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

Discovering heritable modes of MEG spectral power

Brain structure and many brain functions are known to be genetically controlled, but direct links between neuroimaging measures and their underlying cellular-level determinants remain largely undiscovered. Here, we adopt a novel computational method for examining potential similarities in high-dimensional brain imaging data between siblings. We examine oscillatory brain activity measured with magnetoencephalography (MEG) in 201 healthy siblings and apply Bayesian reduced-rank regression to extract a low-dimensional representation of familial features in the participants' spectral power structure. Our results show that the structure of the overall spectral power at 1-90 Hz is a highly conspicuous feature that not only relates siblings to each other but also has very high consistency within participants' own data, irrespective of the exact experimental state of the participant. The analysis is extended by seeking genetic associations for low-dimensional descriptions of the oscillatory brain activity. The observed variability in the MEG spectral power structure was associated with SDK1 (sidekick cell adhesion molecule 1) and suggestively with several other genes that function, for example, in brain development. The current results highlight the potential of sophisticated computational methods in combining molecular and neuroimaging levels for exploring brain functions, even for high-dimensional data limited to a few hundred participants.

A Robust Reduced Rank Graph Regression Method for Neuroimaging Genetic Analysis

To characterize associations between genetic and neuroimaging data, a variety of analytic methods have been proposed in neuroimaging genetic studies. These methods have achieved promising performance by taking into account inherent correlation in either the neuroimaging data or the genetic data alone. In this study, we propose a novel robust reduced rank graph regression based method in a linear regression framework by considering correlations inherent in neuroimaging data and genetic data jointly. Particularly, we model the association analysis problem in a reduced rank regression framework with the genetic data as a feature matrix and the neuroimaging data as a response matrix by jointly considering correlations among the neuroimaging data as well as correlations between the genetic data and the neuroimaging data. A new graph representation of genetic data is adopted to exploit their inherent correlations, in addition to robust loss functions for both the regression and the data representation tasks, and a square-root-operator applied to the robust loss functions for achieving adaptive sample weighting. The resulting optimization problem is solved using an iterative optimization method whose convergence has been theoretically proved. Experimental results on the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset have demonstrated that our method could achieve competitive performance in terms of regression performance between brain structural measures and the Single Nucleotide Polymorphisms (SNPs), compared with state-of-the-art alternative methods.

Lateral Ventricle Enlargement and Cortical Thinning in Idiopathic Normal-pressure Hydrocephalus Patients

We utilized three-dimensional, surface-based, morphometric analysis to investigate ventricle shape between 2 groups: (1) idiopathic normal-pressure hydrocephalus (INPH) patients who had a positive response to the cerebrospinal fluid tap test (CSFTT) and (2) healthy controls. The aims were (1) to evaluate the location of INPH-related structural abnormalities of the lateral ventricles and (2) to investigate relationships between lateral ventricular enlargement and cortical thinning in INPH patients. Thirty-three INPH patients and 23 healthy controls were included in this study. We used sparse canonical correlation analysis to show correlated regions of ventricular surface expansion and cortical thinning. Significant surface expansion in the INPH group was observed mainly in clusters bilaterally located in the superior portion of the lateral ventricles, adjacent to the high convexity of the frontal and parietal regions. INPH patients showed a significant bilateral expansion of both the temporal horns of the lateral ventricles and the medial aspects of the frontal horns of the lateral ventricles to surrounding brain regions, including the medial frontal lobe. Ventricular surface expansion was associated with cortical thinning in the bilateral orbitofrontal cortex, bilateral rostral anterior cingulate cortex, left parahippocampal cortex, left temporal pole, right insula, right inferior temporal cortex, and right fusiform gyrus. These results suggest that patients with INPH have unique patterns of ventricular surface expansion. Our findings encourage future studies to elucidate the underlying mechanism of lateral ventricular morphometric abnormalities in INPH patients.

Quantitative trait loci identification for brain endophenotypes via new additive model with random networks

Motivation

The identification of quantitative trait loci (QTL) is critical to the study of causal relationships between genetic variations and disease abnormalities. We focus on identifying the QTLs associated to the brain endophenotypes in imaging genomics study for Alzheimer's Disease (AD). Existing research works mainly depict the association between single nucleotide polymorphisms (SNPs) and the brain endophenotypes via the linear methods, which may introduce high bias due to the simplicity of the models. Since the influence of QTLs on brain endophenotypes is quite complex, it is desired to design the appropriate non-linear models to investigate the associations of genotypes and endophenotypes.

Results

In this paper, we propose a new additive model to learn the non-linear associations between SNPs and brain endophenotypes in Alzheimer's disease. Our model can be flexibly employed to explain the non-linear influence of QTLs, thus is more adaptive for the complex distribution of the high-throughput biological data. Meanwhile, as an important computational learning theory contribution, we provide the generalization error analysis for the proposed approach. Unlike most previous theoretical analysis under independent and identically distributed samples assumption, our error bound is based on m-dependent observations, which is more appropriate for the high-throughput and noisy biological data. Experiments on the data from Alzheimer's Disease Neuroimaging Initiative (ADNI) cohort demonstrate the promising performance of our approach for identifying biological meaningful SNPs.

Availability and implementation

An executable is available at https://github.com/littleq1991/additive_FNNRW.

Strategies for integrated analysis in imaging genetics studies

Imaging Genetics (IG) integrates neuroimaging and genomic data from the same individual, deepening our knowledge of the biological mechanisms behind neurodevelopmental domains and neurological disorders. Although the literature on IG has exponentially grown over the past years, the majority of studies have mainly analyzed associations between candidate brain regions and individual genetic variants. However, this strategy is not designed to deal with the complexity of neurobiological mechanisms underlying behavioral and neurodevelopmental domains. Moreover, larger sample sizes and increased multidimensionality of this type of data represents a challenge for standardizing modeling procedures in IG research. This review provides a systematic update of the methods and strategies currently used in IG studies, and serves as an analytical framework for researchers working in this field. To complement the functionalities of the Neuroconductor framework, we also describe existing R packages that implement these methodologies. In addition, we present an overview of how these methodological approaches are applied in integrating neuroimaging and genetic data.

Identification of associations between genotypes and longitudinal phenotypes via temporally-constrained group sparse canonical correlation analysis

Motivation

Neuroimaging genetics identifies the relationships between genetic variants (i.e., the single nucleotide polymorphisms) and brain imaging data to reveal the associations from genotypes to phenotypes. So far, most existing machine-learning approaches are widely used to detect the effective associations between genetic variants and brain imaging data at one time-point. However, those associations are based on static phenotypes and ignore the temporal dynamics of the phenotypical changes. The phenotypes across multiple time-points may exhibit temporal patterns that can be used to facilitate the understanding of the degenerative process. In this article, we propose a novel temporally constrained group sparse canonical correlation analysis (TGSCCA) framework to identify genetic associations with longitudinal phenotypic markers.

Results

The proposed TGSCCA method is able to capture the temporal changes in brain from longitudinal phenotypes by incorporating the fused penalty, which requires that the differences between two consecutive canonical weight vectors from adjacent time-points should be small. A new efficient optimization algorithm is designed to solve the objective function. Furthermore, we demonstrate the effectiveness of our algorithm on both synthetic and real data (i.e., the Alzheimer’s Disease Neuroimaging Initiative cohort, including progressive mild cognitive impairment, stable MCI and Normal Control participants). In comparison with conventional SCCA, our proposed method can achieve strong associations and discover phenotypic biomarkers across multiple time-points to guide disease-progressive interpretation.

Availability and implementation

The Matlab code is available at https://sourceforge.net/projects/ibrain-cn/files/.

Whole genome association study of brain-wide imaging phenotypes: A study of the ping cohort

Neuropsychological disorders have a biological basis rooted in brain function, and neuroimaging data are expected to better illuminate the complex genetic basis of neuropsychological disorders. Because they are biological measures, neuroimaging data avoid biases arising from clinical diagnostic criteria that are subject to human understanding and interpretation. A challenge with analyzing neuroimaging data is their high dimensionality and complex spatial relationships. To tackle this challenge, we introduced a novel distance covariance tests that can assess the association between genetic markers and multivariate diffusion tensor imaging measurements, and analyzed a genome-wide association study (GWAS) dataset collected by the Pediatric Imaging, Neurocognition, and Genetics (PING) study. We also considered existing approaches as comparisons. Our results showed that, after correcting for multiplicity, distance covariance tests of the multivariate phenotype yield significantly greater power at detecting genetic markers affecting brain structure than standard mass univariate GWAS of individual neuroimaging biomarkers. Our results underscore the usefulness of utilizing the distance covariance to incorporate neuroimaging data in GWAS.

Fast and Accurate Detection of Complex Imaging Genetics Associations Based on Greedy Projected Distance Correlation

Recent advances in imaging genetics produce large amounts of data including functional MRI images, single nucleotide polymorphisms (SNPs), and cognitive assessments. Understanding the complex interactions among these heterogeneous and complementary data has the potential to help with diagnosis and prevention of mental disorders. However, limited efforts have been made due to the high dimensionality, group structure, and mixed type of these data. In this paper we present a novel method to detect conditional associations between imaging genetics data. We use projected distance correlation to build a conditional dependency graph among high-dimensional mixed data, then use multiple testing to detect significant group level associations (e.g., ROI-gene). In addition, we introduce a scalable algorithm based on orthogonal greedy algorithm, yielding the greedy projected distance correlation (G-PDC). This can reduce the computational cost, which is critical for analyzing large-volume of imaging genomics data. The results from our simulations demonstrate a higher degree of accuracy with GPDC than distance correlation, Pearson's correlation and partial correlation, especially when the correlation is nonlinear. Finally, we apply our method to the Philadelphia Neurodevelopmental data cohort with 866 samples including fMRI images and SNP profiles. The results uncover several statistically significant and biologically interesting interactions, which are further validated with many existing studies. The Matlab code is available at https://sites.google.com/site/jianfang86/gPDC.

Susceptibility of brain atrophy to TRIB3 in Alzheimer's disease, evidence from functional prioritization in imaging genetics

The joint modeling of brain imaging information and genetic data is a promising research avenue to highlight the functional role of genes in determining the pathophysiological mechanisms of Alzheimer's disease (AD). However, since genome-wide association (GWA) studies are essentially limited to the exploration of statistical correlations between genetic variants and phenotype, the validation and interpretation of the findings are usually nontrivial and prone to false positives. To address this issue, in this work, we investigate the functional genetic mechanisms underlying brain atrophy in AD by studying the involvement of candidate variants in known genetic regulatory functions. This approach, here termed functional prioritization, aims at testing the sets of gene variants identified by high-dimensional multivariate statistical modeling with respect to known biological processes to introduce a biology-driven validation scheme. When applied to the Alzheimer's Disease Neuroimaging Initiative (ADNI) cohort, the functional prioritization allowed for identifying a link between tribbles pseudokinase 3 (TRIB3) and the stereotypical pattern of gray matter loss in AD, which was confirmed in an independent validation sample, and that provides evidence about the relation between this gene and known mechanisms of neurodegeneration.

Machine learning shows association between genetic variability in PPARG and cerebral connectivity in preterm infants

Preterm birth affects 11% of births globally; 35% of infants develop long-term neurocognitive problems, and prematurity leads to the loss of 75 million disability adjusted life years per annum worldwide. Imaging studies have shown that these infants have extensive alterations in brain development, but little is known about the molecular or cellular mechanisms involved. This imaging genetics study found a strong association between abnormal cerebral connectivity and variability in the PPARG gene, implicating PPARG signaling in abnormal white-matter development in preterm infants and suggesting a tractable new target for therapeutic research.

Preterm infants show abnormal structural and functional brain development, and have a high risk of long-term neurocognitive problems. The molecular and cellular mechanisms involved are poorly understood, but novel methods now make it possible to address them by examining the relationship between common genetic variability and brain endophenotype. We addressed the hypothesis that variability in the Peroxisome Proliferator Activated Receptor (PPAR) pathway would be related to brain development. We employed machine learning in an unsupervised, unbiased, combined analysis of whole-brain diffusion tractography together with genomewide, single-nucleotide polymorphism (SNP)-based genotypes from a cohort of 272 preterm infants, using Sparse Reduced Rank Regression (sRRR) and correcting for ethnicity and age at birth and imaging. Empirical selection frequencies for SNPs associated with cerebral connectivity ranged from 0.663 to zero, with multiple highly selected SNPs mapping to genes for PPARG (six SNPs), ITGA6 (four SNPs), and FXR1 (two SNPs). SNPs in PPARG were significantly overrepresented (ranked 7–11 and 67 of 556,000 SNPs; P < 2.2 × 10⁻⁷), and were mostly in introns or regulatory regions with predicted effects including protein coding and nonsense-mediated decay. Edge-centric graph-theoretic analysis showed that highly selected white-matter tracts were consistent across the group and important for information transfer (P < 2.2 × 10⁻¹⁷); they most often connected to the insula (P < 6 × 10⁻¹⁷). These results suggest that the inhibited brain development seen in humans exposed to the stress of a premature extrauterine environment is modulated by genetic factors, and that PPARG signaling has a previously unrecognized role in cerebral development.

Groupwise envelope models for imaging genetic analysis

Motivated by searching for associations between genetic variants and brain imaging phenotypes, the aim of this article is to develop a groupwise envelope model for multivariate linear regression in order to establish the association between both multivariate responses and covariates. The groupwise envelope model allows for both distinct regression coefficients and distinct error structures for different groups. Statistically, the proposed envelope model can dramatically improve efficiency of tests and of estimation. Theoretical properties of the proposed model are established. Numerical experiments as well as the analysis of an imaging genetic data set obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) study show the effectiveness of the model in efficient estimation. Data used in preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database.

Neuroimaging genomics in psychiatry-a translational approach

Neuroimaging genomics is a relatively new field focused on integrating genomic and imaging data in order to investigate the mechanisms underlying brain phenotypes and neuropsychiatric disorders. While early work in neuroimaging genomics focused on mapping the associations of candidate gene variants with neuroimaging measures in small cohorts, the lack of reproducible results inspired better-powered and unbiased large-scale approaches. Notably, genome-wide association studies (GWAS) of brain imaging in thousands of individuals around the world have led to a range of promising findings. Extensions of such approaches are now addressing epigenetics, gene–gene epistasis, and gene–environment interactions, not only in brain structure, but also in brain function. Complementary developments in systems biology might facilitate the translation of findings from basic neuroscience and neuroimaging genomics to clinical practice. Here, we review recent approaches in neuroimaging genomics—we highlight the latest discoveries, discuss advantages and limitations of current approaches, and consider directions by which the field can move forward to shed light on brain disorders.

Pattern Discovery in Brain Imaging Genetics via SCCA Modeling with a Generic Non-convex Penalty

Brain imaging genetics intends to uncover associations between genetic markers and neuroimaging quantitative traits. Sparse canonical correlation analysis (SCCA) can discover bi-multivariate associations and select relevant features, and is becoming popular in imaging genetic studies. The L1-norm function is not only convex, but also singular at the origin, which is a necessary condition for sparsity. Thus most SCCA methods impose [Formula: see text]-norm onto the individual feature or the structure level of features to pursuit corresponding sparsity. However, the [Formula: see text]-norm penalty over-penalizes large coefficients and may incurs estimation bias. A number of non-convex penalties are proposed to reduce the estimation bias in regression tasks. But using them in SCCA remains largely unexplored. In this paper, we design a unified non-convex SCCA model, based on seven non-convex functions, for unbiased estimation and stable feature selection simultaneously. We also propose an efficient optimization algorithm. The proposed method obtains both higher correlation coefficients and better canonical loading patterns. Specifically, these SCCA methods with non-convex penalties discover a strong association between the APOE e4 rs429358 SNP and the hippocampus region of the brain. They both are Alzheimer's disease related biomarkers, indicating the potential and power of the non-convex methods in brain imaging genetics.

A quadratically regularized functional canonical correlation analysis for identifying the global structure of pleiotropy with NGS data

Investigating the pleiotropic effects of genetic variants can increase statistical power, provide important information to achieve deep understanding of the complex genetic structures of disease, and offer powerful tools for designing effective treatments with fewer side effects. However, the current multiple phenotype association analysis paradigm lacks breadth (number of phenotypes and genetic variants jointly analyzed at the same time) and depth (hierarchical structure of phenotype and genotypes). A key issue for high dimensional pleiotropic analysis is to effectively extract informative internal representation and features from high dimensional genotype and phenotype data. To explore correlation information of genetic variants, effectively reduce data dimensions, and overcome critical barriers in advancing the development of novel statistical methods and computational algorithms for genetic pleiotropic analysis, we proposed a new statistic method referred to as a quadratically regularized functional CCA (QRFCCA) for association analysis which combines three approaches: (1) quadratically regularized matrix factorization, (2) functional data analysis and (3) canonical correlation analysis (CCA). Large-scale simulations show that the QRFCCA has a much higher power than that of the ten competing statistics while retaining the appropriate type 1 errors. To further evaluate performance, the QRFCCA and ten other statistics are applied to the whole genome sequencing dataset from the TwinsUK study. We identify a total of 79 genes with rare variants and 67 genes with common variants significantly associated with the 46 traits using QRFCCA. The results show that the QRFCCA substantially outperforms the ten other statistics.

Low-Rank Graph-Regularized Structured Sparse Regression for Identifying Genetic Biomarkers

In this paper, we propose a novel sparse regression method for Brain-Wide and Genome-Wide association study. Specifically, we impose a low-rank constraint on the weight coefficient matrix and then decompose it into two low-rank matrices, which find relationships in genetic features and in brain imaging features, respectively. We also introduce a sparse acyclic digraph with sparsity-inducing penalty to take further into account the correlations among the genetic variables, by which it can be possible to identify the representative SNPs that are highly associated with the brain imaging features. We optimize our objective function by jointly tackling low-rank regression and variable selection in a framework. In our method, the low-rank constraint allows us to conduct variable selection with the low-rank representations of the data; the learned low-sparsity weight coefficients allow discarding unimportant variables at the end. The experimental results on the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset showed that the proposed method could select the important SNPs to more accurately estimate the brain imaging features than the state-of-the-art methods.

A Bayesian group sparse multi-task regression model for imaging genetics

MOTIVATION

Recent advances in technology for brain imaging and high-throughput genotyping have motivated studies examining the influence of genetic variation on brain structure. Wang et al. have developed an approach for the analysis of imaging genomic studies using penalized multi-task regression with regularization based on a novel group l2,1-norm penalty which encourages structured sparsity at both the gene level and SNP level. While incorporating a number of useful features, the proposed method only furnishes a point estimate of the regression coefficients; techniques for conducting statistical inference are not provided. A new Bayesian method is proposed here to overcome this limitation.

RESULTS

We develop a Bayesian hierarchical modeling formulation where the posterior mode corresponds to the estimator proposed by Wang et al. and an approach that allows for full posterior inference including the construction of interval estimates for the regression parameters. We show that the proposed hierarchical model can be expressed as a three-level Gaussian scale mixture and this representation facilitates the use of a Gibbs sampling algorithm for posterior simulation. Simulation studies demonstrate that the interval estimates obtained using our approach achieve adequate coverage probabilities that outperform those obtained from the nonparametric bootstrap. Our proposed methodology is applied to the analysis of neuroimaging and genetic data collected as part of the Alzheimer's Disease Neuroimaging Initiative (ADNI), and this analysis of the ADNI cohort demonstrates clearly the value added of incorporating interval estimation beyond only point estimation when relating SNPs to brain imaging endophenotypes.

AVAILABILITY AND IMPLEMENTATION

Software and sample data is available as an R package 'bgsmtr' that can be downloaded from The Comprehensive R Archive Network (CRAN).

CONTACT

nathoo@uvic.ca.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Imaging Genetics and Genomics in Psychiatry: A Critical Review of Progress and Potential

Imaging genetics and genomics research has begun to provide insight into the molecular and genetic architecture of neural phenotypes and the neural mechanisms through which genetic risk for psychopathology may emerge. As it approaches its third decade, imaging genetics is confronted by many challenges, including the proliferation of studies using small sample sizes and diverse designs, limited replication, problems with harmonization of neural phenotypes for meta-analysis, unclear mechanisms, and evidence that effect sizes may be more modest than originally posited, with increasing evidence of polygenicity. These concerns have encouraged the field to grow in many new directions, including the development of consortia and large-scale data collection projects and the use of novel methods (e.g., polygenic approaches, machine learning) that enhance the quality of imaging genetic studies but also introduce new challenges. We critically review progress in imaging genetics and offer suggestions and highlight potential pitfalls of novel approaches. Ultimately, the strength of imaging genetics and genomics lies in their translational and integrative potential with other research approaches (e.g., nonhuman animal models, psychiatric genetics, pharmacologic challenge) to elucidate brain-based pathways that give rise to the vast individual differences in behavior as well as risk for psychopathology.

Robust reduced-rank regression

In high-dimensional multivariate regression problems, enforcing low rank in the coefficient matrix offers effective dimension reduction, which greatly facilitates parameter estimation and model interpretation. However, commonly used reduced-rank methods are sensitive to data corruption, as the low-rank dependence structure between response variables and predictors is easily distorted by outliers. We propose a robust reduced-rank regression approach for joint modelling and outlier detection. The problem is formulated as a regularized multivariate regression with a sparse mean-shift parameterization, which generalizes and unifies some popular robust multivariate methods. An efficient thresholding-based iterative procedure is developed for optimization. We show that the algorithm is guaranteed to converge and that the coordinatewise minimum point produced is statistically accurate under regularity conditions. Our theoretical investigations focus on non-asymptotic robust analysis, demonstrating that joint rank reduction and outlier detection leads to improved prediction accuracy. In particular, we show that redescending ψ-functions can essentially attain the minimax optimal error rate, and in some less challenging problems convex regularization guarantees the same low error rate. The performance of the proposed method is examined through simulation studies and real-data examples.

Joint prediction of multiple scores captures better individual traits from brain images

To probe individual variations in brain organization, population imaging relates features of brain images to rich descriptions of the subjects such as genetic information or behavioral and clinical assessments. Capturing common trends across these measurements is important: they jointly characterize the disease status of patient groups. In particular, mapping imaging features to behavioral scores with predictive models opens the way toward more precise diagnosis. Here we propose to jointly predict all the dimensions (behavioral scores) that make up the individual profiles, using so-called multi-output models. This approach often boosts prediction accuracy by capturing latent shared information across scores. We demonstrate the efficiency of multi-output models on two independent resting-state fMRI datasets targeting different brain disorders (Alzheimer's Disease and schizophrenia). Furthermore, the model with joint prediction generalizes much better to a new cohort: a model learned on one study is more accurately transferred to an independent one. Finally, we show how multi-output models can easily be extended to multi-modal settings, combining heterogeneous data sources for a better overall accuracy.

Mining Outcome-relevant Brain Imaging Genetic Associations via Three-way Sparse Canonical Correlation Analysis in Alzheimer's Disease

Neuroimaging genetics is an emerging field that aims to identify the associations between genetic variants (e.g., single nucleotide polymorphisms (SNPs)) and quantitative traits (QTs) such as brain imaging phenotypes. In recent studies, in order to detect complex multi-SNP-multi-QT associations, bi-multivariate techniques such as various structured sparse canonical correlation analysis (SCCA) algorithms have been proposed and used in imaging genetics studies. However, associations between genetic markers and imaging QTs identified by existing bi-multivariate methods may not be all disease specific. To bridge this gap, we propose an analytical framework, based on three-way sparse canonical correlation analysis (T-SCCA), to explore the intrinsic associations among genetic markers, imaging QTs, and clinical scores of interest. We perform an empirical study using the Alzheimer's Disease Neuroimaging Initiative (ADNI) cohort to discover the relationships among SNPs from AD risk gene APOE, imaging QTs extracted from structural magnetic resonance imaging scans, and cognitive and diagnostic outcomes. The proposed T-SCCA model not only outperforms the traditional SCCA method in terms of identifying strong associations, but also discovers robust outcome-relevant imaging genetic patterns, demonstrating its promise for improving disease-related mechanistic understanding.

Adaptive testing for multiple traits in a proportional odds model with applications to detect SNP-brain network associations

There has been increasing interest in developing more powerful and flexible statistical tests to detect genetic associations with multiple traits, as arising from neuroimaging genetic studies. Most of existing methods treat a single trait or multiple traits as response while treating an SNP as a predictor coded under an additive inheritance mode. In this paper, we follow an earlier approach in treating an SNP as an ordinal response while treating traits as predictors in a proportional odds model (POM). In this way, it is not only easier to handle mixed types of traits, e.g., some quantitative and some binary, but it is also potentially more robust to the commonly adopted additive inheritance mode. More importantly, we develop an adaptive test in a POM so that it can maintain high power across many possible situations. Compared to the existing methods treating multiple traits as responses, e.g., in a generalized estimating equation (GEE) approach, the proposed method can be applied to a high dimensional setting where the number of phenotypes (p) can be larger than the sample size (n), in addition to a usual small P setting. The promising performance of the proposed method was demonstrated with applications to the Alzheimer's Disease Neuroimaging Initiative (ADNI) data, in which either structural MRI driven phenotypes or resting-state functional MRI (rs-fMRI) derived brain functional connectivity measures were used as phenotypes. The applications led to the identification of several top SNPs of biological interest. Furthermore, simulation studies showed competitive performance of the new method, especially for p>n.

Bayesian longitudinal low-rank regression models for imaging genetic data from longitudinal studies

To perform a joint analysis of multivariate neuroimaging phenotypes and candidate genetic markers obtained from longitudinal studies, we develop a Bayesian longitudinal low-rank regression (L2R2) model. The L2R2 model integrates three key methodologies: a low-rank matrix for approximating the high-dimensional regression coefficient matrices corresponding to the genetic main effects and their interactions with time, penalized splines for characterizing the overall time effect, and a sparse factor analysis model coupled with random effects for capturing within-subject spatio-temporal correlations of longitudinal phenotypes. Posterior computation proceeds via an efficient Markov chain Monte Carlo algorithm. Simulations show that the L2R2 model outperforms several other competing methods. We apply the L2R2 model to investigate the effect of single nucleotide polymorphisms (SNPs) on the top 10 and top 40 previously reported Alzheimer disease-associated genes. We also identify associations between the interactions of these SNPs with patient age and the tissue volumes of 93 regions of interest from patients' brain images obtained from the Alzheimer's Disease Neuroimaging Initiative.

ENIGMA and the individual: Predicting factors that affect the brain in 35 countries worldwide

In this review, we discuss recent work by the ENIGMA Consortium (http://enigma.ini.usc.edu) - a global alliance of over 500 scientists spread across 200 institutions in 35 countries collectively analyzing brain imaging, clinical, and genetic data. Initially formed to detect genetic influences on brain measures, ENIGMA has grown to over 30 working groups studying 12 major brain diseases by pooling and comparing brain data. In some of the largest neuroimaging studies to date - of schizophrenia and major depression - ENIGMA has found replicable disease effects on the brain that are consistent worldwide, as well as factors that modulate disease effects. In partnership with other consortia including ADNI, CHARGE, IMAGEN and others1, ENIGMA's genomic screens - now numbering over 30,000 MRI scans - have revealed at least 8 genetic loci that affect brain volumes. Downstream of gene findings, ENIGMA has revealed how these individual variants - and genetic variants in general - may affect both the brain and risk for a range of diseases. The ENIGMA consortium is discovering factors that consistently affect brain structure and function that will serve as future predictors linking individual brain scans and genomic data. It is generating vast pools of normative data on brain measures - from tens of thousands of people - that may help detect deviations from normal development or aging in specific groups of subjects. We discuss challenges and opportunities in applying these predictors to individual subjects and new cohorts, as well as lessons we have learned in ENIGMA's efforts so far.

Joint sparse canonical correlation analysis for detecting differential imaging genetics modules

MOTIVATION

Imaging genetics combines brain imaging and genetic information to identify the relationships between genetic variants and brain activities. When the data samples belong to different classes (e.g. disease status), the relationships may exhibit class-specific patterns that can be used to facilitate the understanding of a disease. Conventional approaches often perform separate analysis on each class and report the differences, but ignore important shared patterns.

RESULTS

In this paper, we develop a multivariate method to analyze the differential dependency across multiple classes. We propose a joint sparse canonical correlation analysis method, which uses a generalized fused lasso penalty to jointly estimate multiple pairs of canonical vectors with both shared and class-specific patterns. Using a data fusion approach, the method is able to detect differentially correlated modules effectively and efficiently. The results from simulation studies demonstrate its higher accuracy in discovering both common and differential canonical correlations compared to conventional sparse CCA. Using a schizophrenia dataset with 92 cases and 116 controls including a single nucleotide polymorphism (SNP) array and functional magnetic resonance imaging data, the proposed method reveals a set of distinct SNP-voxel interaction modules for the schizophrenia patients, which are verified to be both statistically and biologically significant.

AVAILABILITY AND IMPLEMENTATION

The Matlab code is available at https://sites.google.com/site/jianfang86/JSCCA CONTACT: wyp@tulane.eduSupplementary information: Supplementary data are available at Bioinformatics online.

Structured Sparse Low-Rank Regression Model for Brain-Wide and Genome-Wide Associations

With the advances of neuroimaging techniques and genome sequences understanding, the phenotype and genotype data have been utilized to study the brain diseases (known as imaging genetics). One of the most important topics in image genetics is to discover the genetic basis of phenotypic markers and their associations. In such studies, the linear regression models have been playing an important role by providing interpretable results. However, due to their modeling characteristics, it is limited to effectively utilize inherent information among the phenotypes and genotypes, which are helpful for better understanding their associations. In this work, we propose a structured sparse low-rank regression method to explicitly consider the correlations within the imaging phenotypes and the genotypes simultaneously for Brain-Wide and Genome-Wide Association (BW-GWA) study. Specifically, we impose the low-rank constraint as well as the structured sparse constraint on both phenotypes and phenotypes. By using the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset, we conducted experiments of predicting the phenotype data from genotype data and achieved performance improvement by 12.75 % on average in terms of the root-mean-square error over the state-of-the-art methods.

Identifying Multimodal Intermediate Phenotypes Between Genetic Risk Factors and Disease Status in Alzheimer's Disease

Neuroimaging genetics has attracted growing attention and interest, which is thought to be a powerful strategy to examine the influence of genetic variants (i.e., single nucleotide polymorphisms (SNPs)) on structures or functions of human brain. In recent studies, univariate or multivariate regression analysis methods are typically used to capture the effective associations between genetic variants and quantitative traits (QTs) such as brain imaging phenotypes. The identified imaging QTs, although associated with certain genetic markers, may not be all disease specific. A useful, but underexplored, scenario could be to discover only those QTs associated with both genetic markers and disease status for revealing the chain from genotype to phenotype to symptom. In addition, multimodal brain imaging phenotypes are extracted from different perspectives and imaging markers consistently showing up in multimodalities may provide more insights for mechanistic understanding of diseases (i.e., Alzheimer's disease (AD)). In this work, we propose a general framework to exploit multi-modal brain imaging phenotypes as intermediate traits that bridge genetic risk factors and multi-class disease status. We applied our proposed method to explore the relation between the well-known AD risk SNP APOE rs429358 and three baseline brain imaging modalities (i.e., structural magnetic resonance imaging (MRI), fluorodeoxyglucose positron emission tomography (FDG-PET) and F-18 florbetapir PET scans amyloid imaging (AV45)) from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database. The empirical results demonstrate that our proposed method not only helps improve the performances of imaging genetic associations, but also discovers robust and consistent regions of interests (ROIs) across multi-modalities to guide the disease-induced interpretation.

Generalized reduced rank latent factor regression for high dimensional tensor fields, and neuroimaging-genetic applications

We propose a generalized reduced rank latent factor regression model (GRRLF) for the analysis of tensor field responses and high dimensional covariates. The model is motivated by the need from imaging-genetic studies to identify genetic variants that are associated with brain imaging phenotypes, often in the form of high dimensional tensor fields. GRRLF identifies from the structure in the data the effective dimensionality of the data, and then jointly performs dimension reduction of the covariates, dynamic identification of latent factors, and nonparametric estimation of both covariate and latent response fields. After accounting for the latent and covariate effects, GRLLF performs a nonparametric test on the remaining factor of interest. GRRLF provides a better factorization of the signals compared with common solutions, and is less susceptible to overfitting because it exploits the effective dimensionality. The generality and the flexibility of GRRLF also allow various statistical models to be handled in a unified framework and solutions can be efficiently computed. Within the field of neuroimaging, it improves the sensitivity for weak signals and is a promising alternative to existing approaches. The operation of the framework is demonstrated with both synthetic datasets and a real-world neuroimaging example in which the effects of a set of genes on the structure of the brain at the voxel level were measured, and the results compared favorably with those from existing approaches.

Structured sparse CCA for brain imaging genetics via graph OSCAR

BACKGROUND

Recently, structured sparse canonical correlation analysis (SCCA) has received increased attention in brain imaging genetics studies. It can identify bi-multivariate imaging genetic associations as well as select relevant features with desired structure information. These SCCA methods either use the fused lasso regularizer to induce the smoothness between ordered features, or use the signed pairwise difference which is dependent on the estimated sign of sample correlation. Besides, several other structured SCCA models use the group lasso or graph fused lasso to encourage group structure, but they require the structure/group information provided in advance which sometimes is not available.

RESULTS

We propose a new structured SCCA model, which employs the graph OSCAR (GOSCAR) regularizer to encourage those highly correlated features to have similar or equal canonical weights. Our GOSCAR based SCCA has two advantages: 1) It does not require to pre-define the sign of the sample correlation, and thus could reduce the estimation bias. 2) It could pull those highly correlated features together no matter whether they are positively or negatively correlated. We evaluate our method using both synthetic data and real data. Using the 191 ROI measurements of amyloid imaging data, and 58 genetic markers within the APOE gene, our method identifies a strong association between APOE SNP rs429358 and the amyloid burden measure in the frontal region. In addition, the estimated canonical weights present a clear pattern which is preferable for further investigation.

CONCLUSIONS

Our proposed method shows better or comparable performance on the synthetic data in terms of the estimated correlations and canonical loadings. It has successfully identified an important association between an Alzheimer's disease risk SNP rs429358 and the amyloid burden measure in the frontal region.

Probabilistic Modeling of Imaging, Genetics and Diagnosis

We propose a unified Bayesian framework for detecting genetic variants associated with disease by exploiting image-based features as an intermediate phenotype. The use of imaging data for examining genetic associations promises new directions of analysis, but currently the most widely used methods make sub-optimal use of the richness that these data types can offer. Currently, image features are most commonly selected based on their relevance to the disease phenotype. Then, in a separate step, a set of genetic variants is identified to explain the selected features. In contrast, our method performs these tasks simultaneously in order to jointly exploit information in both data types. The analysis yields probabilistic measures of clinical relevance for both imaging and genetic markers. We derive an efficient approximate inference algorithm that handles the high dimensionality of image and genetic data. We evaluate the algorithm on synthetic data and demonstrate that it outperforms traditional models. We also illustrate our method on Alzheimer's Disease Neuroimaging Initiative data.

Multimodal fusion of brain imaging data: A key to finding the missing link(s) in complex mental illness

It is becoming increasingly clear that combining multi-modal brain imaging data is able to provide more information for individual subjects by exploiting the rich multimodal information that exists. However, the number of studies that do true multimodal fusion (i.e. capitalizing on joint information among modalities) is still remarkably small given the known benefits. In part, this is because multi-modal studies require broader expertise in collecting, analyzing, and interpreting the results than do unimodal studies. In this paper, we start by introducing the basic reasons why multimodal data fusion is important and what it can do, and importantly how it can help us avoid wrong conclusions and help compensate for imperfect brain imaging studies. We also discuss the challenges that need to be confronted for such approaches to be more widely applied by the community. We then provide a review of the diverse studies that have used multimodal data fusion (primarily focused on psychosis) as well as provide an introduction to some of the existing analytic approaches. Finally, we discuss some up-and-coming approaches to multi-modal fusion including deep learning and multimodal classification which show considerable promise. Our conclusion is that multimodal data fusion is rapidly growing, but it is still underutilized. The complexity of the human brain coupled with the incomplete measurement provided by existing imaging technology makes multimodal fusion essential in order to mitigate against misdirection and hopefully provide a key to finding the missing link(s) in complex mental illness.

APPLYING SPARSE CODING TO SURFACE MULTIVARIATE TENSOR-BASED MORPHOMETRY TO PREDICT FUTURE COGNITIVE DECLINE

Alzheimer's disease (AD) is a progressive brain disease. Accurate diagnosis of AD and its prodromal stage, mild cognitive impairment, is crucial for clinical trial design. There is also growing interests in identifying brain imaging biomarkers that help evaluate AD risk presymptomatically. Here, we applied a recently developed multivariate tensor-based morphometry (mTBM) method to extract features from hippocampal surfaces, derived from anatomical brain MRI. For such surface-based features, the feature dimension is usually much larger than the number of subjects. We used dictionary learning and sparse coding to effectively reduce the feature dimensions. With the new features, an Adaboost classifier was employed for binary group classification. In tests on publicly available data from the Alzheimers Disease Neuroimaging Initiative, the new framework outperformed several standard imaging measures in classifying different stages of AD. The new approach combines the efficiency of sparse coding with the sensitivity of surface mTBM, and boosts classification performance.

Structured sparse canonical correlation analysis for brain imaging genetics: an improved GraphNet method

MOTIVATION

Structured sparse canonical correlation analysis (SCCA) models have been used to identify imaging genetic associations. These models either use group lasso or graph-guided fused lasso to conduct feature selection and feature grouping simultaneously. The group lasso based methods require prior knowledge to define the groups, which limits the capability when prior knowledge is incomplete or unavailable. The graph-guided methods overcome this drawback by using the sample correlation to define the constraint. However, they are sensitive to the sign of the sample correlation, which could introduce undesirable bias if the sign is wrongly estimated.

RESULTS

We introduce a novel SCCA model with a new penalty, and develop an efficient optimization algorithm. Our method has a strong upper bound for the grouping effect for both positively and negatively correlated features. We show that our method performs better than or equally to three competing SCCA models on both synthetic and real data. In particular, our method identifies stronger canonical correlations and better canonical loading patterns, showing its promise for revealing interesting imaging genetic associations.

AVAILABILITY AND IMPLEMENTATION

The Matlab code and sample data are freely available at http://www.iu.edu/∼shenlab/tools/angscca/

CONTACT

shenli@iu.edu

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Integrative Bayesian analysis of neuroimaging-genetic data with application to cocaine dependence

Neuroimaging and genetic studies provide distinct and complementary information about the structural and biological aspects of a disease. Integrating the two sources of data facilitates the investigation of the links between genetic variability and brain mechanisms among different individuals for various medical disorders. This article presents a general statistical framework for integrative Bayesian analysis of neuroimaging-genetic (iBANG) data, which is motivated by a neuroimaging-genetic study in cocaine dependence. Statistical inference necessitated the integration of spatially dependent voxel-level measurements with various patient-level genetic and demographic characteristics under an appropriate probability model to account for the multiple inherent sources of variation. Our framework uses Bayesian model averaging to integrate genetic information into the analysis of voxel-wise neuroimaging data, accounting for spatial correlations in the voxels. Using multiplicity controls based on the false discovery rate, we delineate voxels associated with genetic and demographic features that may impact diffusion as measured by fractional anisotropy (FA) obtained from DTI images. We demonstrate the benefits of accounting for model uncertainties in both model fit and prediction. Our results suggest that cocaine consumption is associated with FA reduction in most white matter regions of interest in the brain. Additionally, gene polymorphisms associated with GABAergic, serotonergic and dopaminergic neurotransmitters and receptors were associated with FA.

Parallel ICA with multiple references: a semi-blind multivariate approach

High data dimensionality poses a major challenge for imaging genomic studies. To address this issue, a semi-blind multivariate approach, parallel independent component analysis with multiple references (pICA-MR), is proposed. pICA-MR extracts imaging and genetic components in parallel and enhances inter-modality correlations. Prior knowledge is incorporated to emphasize genetic factors with specific attributes. Particularly, pICA-MR can investigate multiple genetic references to explore functional interactions among genes. Simulations demonstrate robust performances with Euclidean distance employed as a metric for reference similarity, where components pointed by the same references are reliably identified and the detection power is significantly improved compared to blind methods.

An introductory review of parallel independent component analysis (p-ICA) and a guide to applying p-ICA to genetic data and imaging phenotypes to identify disease-associated biological pathways and systems in common complex disorders

Complex inherited phenotypes, including those for many common medical and psychiatric diseases, are most likely underpinned by multiple genes contributing to interlocking molecular biological processes, along with environmental factors (Owen et al., 2010). Despite this, genotyping strategies for complex, inherited, disease-related phenotypes mostly employ univariate analyses, e.g., genome wide association. Such procedures most often identify isolated risk-related SNPs or loci, not the underlying biological pathways necessary to help guide the development of novel treatment approaches. This article focuses on the multivariate analysis strategy of parallel (i.e., simultaneous combination of SNP and neuroimage information) independent component analysis (p-ICA), which typically yields large clusters of functionally related SNPs statistically correlated with phenotype components, whose overall molecular biologic relevance is inferred subsequently using annotation software suites. Because this is a novel approach, whose details are relatively new to the field we summarize its underlying principles and address conceptual questions regarding interpretation of resulting data and provide practical illustrations of the method.

FVGWAS: Fast voxelwise genome wide association analysis of large-scale imaging genetic data

More and more large-scale imaging genetic studies are being widely conducted to collect a rich set of imaging, genetic, and clinical data to detect putative genes for complexly inherited neuropsychiatric and neurodegenerative disorders. Several major big-data challenges arise from testing genome-wide (NC>12 million known variants) associations with signals at millions of locations (NV~10(6)) in the brain from thousands of subjects (n~10(3)). The aim of this paper is to develop a Fast Voxelwise Genome Wide Association analysiS (FVGWAS) framework to efficiently carry out whole-genome analyses of whole-brain data. FVGWAS consists of three components including a heteroscedastic linear model, a global sure independence screening (GSIS) procedure, and a detection procedure based on wild bootstrap methods. Specifically, for standard linear association, the computational complexity is O (nNVNC) for voxelwise genome wide association analysis (VGWAS) method compared with O ((NC+NV)n(2)) for FVGWAS. Simulation studies show that FVGWAS is an efficient method of searching sparse signals in an extremely large search space, while controlling for the family-wise error rate. Finally, we have successfully applied FVGWAS to a large-scale imaging genetic data analysis of ADNI data with 708 subjects, 193,275voxels in RAVENS maps, and 501,584 SNPs, and the total processing time was 203,645s for a single CPU. Our FVGWAS may be a valuable statistical toolbox for large-scale imaging genetic analysis as the field is rapidly advancing with ultra-high-resolution imaging and whole-genome sequencing.

2014 Update of 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 initial study, ADNI-1, enrolled 400 subjects with early mild cognitive impairment (MCI), 200 with early AD, and 200 cognitively normal elderly controls. ADNI-1 was extended by a 2-year Grand Opportunities grant in 2009 and by a competitive renewal, ADNI-2, which enrolled an additional 550 participants and will run until 2015. This article reviews all papers published since the inception of the initiative and summarizes the results to the end of 2013. 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 largely consistent with disease trajectories predicted by β-amyloid cascade (Hardy, J Alzheimer's 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 select and combine optimum features from multiple modalities, including MRI, [(18)F]-fluorodeoxyglucose-PET, amyloid PET, CSF biomarkers, and clinical tests; (4) the development of blood biomarkers for AD as potentially noninvasive and low-cost alternatives to CSF biomarkers for AD diagnosis and the assessment of α-syn as an additional biomarker; (5) 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; (6) 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. Multimodal methods incorporating APOE status and longitudinal MRI proved most highly predictive of future decline. Refinements of clinical tests used as outcome measures such as clinical dementia rating-sum of boxes further reduced sample sizes; (7) the pioneering of genome-wide association studies that leverage quantitative imaging and biomarker phenotypes, including longitudinal data, to confirm recently identified loci, CR1, CLU, and PICALM and to identify novel AD risk loci; (8) worldwide impact through the establishment of ADNI-like programs in Japan, Australia, Argentina, Taiwan, China, Korea, Europe, and Italy; (9) understanding the biology and pathobiology of normal aging, MCI, and AD through integration of ADNI biomarker and clinical data 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 (10) the establishment of infrastructure to allow sharing of all raw and processed data without embargo to interested scientific investigators throughout the world.

Equivalence of kernel machine regression and kernel distance covariance for multidimensional phenotype association studies

Associating genetic markers with a multidimensional phenotype is an important yet challenging problem. In this work, we establish the equivalence between two popular methods: kernel-machine regression (KMR), and kernel distance covariance (KDC). KMR is a semiparametric regression framework that models covariate effects parametrically and genetic markers non-parametrically, while KDC represents a class of methods that include distance covariance (DC) and Hilbert-Schmidt independence criterion (HSIC), which are nonparametric tests of independence. We show that the equivalence between the score test of KMR and the KDC statistic under certain conditions can lead to a novel generalization of the KDC test that incorporates covariates. Our contributions are 3-fold: (1) establishing the equivalence between KMR and KDC; (2) showing that the principles of KMR can be applied to the interpretation of KDC; (3) the development of a broader class of KDC statistics, where the class members are statistics corresponding to different kernel combinations. Finally, we perform simulation studies and an analysis of real data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) study. The ADNI study suggest that SNPs of FLJ16124 exhibit pairwise interaction effects that are strongly correlated to the changes of brain region volumes.

Transcriptome-guided amyloid imaging genetic analysis via a novel structured sparse learning algorithm

MOTIVATION

Imaging genetics is an emerging field that studies the influence of genetic variation on brain structure and function. The major task is to examine the association between genetic markers such as single-nucleotide polymorphisms (SNPs) and quantitative traits (QTs) extracted from neuroimaging data. The complexity of these datasets has presented critical bioinformatics challenges that require new enabling tools. Sparse canonical correlation analysis (SCCA) is a bi-multivariate technique used in imaging genetics to identify complex multi-SNP-multi-QT associations. However, most of the existing SCCA algorithms are designed using the soft thresholding method, which assumes that the input features are independent from one another. This assumption clearly does not hold for the imaging genetic data. In this article, we propose a new knowledge-guided SCCA algorithm (KG-SCCA) to overcome this limitation as well as improve learning results by incorporating valuable prior knowledge.

RESULTS

The proposed KG-SCCA method is able to model two types of prior knowledge: one as a group structure (e.g. linkage disequilibrium blocks among SNPs) and the other as a network structure (e.g. gene co-expression network among brain regions). The new model incorporates these prior structures by introducing new regularization terms to encourage weight similarity between grouped or connected features. A new algorithm is designed to solve the KG-SCCA model without imposing the independence constraint on the input features. We demonstrate the effectiveness of our algorithm with both synthetic and real data. For real data, using an Alzheimer's disease (AD) cohort, we examine the imaging genetic associations between all SNPs in the APOE gene (i.e. top AD gene) and amyloid deposition measures among cortical regions (i.e. a major AD hallmark). In comparison with a widely used SCCA implementation, our KG-SCCA algorithm produces not only improved cross-validation performances but also biologically meaningful results.

AVAILABILITY

Software is freely available on request.

GN-SCCA: GraphNet based Sparse Canonical Correlation Analysis for Brain Imaging Genetics

Identifying associations between genetic variants and neuroimaging quantitative traits (QTs) is a popular research topic in brain imaging genetics. Sparse canonical correlation analysis (SCCA) has been widely used to reveal complex multi-SNP-multi-QT associations. Several SCCA methods explicitly incorporate prior knowledge into the model and intend to uncover the hidden structure informed by the prior knowledge. We propose a novel structured SCCA method using Graph constrained Elastic-Net (GraphNet) regularizer to not only discover important associations, but also induce smoothness between coefficients that are adjacent in the graph. In addition, the proposed method incorporates the covariance structure information usually ignored by most SCCA methods. Experiments on simulated and real imaging genetic data show that, the proposed method not only outperforms a widely used SCCA method but also yields an easy-to-interpret biological findings.

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-mixed effects models for candidate genetic mapping in imaging genetic studies

The aim of this paper is to develop a functional-mixed effects modeling (FMEM) framework for the joint analysis of high-dimensional imaging data in a large number of locations (called voxels) of a three-dimensional volume with a set of genetic markers and clinical covariates. Our FMEM is extremely useful for efficiently carrying out the candidate gene approaches in imaging genetic studies. FMEM consists of two novel components including a mixed effects model for modeling nonlinear genetic effects on imaging phenotypes by introducing the genetic random effects at each voxel and a jumping surface model for modeling the variance components of the genetic random effects and fixed effects as piecewise smooth functions of the voxels. Moreover, FMEM naturally accommodates the correlation structure of the genetic markers at each voxel, while the jumping surface model explicitly incorporates the intrinsically spatial smoothness of the imaging data. We propose a novel two-stage adaptive smoothing procedure to spatially estimate the piecewise smooth functions, particularly the irregular functional genetic variance components, while preserving their edges among different piecewise-smooth regions. We develop weighted likelihood ratio tests and derive their exact approximations to test the effect of the genetic markers across voxels. Simulation studies show that FMEM significantly outperforms voxel-wise approaches in terms of higher sensitivity and specificity to identify regions of interest for carrying out candidate genetic mapping in imaging genetic studies. Finally, FMEM is used to identify brain regions affected by three candidate genes including CR1, CD2AP, and PICALM, thereby hoping to shed light on the pathological interactions between these candidate genes and brain structure and function.

Canonical correlation analysis for gene-based pleiotropy discovery

Genome-wide association studies have identified a wealth of genetic variants involved in complex traits and multifactorial diseases. There is now considerable interest in testing variants for association with multiple phenotypes (pleiotropy) and for testing multiple variants for association with a single phenotype (gene-based association tests). Such approaches can increase statistical power by combining evidence for association over multiple phenotypes or genetic variants respectively. Canonical Correlation Analysis (CCA) measures the correlation between two sets of multidimensional variables, and thus offers the potential to combine these two approaches. To apply CCA, we must restrict the number of attributes relative to the number of samples. Hence we consider modules of genetic variation that can comprise a gene, a pathway or another biologically relevant grouping, and/or a set of phenotypes. In order to do this, we use an attribute selection strategy based on a binary genetic algorithm. Applied to a UK-based prospective cohort study of 4286 women (the British Women's Heart and Health Study), we find improved statistical power in the detection of previously reported genetic associations, and identify a number of novel pleiotropic associations between genetic variants and phenotypes. New discoveries include gene-based association of NSF with triglyceride levels and several genes (ACSM3, ERI2, IL18RAP, IL23RAP and NRG1) with left ventricular hypertrophy phenotypes. In multiple-phenotype analyses we find association of NRG1 with left ventricular hypertrophy phenotypes, fibrinogen and urea and pleiotropic relationships of F7 and F10 with Factor VII, Factor IX and cholesterol levels.

Pleiotropy appears when a variation in one gene affects to several non-related phenotypes. The study of this phenomenon can be useful in gene function discovery, but also in the study of the evolution of a gene. In this paper, we present a methodology, based on Canonical Correlation Analysis, which studies gene-centered multiple association of the variation of SNPs in one or a set of genes with one or a set of phenotypes. The resulting methodology can be applied in gene-centered association analysis, multiple association analysis or pleiotropic pattern discovery. We apply this methodology with a genotype dataset and a set of cardiovascular related phenotypes, and discover new gene association between gene NRG1 and phenotypes related with left ventricular hypertrophy, and pleiotropic effects of this gene with other phenotypes as coagulation factors and urea or pleiotropic effects between coagulation related genes F7 and F10 with coagulation factors and cholesterol levels. This methodology could be also used to find multiple associations in other omics datasets.

Sparse models for correlative and integrative analysis of imaging and genetic data

The development of advanced medical imaging technologies and high-throughput genomic measurements has enhanced our ability to understand their interplay as well as their relationship with human behavior by integrating these two types of datasets. However, the high dimensionality and heterogeneity of these datasets presents a challenge to conventional statistical methods; there is a high demand for the development of both correlative and integrative analysis approaches. Here, we review our recent work on developing sparse representation based approaches to address this challenge. We show how sparse models are applied to the correlation and integration of imaging and genetic data for biomarker identification. We present examples on how these approaches are used for the detection of risk genes and classification of complex diseases such as schizophrenia. Finally, we discuss future directions on the integration of multiple imaging and genomic datasets including their interactions such as epistasis.