the foreground of neuroscience research. A connectivity network is characterized by a graph, where nodes represent neural elements such as neurons and brain regions, and links represent statistical dependence that is often encoded in terms of partial correlation. Such a graph is inferred from the matrix-valued neuroimaging data such as electroencephalography and functional magnetic resonance imaging. There have been a good number of successful proposals for sparse precision matrix estimation under normal or matrix normal distribution; however, this family of solutions does not offer a direct statistical significance quantification for the estimated links. In this article, we adopt a matrix normal distribution framework and formulate the brain connectivity analysis as a precision matrix hypothesis testing problem. Based on the separable spatial-temporal dependence structure, we develop oracle and data-driven procedures to test both the global hypothesis that all spatial locations are conditionally independent, and simultaneous tests for identifying conditional dependent spatial locations with false discovery rate control. Our theoretical results show that the data-driven procedures perform asymptotically as well as the oracle procedures and enjoy certain optimality properties. The empirical finite-sample performance of the proposed tests is studied via intensive simulations, and the new tests are applied on a real electroencephalography data analysis.
more » « less- NSF-PAR ID:
- 10486000
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Biometrics
- Volume:
- 73
- Issue:
- 3
- ISSN:
- 0006-341X
- Format(s):
- Medium: X Size: p. 780-791
- Size(s):
- ["p. 780-791"]
- Sponsoring Org:
- National Science Foundation
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Background A lack of in utero imaging data hampers our understanding of the connections in the human fetal brain. Generalizing observations from postmortem subjects and premature newborns is inaccurate due to technical and biological differences.
Purpose To evaluate changes in fetal brain structural connectivity between 23 and 35 weeks postconceptional age using a spatiotemporal atlas of diffusion tensor imaging (DTI).
Study Type Retrospective.
Population Publicly available diffusion atlases, based on 60 healthy women (age 18–45 years) with normal prenatal care, from 23 and 35 weeks of gestation.
Field Strength/Sequence 3.0 Tesla/DTI acquired with diffusion‐weighted echo planar imaging (EPI).
Assessment We performed whole‐brain fiber tractography from DTI images. The cortical plate of each diffusion atlas was segmented and parcellated into 78 regions derived from the Edinburgh Neonatal Atlas (ENA33). Connectivity matrices were computed, representing normalized fiber connections between nodes. We examined the relationship between global efficiency (GE), local efficiency (LE), small‐worldness (SW), nodal efficiency (NE), and betweenness centrality (BC) with gestational age (GA) and with laterality.
Statistical Tests Linear regression was used to analyze changes in GE, LE, NE, and BC throughout gestation, and to assess changes in laterality. The
t ‐tests were used to assess SW.P ‐values were corrected using Holm‐Bonferroni method. A correctedP ‐value <0.05 was considered statistically significant.Results Network analysis revealed a significant weekly increase in GE (5.83%/week, 95% CI 4.32–7.37), LE (5.43%/week, 95% CI 3.63–7.25), and presence of SW across GA. No significant hemisphere differences were found in GE (
P = 0.971) or LE (P = 0.458). Increasing GA was significantly associated with increasing NE in 41 nodes, increasing BC in 3 nodes, and decreasing BC in 2 nodes.Data Conclusion Extensive network development and refinement occur in the second and third trimesters, marked by a rapid increase in global integration and local segregation.
Level of Evidence 3
Technical Efficacy Stage 2
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Background Cognitive training may partially reverse cognitive deficits in people with HIV (PWH). Previous functional MRI (fMRI) studies demonstrate that working memory training (WMT) alters brain activity during working memory tasks, but its effects on resting brain network organization remain unknown.
Purpose To test whether WMT affects PWH brain functional connectivity in resting‐state fMRI (rsfMRI).
Study Type Prospective.
Population A total of 53 PWH (ages 50.7 ± 1.5 years, two women) and 53
HIV ‐seronegative controls (SN , ages 49.5 ± 1.6 years, six women).Field Strength/Sequence Axial single‐shot gradient‐echo echo‐planar imaging at 3.0 T was performed at baseline (TL1), at 1‐month (TL2), and at 6‐months (TL3), after WMT.
Assessment All participants had rsfMRI and clinical assessments (including neuropsychological tests) at TL1 before randomization to Cogmed WMT (adaptive training,
n = 58: 28 PWH, 30 SN; nonadaptive training,n = 48: 25 PWH, 23 SN), 25 sessions over 5–8 weeks. All assessments were repeated at TL2 and at TL3. The functional connectivity estimated by independent component analysis (ICA) or graph theory (GT) metrics (eigenvector centrality, etc.) for different link densities (LDs) were compared between PWH and SN groups at TL1 and TL2.Statistical Tests Two‐way analyses of variance (ANOVA) on GT metrics and two‐sample
t ‐tests on FC or GT metrics were performed. Cognitive (eg memory) measures were correlated with eigenvector centrality (eCent) using Pearson's correlations. The significance level was set atP < 0.05 after false discovery rate correction.Results The ventral default mode network (vDMN) eCent differed between PWH and SN groups at TL1 but not at TL2 (
P = 0.28). In PWH, vDMN eCent changes significantly correlated with changes in the memory ability in PWH (r = −0.62 at LD = 50%) and vDMN eCent before training significantly correlated with memory performance changes (r = 0.53 at LD = 50%).Data Conclusion ICA and GT analyses showed that adaptive WMT normalized graph properties of the vDMN in PWH.
Evidence Level 1
Technical Efficacy 1
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Transcranial magnetic stimulation (TMS) is gaining increasing attention for therapeutic treatment of mental illnesses. However, a clear understanding of its impact to the underlying brain mechanisms is critical for its effective application. For this, we analyze electroencephalography (EEG) response to TMS subthreshold pulse at the left motor cortex from 6 healthy controls and 6 schizophrenia patients. We use principal component analysis (PCA) along sparse nonnegative matrix factorization (NMF), an unsupervised machine learning technique, on brain connectivity data established by sliding window coherence of EEG based source localized data. The source localization was achieved by using the sLORETA algorithm on our EEG data after artifact removal. This, hence, provides high temporal and spatial resolution in the connectivity analysis results, giving advantage over other neuroimaging modalities. PCA aids in establishing the number of common underlying connected subnetworks (say k) across subjects whereas NMF is employed to derive these k spatial and temporal signature subnetwork response to the stimulus. Within these signatures, we studied motor cortical connectivity and found that schizophrenia patients exhibited sensory gating deficits as compared to controls. These findings can act as potential biomarkers to monitor TMS for clinical therapeutic techniques in the future.more » « less
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Summary Medical imaging data with thousands of spatially correlated data points are common in many fields. Methods that account for spatial correlation often require cumbersome matrix evaluations which are prohibitive for data of this size, and thus current work has either used low-rank approximations or analyzed data in blocks. We propose a method that accounts for nonstationarity, functional connectivity of distant regions of interest, and local signals, and can be applied to large multi-subject datasets using spectral methods combined with Markov Chain Monte Carlo sampling. We illustrate using simulated data that properly accounting for spatial dependence improves precision of estimates and yields valid statistical inference. We apply the new approach to study associations between cortical thickness and Alzheimer's disease, and find several regions of the cortex where patients with Alzheimer's disease are thinner on average than healthy controls.
