Discovering genetic associations with high-dimensional neuroimaging phenotypes: A sparse reduced-rank regression approach

Network-guided regression for detecting associations between DNA methylation and gene expression

MOTIVATION

High-throughput profiling in biological research has resulted in the availability of a wealth of data cataloguing the genetic, epigenetic and transcriptional states of cells. These data could yield discoveries that may lead to breakthroughs in the diagnosis and treatment of human disease, but require statistical methods designed to find the most relevant patterns from millions of potential interactions. Aberrant DNA methylation is often a feature of cancer, and has been proposed as a therapeutic target. However, the relationship between DNA methylation and gene expression remains poorly understood.

RESULTS

We propose Network-sparse Reduced-Rank Regression (NsRRR), a multivariate regression framework capable of using prior biological knowledge expressed as gene interaction networks to guide the search for associations between gene expression and DNA methylation signatures. We use simulations to show the advantage of our proposed model in terms of variable selection accuracy over alternative models that do not use prior network information. We discuss an application of NsRRR to The Cancer Genome Atlas datasets on primary ovarian tumours.

AVAILABILITY AND IMPLEMENTATION

R code implementing the NsRRR model is available at http://www2.imperial.ac.uk/∼gmontana

CONTACT

giovanni.montana@kcl.ac.uk

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

The ENIGMA Consortium: large-scale collaborative analyses of neuroimaging and genetic data

The Enhancing NeuroImaging Genetics through Meta-Analysis (ENIGMA) Consortium is a collaborative network of researchers working together on a range of large-scale studies that integrate data from 70 institutions worldwide. Organized into Working Groups that tackle questions in neuroscience, genetics, and medicine, ENIGMA studies have analyzed neuroimaging data from over 12,826 subjects. In addition, data from 12,171 individuals were provided by the CHARGE consortium for replication of findings, in a total of 24,997 subjects. By meta-analyzing results from many sites, ENIGMA has detected factors that affect the brain that no individual site could detect on its own, and that require larger numbers of subjects than any individual neuroimaging study has currently collected. ENIGMA's first project was a genome-wide association study identifying common variants in the genome associated with hippocampal volume or intracranial volume. Continuing work is exploring genetic associations with subcortical volumes (ENIGMA2) and white matter microstructure (ENIGMA-DTI). Working groups also focus on understanding how schizophrenia, bipolar illness, major depression and attention deficit/hyperactivity disorder (ADHD) affect the brain. We review the current progress of the ENIGMA Consortium, along with challenges and unexpected discoveries made on the way.

Genetic analysis of quantitative phenotypes in AD and MCI: imaging, cognition and biomarkers

The Genetics Core of the Alzheimer's Disease Neuroimaging Initiative (ADNI), formally established in 2009, aims to provide resources and facilitate research related to genetic predictors of multidimensional Alzheimer's disease (AD)-related phenotypes. Here, we provide a systematic review of genetic studies published between 2009 and 2012 where either ADNI APOE genotype or genome-wide association study (GWAS) data were used. We review and synthesize ADNI genetic associations with disease status or quantitative disease endophenotypes including structural and functional neuroimaging, fluid biomarker assays, and cognitive performance. We also discuss the diverse analytical strategies used in these studies, including univariate and multivariate analysis, meta-analysis, pathway analysis, and interaction and network analysis. Finally, we perform pathway and network enrichment analyses of these ADNI genetic associations to highlight key mechanisms that may drive disease onset and trajectory. Major ADNI findings included all the top 10 AD genes and several of these (e.g., APOE, BIN1, CLU, CR1, and PICALM) were corroborated by ADNI imaging, fluid and cognitive phenotypes. ADNI imaging genetics studies discovered novel findings (e.g., FRMD6) that were later replicated on different data sets. Several other genes (e.g., APOC1, FTO, GRIN2B, MAGI2, and TOMM40) were associated with multiple ADNI phenotypes, warranting further investigation on other data sets. The broad availability and wide scope of ADNI genetic and phenotypic data has advanced our understanding of the genetic basis of AD and has nominated novel targets for future studies employing next-generation sequencing and convergent multi-omics approaches, and for clinical drug and biomarker development.

Machine learning patterns for neuroimaging-genetic studies in the cloud

Brain imaging is a natural intermediate phenotype to understand the link between genetic information and behavior or brain pathologies risk factors. Massive efforts have been made in the last few years to acquire high-dimensional neuroimaging and genetic data on large cohorts of subjects. The statistical analysis of such data is carried out with increasingly sophisticated techniques and represents a great computational challenge. Fortunately, increasing computational power in distributed architectures can be harnessed, if new neuroinformatics infrastructures are designed and training to use these new tools is provided. Combining a MapReduce framework (TomusBLOB) with machine learning algorithms (Scikit-learn library), we design a scalable analysis tool that can deal with non-parametric statistics on high-dimensional data. End-users describe the statistical procedure to perform and can then test the model on their own computers before running the very same code in the cloud at a larger scale. We illustrate the potential of our approach on real data with an experiment showing how the functional signal in subcortical brain regions can be significantly fit with genome-wide genotypes. This experiment demonstrates the scalability and the reliability of our framework in the cloud with a 2 weeks deployment on hundreds of virtual machines.

A review of multivariate analyses in imaging genetics

Recent advances in neuroimaging technology and molecular genetics provide the unique opportunity to investigate genetic influence on the variation of brain attributes. Since the year 2000, when the initial publication on brain imaging and genetics was released, imaging genetics has been a rapidly growing research approach with increasing publications every year. Several reviews have been offered to the research community focusing on various study designs. In addition to study design, analytic tools and their proper implementation are also critical to the success of a study. In this review, we survey recent publications using data from neuroimaging and genetics, focusing on methods capturing multivariate effects accommodating the large number of variables from both imaging data and genetic data. We group the analyses of genetic or genomic data into either a priori driven or data driven approach, including gene-set enrichment analysis, multifactor dimensionality reduction, principal component analysis, independent component analysis (ICA), and clustering. For the analyses of imaging data, ICA and extensions of ICA are the most widely used multivariate methods. Given detailed reviews of multivariate analyses of imaging data available elsewhere, we provide a brief summary here that includes a recently proposed method known as independent vector analysis. Finally, we review methods focused on bridging the imaging and genetic data by establishing multivariate and multiple genotype-phenotype-associations, including sparse partial least squares, sparse canonical correlation analysis, sparse reduced rank regression and parallel ICA. These methods are designed to extract latent variables from both genetic and imaging data, which become new genotypes and phenotypes, and the links between the new genotype-phenotype pairs are maximized using different cost functions. The relationship between these methods along with their assumptions, advantages, and limitations are discussed.

Population-based studies of myocardial hypertrophy: high resolution cardiovascular magnetic resonance atlases improve statistical power

BACKGROUND

Cardiac phenotypes, such as left ventricular (LV) mass, demonstrate high heritability although most genes associated with these complex traits remain unidentified. Genome-wide association studies (GWAS) have relied on conventional 2D cardiovascular magnetic resonance (CMR) as the gold-standard for phenotyping. However this technique is insensitive to the regional variations in wall thickness which are often associated with left ventricular hypertrophy and require large cohorts to reach significance. Here we test whether automated cardiac phenotyping using high spatial resolution CMR atlases can achieve improved precision for mapping wall thickness in healthy populations and whether smaller sample sizes are required compared to conventional methods.

METHODS

LV short-axis cine images were acquired in 138 healthy volunteers using standard 2D imaging and 3D high spatial resolution CMR. A multi-atlas technique was used to segment and co-register each image. The agreement between methods for end-diastolic volume and mass was made using Bland-Altman analysis in 20 subjects. The 3D and 2D segmentations of the LV were compared to manual labeling by the proportion of concordant voxels (Dice coefficient) and the distances separating corresponding points. Parametric and nonparametric data were analysed with paired t-tests and Wilcoxon signed-rank test respectively. Voxelwise power calculations used the interstudy variances of wall thickness.

RESULTS

The 3D volumetric measurements showed no bias compared to 2D imaging. The segmented 3D images were more accurate than 2D images for defining the epicardium (Dice: 0.95 vs 0.93, P<0.001; mean error 1.3 mm vs 2.2 mm, P<0.001) and endocardium (Dice 0.95 vs 0.93, P<0.001; mean error 1.1 mm vs 2.0 mm, P<0.001). The 3D technique resulted in significant differences in wall thickness assessment at the base, septum and apex of the LV compared to 2D (P<0.001). Fewer subjects were required for 3D imaging to detect a 1 mm difference in wall thickness (72 vs 56, P<0.001).

CONCLUSIONS

High spatial resolution CMR with automated phenotyping provides greater power for mapping wall thickness than conventional 2D imaging and enables a reduction in the sample size required for studies of environmental and genetic determinants of LV wall thickness.

Spherical Topic Models for Imaging Phenotype Discovery in Genetic Studies

In this paper, we use Spherical Topic Models to discover the latent structure of lung disease. This method can be widely employed when a measurement for each subject is provided as a normalized histogram of relevant features. In this paper, the resulting descriptors are used as phenotypes to identify genetic markers associated with the Chronic Obstructive Pulmonary Disease (COPD). Features extracted from images capture the heterogeneity of the disease and therefore promise to improve detection of relevant genetic variants in Genome Wide Association Studies (GWAS). Our generative model is based on normalized histograms of image intensity of each subject and it can be readily extended to other forms of features as long as they are provided as normalized histograms. The resulting algorithm represents the intensity distribution as a combination of meaningful latent factors and mixing co-efficients that can be used for genetic association analysis. This approach is motivated by a clinical hypothesis that COPD symptoms are caused by multiple coexisting disease processes. Our experiments show that the new features enhance the previously detected signal on chromosome 15 with respect to standard respiratory and imaging measurements.

Bayesian Generalized Low Rank Regression Models for Neuroimaging Phenotypes and Genetic Markers

We propose a Bayesian generalized low rank regression model (GLRR) for the analysis of both high-dimensional responses and covariates. This development is motivated by performing searches for associations between genetic variants and brain imaging phenotypes. GLRR integrates a low rank matrix to approximate the high-dimensional regression coefficient matrix of GLRR and a dynamic factor model to model the high-dimensional covariance matrix of brain imaging phenotypes. Local hypothesis testing is developed to identify significant covariates on high-dimensional responses. Posterior computation proceeds via an efficient Markov chain Monte Carlo algorithm. A simulation study is performed to evaluate the finite sample performance of GLRR and its comparison with several competing approaches. We apply GLRR to investigate the impact of 1,071 SNPs on top 40 genes reported by AlzGene database on the volumes of 93 regions of interest (ROI) obtained from Alzheimer's Disease Neuroimaging Initiative (ADNI).

A novel structure-aware sparse learning algorithm for brain imaging genetics

Brain imaging genetics is an emergent research field where the association between genetic variations such as single nucleotide polymorphisms (SNPs) and neuroimaging quantitative traits (QTs) is evaluated. Sparse canonical correlation analysis (SCCA) is a bi-multivariate analysis method that has the potential to reveal complex multi-SNP-multi-QT associations. Most existing SCCA algorithms are designed using the soft threshold strategy, which assumes that the features in the data are independent from each other. This independence assumption usually does not hold in imaging genetic data, and thus inevitably limits the capability of yielding optimal solutions. We propose a novel structure-aware SCCA (denoted as S2CCA) algorithm to not only eliminate the independence assumption for the input data, but also incorporate group-like structure in the model. Empirical comparison with a widely used SCCA implementation, on both simulated and real imaging genetic data, demonstrated that S2CCA could yield improved prediction performance and biologically meaningful findings.

Guided exploration of genomic risk for gray matter abnormalities in schizophrenia using parallel independent component analysis with reference

One application of imaging genomics is to explore genetic variants associated with brain structure and function, presenting a new means of mapping genetic influences on mental disorders. While there is growing interest in performing genome-wide searches for determinants, it remains challenging to identify genetic factors of small effect size, especially in limited sample sizes. In an attempt to address this issue, we propose to take advantage of a priori knowledge, specifically to extend parallel independent component analysis (pICA) to incorporate a reference (pICA-R), aiming to better reveal relationships between hidden factors of a particular attribute. The new approach was first evaluated on simulated data for its performance under different configurations of effect size and dimensionality. Then pICA-R was applied to a 300-participant (140 schizophrenia (SZ) patients versus 160 healthy controls) dataset consisting of structural magnetic resonance imaging (sMRI) and single nucleotide polymorphism (SNP) data. Guided by a reference SNP set derived from ANK3, a gene implicated by the Psychiatric Genomic Consortium SZ study, pICA-R identified one pair of SNP and sMRI components with a significant loading correlation of 0.27 (p=1.64×10(-6)). The sMRI component showed a significant group difference in loading parameters between patients and controls (p=1.33×10(-15)), indicating SZ-related reduction in gray matter concentration in prefrontal and temporal regions. The linked SNP component also showed a group difference (p=0.04) and was predominantly contributed to by 1030 SNPs. The effect of these top contributing SNPs was verified using association test results of the Psychiatric Genomic Consortium SZ study, where the 1030 SNPs exhibited significant SZ enrichment compared to the whole genome. In addition, pathway analyses indicated the genetic component majorly relating to neurotransmitter and nervous system signaling pathways. Given the simulation and experiment results, pICA-R may prove a promising multivariate approach for use in imaging genomics to discover reliable genetic risk factors under a scenario of relatively high dimensionality and small effect size.

Random forests on Hadoop for genome-wide association studies of multivariate neuroimaging phenotypes

MOTIVATION

Multivariate quantitative traits arise naturally in recent neuroimaging genetics studies, in which both structural and functional variability of the human brain is measured non-invasively through techniques such as magnetic resonance imaging (MRI). There is growing interest in detecting genetic variants associated with such multivariate traits, especially in genome-wide studies. Random forests (RFs) classifiers, which are ensembles of decision trees, are amongst the best performing machine learning algorithms and have been successfully employed for the prioritisation of genetic variants in case-control studies. RFs can also be applied to produce gene rankings in association studies with multivariate quantitative traits, and to estimate genetic similarities measures that are predictive of the trait. However, in studies involving hundreds of thousands of SNPs and high-dimensional traits, a very large ensemble of trees must be inferred from the data in order to obtain reliable rankings, which makes the application of these algorithms computationally prohibitive.

RESULTS

We have developed a parallel version of the RF algorithm for regression and genetic similarity learning tasks in large-scale population genetic association studies involving multivariate traits, called PaRFR (Parallel Random Forest Regression). Our implementation takes advantage of the MapReduce programming model and is deployed on Hadoop, an open-source software framework that supports data-intensive distributed applications. Notable speed-ups are obtained by introducing a distance-based criterion for node splitting in the tree estimation process. PaRFR has been applied to a genome-wide association study on Alzheimer's disease (AD) in which the quantitative trait consists of a high-dimensional neuroimaging phenotype describing longitudinal changes in the human brain structure. PaRFR provides a ranking of SNPs associated to this trait, and produces pair-wise measures of genetic proximity that can be directly compared to pair-wise measures of phenotypic proximity. Several known AD-related variants have been identified, including APOE4 and TOMM40. We also present experimental evidence supporting the hypothesis of a linear relationship between the number of top-ranked mutated states, or frequent mutation patterns, and an indicator of disease severity.

AVAILABILITY

The Java codes are freely available at http://www2.imperial.ac.uk/~gmontana.

Genetics of the connectome

Connectome genetics attempts to discover how genetic factors affect brain connectivity. Here we review a variety of genetic analysis methods--such as genome-wide association studies (GWAS), linkage and candidate gene studies--that have been fruitfully adapted to imaging data to implicate specific variants in the genome for brain-related traits. Studies that emphasized the genetic influences on brain connectivity. Some of these analyses of brain integrity and connectivity using diffusion MRI, and others have mapped genetic effects on functional networks using resting state functional MRI. Connectome-wide genome-wide scans have also been conducted, and we review the multivariate methods required to handle the extremely high dimension of the genomic and network data. We also review some consortium efforts, such as ENIGMA, that offer the power to detect robust common genetic associations using phenotypic harmonization procedures and meta-analysis. Current work on connectome genetics is advancing on many fronts and promises to shed light on how disease risk genes affect the brain. It is already discovering new genetic loci and even entire genetic networks that affect brain organization and connectivity.

Genetic influences of resting state fMRI activity in language-related brain regions in healthy controls and schizophrenia patients: a pilot study

Individuals with schizophrenia show a broad range of language impairments, similar to those observed in reading disability (RD). Genetic linkage and association studies of RD have identified a number of candidate RD-genes that are associated with neuronal migration. Some individuals with schizophrenia also show evidence of impaired cortical neuronal migration. We have previously linked RD-related genes with gray matter distributions in healthy controls and schizophrenia. The aim of the current study was to extend these structural findings and to examine links between putative RD-genes and functional connectivity of language-related regions in healthy controls (n = 27) and schizophrenia (n = 28). Parallel independent component analysis (parallel-ICA) was used to examine the relationship between language-related regions extracted from resting-state fMRI and 16 single nucleotide polymorphisms (SNPs) spanning 5 RD-related genes. Parallel-ICA identified four significant fMRI-SNP relationships. A Left Broca-Superior/Inferior Parietal network was related to two KIAA0319 SNPs in controls but not in schizophrenia. For both diagnostic groups, a Broca-Medial Parietal network was related to two DCDC2 SNPs, while a Left Wernicke-Fronto-Occipital network was related to two KIAA0319 SNPs. A Bilateral Wernicke-Fronto-Parietal network was related to one KIAA0319 SNP only in controls. Thus, RD-genes influence functional connectivity in language-related regions, but no RD-gene uniquely affected network function in schizophrenia as compared to controls. This is in contrast with our previous study where RD-genes affected gray matter distribution in some structural networks in schizophrenia but not in controls. Thus these RD-genes may exert a more important influence on structure rather than function of language-related networks in schizophrenia.

The Alzheimer's Disease Neuroimaging Initiative: a review of papers published since its inception

The Alzheimer's Disease Neuroimaging Initiative (ADNI) is an ongoing, longitudinal, multicenter study designed to develop clinical, imaging, genetic, and biochemical biomarkers for the early detection and tracking of Alzheimer's disease (AD). The study aimed to enroll 400 subjects with early mild cognitive impairment (MCI), 200 subjects with early AD, and 200 normal control subjects; $67 million funding was provided by both the public and private sectors, including the National Institute on Aging, 13 pharmaceutical companies, and 2 foundations that provided support through the Foundation for the National Institutes of Health. This article reviews all papers published since the inception of the initiative and summarizes the results as of February 2011. The major accomplishments of ADNI have been as follows: (1) the development of standardized methods for clinical tests, magnetic resonance imaging (MRI), positron emission tomography (PET), and cerebrospinal fluid (CSF) biomarkers in a multicenter setting; (2) elucidation of the patterns and rates of change of imaging and CSF biomarker measurements in control subjects, MCI patients, and AD patients. CSF biomarkers are consistent with disease trajectories predicted by β-amyloid cascade (Hardy, J Alzheimers Dis 2006;9(Suppl 3):151-3) and tau-mediated neurodegeneration hypotheses for AD, whereas brain atrophy and hypometabolism levels show predicted patterns but exhibit differing rates of change depending on region and disease severity; (3) the assessment of alternative methods of diagnostic categorization. Currently, the best classifiers combine optimum features from multiple modalities, including MRI, [(18)F]-fluorodeoxyglucose-PET, CSF biomarkers, and clinical tests; (4) the development of methods for the early detection of AD. CSF biomarkers, β-amyloid 42 and tau, as well as amyloid PET may reflect the earliest steps in AD pathology in mildly symptomatic or even nonsymptomatic subjects, and are leading candidates for the detection of AD in its preclinical stages; (5) the improvement of clinical trial efficiency through the identification of subjects most likely to undergo imminent future clinical decline and the use of more sensitive outcome measures to reduce sample sizes. Baseline cognitive and/or MRI measures generally predicted future decline better than other modalities, whereas MRI measures of change were shown to be the most efficient outcome measures; (6) the confirmation of the AD risk loci CLU, CR1, and PICALM and the identification of novel candidate risk loci; (7) worldwide impact through the establishment of ADNI-like programs in Europe, Asia, and Australia; (8) understanding the biology and pathobiology of normal aging, MCI, and AD through integration of ADNI biomarker data with clinical data from ADNI to stimulate research that will resolve controversies about competing hypotheses on the etiopathogenesis of AD, thereby advancing efforts to find disease-modifying drugs for AD; and (9) the establishment of infrastructure to allow sharing of all raw and processed data without embargo to interested scientific investigators throughout the world. The ADNI study was extended by a 2-year Grand Opportunities grant in 2009 and a renewal of ADNI (ADNI-2) in October 2010 through to 2016, with enrollment of an additional 550 participants.

Penalized likelihood phenotyping: unifying voxelwise analyses and multi-voxel pattern analyses in neuroimaging: penalized likelihood phenotyping

Neuroimage phenotyping for psychiatric and neurological disorders is performed using voxelwise analyses also known as voxel based analyses or morphometry (VBM). A typical voxelwise analysis treats measurements at each voxel (e.g., fractional anisotropy, gray matter probability) as outcome measures to study the effects of possible explanatory variables (e.g., age, group) in a linear regression setting. Furthermore, each voxel is treated independently until the stage of correction for multiple comparisons. Recently, multi-voxel pattern analyses (MVPA), such as classification, have arisen as an alternative to VBM. The main advantage of MVPA over VBM is that the former employ multivariate methods which can account for interactions among voxels in identifying significant patterns. They also provide ways for computer-aided diagnosis and prognosis at individual subject level. However, compared to VBM, the results of MVPA are often more difficult to interpret and prone to arbitrary conclusions. In this paper, first we use penalized likelihood modeling to provide a unified framework for understanding both VBM and MVPA. We then utilize statistical learning theory to provide practical methods for interpreting the results of MVPA beyond commonly used performance metrics, such as leave-one-out-cross validation accuracy and area under the receiver operating characteristic (ROC) curve. Additionally, we demonstrate that there are challenges in MVPA when trying to obtain image phenotyping information in the form of statistical parametric maps (SPMs), which are commonly obtained from VBM, and provide a bootstrap strategy as a potential solution for generating SPMs using MVPA. This technique also allows us to maximize the use of available training data. We illustrate the empirical performance of the proposed framework using two different neuroimaging studies that pose different levels of challenge for classification using MVPA.

IMAGING GENETICS VIA SPARSE CANONICAL CORRELATION ANALYSIS

The collection of brain images from populations of subjects who have been genotyped with genome-wide scans makes it feasible to search for genetic effects on the brain. Even so, multivariate methods are sorely needed that can search both images and the genome for relationships, making use of the correlation structure of both datasets. Here we investigate the use of sparse canonical correlation analysis (CCA) to home in on sets of genetic variants that explain variance in a set of images. We extend recent work on penalized matrix decomposition to account for the correlations in both datasets. Such methods show promise in imaging genetics as they exploit the natural covariance in the datasets. They also avoid an astronomically heavy statistical correction for searching the whole genome and the entire image for promising associations.

Applying tensor-based morphometry to parametric surfaces can improve MRI-based disease diagnosis

Many methods have been proposed for computer-assisted diagnostic classification. Full tensor information and machine learning with 3D maps derived from brain images may help detect subtle differences or classify subjects into different groups. Here we develop a new approach to apply tensor-based morphometry to parametric surface models for diagnostic classification. We use this approach to identify cortical surface features for use in diagnostic classifiers. First, with holomorphic 1-forms, we compute an efficient and accurate conformal mapping from a multiply connected mesh to the so-called slit domain. Next, the surface parameterization approach provides a natural way to register anatomical surfaces across subjects using a constrained harmonic map. To analyze anatomical differences, we then analyze the full Riemannian surface metric tensors, which retain multivariate information on local surface geometry. As the number of voxels in a 3D image is large, sparse learning is a promising method to select a subset of imaging features and to improve classification accuracy. Focusing on vertices with greatest effect sizes, we train a diagnostic classifier using the surface features selected by an L1-norm based sparse learning method. Stability selection is applied to validate the selected feature sets. We tested the algorithm on MRI-derived cortical surfaces from 42 subjects with genetically confirmed Williams syndrome and 40 age-matched controls, multivariate statistics on the local tensors gave greater effect sizes for detecting group differences relative to other TBM-based statistics including analysis of the Jacobian determinant and the largest eigenvalue of the surface metric. Our method also gave reasonable classification results relative to the Jacobian determinant, the pair of eigenvalues of the Jacobian matrix and volume features. This analysis pipeline may boost the power of morphometry studies, and may assist with image-based classification.

Joint modeling of imaging and genetics

We propose a unified Bayesian framework for detecting genetic variants associated with a disease while exploiting image-based features as an intermediate phenotype. Traditionally, imaging genetics methods comprise two separate steps. First, image features are selected based on their relevance to the disease phenotype. Second, a set of genetic variants are identified to explain the selected features. In contrast, our method performs these tasks simultaneously to ultimately assign probabilistic measures of relevance to both genetic and imaging markers. We derive an efficient approximate inference algorithm that handles high dimensionality of imaging genetic data. We evaluate the algorithm on synthetic data and show that it outperforms traditional models. We also illustrate the application of the method on ADNI data.

Identification of gene pathways implicated in Alzheimer's disease using longitudinal imaging phenotypes with sparse regression

We present a new method for the detection of gene pathways associated with a multivariate quantitative trait, and use it to identify causal pathways associated with an imaging endophenotype characteristic of longitudinal structural change in the brains of patients with Alzheimer's disease (AD). Our method, known as pathways sparse reduced-rank regression (PsRRR), uses group lasso penalised regression to jointly model the effects of genome-wide single nucleotide polymorphisms (SNPs), grouped into functional pathways using prior knowledge of gene-gene interactions. Pathways are ranked in order of importance using a resampling strategy that exploits finite sample variability. Our application study uses whole genome scans and MR images from 99 probable AD patients and 164 healthy elderly controls in the Alzheimer's Disease Neuroimaging Initiative (ADNI) database. 66,182 SNPs are mapped to 185 gene pathways from the KEGG pathway database. Voxel-wise imaging signatures characteristic of AD are obtained by analysing 3D patterns of structural change at 6, 12 and 24 months relative to baseline. High-ranking, AD endophenotype-associated pathways in our study include those describing insulin signalling, vascular smooth muscle contraction and focal adhesion. All of these have been previously implicated in AD biology. In a secondary analysis, we investigate SNPs and genes that may be driving pathway selection. High ranking genes include a number previously linked in gene expression studies to β-amyloid plaque formation in the AD brain (PIK3R3,PIK3CG,PRKCAandPRKCB), and to AD related changes in hippocampal gene expression (ADCY2, ACTN1, ACACA, and GNAI1). Other high ranking previously validated AD endophenotype-related genes include CR1, TOMM40 and APOE.

Increasing power for voxel-wise genome-wide association studies: the random field theory, least square kernel machines and fast permutation procedures

Imaging traits are thought to have more direct links to genetic variation than diagnostic measures based on cognitive or clinical assessments and provide a powerful substrate to examine the influence of genetics on human brains. Although imaging genetics has attracted growing attention and interest, most brain-wide genome-wide association studies focus on voxel-wise single-locus approaches, without taking advantage of the spatial information in images or combining the effect of multiple genetic variants. In this paper we present a fast implementation of voxel- and cluster-wise inferences based on the random field theory to fully use the spatial information in images. The approach is combined with a multi-locus model based on least square kernel machines to associate the joint effect of several single nucleotide polymorphisms (SNP) with imaging traits. A fast permutation procedure is also proposed which significantly reduces the number of permutations needed relative to the standard empirical method and provides accurate small p-value estimates based on parametric tail approximation. We explored the relation between 448,294 single nucleotide polymorphisms and 18,043 genes in 31,662 voxels of the entire brain across 740 elderly subjects from the Alzheimer's disease neuroimaging initiative (ADNI). Structural MRI scans were analyzed using tensor-based morphometry (TBM) to compute 3D maps of regional brain volume differences compared to an average template image based on healthy elderly subjects. We find method to be more sensitive compared with voxel-wise single-locus approaches. A number of genes were identified as having significant associations with volumetric changes. The most associated gene was GRIN2B, which encodes the N-methyl-d-aspartate (NMDA) glutamate receptor NR2B subunit and affects both the parietal and temporal lobes in human brains. Its role in Alzheimer's disease has been widely acknowledged and studied, suggesting the validity of the approach. The various advantages over existing approaches indicate a great potential offered by this novel framework to detect genetic influences on human brains.

Discovery and Replication of Gene Influences on Brain Structure Using LASSO Regression

We implemented least absolute shrinkage and selection operator (LASSO) regression to evaluate gene effects in genome-wide association studies (GWAS) of brain images, using an MRI-derived temporal lobe volume measure from 729 subjects scanned as part of the Alzheimer's Disease Neuroimaging Initiative (ADNI). Sparse groups of SNPs in individual genes were selected by LASSO, which identifies efficient sets of variants influencing the data. These SNPs were considered jointly when assessing their association with neuroimaging measures. We discovered 22 genes that passed genome-wide significance for influencing temporal lobe volume. This was a substantially greater number of significant genes compared to those found with standard, univariate GWAS. These top genes are all expressed in the brain and include genes previously related to brain function or neuropsychiatric disorders such as MACROD2, SORCS2, GRIN2B, MAGI2, NPAS3, CLSTN2, GABRG3, NRXN3, PRKAG2, GAS7, RBFOX1, ADARB2, CHD4, and CDH13. The top genes we identified with this method also displayed significant and widespread post hoc effects on voxelwise, tensor-based morphometry (TBM) maps of the temporal lobes. The most significantly associated gene was an autism susceptibility gene known as MACROD2. We were able to successfully replicate the effect of the MACROD2 gene in an independent cohort of 564 young, Australian healthy adult twins and siblings scanned with MRI (mean age: 23.8 ± 2.2 SD years). Our approach powerfully complements univariate techniques in detecting influences of genes on the living brain.

Predicting white matter integrity from multiple common genetic variants

Several common genetic variants have recently been discovered that appear to influence white matter microstructure, as measured by diffusion tensor imaging (DTI). Each genetic variant explains only a small proportion of the variance in brain microstructure, so we set out to explore their combined effect on the white matter integrity of the corpus callosum. We measured six common candidate single-nucleotide polymorphisms (SNPs) in the COMT, NTRK1, BDNF, ErbB4, CLU, and HFE genes, and investigated their individual and aggregate effects on white matter structure in 395 healthy adult twins and siblings (age: 20-30 years). All subjects were scanned with 4-tesla 94-direction high angular resolution diffusion imaging. When combined using mixed-effects linear regression, a joint model based on five of the candidate SNPs (COMT, NTRK1, ErbB4, CLU, and HFE) explained ≈ 6% of the variance in the average fractional anisotropy (FA) of the corpus callosum. This predictive model had detectable effects on FA at 82% of the corpus callosum voxels, including the genu, body, and splenium. Predicting the brain's fiber microstructure from genotypes may ultimately help in early risk assessment, and eventually, in personalized treatment for neuropsychiatric disorders in which brain integrity and connectivity are affected.

Glutamate gene polymorphisms predict brain volumes in multiple sclerosis

Background:

Several genetic markers have been associated with multiple sclerosis (MS) susceptibility; however, uncovering the genetic aetiology of the complex phenotypic expression of MS has been more difficult so far. The most common approach in imaging genetics is based on mass-univariate linear modelling (MULM), which faces several limitations.

Objective:

Here we apply a novel multivariate statistical model, sparse reduced-rank regression (sRRR), to identify possible associations of glutamate related single nucleotide polymorphisms (SNPs) and multiple MRI-derived phenotypes in MS.

Methods:

Seven phenotypes related to brain and lesion volumes for a total number of 326 relapsing–remitting and secondary-progressive MS patients and a total of 3809 glutamate related and control SNPs were analysed with sRRR, which resulted in a ranking of SNPs in decreasing order of importance (‘selection probability’). Lasso regression and MULM were used as comparative statistical techniques to assess consistency of the most important associations over different statistical models.

Results:

Five SNPs within the NMDA-receptor-2A-subunit (GRIN2A) domain were identified by sRRR in association with normalized brain volume (NBV), normalized grey matter volume and normalized white matter volume (NMWM). The association between GRIN2A and both NBV and NWMV was confirmed in MULM and Lasso analysis.

Conclusions:

Using a novel, multivariate regression model confirmed by two other statistical approaches we show associations between GRIN2A SNPs and phenotypic variation in NBV and NWMV in this first exploratory study. Replications in independent datasets are now necessary to validate these findings.

Significant correlation between a set of genetic polymorphisms and a functional brain network revealed by feature selection and sparse Partial Least Squares

Brain imaging is increasingly recognised as an intermediate phenotype to understand the complex path between genetics and behavioural or clinical phenotypes. In this context, a first goal is to propose methods to identify the part of genetic variability that explains some neuroimaging variability. Classical univariate approaches often ignore the potential joint effects that may exist between genes or the potential covariations between brain regions. In this paper, we propose instead to investigate an exploratory multivariate method in order to identify a set of Single Nucleotide Polymorphisms (SNPs) covarying with a set of neuroimaging phenotypes derived from functional Magnetic Resonance Imaging (fMRI). Recently, Partial Least Squares (PLS) regression or Canonical Correlation Analysis (CCA) have been proposed to analyse DNA and transcriptomics. Here, we propose to transpose this idea to the DNA vs. imaging context. However, in very high-dimensional settings like in imaging genetics studies, such multivariate methods may encounter overfitting issues. Thus we investigate the use of different strategies of regularisation and dimension reduction techniques combined with PLS or CCA to face the very high dimensionality of imaging genetics studies. We propose a comparison study of the different strategies on a simulated dataset first and then on a real dataset composed of 94 subjects, around 600,000 SNPs and 34 functional MRI lateralisation indexes computed from reading and speech comprehension contrast maps. We estimate the generalisability of the multivariate association with a cross-validation scheme and demonstrate the significance of this link, using a permutation procedure. Univariate selection appears to be necessary to reduce the dimensionality. However, the significant association uncovered by this two-step approach combining univariate filtering and L1-regularised PLS suggests that discovering meaningful genetic associations calls for a multivariate approach.

PREDICTING TEMPORAL LOBE VOLUME ON MRI FROM GENOTYPES USING L(1)-L(2) REGULARIZED REGRESSION

Penalized or sparse regression methods are gaining increasing attention in imaging genomics, as they can select optimal regressors from a large set of predictors whose individual effects are small or mostly zero. We applied a multivariate approach, based on L(1)-L(2)-regularized regression (elastic net) to predict a magnetic resonance imaging (MRI) tensor-based morphometry-derived measure of temporal lobe volume from a genome-wide scan in 740 Alzheimer's Disease Neuroimaging Initiative (ADNI) subjects. We tuned the elastic net model's parameters using internal crossvalidation and evaluated the model on independent test sets. Compared to 100,000 permutations performed with randomized imaging measures, the predictions were found to be statistically significant (p ~ 0.001). The rs9933137 variant in the RBFOX1 gene was a highly contributory genotype, along with rs10845840 in GRIN2B and rs2456930, discovered previously in a univariate genomewide search.

The challenges and promise of neuroimaging in psychiatry

Neuroimaging is central to the quest for a biological foundation of psychiatric diagnosis but so far has not yielded clinically relevant biomarkers for mental disorders. This review addresses potential reasons for this limitation and discusses refinements of paradigms and analytic techniques that may yield improved diagnostic and prognostic accuracy. Neuroimaging can also be used to probe genetically defined biological pathways underlying mental disorders, for example through the genetic imaging of variants discovered in genome-wide association studies. These approaches may ultimately reveal mechanisms through which genes contribute to psychiatric symptoms and how pharmacological and psychological interventions exert their effects.

Identification of cancer cell-line origins using fluorescence image-based phenomic screening

Universal phenotyping techniques that can discriminate among various states of biological systems have great potential. We applied 557 fluorescent library compounds to NCI's 60 human cancer cell-lines (NCI-60) to generate a systematic fluorescence phenotypic profiling data. By the kinetic fluorescence intensity analysis, we successfully discriminated the organ origin of all the 60 cell-lines.

An ICA with reference approach in identification of genetic variation and associated brain networks

To address the statistical challenges associated with genome-wide association studies, we present an independent component analysis (ICA) with reference approach to target a specific genetic variation and associated brain networks. First, a small set of single nucleotide polymorphisms (SNPs) are empirically chosen to reflect a feature of interest and these SNPs are used as a reference when applying ICA to a full genomic SNP array. After extracting the genetic component maximally representing the characteristics of the reference, we test its association with brain networks in functional magnetic resonance imaging (fMRI) data. The method was evaluated on both real and simulated datasets. Simulation demonstrates that ICA with reference can extract a specific genetic factor, even when the variance accounted for by such a factor is so small that a regular ICA fails. Our real data application from 48 schizophrenia patients (SZs) and 40 healthy controls (HCs) include 300K SNPs and fMRI images in an auditory oddball task. Using SNPs with allelic frequency difference in two groups as a reference, we extracted a genetic component that maximally differentiates patients from controls (p < 4 × 10⁻¹⁷), and discovered a brain functional network that was significantly associated with this genetic component (p < 1 × 10⁻⁴). The regions in the functional network mainly locate in the thalamus, anterior and posterior cingulate gyri. The contributing SNPs in the genetic factor mainly fall into two clusters centered at chromosome 7q21 and chromosome 5q35. The findings from the schizophrenia application are in concordance with previous knowledge about brain regions and gene function. All together, the results suggest that the ICA with reference can be particularly useful to explore the whole genome to find a specific factor of interest and further study its effect on brain.

Fast identification of biological pathways associated with a quantitative trait using group lasso with overlaps

Where causal SNPs (single nucleotide polymorphisms) tend to accumulate within biological pathways, the incorporation of prior pathways information into a statistical model is expected to increase the power to detect true associations in a genetic association study. Most existing pathways-based methods rely on marginal SNP statistics and do not fully exploit the dependence patterns among SNPs within pathways.We use a sparse regression model, with SNPs grouped into pathways, to identify causal pathways associated with a quantitative trait. Notable features of our "pathways group lasso with adaptive weights" (P-GLAW) algorithm include the incorporation of all pathways in a single regression model, an adaptive pathway weighting procedure that accounts for factors biasing pathway selection, and the use of a bootstrap sampling procedure for the ranking of important pathways. P-GLAW takes account of the presence of overlapping pathways and uses a novel combination of techniques to optimise model estimation, making it fast to run, even on whole genome datasets.In a comparison study with an alternative pathways method based on univariate SNP statistics, our method demonstrates high sensitivity and specificity for the detection of important pathways, showing the greatest relative gains in performance where marginal SNP effect sizes are small.

Sparse reduced-rank regression detects genetic associations with voxel-wise longitudinal phenotypes in Alzheimer's disease

Scanning the entire genome in search of variants related to imaging phenotypes holds great promise in elucidating the genetic etiology of neurodegenerative disorders. Here we discuss the application of a penalized multivariate model, sparse reduced-rank regression (sRRR), for the genome-wide detection of markers associated with voxel-wise longitudinal changes in the brain caused by Alzheimer's disease (AD). Using a sample from the Alzheimer's Disease Neuroimaging Initiative database, we performed three separate studies that each compared two groups of individuals to identify genes associated with disease development and progression. For each comparison we took a two-step approach: initially, using penalized linear discriminant analysis, we identified voxels that provide an imaging signature of the disease with high classification accuracy; then we used this multivariate biomarker as a phenotype in a genome-wide association study, carried out using sRRR. The genetic markers were ranked in order of importance of association to the phenotypes using a data re-sampling approach. Our findings confirmed the key role of the APOE and TOMM40 genes but also highlighted some novel potential associations with AD.

Hippocampal surface mapping of genetic risk factors in AD via sparse learning models

Genetic mapping of hippocampal shape, an under-explored area, has strong potential as a neurodegeneration biomarker for AD and MCI. This study investigates the genetic effects of top candidate single nucleotide polymorphisms (SNPs) on hippocampal shape features as quantitative traits (QTs) in a large cohort. FS+LDDMM was used to segment hippocampal surfaces from MRI scans and shape features were extracted after surface registration. Elastic net (EN) and sparse canonical correlation analysis (SCCA) were proposed to examine SNP-QT associations, and compared with multiple regression (MR). Although similar in power, EN yielded substantially fewer predictors than MR. Detailed surface mapping of global and localized genetic effects were identified by MR and EN to reveal multi-SNP-single-QT relationships, and by SCCA to discover multi-SNP-multi-QT associations. Shape analysis identified stronger SNP-QT correlations than volume analysis. Sparse multivariate models have greater power to reveal complex SNP-QT relationships. Genetic analysis of quantitative shape features has considerable potential for enhancing mechanistic understanding of complex disorders like AD.

The Alzheimer's Disease Neuroimaging Initiative: a review of papers published since its inception

The Alzheimer's Disease Neuroimaging Initiative (ADNI) is an ongoing, longitudinal, multicenter study designed to develop clinical, imaging, genetic, and biochemical biomarkers for the early detection and tracking of Alzheimer's disease (AD). The study aimed to enroll 400 subjects with early mild cognitive impairment (MCI), 200 subjects with early AD, and 200 normal control subjects; $67 million funding was provided by both the public and private sectors, including the National Institute on Aging, 13 pharmaceutical companies, and 2 foundations that provided support through the Foundation for the National Institutes of Health. This article reviews all papers published since the inception of the initiative and summarizes the results as of February 2011. The major accomplishments of ADNI have been as follows: (1) the development of standardized methods for clinical tests, magnetic resonance imaging (MRI), positron emission tomography (PET), and cerebrospinal fluid (CSF) biomarkers in a multicenter setting; (2) elucidation of the patterns and rates of change of imaging and CSF biomarker measurements in control subjects, MCI patients, and AD patients. CSF biomarkers are consistent with disease trajectories predicted by β-amyloid cascade (Hardy, J Alzheimers Dis 2006;9(Suppl 3):151-3) and tau-mediated neurodegeneration hypotheses for AD, whereas brain atrophy and hypometabolism levels show predicted patterns but exhibit differing rates of change depending on region and disease severity; (3) the assessment of alternative methods of diagnostic categorization. Currently, the best classifiers combine optimum features from multiple modalities, including MRI, [(18)F]-fluorodeoxyglucose-PET, CSF biomarkers, and clinical tests; (4) the development of methods for the early detection of AD. CSF biomarkers, β-amyloid 42 and tau, as well as amyloid PET may reflect the earliest steps in AD pathology in mildly symptomatic or even nonsymptomatic subjects, and are leading candidates for the detection of AD in its preclinical stages; (5) the improvement of clinical trial efficiency through the identification of subjects most likely to undergo imminent future clinical decline and the use of more sensitive outcome measures to reduce sample sizes. Baseline cognitive and/or MRI measures generally predicted future decline better than other modalities, whereas MRI measures of change were shown to be the most efficient outcome measures; (6) the confirmation of the AD risk loci CLU, CR1, and PICALM and the identification of novel candidate risk loci; (7) worldwide impact through the establishment of ADNI-like programs in Europe, Asia, and Australia; (8) understanding the biology and pathobiology of normal aging, MCI, and AD through integration of ADNI biomarker data with clinical data from ADNI to stimulate research that will resolve controversies about competing hypotheses on the etiopathogenesis of AD, thereby advancing efforts to find disease-modifying drugs for AD; and (9) the establishment of infrastructure to allow sharing of all raw and processed data without embargo to interested scientific investigators throughout the world. The ADNI study was extended by a 2-year Grand Opportunities grant in 2009 and a renewal of ADNI (ADNI-2) in October 2010 through to 2016, with enrollment of an additional 550 participants.

Multilocus genetic analysis of brain images

The quest to identify genes that influence disease is now being extended to find genes that affect biological markers of disease, or endophenotypes. Brain images, in particular, provide exquisitely detailed measures of anatomy, function, and connectivity in the living brain, and have identified characteristic features for many neurological and psychiatric disorders. The emerging field of imaging genomics is discovering important genetic variants associated with brain structure and function, which in turn influence disease risk and fundamental cognitive processes. Statistical approaches for testing genetic associations are not straightforward to apply to brain images because the data in brain images is spatially complex and generally high dimensional. Neuroimaging phenotypes typically include 3D maps across many points in the brain, fiber tracts, shape-based analyses, and connectivity matrices, or networks. These complex data types require new methods for data reduction and joint consideration of the image and the genome. Image-wide, genome-wide searches are now feasible, but they can be greatly empowered by sparse regression or hierarchical clustering methods that isolate promising features, boosting statistical power. Here we review the evolution of statistical approaches to assess genetic influences on the brain. We outline the current state of multivariate statistics in imaging genomics, and future directions, including meta-analysis. We emphasize the power of novel multivariate approaches to discover reliable genetic influences with small effect sizes.

Discovery and replication of dopamine-related gene effects on caudate volume in young and elderly populations (N=1198) using genome-wide search

The caudate is a subcortical brain structure implicated in many common neurological and psychiatric disorders. To identify specific genes associated with variations in caudate volume, structural magnetic resonance imaging and genome-wide genotypes were acquired from two large cohorts, the Alzheimer's Disease NeuroImaging Initiative (ADNI; N=734) and the Brisbane Adolescent/Young Adult Longitudinal Twin Study (BLTS; N=464). In a preliminary analysis of heritability, around 90% of the variation in caudate volume was due to genetic factors. We then conducted genome-wide association to find common variants that contribute to this relatively high heritability. Replicated genetic association was found for the right caudate volume at single-nucleotide polymorphism rs163030 in the ADNI discovery sample (P=2.36 × 10⁻⁶) and in the BLTS replication sample (P=0.012). This genetic variation accounted for 2.79 and 1.61% of the trait variance, respectively. The peak of association was found in and around two genes, WDR41 and PDE8B, involved in dopamine signaling and development. In addition, a previously identified mutation in PDE8B causes a rare autosomal-dominant type of striatal degeneration. Searching across both samples offers a rigorous way to screen for genes consistently influencing brain structure at different stages of life. Variants identified here may be relevant to common disorders affecting the caudate.

Voxelwise gene-wide association study (vGeneWAS): multivariate gene-based association testing in 731 elderly subjects

Imaging traits provide a powerful and biologically relevant substrate to examine the influence of genetics on the brain. Interest in genome-wide, brain-wide search for influential genetic variants is growing, but has mainly focused on univariate, SNP-based association tests. Moving to gene-based multivariate statistics, we can test the combined effect of multiple genetic variants in a single test statistic. Multivariate models can reduce the number of statistical tests in gene-wide or genome-wide scans and may discover gene effects undetectable with SNP-based methods. Here we present a gene-based method for associating the joint effect of single nucleotide polymorphisms (SNPs) in 18,044 genes across 31,662 voxels of the whole brain in 731 elderly subjects (mean age: 75.56±6.82SD years; 430 males) from the Alzheimer's Disease Neuroimaging Initiative (ADNI). Structural MRI scans were analyzed using tensor-based morphometry (TBM) to compute 3D maps of regional brain volume differences compared to an average template image based on healthy elderly subjects. Using the voxel-level volume difference values as the phenotype, we selected the most significantly associated gene (out of 18,044) at each voxel across the brain. No genes identified were significant after correction for multiple comparisons, but several known candidates were re-identified, as were other genes highly relevant to brain function. GAB2, which has been previously associated with late-onset AD, was identified as the top gene in this study, suggesting the validity of the approach. This multivariate, gene-based voxelwise association study offers a novel framework to detect genetic influences on the brain.

Penalized least squares regression methods and applications to neuroimaging

The goals of this paper are to review the most popular methods of predictor selection in regression models, to explain why some fail when the number P of explanatory variables exceeds the number N of participants, and to discuss alternative statistical methods that can be employed in this case. We focus on penalized least squares methods in regression models, and discuss in detail two such methods that are well established in the statistical literature, the LASSO and Elastic Net. We introduce bootstrap enhancements of these methods, the BE-LASSO and BE-Enet, that allow the user to attach a measure of uncertainty to each variable selected. Our work is motivated by a multimodal neuroimaging dataset that consists of morphometric measures (volumes at several anatomical regions of interest), white matter integrity measures from diffusion weighted data (fractional anisotropy, mean diffusivity, axial diffusivity and radial diffusivity) and clinical and demographic variables (age, education, alcohol and drug history). In this dataset, the number P of explanatory variables exceeds the number N of participants. We use the BE-LASSO and BE-Enet to provide the first statistical analysis that allows the assessment of neurocognitive performance from high dimensional neuroimaging and clinical predictors, including their interactions. The major novelty of this analysis is that biomarker selection and dimension reduction are accomplished with a view towards obtaining good predictions for the outcome of interest (i.e., the neurocognitive indices), unlike principal component analysis that are performed only on the predictors' space independently of the outcome of interest.