Authored by Runa Bhaumik*
Abstract
Aberrant activities in the complex human brain network can lead to various neurological disorders such as multiple sclerosis, Parkinson’s disease, Alzheimer’s disease and Autism Spectrum Disorder (ASD). Functional Magnetic Resonance Imaging (fMRI) has emerged as an important tool to delineate the neural networks affected by such diseases, particularly ASD. In seeking for earlier diagnosis, we aimed to find biomarkers through the analysis of resting state fMRI images. In this article, we present a holistic approach to detect disrupted connectivities in whole brain studies. Our meta analytic approach addresses multidimensional heterogeneities in the context of multiple ROIs borrowing strength from all sites. Results are illustrated with a large data set known as Autism Brain Imaging Data Exchange (ABIDE), which includes 361 subjects from eight medical centers. Our results are consistent with previous studies in Autism research. These interrupted regions are involved in language processing, social cognition, auditory effect on social communication which are associated with ASD. We believe that our findings have addressed the variations due to different hierarchies and thus lead to more reliable identification of therapeutic targets for intervention. Our disciplined study can be used for early detection of subjects who are at a higher risk of developing neurological disorders.
Keywords: Functional magnetic resonance imaging; Meta-analysis; Mixed-effects; False discovery rate; Hierarchical designs.
Abbreviations: ABIDE: Autism Brain Imaging Data Exchange; fMRI: Functional Magnetic Resonance Imaging; ASD: Autism Spectrum Disorder; TBI: Traumatic Brain Injury; ROI: Region of Interest; FDR: False Discovery Rate; INDI: International Neuroimaging Data-Sharing Initiative
Introduction
The area of neurological disease research requires adequate statistical inferential methods appropriate for addressing unique aspects of neuroimaging data. In neural connectivity research, we detect disrupted connectivities for targeting treatment interventions for therapeutic benefit. A detailed understanding of how brains with neurological conditions (e.g. autism, depression, traumatic brain injury (TBI) etc.) differ from healthy brains is fundamental to the development of treatments for these conditions. Disrupted network connectivity between distant brain regions has been reported among individuals with ASD [1-5]. These reports showed both increased and decreased connectivities in brain regions including default mode network, social brain regions, attentional regions, visual search regions and corticostriatal connections. However, knowing the specificity of diagnosis criteria (American Psychiatric Association 2013), there is hope that some (possibly complex) patterns of brain features may be unique to the disorder and it is worth to continue the research.
The primary goal of psychiatric neuroimaging research is to identify objective biomarkers that may inform the diagnosis and treatment of brain-based disorders. Data-intensive machine learning methods are a promising tool for investigating the replicability of patterns of brain function across larger, more heterogeneous data sets Varoquaux and Thirion, (2014). Several studies have shown that data-intensive machine learning methods are a promising tool for identification of objective biomarkers. They have used a brain imaging data from a worldwide multi-site database known as ABIDE (Autism Brain Imaging Data Exchange), where data gathered across different scanners, with different field strengths and different acquisition schemes [5-7]. These studies revealed that acquisition site has significant effects on image properties. To alleviate the problem of between site variation, several studies [3,6,8,9] applied domain adaptation machine learning algorithms to classify ASDs from HCs using cross-site evaluation strategy.
In this article, we propose a meta analytic approach utilizing mixed-effects model to detect disrupted connectivities by controlling the false discovery rate (FDR) for better confidence in a group comparison study at the region of interest (ROI) level using data from multiple independent studies.
Functional connectivity of ROIs is generally measured by the Pearson correlation coefficient, and a disrupted connectivity is detected by a t-test in a group comparison study while comparing a link (connection between two ROIs) of a neurological condition group with the corresponding link of a healthy control group. However, when a large number of ROIs is involved in such studies, the problem becomes challenging as ROIs nested within the same brain are expected to be correlated, and an adjustment of the type I error rate becomes necessary in order to control the false discoveries. In our previous research, mixed-effects models have been used to address within-subject and between-group heterogeneities [10]. These models had three important features. First, it addressed the within-subject correlations resulting from subject-specific links nested within the same brain. Second, unlike previous mixed-effects approaches as described in [11-14], we did not assume equal variance among the autism and control groups and across links. Our assumption of unequal variances addressed both within-subject and between-group variability in the model. Third, our model compared two groups not at the global level, but at the local level. This is important for the goals of these types of studies, as the neurological condition group can vary from the control group at the link level. Our approach utilized a random subject effect to account for the correlation of multiple regions of interest within each subject, and allows each link to have a unique estimate of mean and variance for each group separately. Furthermore, the fixed effects parameters enabled us to detect disrupted connectivities at the link level for correlated measures with heterogeneities across groups. Our pragmatic approach was realistic, as it addressed the complexity of hierarchy while maintaining flexibility compared to other mixed-effects models used in the literature.
We generalize the concept of meta-analysis from a single effect size to multiple effect sizes. Generally, in meta-analysis, summary statistics from independent studies are combined to estimate the effect size [15]. In the presence of heterogeneity, model-based approaches of meta-analysis have been discussed [16-18]. In this article, estimated link specific parameters of the aforementioned mixed-effects model are used to estimate effect sizes. These effect sizes obtained from each study are then combined for every link to get the link specific effect size that measures the difference of connectivity of two groups at the link level. Thus, our meta-analysis approach estimates link specific combined connectivity, borrowing strength from all studies and addressing multidimensional heterogeneities in the context of multiple ROIs. In addition, the concept of FDR was developed with the goal of avoiding too many false positives while attaining more power to detect true positives [19] in multiple comparisons. In order to implement the FDR method, a q-value (FDR level) is required which represents the minimum FDR at which the test can be called significant. The novelty of this article is the determination of the FDR level by a rigorous exploration of p-values in order to estimate the proportion of true null hypotheses, and also to find the most suitable q-value cutoff necessary to get the optimal result.
Finally, to evaluate the proposed meta-analytic approach, we compared our results with some regularized regression models (LASSO, Elastic Net), and an embedded learning regression method (Random Forest) with a 10-fold cross validation scheme. Feature selection approaches select the most important disrupted links without going through hypothesis testing. Comparing results between the modeling approach and feature selection approaches, we are now able to examine the agreement between these two different sets of procedures. Based on the discoveries we made, we are able to determine some hubs of disruptions and their locations in known networks for interventions.
We organize the article as follows. In Section 2, we introduced methods and dataset used in this article. In Section 3, we generalize the meta-analysis concept using the parameters estimated by the mixed-effects model, discuss related hypotheses, and outline multiple testing procedures to control false discoveries. We further discuss briefly LASSO, Elastic Net and Random Forest. In this section, we also provide a rationale for the use of FDR instead of controlling type 1 error rate. In Section 4, we provide results from a study related to ASD (Autism Spectrum Disorders). We then discuss how these networks help us in correlating neurobehavioral symptoms in autistic subjects. Furthermore, we compare our model based results with Bayesian hierarchical method, feature selection approaches, and graph theory methodology. This section also examines the links found to be significant, identifies hubs of disruptions, and develops networks based on these hubs. We conclude the paper with some discussion in Section.
Methods and Materials
Dataset
For illustration, we study resting state fMRI data obtained from seven sites in Autism Brain Imaging Data Exchange (ABIDE) repository [20]. Data were collected from ABIDE site, which is a part of the 1000 Functional Connectome Project/International Neuroimaging Data-sharing Initiative (INDI) (http://fcon1000. projects.nitrc.org). The Autism Brain Imaging Data Exchange (ABIDE) is an open-access multi-site image repository consisting of structural and rs-fMRI scans from ASD and TD individuals [20]. For our work, we use fMRI measurements from 8 medical centers (sites). Acquisition parameters, protocol information can be obtained at ABIDE site http://fcon-1000.projects.nitrc.org/in di/ abide/. We use preprocessed data using Connectome Computation System (CCS) pipeline as described at ABIDE sites. The number of subjects at each site is summarized in Table 1. All the sites except for NYU have fewer than 60 subjects. In total, we use 361 subjects, consisting of 189 healthy controls and 172 autistic subjects. Connectivity maps are obtained utilizing CONN toolbox (http:// www.nitrc.org/projects/conn). Using 42 bilateral Brodmanns [10] regions of interest (ROI), bivariate correlations are calculated between each pair of ROIs. The rs-fMRI network is captured by an 84×84 symmetric matrix of nodes. We extract the upper triangle elements of the functional connectivity matrix as classification features, i.e. the feature space for classification was spanned by the (84×83)/2=3486-dimensional feature vectors. A list of all Brodmanns regions with their assigned numbers is given in [10].
Mixed-effects model
The mixed-effects model that we would like to develop should (i) have discriminating power for detecting disrupted connectivity at the link level while comparing two groups, (ii) be flexible enough to incorporate heterogeneities over links as well as across groups, and (iii) address correlations of multiple measures nested within subjects. We try to fulfill the normality assumption of random components by Fisher z transformation of the Pearson correlation measured for the connectivity of two regions. It is described in our paper [10].
Meta-analysis
In this section, we introduce the concept of meta-analysis in detecting disrupted connectivities. The fundamental difference between traditional meta-analysis and what we propose is that the former is based on a summary statistic, whereas our approach first uses a mixed-effects model and subsequently performs metaanalysis using parameter estimates from the model. An additional challenge that we encounter is from testing one hypothesis to multiple hypotheses while implementing meta-analysis.
The main reason that different studies lead to different conclusions is that these studies are often performed at a single center with a relatively small sample. Results from a single-center study suffer from both type I and type II errors. As the number of regions under study is large (in our case, 3864 different links), the chance of making a type I error cannot be ignored and must be controlled. An analysis that combines data from multiple studies should reduce the number of false positives under the assumption that false positives occur randomly across different regions. Pooling data from various studies can increase the reliability of findings and power of statistical analysis. This brings in the notion of metaanalysis. Meta-analysis has been shown to be superior to singlesite analysis as it reduces both the number of false positive and false negative results [4]. However, previous meta-analyses have not explicitly addressed the difference between sites (studies) or between site heterogeneity. In neuroimaging studies, the difference between sites can be caused by variations in scanner strength [21], study population [22] and analysis methods [23]. Inter-study variation can be a significant source of variation in neuroimaging studies [24, 21]. Many studies have shown that meta-analysis is a technique that makes efficient use of multi-site neuroimaging data [25]. In terms of the statistical testing framework, the hypothesis test for the effect size, denoted by θ, determined by the difference in mean between experimental and control group can be tested by
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