Functional CAR Models for Large Spatially Correlated Functional Datasets

Zhang, Linlin; Baladandayuthapani, Veerabhadran; Zhu, Hongxiao; Baggerly, Keith A.; Majewski, Tadeusz; Czerniak, Bogdan; Morris, Jeffrey S.

doi:10.1080/01621459.2015.1042581

Cited by 52 publications

(32 citation statements)

References 45 publications

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“…For functional data indexed by points on a lattice, one could also assume local correlation patterns. For example, Zhang et al (2015) used conditional autoregressive (CAR) assumptions to model local correlations between functions on a lattice, which can also be easily incorporated into our framework.…”

Section: Discussionmentioning

confidence: 99%

Robust and Gaussian spatial functional regression models for analysis of event-related potentials

et al. 2018

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Event-related potentials (ERPs) summarize electrophysiological brain response to specific stimuli. They can be considered as correlated functions of time with both spatial correlation across electrodes and nested correlations within subjects. Commonly used analytical methods for ERPs often focus on pre-determined extracted components and/or ignore the correlation among electrodes or subjects, which can miss important insights, and tend to be sensitive to outlying subjects, time points or electrodes. Motivated by ERP data in a smoking cessation study, we introduce a Bayesian spatial functional regression framework that models the entire ERPs as spatially correlated functional responses and the stimulus types as covariates. This novel framework relies on mixed models to characterize the effects of stimuli while simultaneously accounting for the multilevel correlation structure. The spatial correlation among the ERP profiles is captured through basis-space Matérn assumptions that allow either separable or nonseparable spatial correlations over time. We induce both adaptive regularization over time and spatial smoothness across electrodes via a correlated normal-exponential-gamma (CNEG) prior on the fixed effect coefficient functions. Our proposed framework includes both Gaussian models as well as robust models using heavier-tailed distributions to make the regression automatically robust to outliers. We introduce predictive methods to select among Gaussian vs. robust models and models with separable vs. non-separable spatiotemporal correlation structures. Our proposed analysis produces global tests for stimuli effects across entire time (or time-frequency) and electrode domains, plus multiplicity-adjusted pointwise inference based on experiment-wise error rate or false discovery rate to flag spatiotemporal (or spatio-temporal-frequency) regions that characterize stimuli differences, and can also produce inference for any prespecified waveform components. Our analysis of the smoking cessation ERP data set reveals numerous effects across different types of visual stimuli.

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Section: Discussionmentioning

confidence: 99%

Robust and Gaussian spatial functional regression models for analysis of event-related potentials

et al. 2018

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“…Although motivated and generated in the context of resting‐state functional connectivity analysis, the proposed methods can be easily generalized to other data such as gene network tests for different groups or protein network tests under different conditions . The proposed methods can also be applied to detect changes in structural connectivity derived by fiber tractography.…”

Section: Discussionmentioning

confidence: 99%

Edgewise and subgraph‐level tests for brain networks

Chen

Zhao

Porges

et al. 2016

Statistics in Medicine

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Resting-state functional magnetic resonance image (rsfMRI) is a useful technique for investigating brain functional connectivity at rest. In this work, we develop flexible regression models and methods for determining differences in resting-state functional connectivity as a function of age, gender, drug intervention, or neuropsychiatric disorders. We propose two complementary methods for identifying changes of edges and subgraphs. 1) For detecting changes of edges, we select the optimal model at each edge, and then conduct contrast tests to identify the effects of the important variables while controlling the familywise error rate (FWER). 2) We adopt the network based statistics (NBS) method to improve power by incorporating the graph topological structure. Both methods have wide applications for low signal-to-noise ratio data. We propose stability criteria for the choice of threshold in the NBS procedure and utilize efficient massive parallel procedure to speed up the estimation and inference procedure. Results from our simulation studies show that the thresholds chosen by the proposed stability criteria outperform the Bonferroni threshold. To demonstrate applicability, we use both methods in the context of the Oxytocin and Aging Study to determine effects of age, gender, and drug treatment on resting-state functional connectivity, as well as in the context of the Autism Brain Imaging Data Exchange Study to determine effects of autism spectrum disorder on functional connectivity at rest.

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“…In this case, the random effect functions U hm ( t ) are iid mean zero Gaussian Processes with intrafunctional covariance cov{ U hm ( t 1 ) , U hm ( t 2 )} = Q h ( t 1 , t 2 ) and the residual error functions E i ( t ) are iid mean zero Gaussian Processes with intrafunctional covariance cov{ E i ( t 1 ) ,E i ( t 2 )} = S ( t 1 , t 2 ). Other extensions of this framework allow the option of conditional autoregressive (CAR) (Zhang et al, 2014) or Matern spatial covariance or AR( p ) temporal interfunctional correlation structures in the residual errors (Zhu et al, 2014). Although focusing on Gaussian regression here, a robust version of this framework assuming heavier tailed distributions on the random effects or residuals is available (Zhu et al, 2011) if robustness to outliers is desired, and can also be utilized with any other features or modeling components in the BayesFMM framework.…”

Section: Methodsmentioning

confidence: 99%

Bayesian Semiparametric Functional Mixed Models for Serially Correlated Functional Data, With Application to Glaucoma Data

Lee

Miranda

Rausch

et al. 2018

Journal of the American Statistical Association

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Glaucoma, a leading cause of blindness, is characterized by optic nerve damage related to intraocular pressure (IOP), but its full etiology is unknown. Researchers at UAB have devised a custom device to measure scleral strain continuously around the eye under fixed levels of IOP, which here is used to assess how strain varies around the posterior pole, with IOP, and across glaucoma risk factors such as age. The hypothesis is that scleral strain decreases with age, which could alter biomechanics of the optic nerve head and cause damage that could eventually lead to glaucoma. To evaluate this hypothesis, we adapted Bayesian Functional Mixed Models to model these complex data consisting of correlated functions on spherical scleral surface, with nonparametric age effects allowed to vary in magnitude and smoothness across the scleral surface, multi-level random effect functions to capture within-subject correlation, and functional growth curve terms to capture serial correlation across IOPs that can vary around the scleral surface. Our method yields fully Bayesian inference on the scleral surface or any aggregation or transformation thereof, and reveals interesting insights into the biomechanical etiology of glaucoma. The general modeling framework described is very flexible and applicable to many complex, high-dimensional functional data.

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Functional CAR Models for Large Spatially Correlated Functional Datasets

Cited by 52 publications

References 45 publications

Robust and Gaussian spatial functional regression models for analysis of event-related potentials

Robust and Gaussian spatial functional regression models for analysis of event-related potentials

Edgewise and subgraph‐level tests for brain networks

Bayesian Semiparametric Functional Mixed Models for Serially Correlated Functional Data, With Application to Glaucoma Data

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