Modeling the Spatial and Temporal Dependence in fMRI Data

Summary Functional magnetic resonance imaging (fMRI) data sets are large and characterized by complex dependence structures driven by highly sophisticated neurophysiology and aspects of the experimental designs. Typical analyses investigating task‐related changes in measured brain activity use a two‐stage procedure in which the first stage involves subject‐specific models and the second‐stage specifies group (or population) level parameters. Customarily, the first‐level accounts for temporal correlations between the serial scans acquired during one scanning session. Despite accounting for these correlations, fMRI studies often include multiple sessions and temporal dependencies may persist between the corresponding estimates of mean neural activity. Further, spatial correlations between brain activity measurements in different locations are often unaccounted for in statistical modeling and estimation. We propose a two‐stage, spatio‐temporal, autoregressive model that simultaneously accounts for spatial dependencies between voxels within the same anatomical region and for temporal dependencies between a subject's estimates from multiple sessions. We develop an algorithm that leverages the special structure of our covariance model, enabling relatively fast and efficient estimation. Using our proposed method, we analyze fMRI data from a study of inhibitory control in cocaine addicts.     

Double‐wavelet transform for multisubject task‐induced functional magnetic resonance imaging data

The goal of this article is to model multisubject task‐induced functional magnetic resonance imaging (fMRI) response among predefined regions of interest (ROIs) of the human brain. Conventional approaches to fMRI analysis only take into account temporal correlations, but do not rigorously model the underlying spatial correlation due to the complexity of estimating and inverting the high dimensional spatio‐temporal covariance matrix. Other spatio‐temporal model approaches estimate the covariance matrix with the assumption of stationary time series, which is not always feasible. To address these limitations, we propose a double‐wavelet approach for modeling the spatio‐temporal brain process. Working with wavelet coefficients simplifies temporal and spatial covariance structure because under regularity conditions, wavelet coefficients are approximately uncorrelated. Different wavelet functions were used to capture different correlation structures in the spatio‐temporal model. The main advantages of the wavelet approach are that it is scalable and that it deals with nonstationarity in brain signals. Simulation studies showed that our method could reduce false‐positive and false‐negative rates by taking into account spatial and temporal correlations simultaneously. We also applied our method to fMRI data to study activation in prespecified ROIs in the prefontal cortex. Data analysis showed that the result using the double‐wavelet approach was more consistent than the conventional approach when sample size decreased.     

Smooth individual level covariates adjustment in disease mapping

Spatial models for disease mapping should ideally account for covariates measured both at individual and area levels. The newly available “indiCAR” model fits the popular conditional autoregresssive (CAR) model by accommodating both individual and group level covariates while adjusting for spatial correlation in the disease rates. This algorithm has been shown to be effective but assumes log‐linear associations between individual level covariates and outcome. In many studies, the relationship between individual level covariates and the outcome may be non‐log‐linear, and methods to track such nonlinearity between individual level covariate and outcome in spatial regression modeling are not well developed. In this paper, we propose a new algorithm, smooth‐indiCAR, to fit an extension to the popular conditional autoregresssive model that can accommodate both linear and nonlinear individual level covariate effects while adjusting for group level covariates and spatial correlation in the disease rates. In this formulation, the effect of a continuous individual level covariate is accommodated via penalized splines. We describe a two‐step estimation procedure to obtain reliable estimates of individual and group level covariate effects where both individual and group level covariate effects are estimated separately. This distributed computing framework enhances its application in the Big Data domain with a large number of individual/group level covariates. We evaluate the performance of smooth‐indiCAR through simulation. Our results indicate that the smooth‐indiCAR method provides reliable estimates of all regression and random effect parameters. We illustrate our proposed methodology with an analysis of data on neutropenia admissions in New South Wales (NSW), Australia.     

Joint Spatial Modeling of Recurrent Infection and Growth with Processes under Intermittent Observation

Summary In this article, we present a new statistical methodology for longitudinal studies in forestry, where trees are subject to recurrent infection, and the hazard of infection depends on tree growth over time. Understanding the nature of this dependence has important implications for reforestation and breeding programs. Challenges arise for statistical analysis in this setting with sampling schemes leading to panel data, exhibiting dynamic spatial variability, and incomplete covariate histories for hazard regression. In addition, data are collected at a large number of locations, which poses computational difficulties for spatiotemporal modeling. A joint model for infection and growth is developed wherein a mixed nonhomogeneous Poisson process, governing recurring infection, is linked with a spatially dynamic nonlinear model representing the underlying height growth trajectories. These trajectories are based on the von Bertalanffy growth model and a spatially varying parameterization is employed. Spatial variability in growth parameters is modeled through a multivariate spatial process derived through kernel convolution. Inference is conducted in a Bayesian framework with implementation based on hybrid Monte Carlo. Our methodology is applied for analysis in an 11‐year study of recurrent weevil infestation of white spruce in British Columbia.     

Joint generalized models for multidimensional outcomes: A case study of neuroscience data from multimodalities

This paper is motivated from the analysis of neuroscience data in a study of neural and muscular mechanisms of muscle fatigue. Multidimensional outcomes of different natures were obtained simultaneously from multiple modalities, including handgrip force, electromyography (EMG), and functional magnetic resonance imaging (fMRI). We first study individual modeling of the univariate response depending on its nature. A mixed‐effects beta model and a mixed‐effects simplex model are compared for modeling the force/EMG percentages. A mixed‐effects negative‐binomial model is proposed for modeling the fMRI counts. Then, I present a joint modeling approach to model the multidimensional outcomes together, which allows us to not only estimate the covariate effects but also to evaluate the strength of association among the multiple responses from different modalities. A simulation study is conducted to quantify the possible benefits by the new approaches in finite sample situations. Finally, the analysis of the fatigue data is illustrated with the use of the proposed methods.     

Eigenvector Centrality Mapping for Analyzing Connectivity Patterns in fMRI Data of the Human Brain

Functional magnetic resonance data acquired in a task-absent condition (“resting state”) require new data analysis techniques that do not depend on an activation model. In this work, we introduce an alternative assumption- and parameter-free method based on a particular form of node centrality called eigenvector centrality. Eigenvector centrality attributes a value to each voxel in the brain such that a voxel receives a large value if it is strongly correlated with many other nodes that are themselves central within the network. Google''s PageRank algorithm is a variant of eigenvector centrality. Thus far, other centrality measures - in particular “betweenness centrality” - have been applied to fMRI data using a pre-selected set of nodes consisting of several hundred elements. Eigenvector centrality is computationally much more efficient than betweenness centrality and does not require thresholding of similarity values so that it can be applied to thousands of voxels in a region of interest covering the entire cerebrum which would have been infeasible using betweenness centrality. Eigenvector centrality can be used on a variety of different similarity metrics. Here, we present applications based on linear correlations and on spectral coherences between fMRI times series. This latter approach allows us to draw conclusions of connectivity patterns in different spectral bands. We apply this method to fMRI data in task-absent conditions where subjects were in states of hunger or satiety. We show that eigenvector centrality is modulated by the state that the subjects were in. Our analyses demonstrate that eigenvector centrality is a computationally efficient tool for capturing intrinsic neural architecture on a voxel-wise level.     

Evaluating regional resiliency of coastal wetlands to sea level rise through hypsometry‐based modeling

Sea level rise (SLR) threatens coastal wetlands worldwide, yet the fate of individual wetlands will vary based on local topography, wetland morphology, sediment dynamics, hydrologic processes, and plant‐mediated feedbacks. Local variability in these factors makes it difficult to predict SLR effects across wetlands or to develop a holistic regional perspective on SLR response for a diversity of wetland types. To improve regional predictions of SLR impacts to coastal wetlands, we developed a model that addresses the scale‐dependent factors controlling SLR response and accommodates different levels of data availability. The model quantifies SLR‐driven habitat conversion within wetlands across a region by predicting changes in individual wetland hypsometry. This standardized approach can be applied to all wetlands in a region regardless of data availability, making it ideal for modeling SLR response across a range of scales. Our model was applied to 105 wetlands in southern California that spanned a broad range of typology and data availability. Our findings suggest that if wetlands are confined to their current extents, the region will lose 12% of marsh habitats (vegetated marsh and unvegetated flats) with 0.6 m of SLR (projected for 2050) and 48% with 1.7 m of SLR (projected for 2100). Habitat conversion was more drastic in wetlands with larger proportions of marsh habitats relative to subtidal habitats and occurred more rapidly in small lagoons relative to larger sites. Our assessment can inform management of coastal wetland vulnerability, improve understanding of the SLR drivers relevant to individual wetlands, and highlight significant data gaps that impede SLR response modeling across spatial scales. This approach augments regional SLR assessments by considering spatial variability in SLR response drivers, addressing data gaps, and accommodating wetland diversity, which will provide greater insights into regional SLR response that are relevant to coastal management and restoration efforts.     

Multiscale Adaptive Marginal Analysis of Longitudinal Neuroimaging Data with Time‐Varying Covariates

Summary Neuroimaging data collected at repeated occasions are gaining increasing attention in the neuroimaging community due to their potential in answering questions regarding brain development, aging, and neurodegeneration. These datasets are large and complicated, characterized by the intricate spatial dependence structure of each response image, multiple response images per subject, and covariates that may vary with time. We propose a multiscale adaptive generalized method of moments (MA‐GMM) approach to estimate marginal regression models for imaging datasets that contain time‐varying, spatially related responses and some time‐varying covariates. Our method categorizes covariates into types to determine the valid moment conditions to combine during estimation. Further, instead of assuming independence of voxels (the components that make up each subject’s response image at each time point) as many current neuroimaging analysis techniques do, this method “adaptively smoothes” neuroimaging response data, computing parameter estimates by iteratively building spheres around each voxel and combining observations within the spheres with weights. MA‐GMM’s development adds to the few available modeling approaches intended for longitudinal imaging data analysis. Simulation studies and an analysis of a real longitudinal imaging dataset from the Alzheimer’s Disease Neuroimaging Initiative are used to assess the performance of MA‐GMM. Martha Skup, Hongtu Zhu, and Heping Zhang for the Alzheimer’s Disease Neuroimaging Initiative.     

Spatial Cluster Detection for Weighted Outcomes Using Cumulative Geographic Residuals

Summary Spatial cluster detection is an important methodology for identifying regions with excessive numbers of adverse health events without making strong model assumptions on the underlying spatial dependence structure. Previous work has focused on point or individual‐level outcome data and few advances have been made when the outcome data are reported at an aggregated level, for example, at the county‐ or census‐tract level. This article proposes a new class of spatial cluster detection methods for point or aggregate data, comprising of continuous, binary, and count data. Compared with the existing spatial cluster detection methods it has the following advantages. First, it readily incorporates region‐specific weights, for example, based on a region's population or a region's outcome variance, which is the key for aggregate data. Second, the established general framework allows for area‐level and individual‐level covariate adjustment. A simulation study is conducted to evaluate the performance of the method. The proposed method is then applied to assess spatial clustering of high Body Mass Index in a health maintenance organization population in the Seattle, Washington, USA area.     

Disentangling elevational richness: a multi‐scale hierarchical Bayesian occupancy model of Colorado ant communities

Understanding the forces that shape the distribution of biodiversity across spatial scales is central in ecology and critical to effective conservation. To assess effects of possible richness drivers, we sampled ant communities on four elevational transects across two mountain ranges in Colorado, USA, with seven or eight sites on each transect and twenty repeatedly sampled pitfall trap pairs at each site each for a total of 90 d. With a multi‐scale hierarchical Bayesian community occupancy model, we simultaneously evaluated the effects of temperature, productivity, area, habitat diversity, vegetation structure, and temperature variability on ant richness at two spatial scales, quantifying detection error and genus‐level phylogenetic effects. We fit the model with data from one mountain range and tested predictive ability with data from the other mountain range. In total, we detected 105 ant species, and richness peaked at intermediate elevations on each transect. Species‐specific thermal preferences drove richness at each elevation with marginal effects of site‐scale productivity. Trap‐scale richness was primarily influenced by elevation‐scale variables along with a negative impact of canopy cover. Soil diversity had a marginal negative effect while daily temperature variation had a marginal positive effect. We detected no impact of area, land cover diversity, trap‐scale productivity, or tree density. While phylogenetic relationships among genera had little influence, congeners tended to respond similarly. The hierarchical model, trained on data from the first mountain range, predicted the trends on the second mountain range better than multiple regression, reducing root mean squared error up to 65%. Compared to a more standard approach, this modeling framework better predicts patterns on a novel mountain range and provides a nuanced, detailed evaluation of ant communities at two spatial scales.     

Uncertainties in the projection of species distributions related to general circulation models

Ecological Niche Models (ENMs) are increasingly used by ecologists to project species potential future distribution. However, the application of such models may be challenging, and some caveats have already been identified. While studies have generally shown that projections may be sensitive to the ENM applied or the emission scenario, to name just a few, the sensitivity of ENM‐based scenarios to General Circulation Models (GCMs) has been often underappreciated. Here, using a multi‐GCM and multi‐emission scenario approach, we evaluated the variability in projected distributions under future climate conditions. We modeled the ecological realized niche (sensu Hutchinson) and predicted the baseline distribution of species with contrasting spatial patterns and representative of two major functional groups of European trees: the dwarf birch and the sweet chestnut. Their future distributions were then projected onto future climatic conditions derived from seven GCMs and four emissions scenarios using the new Representative Concentration Pathways (RCPs) developed for the Intergovernmental Panel on Climate Change (IPCC) AR5 report. Uncertainties arising from GCMs and those resulting from emissions scenarios were quantified and compared. Our study reveals that scenarios of future species distribution exhibit broad differences, depending not only on emissions scenarios but also on GCMs. We found that the between‐GCM variability was greater than the between‐RCP variability for the next decades and both types of variability reached a similar level at the end of this century. Our result highlights that a combined multi‐GCM and multi‐RCP approach is needed to better consider potential trajectories and uncertainties in future species distributions. In all cases, between‐GCM variability increases with the level of warming, and if nothing is done to alleviate global warming, future species spatial distribution may become more and more difficult to anticipate. When future species spatial distributions are examined, we propose to use a large number of GCMs and RCPs to better anticipate potential trajectories and quantify uncertainties.     

Analysis of the neuronal selectivity underlying low fMRI signals

BACKGROUND: A prevailing assumption in neuroimaging studies is that relatively low fMRI signals are due to weak neuronal activation, and, therefore, they are commonly ignored. However, lower fMRI signals may also result from intense activation by highly selective, albeit small, subsets of neurons in the imaged voxel. We report on an approach that could form a basis for resolving this ambiguity imposed by the low (mm range) spatial resolution of fMRI. Our approach employs fMR-adaptation as an indicator for highly active neuronal populations even when the measured fMRI signal is low.RESULTS: In this study, we first showed that fMRI-adaptation is diminished when overall neuronal activity is lowered substantially by reducing image contrast. We then applied the same adaptation paradigm, but this time we lowered the fMRI signal by changing object shape. While the overall fMRI signal in category-related regions such as the face-related pFs was drastically reduced for non-face stimuli, the adaptation level obtained for these stimuli remained high. We hypothesize that the relatively greater adaptation level following exposure to "nonoptimal" object shapes is indicative of small subsets of neurons responding vigorously to these "nonoptimal" objects even when the overall fMRI activity is low.CONCLUSIONS: Our results show that fMR-adaptation can be used to differentiate between neuronal activation patterns that appear similar in the overall fMRI signal. The results suggest that it may be possible to employ fMR-adaptation to reveal functionally heterogeneous islands of activity, which are too small to image using conventional imaging methods.     

Learning brain dynamics for decoding and predicting individual differences

Insights from functional Magnetic Resonance Imaging (fMRI), as well as recordings of large numbers of neurons, reveal that many cognitive, emotional, and motor functions depend on the multivariate interactions of brain signals. To decode brain dynamics, we propose an architecture based on recurrent neural networks to uncover distributed spatiotemporal signatures. We demonstrate the potential of the approach using human fMRI data during movie-watching data and a continuous experimental paradigm. The model was able to learn spatiotemporal patterns that supported 15-way movie-clip classification (∼90%) at the level of brain regions, and binary classification of experimental conditions (∼60%) at the level of voxels. The model was also able to learn individual differences in measures of fluid intelligence and verbal IQ at levels comparable to that of existing techniques. We propose a dimensionality reduction approach that uncovers low-dimensional trajectories and captures essential informational (i.e., classification related) properties of brain dynamics. Finally, saliency maps and lesion analysis were employed to characterize brain-region/voxel importance, and uncovered how dynamic but consistent changes in fMRI activation influenced decoding performance. When applied at the level of voxels, our framework implements a dynamic version of multivariate pattern analysis. Our approach provides a framework for visualizing, analyzing, and discovering dynamic spatially distributed brain representations during naturalistic conditions.     

A Hierarchical Bayesian Model for Spatial Prediction of Multivariate Non‐Gaussian Random Fields

Summary As most georeferenced data sets are multivariate and concern variables of different types, spatial mapping methods must be able to deal with such data. The main difficulties are the prediction of non‐Gaussian variables and the modeling of the dependence between processes. The aim of this article is to present a new hierarchical Bayesian approach that permits simultaneous modeling of dependent Gaussian, count, and ordinal spatial fields. This approach is based on spatial generalized linear mixed models. We use a moving average approach to model the spatial dependence between the processes. The method is first validated through a simulation study. We show that the multivariate model has better predictive abilities than the univariate one. Then the multivariate spatial hierarchical model is applied to a real data set collected in French Guiana to predict topsoil patterns.     

Robust joint modeling of longitudinal measurements and time to event data using normal/independent distributions: A Bayesian approach

Joint modeling of longitudinal data and survival data has been used widely for analyzing AIDS clinical trials, where a biological marker such as CD4 count measurement can be an important predictor of survival. In most of these studies, a normal distribution is used for modeling longitudinal responses, which leads to vulnerable inference in the presence of outliers in longitudinal measurements. Powerful distributions for robust analysis are normal/independent distributions, which include univariate and multivariate versions of the Student's t, the slash and the contaminated normal distributions in addition to the normal. In this paper, a linear‐mixed effects model with normal/independent distribution for both random effects and residuals and Cox's model for survival time are used. For estimation, a Bayesian approach using Markov Chain Monte Carlo is adopted. Some simulation studies are performed for illustration of the proposed method. Also, the method is illustrated on a real AIDS data set and the best model is selected using some criteria.     

A Sparse Representation-Based Algorithm for Pattern Localization in Brain Imaging Data Analysis

Considering the two-class classification problem in brain imaging data analysis, we propose a sparse representation-based multi-variate pattern analysis (MVPA) algorithm to localize brain activation patterns corresponding to different stimulus classes/brain states respectively. Feature selection can be modeled as a sparse representation (or sparse regression) problem. Such technique has been successfully applied to voxel selection in fMRI data analysis. However, single selection based on sparse representation or other methods is prone to obtain a subset of the most informative features rather than all. Herein, our proposed algorithm recursively eliminates informative features selected by a sparse regression method until the decoding accuracy based on the remaining features drops to a threshold close to chance level. In this way, the resultant feature set including all the identified features is expected to involve all the informative features for discrimination. According to the signs of the sparse regression weights, these selected features are separated into two sets corresponding to two stimulus classes/brain states. Next, in order to remove irrelevant/noisy features in the two selected feature sets, we perform a nonparametric permutation test at the individual subject level or the group level. In data analysis, we verified our algorithm with a toy data set and an intrinsic signal optical imaging data set. The results show that our algorithm has accurately localized two class-related patterns. As an application example, we used our algorithm on a functional magnetic resonance imaging (fMRI) data set. Two sets of informative voxels, corresponding to two semantic categories (i.e., “old people” and “young people”), respectively, are obtained in the human brain.     

Modeling spatiotemporal abundance of mobile wildlife in highly variable environments using boosted GAMLSS hurdle models

Modeling organism distributions from survey data involves numerous statistical challenges, including accounting for zero‐inflation, overdispersion, and selection and incorporation of environmental covariates. In environments with high spatial and temporal variability, addressing these challenges often requires numerous assumptions regarding organism distributions and their relationships to biophysical features. These assumptions may limit the resolution or accuracy of predictions resulting from survey‐based distribution models. We propose an iterative modeling approach that incorporates a negative binomial hurdle, followed by modeling of the relationship of organism distribution and abundance to environmental covariates using generalized additive models (GAM) and generalized additive models for location, scale, and shape (GAMLSS). Our approach accounts for key features of survey data by separating binary (presence‐absence) from count (abundance) data, separately modeling the mean and dispersion of count data, and incorporating selection of appropriate covariates and response functions from a suite of potential covariates while avoiding overfitting. We apply our modeling approach to surveys of sea duck abundance and distribution in Nantucket Sound (Massachusetts, USA), which has been proposed as a location for offshore wind energy development. Our model results highlight the importance of spatiotemporal variation in this system, as well as identifying key habitat features including distance to shore, sediment grain size, and seafloor topographic variation. Our work provides a powerful, flexible, and highly repeatable modeling framework with minimal assumptions that can be broadly applied to the modeling of survey data with high spatiotemporal variability. Applying GAMLSS models to the count portion of survey data allows us to incorporate potential overdispersion, which can dramatically affect model results in highly dynamic systems. Our approach is particularly relevant to systems in which little a priori knowledge is available regarding relationships between organism distributions and biophysical features, since it incorporates simultaneous selection of covariates and their functional relationships with organism responses.     

Spatio-temporal modeling of localized brain activity

Functional neuroimaging, including positron emission tomography (PET) and functional magnetic resonance imaging (fMRI), plays an important role in identifying specific brain regions associated with experimental stimuli or psychiatric disorders such as schizophrenia. PET and fMRI produce massive data sets that contain both temporal correlations from repeated scans and complex spatial correlations. Several methods exist for handling temporal correlations, some of which rely on transforming the response data to induce either a known or an independence covariance structure. Despite the presence of spatial correlations between the volume elements (voxels) comprising a brain scan, conventional methods perform voxel-by-voxel analyses of measured brain activity. We propose a two-stage spatio-temporal model for the estimation and testing of localized activity. Our second-stage model specifies a spatial auto-regression, capturing correlations within neural processing clusters defined by a data-driven cluster analysis. We use maximum likelihood methods to estimate parameters from our spatial autoregressive model. Our model protects against type-I errors, enables the detection of both localized and regional activations (including volume of interest effects), provides information on functional connectivity in the brain, and establishes a framework to produce spatially smoothed maps of distributed brain activity for each individual. We illustrate the application of our model using PET data from a study of working memory in individuals with schizophrenia.     

A flexible cure rate model for spatially correlated survival data based on generalized extreme value distribution and Gaussian process priors

Our present work proposes a new survival model in a Bayesian context to analyze right‐censored survival data for populations with a surviving fraction, assuming that the log failure time follows a generalized extreme value distribution. Many applications require a more flexible modeling of covariate information than a simple linear or parametric form for all covariate effects. It is also necessary to include the spatial variation in the model, since it is sometimes unexplained by the covariates considered in the analysis. Therefore, the nonlinear covariate effects and the spatial effects are incorporated into the systematic component of our model. Gaussian processes (GPs) provide a natural framework for modeling potentially nonlinear relationship and have recently become extremely powerful in nonlinear regression. Our proposed model adopts a semiparametric Bayesian approach by imposing a GP prior on the nonlinear structure of continuous covariate. With the consideration of data availability and computational complexity, the conditionally autoregressive distribution is placed on the region‐specific frailties to handle spatial correlation. The flexibility and gains of our proposed model are illustrated through analyses of simulated data examples as well as a dataset involving a colon cancer clinical trial from the state of Iowa.