Meta Analysis of Functional Neuroimaging Data via Bayesian Spatial Point Processes

SPARTIN: a Bayesian method for the quantification and characterization of cell type interactions in spatial pathology data

Introduction: The acquisition of high-resolution digital pathology imaging data has sparked the development of methods to extract context-specific features from such complex data. In the context of cancer, this has led to increased exploration of the tumor microenvironment with respect to the presence and spatial composition of immune cells. Spatial statistical modeling of the immune microenvironment may yield insights into the role played by the immune system in the natural development of cancer as well as downstream therapeutic interventions. Methods: In this paper, we present SPatial Analysis of paRtitioned Tumor-Immune imagiNg (SPARTIN), a Bayesian method for the spatial quantification of immune cell infiltration from pathology images. SPARTIN uses Bayesian point processes to characterize a novel measure of local tumor-immune cell interaction, Cell Type Interaction Probability (CTIP). CTIP allows rigorous incorporation of uncertainty and is highly interpretable, both within and across biopsies, and can be used to assess associations with genomic and clinical features. Results: Through simulations, we show SPARTIN can accurately distinguish various patterns of cellular interactions as compared to existing methods. Using SPARTIN, we characterized the local spatial immune cell infiltration within and across 335 melanoma biopsies and evaluated their association with genomic, phenotypic, and clinical outcomes. We found that CTIP was significantly (negatively) associated with deconvolved immune cell prevalence scores including CD8+ T-Cells and Natural Killer cells. Furthermore, average CTIP scores differed significantly across previously established transcriptomic classes and significantly associated with survival outcomes. Discussion: SPARTIN provides a general framework for investigating spatial cellular interactions in high-resolution digital histopathology imaging data and its associations with patient level characteristics. The results of our analysis have potential implications relevant to both treatment and prognosis in the context of Skin Cutaneous Melanoma. The R-package for SPARTIN is available at https://github.com/bayesrx/SPARTIN along with a visualization tool for the images and results at: https://nateosher.github.io/SPARTIN.

The impact of sociality and affective valence on brain activation: A meta-analysis

Thirty years of neuroimaging reveal the set of brain regions consistently associated with pleasant and unpleasant affect in humans-or the neural reference space for valence. Yet some of humans' most potent affective states occur in the context of other humans. Prior work has yet to differentiate how the neural reference space for valence varies as a product of the sociality of affective stimuli. To address this question, we meta-analyzed across 614 social and non-social affective neuroimaging contrasts, summarizing the brain regions that are consistently activated for social and non-social affective information. We demonstrate that across the literature, social and non-social affective stimuli yield overlapping activations within regions associated with visceromotor control, including the amygdala, hypothalamus, anterior cingulate cortex and insula. However, we find that social processing differs from non-social affective processing in that it involves additional cortical activations in the medial prefrontal and posterior cingulum that have been associated with mentalizing and prediction. A Bayesian classifier was able to differentiate unpleasant from pleasant affect, but not social from non-social affective states. Moreover, it was not able to classify unpleasantness from pleasantness at the highest levels of sociality. These findings suggest that highly social scenarios may be equally salient to humans, regardless of their valence.

Online two-way estimation and inference via linear mixed-effects models

In this article, we tackle the estimation and inference problem of analyzing distributed streaming data that is collected continuously over multiple data sites. We propose an online two-way approach via linear mixed-effects models. We explicitly model the site-specific effects as random-effect terms, and tackle both between-site heterogeneity and within-site correlation. We develop an online updating procedure that does not need to re-access the previous data and can efficiently update the parameter estimate, when either new data sites, or new streams of sample observations of the existing data sites, become available. We derive the non-asymptotic error bound for our proposed online estimator, and show that it is asymptotically equivalent to the offline counterpart based on all the raw data. We compare with some key alternative solutions both analytically and numerically, and demonstrate the advantages of our proposal. We further illustrate our method with two data applications.

Spatial Statistical Models: An Overview under the Bayesian Approach

Spatial documentation is exponentially increasing given the availability of Big Data in the Internet of Things, enabled by device miniaturization and data storage capacity. Bayesian spatial statistics is a useful statistical tool to determine the dependence structure and hidden patterns in space through prior knowledge and data likelihood. However, this class of modeling is not yet well explored when compared to adopting classification and regression in machine-learning models, in which the assumption of the spatiotemporal independence of the data is often made, that is an inexistent or very weak dependence. Thus, this systematic review aims to address the main models presented in the literature over the past 20 years, identifying the gaps and research opportunities. Elements such as random fields, spatial domains, prior specification, the covariance function, and numerical approximations are discussed. This work explores the two subclasses of spatial smoothing: global and local.

Multivariate Temporal Point Process Regression

Point process modeling is gaining increasing attention, as point process type data are emerging in a large variety of scientific applications. In this article, motivated by a neuronal spike trains study, we propose a novel point process regression model, where both the response and the predictor can be a high-dimensional point process. We model the predictor effects through the conditional intensities using a set of basis transferring functions in a convolutional fashion. We organize the corresponding transferring coefficients in the form of a three-way tensor, then impose the low-rank, sparsity, and subgroup structures on this coefficient tensor. These structures help reduce the dimensionality, integrate information across different individual processes, and facilitate the interpretation. We develop a highly scalable optimization algorithm for parameter estimation. We derive the large sample error bound for the recovered coefficient tensor, and establish the subgroup identification consistency, while allowing the dimension of the multivariate point process to diverge. We demonstrate the efficacy of our method through both simulations and a cross-area neuronal spike trains analysis in a sensory cortex study.

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.

A Cortical Surface-Based Meta-Analysis of Human Reasoning

Recent advances in neuroimaging have augmented numerous findings in the human reasoning process but have yielded varying results. One possibility for this inconsistency is that reasoning is such an intricate cognitive process, involving attention, memory, executive functions, symbolic processing, and fluid intelligence, whereby various brain regions are inevitably implicated in orchestrating the process. Therefore, researchers have used meta-analyses for a better understanding of neural mechanisms of reasoning. However, previous meta-analysis techniques include weaknesses such as an inadequate representation of the cortical surface’s highly folded geometry. Accordingly, we developed a new meta-analysis method called Bayesian meta-analysis of the cortical surface (BMACS). BMACS offers a fast, accurate, and accessible inference of the spatial patterns of cognitive processes from peak brain activations across studies by applying spatial point processes to the cortical surface. Using BMACS, we found that the common pattern of activations from inductive and deductive reasoning was colocalized with the multiple-demand system, indicating that reasoning is a high-level convergence of complex cognitive processes. We hope surface-based meta-analysis will be facilitated by BMACS, bringing more profound knowledge of various cognitive processes.

Resting State Functional Connectivity of Brain With Electroconvulsive Therapy in Depression: Meta-Analysis to Understand Its Mechanisms

Introduction: Electroconvulsive therapy (ECT) is a commonly used brain stimulation treatment for treatment-resistant or severe depression. This study was planned to find the effects of ECT on brain connectivity by conducting a systematic review and coordinate-based meta-analysis of the studies performing resting state fMRI (rsfMRI) in patients with depression receiving ECT. Methods: We systematically searched the databases published up to July 31, 2020, for studies in patients having depression that compared resting-state functional connectivity (rsFC) before and after a course of pulse wave ECT. Meta-analysis was performed using the activation likelihood estimation method after extracting details about coordinates, voxel size, and method for correction of multiple comparisons corresponding to the significant clusters and the respective rsFC analysis measure with its method of extraction. Results: Among 41 articles selected for full-text review, 31 articles were included in the systematic review. Among them, 13 articles were included in the meta-analysis, and a total of 73 foci of 21 experiments were examined using activation likelihood estimation in 10 sets. Using the cluster-level interference method, one voxel-wise analysis with the measure of amplitude of low frequency fluctuations and one seed-voxel analysis with the right hippocampus showed a significant reduction (p < 0.0001) in the left cingulate gyrus (dorsal anterior cingulate cortex) and a significant increase (p < 0.0001) in the right hippocampus with the right parahippocampal gyrus, respectively. Another analysis with the studies implementing network-wise (posterior default mode network: dorsomedial prefrontal cortex) resting state functional connectivity showed a significant increase (p < 0.001) in bilateral posterior cingulate cortex. There was considerable variability as well as a few key deficits in the preprocessing and analysis of the neuroimages and the reporting of results in the included studies. Due to lesser studies, we could not do further analysis to address the neuroimaging variability and subject-related differences. Conclusion: The brain regions noted in this meta-analysis are reasonably specific and distinguished, and they had significant changes in resting state functional connectivity after a course of ECT for depression. More studies with better neuroimaging standards should be conducted in the future to confirm these results in different subgroups of depression and with varied aspects of ECT.

NeuroQuery, comprehensive meta-analysis of human brain mapping

Reaching a global view of brain organization requires assembling evidence on widely different mental processes and mechanisms. The variety of human neuroscience concepts and terminology poses a fundamental challenge to relating brain imaging results across the scientific literature. Existing meta-analysis methods perform statistical tests on sets of publications associated with a particular concept. Thus, large-scale meta-analyses only tackle single terms that occur frequently. We propose a new paradigm, focusing on prediction rather than inference. Our multivariate model predicts the spatial distribution of neurological observations, given text describing an experiment, cognitive process, or disease. This approach handles text of arbitrary length and terms that are too rare for standard meta-analysis. We capture the relationships and neural correlates of 7547 neuroscience terms across 13 459 neuroimaging publications. The resulting meta-analytic tool, neuroquery.org, can ground hypothesis generation and data-analysis priors on a comprehensive view of published findings on the brain.

False-positive neuroimaging: Undisclosed flexibility in testing spatial hypotheses allows presenting anything as a replicated finding

Hypothesis testing in neuroimaging studies relies heavily on treating named anatomical regions (e.g., "the amygdala") as unitary entities. Though data collection and analyses are conducted at the voxel level, inferences are often based on anatomical regions. The discrepancy between the unit of analysis and the unit of inference leads to ambiguity and flexibility in analyses that can create a false sense of reproducibility. For example, hypothesizing effects on "amygdala activity" does not provide a falsifiable and reproducible definition of precisely which voxels or which patterns of activation should be observed. Rather, it comprises a large number of unspecified sub-hypotheses, leaving room for flexible interpretation of findings, which we refer to as "model degrees of freedom." From a survey of 135 functional Magnetic Resonance Imaging studies in which researchers claimed replications of previous findings, we found that 42.2% of the studies did not report any quantitative evidence for replication such as activation peaks. Only 14.1% of the papers used exact coordinate-based or a priori pattern-based models. Of the studies that reported peak information, 42.9% of the 'replicated' findings had peak coordinates more than 15 mm away from the 'original' findings, suggesting that different brain locations were activated, even when studies claimed to replicate prior results. To reduce the flexible and qualitative region-level tests in neuroimaging studies, we recommend adopting quantitative spatial models and tests to assess the spatial reproducibility of findings. Techniques reviewed here include permutation tests on peak distance, Bayesian MANOVA, and a priori multivariate pattern-based models. These practices will help researchers to establish precise and falsifiable spatial hypotheses, promoting a cumulative science of neuroimaging.

Bayesian meta-analysis of fMRI image data

We composed an R-based script for Image-based Bayesian random-effect meta-analysis of previous fMRI studies. It meta-analyzes second-level test results of the studies and calculates Bayes Factors indicating whether the effect in each voxel is significantly different from zero. We compared results from Bayesian and classical meta-analyses by examining the overlap between the result from each method and that created by NeuroSynth as the target. As an example, we analyzed previous fMRI studies focusing on working memory extracted from NeuroSynth. The result from our Bayesian method showed a greater overlap than the classical method. In addition, Bayes Factors proved a better way to examine whether the evidence supported hypotheses than p-values. Given these, Bayesian meta-analysis provides neuroscientists with an alternative meta-analysis method for fMRI studies given the improved overlap with the NeuroSynth result and the practical and epistemological value of Bayes Factors that can directly test the presence of an effect.

Bayesian log-Gaussian Cox process regression: with applications to meta-analysis of neuroimaging working memory studies

Working memory (WM) was one of the first cognitive processes studied with functional magnetic resonance imaging (fMRI). With now over 20 years of studies on WM, each study with tiny sample sizes, there is a need for meta-analysis to identify the brain regions consistently activated by WM tasks, and to understand the inter-study variation in those activations. However, current methods in the field cannot fully account for the spatial nature of neuroimaging meta-analysis data or the heterogeneity observed among WM studies. In this work, we propose a fully Bayesian random-effects meta-regression model based on log-Gaussian Cox processes, which can be used for meta-analysis of neuroimaging studies. An efficient MCMC scheme for posterior simulations is presented which makes use of some recent advances in parallel computing using graphics processing units (GPUs). Application of the proposed model to a real dataset provides valuable insights regarding the function of the WM.

Assessing robustness against potential publication bias in Activation Likelihood Estimation (ALE) meta-analyses for fMRI

The importance of integrating research findings is incontrovertible and procedures for coordinate-based meta-analysis (CBMA) such as Activation Likelihood Estimation (ALE) have become a popular approach to combine results of fMRI studies when only peaks of activation are reported. As meta-analytical findings help building cumulative knowledge and guide future research, not only the quality of such analyses but also the way conclusions are drawn is extremely important. Like classical meta-analyses, coordinate-based meta-analyses can be subject to different forms of publication bias which may impact results and invalidate findings. The file drawer problem refers to the problem where studies fail to get published because they do not obtain anticipated results (e.g. due to lack of statistical significance). To enable assessing the stability of meta-analytical results and determine their robustness against the potential presence of the file drawer problem, we present an algorithm to determine the number of noise studies that can be added to an existing ALE fMRI meta-analysis before spatial convergence of reported activation peaks over studies in specific regions is no longer statistically significant. While methods to gain insight into the validity and limitations of results exist for other coordinate-based meta-analysis toolboxes, such as Galbraith plots for Multilevel Kernel Density Analysis (MKDA) and funnel plots and egger tests for seed-based d mapping, this procedure is the first to assess robustness against potential publication bias for the ALE algorithm. The method assists in interpreting meta-analytical results with the appropriate caution by looking how stable results remain in the presence of unreported information that may differ systematically from the information that is included. At the same time, the procedure provides further insight into the number of studies that drive the meta-analytical results. We illustrate the procedure through an example and test the effect of several parameters through extensive simulations. Code to generate noise studies is made freely available which enables users to easily use the algorithm when interpreting their results.

Voxel-based meta-analysis via permutation of subject images (PSI): Theory and implementation for SDM

Coordinate-based meta-analyses (CBMA) are very useful for summarizing the large number of voxel-based neuroimaging studies of normal brain functions and brain abnormalities in neuropsychiatric disorders. However, current CBMA methods do not conduct common voxelwise tests, but rather a test of convergence, which relies on some spatial assumptions that data may seldom meet, and has lower statistical power when there are multiple effects. Here we present a new algorithm that can use standard voxelwise tests and, importantly, conducts a standard permutation of subject images (PSI). Its main steps are: a) multiple imputation of study images; b) imputation of subject images; and c) subject-based permutation test to control the familywise error rate (FWER). The PSI algorithm is general and we believe that developers might implement it for several CBMA methods. We present here an implementation of PSI for seed-based d mapping (SDM) method, which additionally benefits from the use of effect sizes, random-effects models, Freedman-Lane-based permutations and threshold-free cluster enhancement (TFCE) statistics, among others. Finally, we also provide an empirical validation of the control of the FWER in SDM-PSI, which showed that it might be too conservative. We hope that the neuroimaging meta-analytic community will welcome this new algorithm and method.

Spatial Bayesian latent factor regression modeling of coordinate-based meta-analysis data

Now over 20 years old, functional MRI (fMRI) has a large and growing literature that is best synthesised with meta-analytic tools. As most authors do not share image data, only the peak activation coordinates (foci) reported in the article are available for Coordinate-Based Meta-Analysis (CBMA). Neuroimaging meta-analysis is used to (i) identify areas of consistent activation; and (ii) build a predictive model of task type or cognitive process for new studies (reverse inference). To simultaneously address these aims, we propose a Bayesian point process hierarchical model for CBMA. We model the foci from each study as a doubly stochastic Poisson process, where the study-specific log intensity function is characterized as a linear combination of a high-dimensional basis set. A sparse representation of the intensities is guaranteed through latent factor modeling of the basis coefficients. Within our framework, it is also possible to account for the effect of study-level covariates (meta-regression), significantly expanding the capabilities of the current neuroimaging meta-analysis methods available. We apply our methodology to synthetic data and neuroimaging meta-analysis datasets.

The coordinate-based meta-analysis of neuroimaging data

Neuroimaging meta-analysis is an area of growing interest in statistics. The special characteristics of neuroimaging data render classical meta-analysis methods inapplicable and therefore new methods have been developed. We review existing methodologies, explaining the benefits and drawbacks of each. A demonstration on a real dataset of emotion studies is included. We discuss some still-open problems in the field to highlight the need for future research.

Characterizing cross-subject spatial interaction patterns in functional magnetic resonance imaging studies: A two-stage point-process model

We develop a two-stage spatial point process model that introduces new characterizations of activation patterns in multisubject functional Magnetic Resonance Imaging (fMRI) studies. Conventionally multisubject fMRI methods rely on combining information across subjects one voxel at a time in order to identify locations of peak activation in the brain. The two-stage model that we develop here addresses shortcomings of standard methods by explicitly modeling the spatial structure of functional signals and recognizing that corresponding cross-subject functional signals can be spatially misaligned. In our first stage analysis, we introduce a marked spatial point process model that captures the spatial features of the functional response and identifies a configuration of activation units for each subject. The locations of these activation units are used as input for the second stage model. The point process model of the second stage analysis is developed to characterize multisubject activation patterns by estimating the strength of cross-subject interactions at different spatial ranges. The model uses spatial neighborhoods to account for the cross-subject spatial misalignment in corresponding functional units. We applied our methods to an fMRI study of 21 individuals who performed an attention test. We identified four brain regions that are involved in the test and found that our model results agree well with our understanding of how these regions engage with the tasks performed during the attention test. Our results highlighted that cross-subject interactions are stronger in brain areas that have a more specific function in performing the experimental tasks than in other areas.

Bayesian Computation for Log-Gaussian Cox Processes: A Comparative Analysis of Methods

The Log-Gaussian Cox Process is a commonly used model for the analysis of spatial point pattern data. Fitting this model is difficult because of its doubly-stochastic property, i.e., it is an hierarchical combination of a Poisson process at the first level and a Gaussian Process at the second level. Various methods have been proposed to estimate such a process, including traditional likelihood-based approaches as well as Bayesian methods. We focus here on Bayesian methods and several approaches that have been considered for model fitting within this framework, including Hamiltonian Monte Carlo, the Integrated nested Laplace approximation, and Variational Bayes. We consider these approaches and make comparisons with respect to statistical and computational efficiency. These comparisons are made through several simulation studies as well as through two applications, the first examining ecological data and the second involving neuroimaging data.

Identifying Activation Centers with Spatial Cox Point Processes Using fMRI Data

We developed a Bayesian clustering method to identify significant regions of brain activation. Coordinate-based meta data originating from functional magnetic resonance imaging (fMRI) were of primary interest. Individual fMRI has the ability to measure the intensity of blood flow and oxygen to a location within the brain that was activated by a given thought or emotion. The proposed method performed clustering on two levels, latent foci center and study activation center, with a spatial Cox point process utilizing the Dirichlet process to describe the distribution of foci. Intensity was modeled as a function of distance between the focus and the center of the cluster of foci using a Gaussian kernel. Simulation studies were conducted to evaluate the sensitivity and robustness of the method with respect to cluster identification and underlying data distributions. We applied the method to a meta data set to identify emotion foci centers.

Involvement of Sensory Regions in Affective Experience: A Meta-Analysis

A growing body of work suggests that sensory processes may also contribute to affective experience. In this study, we performed a meta-analysis of affective experiences driven through visual, auditory, olfactory, gustatory, and somatosensory stimulus modalities including study contrasts that compared affective stimuli to matched neutral control stimuli. We found, first, that limbic and paralimbic regions, including the amygdala, anterior insula, pre-supplementary motor area, and portions of orbitofrontal cortex were consistently engaged across two or more modalities. Second, early sensory input regions in occipital, temporal, piriform, mid-insular, and primary sensory cortex were frequently engaged during affective experiences driven by visual, auditory, olfactory, gustatory, and somatosensory inputs. A classification analysis demonstrated that the pattern of neural activity across a contrast map diagnosed the stimulus modality driving the affective experience. These findings suggest that affective experiences are constructed from activity that is distributed across limbic and paralimbic brain regions and also activity in sensory cortical regions.

A Bayesian model of category-specific emotional brain responses

Understanding emotion is critical for a science of healthy and disordered brain function, but the neurophysiological basis of emotional experience is still poorly understood. We analyzed human brain activity patterns from 148 studies of emotion categories (2159 total participants) using a novel hierarchical Bayesian model. The model allowed us to classify which of five categories--fear, anger, disgust, sadness, or happiness--is engaged by a study with 66% accuracy (43-86% across categories). Analyses of the activity patterns encoded in the model revealed that each emotion category is associated with unique, prototypical patterns of activity across multiple brain systems including the cortex, thalamus, amygdala, and other structures. The results indicate that emotion categories are not contained within any one region or system, but are represented as configurations across multiple brain networks. The model provides a precise summary of the prototypical patterns for each emotion category, and demonstrates that a sufficient characterization of emotion categories relies on (a) differential patterns of involvement in neocortical systems that differ between humans and other species, and (b) distinctive patterns of cortical-subcortical interactions. Thus, these findings are incompatible with several contemporary theories of emotion, including those that emphasize emotion-dedicated brain systems and those that propose emotion is localized primarily in subcortical activity. They are consistent with componential and constructionist views, which propose that emotions are differentiated by a combination of perceptual, mnemonic, prospective, and motivational elements. Such brain-based models of emotion provide a foundation for new translational and clinical approaches.

Bayesian Models for fMRI Data Analysis

Functional magnetic resonance imaging (fMRI), a noninvasive neuroimaging method that provides an indirect measure of neuronal activity by detecting blood flow changes, has experienced an explosive growth in the past years. Statistical methods play a crucial role in understanding and analyzing fMRI data. Bayesian approaches, in particular, have shown great promise in applications. A remarkable feature of fully Bayesian approaches is that they allow a flexible modeling of spatial and temporal correlations in the data. This paper provides a review of the most relevant models developed in recent years. We divide methods according to the objective of the analysis. We start from spatio-temporal models for fMRI data that detect task-related activation patterns. We then address the very important problem of estimating brain connectivity. We also touch upon methods that focus on making predictions of an individual's brain activity or a clinical or behavioral response. We conclude with a discussion of recent integrative models that aim at combining fMRI data with other imaging modalities, such as EEG/MEG and DTI data, measured on the same subjects. We also briefly discuss the emerging field of imaging genetics.

Functional Specialization and Flexibility in Human Association Cortex

The association cortex supports cognitive functions enabling flexible behavior. Here, we explored the organization of human association cortex by mathematically formalizing the notion that a behavioral task engages multiple cognitive components, which are in turn supported by multiple overlapping brain regions. Application of the model to a large data set of neuroimaging experiments (N = 10 449) identified complex zones of frontal and parietal regions that ranged from being highly specialized to highly flexible. The network organization of the specialized and flexible regions was explored with an independent resting-state fMRI data set (N = 1000). Cortical regions specialized for the same components were strongly coupled, suggesting that components function as partially isolated networks. Functionally flexible regions participated in multiple components to different degrees. This heterogeneous selectivity was predicted by the connectivity between flexible and specialized regions. Functionally flexible regions might support binding or integrating specialized brain networks that, in turn, contribute to the ability to execute multiple and varied tasks.

Coordinate based meta-analysis of functional neuroimaging data using activation likelihood estimation; full width half max and group comparisons

Coordinate based meta-analysis (CBMA) is used to find regions of consistent activation across fMRI and PET studies selected for their functional relevance to a hypothesis. Results are clusters of foci where multiple studies report in the same spatial region, indicating functional relevance. Contrast meta-analysis finds regions where there are consistent differences in activation pattern between two groups. The activation likelihood estimate methods tackle these problems, but require a specification of uncertainty in foci location: the full width half max (FWHM). Results are sensitive to FWHM. Furthermore, contrast meta-analysis requires correction for multiple statistical tests. Consequently it is sensitive only to very significant localised differences that produce very small p-values, which remain significant after correction; subtle diffuse differences between the groups can be overlooked. In this report we redefine the FWHM parameter, by analogy with a density clustering algorithm, and provide a method to estimate it. The FWHM is modified to account for the number of studies in the analysis, and represents a substantial change to the CBMA philosophy that can be applied to the current algorithms. Consequently we observe more reliable detection of clusters when there are few studies in the CBMA, and a decreasing false positive rate with larger study numbers. By contrast the standard definition (FWHM independent of the number of studies) is demonstrated to paradoxically increase the false positive rate as the number of studies increases, while reducing ability to detect true clusters for small numbers of studies. We also provide an algorithm for contrast meta-analysis, which includes a correction for multiple correlated tests that controls for the proportion of false clusters expected under the null hypothesis. Furthermore, we detail an omnibus test of difference between groups that is more sensitive than contrast meta-analysis when differences are diffuse. This test is useful where contrast meta-analysis is unrevealing.

Identifying functional co-activation patterns in neuroimaging studies via poisson graphical models

Studying the interactions between different brain regions is essential to achieve a more complete understanding of brain function. In this article, we focus on identifying functional co-activation patterns and undirected functional networks in neuroimaging studies. We build a functional brain network, using a sparse covariance matrix, with elements representing associations between region-level peak activations. We adopt a penalized likelihood approach to impose sparsity on the covariance matrix based on an extended multivariate Poisson model. We obtain penalized maximum likelihood estimates via the expectation-maximization (EM) algorithm and optimize an associated tuning parameter by maximizing the predictive log-likelihood. Permutation tests on the brain co-activation patterns provide region pair and network-level inference. Simulations suggest that the proposed approach has minimal biases and provides a coverage rate close to 95% of covariance estimations. Conducting a meta-analysis of 162 functional neuroimaging studies on emotions, our model identifies a functional network that consists of connected regions within the basal ganglia, limbic system, and other emotion-related brain regions. We characterize this network through statistical inference on region-pair connections as well as by graph measures.

REGULARIZED 3D FUNCTIONAL REGRESSION FOR BRAIN IMAGE DATA VIA HAAR WAVELETS

The primary motivation and application in this article come from brain imaging studies on cognitive impairment in elderly subjects with brain disorders. We propose a regularized Haar wavelet-based approach for the analysis of three-dimensional brain image data in the framework of functional data analysis, which automatically takes into account the spatial information among neighboring voxels. We conduct extensive simulation studies to evaluate the prediction performance of the proposed approach and its ability to identify related regions to the outcome of interest, with the underlying assumption that only few relatively small subregions are truly predictive of the outcome of interest. We then apply the proposed approach to searching for brain subregions that are associated with cognition using PET images of patients with Alzheimer's disease, patients with mild cognitive impairment, and normal controls.

Group-wise FMRI activation detection on DICCCOL landmarks

Group-wise activation detection in task-based fMRI has been widely used because of its robustness to noises and its capacity to deal with variability of individual brains. However, current group-wise fMRI activation detection methods typically rely on the co-registration of individual brains' fMRI images, which has difficulty in dealing with the remarkable anatomic variation of different brains. As a consequence, the resulted misalignments could significantly degrade the required inter-subject correspondences, thus substantially reducing the sensitivity and specificity of group-wise fMRI activation detection. To deal with these challenges, this paper presents a novel approach to detecting group-wise fMRI activation on our recently developed and validated Dense Individualized and Common Connectivity-based Cortical Landmarks (DICCCOL). The basic idea here is that the first-level general linear model (GLM) analysis is first performed on the fMRI signal of each corresponding DICCCOL landmark in individual brain's own space, and then the estimated effect sizes of the same landmark from a group of subjects are statistically assessed with the mixed-effect model at the group level. Finally, the consistently activated DICCCOL landmarks are determined and declared in a group-wise fashion in response to external block-based stimuli. Our experimental results have demonstrated that the proposed approach can detect meaningful activations.

Cluster-extent based thresholding in fMRI analyses: pitfalls and recommendations

Cluster-extent based thresholding is currently the most popular method for multiple comparisons correction of statistical maps in neuroimaging studies, due to its high sensitivity to weak and diffuse signals. However, cluster-extent based thresholding provides low spatial specificity; researchers can only infer that there is signal somewhere within a significant cluster and cannot make inferences about the statistical significance of specific locations within the cluster. This poses a particular problem when one uses a liberal cluster-defining primary threshold (i.e., higher p-values), which often produces large clusters spanning multiple anatomical regions. In such cases, it is impossible to reliably infer which anatomical regions show true effects. From a survey of 814 functional magnetic resonance imaging (fMRI) studies published in 2010 and 2011, we show that the use of liberal primary thresholds (e.g., p<.01) is endemic, and that the largest determinant of the primary threshold level is the default option in the software used. We illustrate the problems with liberal primary thresholds using an fMRI dataset from our laboratory (N=33), and present simulations demonstrating the detrimental effects of liberal primary thresholds on false positives, localization, and interpretation of fMRI findings. To avoid these pitfalls, we recommend several analysis and reporting procedures, including 1) setting primary p<.001 as a default lower limit; 2) using more stringent primary thresholds or voxel-wise correction methods for highly powered studies; and 3) adopting reporting practices that make the level of spatial precision transparent to readers. We also suggest alternative and supplementary analysis methods.

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.

Spatial Bayesian Variable Selection Models on Functional Magnetic Resonance Imaging Time-Series Data

A common objective of fMRI (functional magnetic resonance imaging) studies is to determine subject-specific areas of increased blood oxygenation level dependent (BOLD) signal contrast in response to a stimulus or task, and hence to infer regional neuronal activity. We posit and investigate a Bayesian approach that incorporates spatial and temporal dependence and allows for the task-related change in the BOLD signal to change dynamically over the scanning session. In this way, our model accounts for potential learning effects in addition to other mechanisms of temporal drift in task-related signals. We study the properties of the model through its performance on simulated and real data sets.

Multiple testing corrections, nonparametric methods, and random field theory

I provide a selective review of the literature on the multiple testing problem in fMRI. By drawing connections with the older modalities, PET in particular, and how software implementations have tracked (or lagged behind) theoretical developments, my narrative aims to give the methodological researcher a historical perspective on this important aspect of fMRI data analysis.

The future of functional MRI in clinical medicine

In the last 20 years or so, functional MRI has matured very rapidly from being an experimental imaging method in the hands of a few labs to being a very widely available and widely used workhorse of cognitive neuroscience and clinical neuroscience research internationally. FMRI studies have had a considerable impact on our understanding of brain system phenotypes of neurological and psychiatric disorders; and some impact already on development of new therapeutics. However, the direct benefit of fMRI to individual patients with brain disorders has so far been minimal. Here I provide a personal perspective on what has already been achieved, and imagine how the further development of fMRI over the medium term might lead to even greater engagement with clinical medicine.