Modeling the spatial and temporal dependence in FMRI data

Leveraging the adolescent brain cognitive development study to improve behavioral prediction from neuroimaging in smaller replication samples

Neuroimaging is a popular method to map brain structural and functional patterns to complex human traits. Recently published observations cast doubt upon these prospects, particularly for prediction of cognitive traits from structural and resting state functional magnetic resonance imaging (MRI). We leverage baseline data from thousands of children in the Adolescent Brain Cognitive DevelopmentSM Study to inform the replication sample size required with univariate and multivariate methods across different imaging modalities to detect reproducible brain-behavior associations. We demonstrate that by applying multivariate methods to high-dimensional brain imaging data, we can capture lower dimensional patterns of structural and functional brain architecture that correlate robustly with cognitive phenotypes and are reproducible with only 41 individuals in the replication sample for working memory-related functional MRI, and ~ 100 subjects for structural and resting state MRI. Even with 100 random re-samplings of 100 subjects in discovery, prediction can be adequately powered with 66 subjects in replication for multivariate prediction of cognition with working memory task functional MRI. These results point to an important role for neuroimaging in translational neurodevelopmental research and showcase how findings in large samples can inform reproducible brain-behavior associations in small sample sizes that are at the heart of many research programs and grants.

Identifying covariate-related subnetworks for whole-brain connectome analysis

Whole-brain connectome data characterize the connections among distributed neural populations as a set of edges in a large network, and neuroscience research aims to systematically investigate associations between brain connectome and clinical or experimental conditions as covariates. A covariate is often related to a number of edges connecting multiple brain areas in an organized structure. However, in practice, neither the covariate-related edges nor the structure is known. Therefore, the understanding of underlying neural mechanisms relies on statistical methods that are capable of simultaneously identifying covariate-related connections and recognizing their network topological structures. The task can be challenging because of false-positive noise and almost infinite possibilities of edges combining into subnetworks. To address these challenges, we propose a new statistical approach to handle multivariate edge variables as outcomes and output covariate-related subnetworks. We first study the graph properties of covariate-related subnetworks from a graph and combinatorics perspective and accordingly bridge the inference for individual connectome edges and covariate-related subnetworks. Next, we develop efficient algorithms to exact covariate-related subnetworks from the whole-brain connectome data with an $\ell_0$ norm penalty. We validate the proposed methods based on an extensive simulation study, and we benchmark our performance against existing methods. Using our proposed method, we analyze two separate resting-state functional magnetic resonance imaging data sets for schizophrenia research and obtain highly replicable disease-related subnetworks.

Leveraging the Adolescent Brain Cognitive Development Study to improve behavioral prediction from neuroimaging in smaller replication samples

Magnetic resonance imaging (MRI) is a popular and useful non-invasive method to map patterns of brain structure and function to complex human traits. Recently published observations in multiple large scale studies cast doubt upon these prospects, particularly for prediction of cognitive traits from structural and resting state functional MRI, which seems to account for little behavioral variability. We leverage baseline data from thousands of children in the Adolescent Brain Cognitive DevelopmentSM (ABCD®) Study to inform the replication sample size required with both univariate and multivariate methods across different imaging modalities to detect reproducible brain-behavior associations. We demonstrate that by applying multivariate methods to high-dimensional brain imaging data, we can capture lower dimensional patterns of structural and functional brain architecture that correlate robustly with cognitive phenotypes and are reproducible with only 41 individuals in the replication sample for working memory-related functional MRI, and ~100 subjects for structural MRI. Even with 100 random re-samplings of 50 subjects in the discovery sample, prediction can be adequately powered with 98 subjects in the replication sample for multivariate prediction of cognition with working memory task functional MRI. These results point to an important role for neuroimaging in translational neurodevelopmental research and showcase how findings in large samples can inform reproducible brain-behavior associations in small sample sizes that are at the heart of many investigators' research programs and grants.

Bayesian Spatial Blind Source Separation via the Thresholded Gaussian Process

Blind source separation (BSS) aims to separate latent source signals from their mixtures. For spatially dependent signals in high dimensional and large-scale data, such as neuroimaging, most existing BSS methods do not take into account the spatial dependence and the sparsity of the latent source signals. To address these major limitations, we propose a Bayesian spatial blind source separation (BSP-BSS) approach for neuroimaging data analysis. We assume the expectation of the observed images as a linear mixture of multiple sparse and piece-wise smooth latent source signals, for which we construct a new class of Bayesian nonparametric prior models by thresholding Gaussian processes. We assign the vMF priors to mixing coefficients in the model. Under some regularity conditions, we show that the proposed method has several desirable theoretical properties including the large support for the priors, the consistency of joint posterior distribution of the latent source intensity functions and the mixing coefficients, and the selection consistency on the number of latent sources. We use extensive simulation studies and an analysis of the resting-state fMRI data in the Autism Brain Imaging Data Exchange (ABIDE) study to demonstrate that BSP-BSS outperforms the existing method for separating latent brain networks and detecting activated brain activation in the latent sources.

An integrated cluster-wise significance measure for fMRI analysis

Cluster-wise inference is widely used in fMRI analysis. The cluster-level statistic is often obtained by counting the number of intra-cluster voxels which surpass a voxel-level statistical significance threshold. This measure can be sub-optimal regarding the power and false-positive error rate because the suprathreshold voxel count neglects the voxel-wise significance levels and ignores the dependence between voxels. This article aims to provide a new Integrated Cluster-wise significance Measure (ICM) for cluster-level significance determination in cluster-wise fMRI analysis by integrating cluster extent, voxel-level significance (e.g., p values), and activation dependence between within-cluster voxels. We develop a computationally efficient strategy for ICM based on probabilistic approximation theories. Consequently, the computational load for ICM-based cluster-wise inference (e.g., permutation tests) is affordable. We validate the proposed method via extensive simulations and then apply it to two fMRI data sets. The results demonstrate that ICM can improve the power with well-controlled family-wise error (FWE).

Evolutional Neural Architecture Search for Optimization of Spatiotemporal Brain Network Decomposition

Using deep neural networks (DNNs) to explore spatial patterns and temporal dynamics of human brain activities has been an important yet challenging problem because the artificial neural networks are hard to be designed manually. There have been several promising deep learning methods, e.g., deep belief network (DBN), convolutional neural network (CNN), and deep sparse recurrent auto-encoder (DSRAE), that can decompose neuroscientific and meaningful spatiotemporal patterns from 4D functional Magnetic Resonance Imaging (fMRI) data. However, those previous studies still depend on hand-crafted neural network architectures and hyperparameters, which are not optimal in various senses. In this paper, we employ the evolutionary algorithms (EA) to optimize the deep neural architecture of DSRAE by minimizing the expected loss of initialized models, named eNAS-DSRAE (evolutionary Neural Architecture Search on Deep Sparse Recurrent Auto-Encoder). Also, validation experiments are designed and performed on the publicly available human connectome project (HCP) 900 datasets, and the results achieved by the optimized eNAS-DSRAE suggested that our framework can successfully identify the spatiotemporal features and perform better than the hand-crafted neural network models. To our best knowledge, the proposed eNAS-DSRAE is not only among the earliest NAS models that can extract connectome-scale meaningful spatiotemporal brain networks from 4D fMRI data, but also is an effective framework to optimize the RNN-based models.

Bayes estimate of primary threshold in clusterwise functional magnetic resonance imaging inferences

Clusterwise statistical inference is the most widely used technique for functional magnetic resonance imaging (fMRI) data analyses. Clusterwise statistical inference consists of two steps: (i) primary thresholding that excludes less significant voxels by a prespecified cut-off (eg, p < . 001 ); and (ii) clusterwise thresholding that controls the familywise error rate caused by clusters consisting of false positive suprathreshold voxels. The selection of the primary threshold is critical because it determines both statistical power and false discovery rate (FDR). However, in most existing statistical packages, the primary threshold is selected based on prior knowledge (eg, p < . 001 ) without taking into account the information in the data. In this article, we propose a data-driven approach to algorithmically select the optimal primary threshold based on an empirical Bayes framework. We evaluate the proposed model using extensive simulation studies and real fMRI data. In the simulation, we show that our method can effectively increase statistical power by 20% to over 100% while effectively controlling the FDR. We then investigate the brain response to the dose-effect of chlorpromazine in patients with schizophrenia by analyzing fMRI scans and generate consistent results.

Simultaneous spatial-temporal decomposition for connectome-scale brain networks by deep sparse recurrent auto-encoder

Exploring the spatial patterns and temporal dynamics of human brain activity has been of great interest, in the quest to better understand connectome-scale brain networks. Though modeling spatial and temporal patterns of functional brain networks have been researched for a long time, the development of a unified and simultaneous spatial-temporal model has yet to be realized. For instance, although some deep learning methods have been proposed recently in order to model functional brain networks, most of them can only represent either spatial or temporal perspective of functional Magnetic Resonance Imaging (fMRI) data and rarely model both domains simultaneously. Due to the recent success in applying sequential auto-encoders for brain decoding, in this paper, we propose a deep sparse recurrent auto-encoder (DSRAE) to be applied unsupervised to learn spatial patterns and temporal fluctuations of brain networks at the same time. The proposed DSRAE was evaluated and validated based on three tasks of the publicly available Human Connectome Project (HCP) fMRI dataset, resulting with promising evidence. To the best of our knowledge, the proposed DSRAE is among the early efforts in developing unified models that can extract connectome-scale spatial-temporal networks from 4D fMRI data simultaneously.

Bayesian modeling of dependence in brain connectivity data

Brain connectivity studies often refer to brain areas as graph nodes and connections between nodes as edges, and aim to identify neuropsychiatric phenotype-related connectivity patterns. When performing group-level brain connectivity alternation analyses, it is critical to model the dependence structure between multivariate connectivity edges to achieve accurate and efficient estimates of model parameters. However, specifying and estimating dependencies between connectivity edges presents formidable challenges because (i) the dimensionality of parameters in the covariance matrix is high (of the order of the fourth power of the number of nodes); (ii) the covariance between a pair of edges involves four nodes with spatial location information; and (iii) the dependence structure between edges can be related to unknown network topological structures. Existing methods for large covariance/precision matrix regularization and spatial closeness-based dependence structure specification/estimation models may not fully address the complexity and challenges. We develop a new Bayesian nonparametric model that unifies information from brain network areas (nodes), connectivity (edges), and covariance between edges by constructing the function of covariance matrix based on the underlying network topological structure. We perform parameter estimation using an efficient Markov chain Monte Carlo algorithm. We apply our method to resting-state functional magnetic resonance imaging data from 60 subjects of a schizophrenia study and simulated data to demonstrate the performance of our method.

Spatial and spatio-temporal statistical analyses of retinal images: a review of methods and applications

Background

Clinical research and management of retinal diseases greatly depend on the interpretation of retinal images and often longitudinally collected images. Retinal images provide context for spatial data, namely the location of specific pathologies within the retina. Longitudinally collected images can show how clinical events at one point can affect the retina over time. In this review, we aimed to assess statistical approaches to spatial and spatio-temporal data in retinal images. We also review the spatio-temporal modelling approaches used in other medical image types.

Methods

We conducted a comprehensive literature review of both spatial or spatio-temporal approaches and non-spatial approaches to the statistical analysis of retinal images. The key methodological and clinical characteristics of published papers were extracted. We also investigated whether clinical variables and spatial correlation were accounted for in the analysis.

Results

Thirty-four papers that included retinal imaging data were identified for full-text information extraction. Only 11 (32.4%) papers used spatial or spatio-temporal statistical methods to analyse images, others (23 papers, 67.6%) used non-spatial methods. Twenty-eight (82.4%) papers reported images collected cross-sectionally, while 6 (17.6%) papers reported analyses on images collected longitudinally. In imaging areas outside of ophthalmology, 19 papers were identified with spatio-temporal analysis, and multiple statistical methods were recorded.

Conclusions

In future statistical analyses of retinal images, it will be beneficial to clearly define and report the spatial distributions studied, report the spatial correlations, combine imaging data with clinical variables into analysis if available, and clearly state the software or packages used.

Fighting or embracing multiplicity in neuroimaging? neighborhood leverage versus global calibration

Neuroimaging faces the daunting challenge of multiple testing - an instance of multiplicity - that is associated with two other issues to some extent: low inference efficiency and poor reproducibility. Typically, the same statistical model is applied to each spatial unit independently in the approach of massively univariate modeling. In dealing with multiplicity, the general strategy employed in the field is the same regardless of the specifics: trust the local "unbiased" effect estimates while adjusting the extent of statistical evidence at the global level. However, in this approach, modeling efficiency is compromised because each spatial unit (e.g., voxel, region, matrix element) is treated as an isolated and independent entity during massively univariate modeling. In addition, the required step of multiple testing "correction" by taking into consideration spatial relatedness, or neighborhood leverage, can only partly recoup statistical efficiency, resulting in potentially excessive penalization as well as arbitrariness due to thresholding procedures. Moreover, the assigned statistical evidence at the global level heavily relies on the data space (whole brain or a small volume). The present paper reviews how Stein's paradox (1956) motivates a Bayesian multilevel (BML) approach that, rather than fighting multiplicity, embraces it to our advantage through a global calibration process among spatial units. Global calibration is accomplished via a Gaussian distribution for the cross-region effects whose properties are not a priori specified, but a posteriori determined by the data at hand through the BML model. Our framework therefore incorporates multiplicity as integral to the modeling structure, not a separate correction step. By turning multiplicity into a strength, we aim to achieve five goals: 1) improve the model efficiency with a higher predictive accuracy, 2) control the errors of incorrect magnitude and incorrect sign, 3) validate each model relative to competing candidates, 4) reduce the reliance and sensitivity on the choice of data space, and 5) encourage full results reporting. Our modeling proposal reverberates with recent proposals to eliminate the dichotomization of statistical evidence ("significant" vs. "non-significant"), to improve the interpretability of study findings, as well as to promote reporting the full gamut of results (not only "significant" ones), thereby enhancing research transparency and reproducibility.

Detecting and Testing Altered Brain Connectivity Networks with K-partite Network Topology

Emerging brain connectivity network studies suggest that interactions between various distributed neuronal populations may be characterized by an organized complex topological structure. Many neuropsychiatric disorders are associated with altered topological patterns of brain connectivity. Therefore, a key inquiry of connectivity analysis is to detect group-level differentially expressed connectome patterns from the massive neuroimaging data. Recently, statistical methods have been developed to detect differentially expressed connectivity features at a subnetwork level, extending more commonly applied edge level analysis. However, the graph topological structures in these methods are limited to community/cliques which may not effectively uncover the underlying complex and disease-related brain circuits/subnetworks. Building on these previous subnetwork detection methods, a new statistical approach is developed to automatically identify the latent differentially expressed brain connectivity subnetworks with k-partite graph topological structures from large brain connectivity matrices. In addition, statistical inferential techniques are provided to test the detected topological structure. The new methods are evaluated via extensive simulation studies and then applied to resting state fMRI data (24 cases and 18 controls) for Parkinson's disease research. A differentially expressed connectivity network with the k-partite graph topological structure is detected which reveals underlying neural features distinguishing Parkinson's disease patients from healthy control subjects.

Copula-based semiparametric models for spatiotemporal data

The joint analysis of spatial and temporal processes poses computational challenges due to the data's high dimensionality. Furthermore, such data are commonly non-Gaussian. In this paper, we introduce a copula-based spatiotemporal model for analyzing spatiotemporal data and propose a semiparametric estimator. The proposed algorithm is computationally simple, since it models the marginal distribution and the spatiotemporal dependence separately. Instead of assuming a parametric distribution, the proposed method models the marginal distributions nonparametrically and thus offers more flexibility. The method also provides a convenient way to construct both point and interval predictions at new times and locations, based on the estimated conditional quantiles. Through a simulation study and an analysis of wind speeds observed along the border between Oregon and Washington, we show that our method produces more accurate point and interval predictions for skewed data than those based on normality assumptions.

A TESTING BASED APPROACH TO THE DISCOVERY OF DIFFERENTIALLY CORRELATED VARIABLE SETS

Given data obtained under two sampling conditions, it is often of interest to identify variables that behave differently in one condition than in the other. We introduce a method for differential analysis of second-order behavior called Differential Correlation Mining (DCM). The DCM method identifies differentially correlated sets of variables, with the property that the average pairwise correlation between variables in a set is higher under one sample condition than the other. DCM is based on an iterative search procedure that adaptively updates the size and elements of a candidate variable set. Updates are performed via hypothesis testing of individual variables, based on the asymptotic distribution of their average differential correlation. We investigate the performance of DCM by applying it to simulated data as well as to recent experimental datasets in genomics and brain imaging.

STGP: Spatio-temporal Gaussian process models for longitudinal neuroimaging data

Longitudinal neuroimaging data plays an important role in mapping the neural developmental profile of major neuropsychiatric and neurodegenerative disorders and normal brain. The development of such developmental maps is critical for the prevention, diagnosis, and treatment of many brain-related diseases. The aim of this paper is to develop a spatio-temporal Gaussian process (STGP) framework to accurately delineate the developmental trajectories of brain structure and function, while achieving better prediction by explicitly incorporating the spatial and temporal features of longitudinal neuroimaging data. Our STGP integrates a functional principal component model (FPCA) and a partition parametric space-time covariance model to capture the medium-to-large and small-to-medium spatio-temporal dependence structures, respectively. We develop a three-stage efficient estimation procedure as well as a predictive method based on a kriging technique. Two key novelties of STGP are that it can efficiently use a small number of parameters to capture complex non-stationary and non-separable spatio-temporal dependence structures and that it can accurately predict spatio-temporal changes. We illustrate STGP using simulated data sets and two real data analyses including longitudinal positron emission tomography data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) and longitudinal lateral ventricle surface data from a longitudinal study of early brain development.

A Bayesian hierarchical framework for modeling brain connectivity for neuroimaging data

We propose a novel Bayesian hierarchical model for brain imaging data that unifies voxel-level (the most localized unit of measure) and region-level brain connectivity analyses, and yields population-level inferences. Functional connectivity generally refers to associations in brain activity between distinct locations. The first level of our model summarizes brain connectivity for cross-region voxel pairs using a two-component mixture model consisting of connected and nonconnected voxels. We use the proportion of connected voxel pairs to define a new measure of connectivity strength, which reflects the breadth of between-region connectivity. Furthermore, we evaluate the impact of clinical covariates on connectivity between region-pairs at a population level. We perform parameter estimation using Markov chain Monte Carlo (MCMC) techniques, which can be executed quickly relative to the number of model parameters. We apply our method to resting-state functional magnetic resonance imaging (fMRI) data from 32 subjects with major depression and simulated data to demonstrate the properties of our method.

Quantification of the statistical effects of spatiotemporal processing of nontask FMRI data

Nontask functional magnetic resonance imaging (fMRI) has become one of the most popular noninvasive areas of brain mapping research for neuroscientists. In nontask fMRI, various sources of "noise" corrupt the measured blood oxygenation level-dependent signal. Many studies have aimed to attenuate the noise in reconstructed voxel measurements through spatial and temporal processing operations. While these solutions make the data more "appealing," many commonly used processing operations induce artificial correlations in the acquired data. As such, it becomes increasingly more difficult to derive the true underlying covariance structure once the data have been processed. As the goal of nontask fMRI studies is to determine, utilize, and analyze the true covariance structure of acquired data, such processing can lead to inaccurate and misleading conclusions drawn from the data if they are unaccounted for in the final connectivity analysis. In this article, we develop a framework that represents the spatiotemporal processing and reconstruction operations as linear operators, providing a means of precisely quantifying the correlations induced or modified by such processing rather than by performing lengthy Monte Carlo simulations. A framework of this kind allows one to appropriately model the statistical properties of the processed data, optimize the data processing pipeline, characterize excessive processing, and draw more accurate functional connectivity conclusions.

SGPP: spatial Gaussian predictive process models for neuroimaging data

The aim of this paper is to develop a spatial Gaussian predictive process (SGPP) framework for accurately predicting neuroimaging data by using a set of covariates of interest, such as age and diagnostic status, and an existing neuroimaging data set. To achieve a better prediction, we not only delineate spatial association between neuroimaging data and covariates, but also explicitly model spatial dependence in neuroimaging data. The SGPP model uses a functional principal component model to capture medium-to-long-range (or global) spatial dependence, while SGPP uses a multivariate simultaneous autoregressive model to capture short-range (or local) spatial dependence as well as cross-correlations of different imaging modalities. We propose a three-stage estimation procedure to simultaneously estimate varying regression coefficients across voxels and the global and local spatial dependence structures. Furthermore, we develop a predictive method to use the spatial correlations as well as the cross-correlations by employing a cokriging technique, which can be useful for the imputation of missing imaging data. Simulation studies and real data analysis are used to evaluate the prediction accuracy of SGPP and show that SGPP significantly outperforms several competing methods, such as voxel-wise linear model, in prediction. Although we focus on the morphometric variation of lateral ventricle surfaces in a clinical study of neurodevelopment, it is expected that SGPP is applicable to other imaging modalities and features.

Massively parallel nonparametric regression, with an application to developmental brain mapping

We propose a penalized spline approach to performing large numbers of parallel non-parametric analyses of either of two types: restricted likelihood ratio tests of a parametric regression model versus a general smooth alternative, and nonparametric regression. Compared with naïvely performing each analysis in turn, our techniques reduce computation time dramatically. Viewing the large collection of scatterplot smooths produced by our methods as functional data, we develop a clustering approach to summarize and visualize these results. Our approach is applicable to ultra-high-dimensional data, particularly data acquired by neuroimaging; we illustrate it with an analysis of developmental trajectories of functional connectivity at each of approximately 70000 brain locations. Supplementary materials, including an appendix and an R package, are available online.

Spatial-temporal modelling of fMRI data through spatially regularized mixture of hidden process models

Previous work investigated a range of spatio-temporal constraints for fMRI data analysis to provide robust detection of neural activation. We present a mixture-based method for the spatio-temporal modelling of fMRI data. This approach assumes that fMRI time series are generated by a probabilistic superposition of a small set of spatio-temporal prototypes (mixture components). Each prototype comprises a temporal model that explains fMRI signals on a single voxel and the model's "region of influence" through a spatial prior over the voxel space. As the key ingredient of our temporal model, the Hidden Process Model (HPM) framework proposed in Hutchinson et al. (2009) is adopted to infer the overlapping cognitive processes triggered by stimuli. Unlike the original HPM framework, we use a parametric model of Haemodynamic Response Function (HRF) so that biological constraints are naturally incorporated in the HRF estimation. The spatial priors are defined in terms of a parameterised distribution. Thus, the total number of parameters in the model does not depend on the number of voxels. The resulting model provides a conceptually principled and computationally efficient approach to identify spatio-temporal patterns of neural activation from fMRI data, in contrast to most conventional approaches in the literature focusing on the detection of spatial patterns. We first verify the proposed model in a controlled experimental setting using synthetic data. The model is further validated on real fMRI data obtained from a rapid event-related visual recognition experiment (Mayhew et al., 2012). Our model enables us to evaluate in a principled manner the variability of neural activations within individual regions of interest (ROIs). The results strongly suggest that, compared with occipitotemporal regions, the frontal ones are less homogeneous, requiring two HPM prototypes per region. Despite the rapid event-related experimental design, the model is capable of disentangling the perceptual judgement and motor response processes that are both activated in the frontal ROIs. Spatio-temporal heterogeneity in the frontal regions seems to be associated with diverse dynamic localizations of the two hidden processes in different subregions of frontal ROIs.

Brain Imaging Analysis

The increasing availability of brain imaging technologies has led to intense neuroscientific inquiry into the human brain. Studies often investigate brain function related to emotion, cognition, language, memory, and numerous other externally induced stimuli as well as resting-state brain function. Studies also use brain imaging in an attempt to determine the functional or structural basis for psychiatric or neurological disorders and, with respect to brain function, to further examine the responses of these disorders to treatment. Neuroimaging is a highly interdisciplinary field, and statistics plays a critical role in establishing rigorous methods to extract information and to quantify evidence for formal inferences. Neuroimaging data present numerous challenges for statistical analysis, including the vast amounts of data collected from each individual and the complex temporal and spatial dependence present. We briefly provide background on various types of neuroimaging data and analysis objectives that are commonly targeted in the field. We present a survey of existing methods targeting these objectives and identify particular areas offering opportunities for future statistical contribution.

Voxelwise multivariate analysis of multimodality magnetic resonance imaging

Most brain magnetic resonance imaging (MRI) studies concentrate on a single MRI contrast or modality, frequently structural MRI. By performing an integrated analysis of several modalities, such as structural, perfusion-weighted, and diffusion-weighted MRI, new insights may be attained to better understand the underlying processes of brain diseases. We compare two voxelwise approaches: (1) fitting multiple univariate models, one for each outcome and then adjusting for multiple comparisons among the outcomes and (2) fitting a multivariate model. In both cases, adjustment for multiple comparisons is performed over all voxels jointly to account for the search over the brain. The multivariate model is able to account for the multiple comparisons over outcomes without assuming independence because the covariance structure between modalities is estimated. Simulations show that the multivariate approach is more powerful when the outcomes are correlated and, even when the outcomes are independent, the multivariate approach is just as powerful or more powerful when at least two outcomes are dependent on predictors in the model. However, multiple univariate regressions with Bonferroni correction remain a desirable alternative in some circumstances. To illustrate the power of each approach, we analyze a case control study of Alzheimer's disease, in which data from three MRI modalities are available.

A Novel Support Vector Classifier for Longitudinal High-dimensional Data and Its Application to Neuroimaging Data

Recent technological advances have made it possible for many studies to collect high dimensional data (HDD) longitudinally, for example images collected during different scanning sessions. Such studies may yield temporal changes of selected features that, when incorporated with machine learning methods, are able to predict disease status or responses to a therapeutic treatment. Support vector machine (SVM) techniques are robust and effective tools well-suited for the classification and prediction of HDD. However, current SVM methods for HDD analysis typically consider cross-sectional data collected during one time period or session (e.g. baseline). We propose a novel support vector classifier (SVC) for longitudinal HDD that allows simultaneous estimation of the SVM separating hyperplane parameters and temporal trend parameters, which determine the optimal means to combine the longitudinal data for classification and prediction. Our approach is based on an augmented reproducing kernel function and uses quadratic programming for optimization. We demonstrate the use and potential advantages of our proposed methodology using a simulation study and a data example from the Alzheimer's disease Neuroimaging Initiative. The results indicate that our proposed method leverages the additional longitudinal information to achieve higher accuracy than methods using only cross-sectional data and methods that combine longitudinal data by naively expanding the feature space.