A review of multivariate analyses in imaging genetics
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paper_title: Brain vs Behavior: An Effect Size Comparison of Neuroimaging and Cognitive Studies of Genetic Risk for Schizophrenia

paper_content:

Genetic variants associated with increased risk for schizophrenia (SZ) are hypothesized to be more penetrant at the level of brain structure and function than at the level of behavior. However, to date the relative sensitivity of imaging vs cognitive measures of these variants has not been quantified. We considered effect sizes associated with cognitive and imaging studies of 9 robust SZ risk genes (DAOA, DISC1, DTNBP1, NRG1, RGS4, NRGN, CACNA1C, TCF4, and ZNF804A) published between January 2005–November 2011. Summary data was used to calculate estimates of effect size for each significant finding. The mean effect size for each study was categorized as small, medium, or large and the relative frequency of each category was compared between modalities and across genes. Random effects meta-analysis was used to consider the impact of experimental methodology on effect size. Imaging studies reported mostly medium or large effects, whereas cognitive investigations commonly reported small effects. Meta-analysis confirmed that imaging studies were associated with larger effects. Effect size estimates were negatively correlated with sample size but did not differ as a function of gene nor imaging modality. These observations support the notion that SZ risk variants show larger effects, and hence greater penetrance, when characterized using indices of brain structure and function than when indexed by cognitive measures. However, it remains to be established whether this holds true for individual risk variants, imaging modalities, or cognitive functions, and how such effects may be mediated by a relationship with sample size and other aspects of experimental variability.
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paper_title: Effect of COMT Val108/158 Met genotype on frontal lobe function and risk for schizophrenia

paper_content:

Abnormalities of prefrontal cortical function are prominent features of schizophrenia and have been associated with genetic risk, suggesting that susceptibility genes for schizophrenia may impact on the molecular mechanisms of prefrontal function. A potential susceptibility mechanism involves regulation of prefrontal dopamine, which modulates the response of prefrontal neurons during working memory. We examined the relationship of a common functional polymorphism (Val108/158 Met) in the catechol-O-methyltransferase (COMT) gene, which accounts for a 4-fold variation in enzyme activity and dopamine catabolism, with both prefrontally mediated cognition and prefrontal cortical physiology. In 175 patients with schizophrenia, 219 unaffected siblings, and 55 controls, COMT genotype was related in allele dosage fashion to performance on the Wisconsin Card Sorting Test of executive cognition and explained 4% of variance (P = 0.001) in frequency of perseverative errors. Consistent with other evidence that dopamine enhances prefrontal neuronal function, the load of the low-activity Met allele predicted enhanced cognitive performance. We then examined the effect of COMT genotype on prefrontal physiology during a working memory task in three separate subgroups (n = 11–16) assayed with functional MRI. Met allele load consistently predicted a more efficient physiological response in prefrontal cortex. Finally, in a family-based association analysis of 104 trios, we found a significant increase in transmission of the Val allele to the schizophrenic offspring. These data suggest that the COMT Val allele, because it increases prefrontal dopamine catabolism, impairs prefrontal cognition and physiology, and by this mechanism slightly increases risk for schizophrenia.
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paper_title: Imaging Genetics: Perspectives from Studies of Genetically Driven Variation in Serotonin Function and Corticolimbic Affective Processing

paper_content:

Advances in molecular biology and neuroimaging have provided a unique opportunity to explore the relationships between genes, brain, and behavior. In this review, we will briefly outline the rationale for studying genetic effects on brain function with neuroimaging. We will then use studies of genetically driven variation in serotonin transporter function on corticolimbic structure and function to highlight the effectiveness of this strategy to delineate biological pathways and mechanisms by which individual differences in brain function emerge and potentially bias behavior and risk for psychiatric illness. In a series of studies, a relatively frequent regulatory variant of the human serotonin transporter gene (5-HTTLPR) has been demonstrated to bias the reactivity of the amygdala to salient environmental cues. Moreover, the 5-HTTLPR affects the development of a broader corticolimbic circuit and alters the functional integration of emotional information between the amygdala and medial prefrontal cortex. In turn, corticolimbic circuit function predicts individual differences in an experimental index of temperamental anxiety and, thus, might reflect a predictive biological marker of increased risk for mood disorders associated with the 5-HTTLPR.
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paper_title: Common polygenic variation contributes to risk of schizophrenia and bipolar disorder

paper_content:

Schizophrenia is a severe mental disorder with a lifetime risk of about 1%, characterized by hallucinations, delusions and cognitive deficits, with heritability estimated at up to 80%. We performed a genome-wide association study of 3,322 European individuals with schizophrenia and 3,587 controls. Here we show, using two analytic approaches, the extent to which common genetic variation underlies the risk of schizophrenia. First, we implicate the major histocompatibility complex. Second, we provide molecular genetic evidence for a substantial polygenic component to the risk of schizophrenia involving thousands of common alleles of very small effect. We show that this component also contributes to the risk of bipolar disorder, but not to several non-psychiatric diseases.
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paper_title: Abundant Pleiotropy in Human Complex Diseases and Traits

paper_content:

We present a systematic review of pleiotropy among SNPs and genes reported to show genome-wide association with common complex diseases and traits. We find abundant evidence of pleiotropy; 233 (16.9%) genes and 77 (4.6%) SNPs show pleiotropic effects. SNP pleiotropic status was associated with gene location (p = 0.024; pleiotropic SNPs more often exonic [14.5% versus 4.9% for nonpleiotropic, trait-associated SNPs] and less often intergenic [15.8% versus 23.6%]), "predicted transcript consequence" (p = 0.001; pleiotropic SNPs more often predicted to be structurally deleterious [5% versus 0.4%] but not more often in regulatory sequences), and certain disease classes. We develop a method to calculate the likelihood that pleiotropic links between traits occurred more often than expected and demonstrate that this approach can identify etiological links that are already known (such as between fetal hemoglobin and malaria risk) and those that are not yet established (e.g., between plasma campesterol levels and gallstones risk; and between immunoglobulin A and juvenile idiopathic arthritis). Examples of pleiotropy will accumulate over time, but it is already clear that pleiotropy is a common property of genes and SNPs associated with disease traits, and this will have implications for identification of molecular targets for drug development, future genetic risk-profiling, and classification of diseases.
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paper_title: Correlation-based multivariate analysis of genetic influence on brain volume

paper_content:

Considerable research effort has focused on achieving a better understanding of the genetic correlates of individual differences in volumetric and morphological brain measures. The importance of these efforts is underlined by evidence suggesting that brain changes in a number of neuropsychiatric disorders are at least partly genetic in origin. The currently used methods to study these relationships are mostly based on single-genotype univariate analysis techniques. These methods are limited as multiple genes are likely to interact with each other in their influences on brain structure and function. In this paper we present a feasibility study where we show that by using kernel correlation analysis, with a new genotypes representation, it is possible to analyse the relative associations of several genetic polymorphisms with brain structure. The implementation of the method is demonstrated on genetic and structural magnetic resonance imaging (MRI) data acquired from a group of 16 healthy subjects by showing the multivariate genetic influence on grey and white matter.
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paper_title: Neuroimaging Endophenotypes: Strategies for Finding Genes Influencing Brain Structure and Function

paper_content:

It is vitally important to identify the genetic determinants of complex brain-related disorders such as autism, dementia, mood disorders, and schizophrenia. However, the search for genes predis- posing individuals to these illnesses has been hampered by their genetic and phenotypic complexity and by reliance upon phenomenologically based qualitative diagnostic systems. Neuroimaging endo- phenotypes are quantitative indicators of brain structure or function that index genetic liability for an illness. These indices will significantly improve gene discovery and help us to understand the func- tional consequences of specific genes at the level of systems neuroscience. Here, we review the feasibil- ity of using neuroanatomic and neuropsychological measures as endophenotypes for brain-related dis- orders. Specifically, we examine specific indices of brain structure or function that are genetically influ- enced and associated with neurological and psychiatric illness. In addition, we review genetic approaches that capitalize on the use of quantitative traits, including those derived from brain images. Hum Brain Mapp 28:488-501, 2007. V C 2007 Wiley-Liss, Inc.
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paper_title: False positives in neuroimaging genetics using voxel-based morphometry data

paper_content:

Voxel-wise statistical inference is commonly used to identify significant experimental effects or group differences in both functional and structural studies of the living brain. Tests based on the size of spatially extended clusters of contiguous suprathreshold voxels are also widely used due to their typically increased statistical power. In “imaging genetics”, such tests are used to identify regions of the brain that are associated with genetic variation. However, concerns have been raised about the adequate control of rejection rates in studies of this type. A previous study tested the effect of a set of ‘null’ SNPs on brain structure and function, and found that false positive rates were well-controlled. However, no similar analysis of false positive rates in an imaging genetic study using cluster size inference has yet been undertaken. ::: ::: We measured false positive rates in an investigation of the effect of 700 pre-selected null SNPs on grey matter volume using voxel-based morphometry (VBM). As VBM data exhibit spatially-varying smoothness, we used both non-stationary and stationary cluster size tests in our analysis. Image and genotype data on 181 subjects with mild cognitive impairment were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI). At a nominal significance level of 5%, false positive rates were found to be well-controlled (3.9–5.6%), using a relatively high cluster-forming threshold, αc = 0.001, on images smoothed with a 12 mm Gaussian kernel. Tests were however anticonservative at lower cluster-forming thresholds (αc = 0.01, 0.05), and for images smoothed using a 6 mm Gaussian kernel. Here false positive rates ranged from 9.8 to 67.6%. In a further analysis, false positive rates using simulated data were observed to be well-controlled across a wide range of conditions. ::: ::: While motivated by imaging genetics, our findings apply to any VBM study, and suggest that parametric cluster size inference should only be used with high cluster-forming thresholds and smoothness. We would advocate the use of nonparametric methods in other cases.
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paper_title: Imaging genetics of schizophrenia

paper_content:

Recent years have seen an explosive growth of interest in the application of imaging genetics to understand neurogenetic mechanisms of schizophrenia. Imaging genetics applies structural and functional neuroimaging to study subjects carrying genetic risk variants that relate to a psychiatric disorder. We review selected aspects of this literature, starting with a widely studied candidate gene - the catechol-0-methyltransferase gene (COMT)- discussing other candidate genes in the dopaminergic system, and then discussing variants with genome-wide support. In future perspectives, approaches to characterize epistatic effects, the identification of new risk genes through forward-genetic approaches using imaging phenotypes, and the study of rare structural variants are considered.
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paper_title: Imaging genetics—days of future past

paper_content:

Abstract Imaging genetics provides a unique tool with which to explore and evaluate the functional impact of brain-relevant genetic polymorphisms with the potential to understand their impact on behavior. Because statistical association with clinical diagnosis does not establish biological significance nor identify a mechanism of risk, imaging genetics is a uniquely valuable strategy for extending statistical evidence with biological data. Applications include identifying biologic mechanisms and pathways that mediate individual differences in complex behaviors and vulnerability to disease, and conversely identifying genes that contribute to functional variation in brain circuitry. Additionally, neuroimaging genetics can validate data that suggest an association with psychiatric illness as well as providing evidence of the mechanism of risk. This review also outlines several critical principles of imaging genetics including a rational approach to the selection of candidate genes, the selection of task paradigms that could be plausibly linked to the biology of the gene of interest, and careful control of non-genetic factors. The future of imaging genetics holds great promise for brain research and for biologic validation of genetic validation in CNS disorders, but a disciplined application of the basic principles outlined in this review is critical.
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paper_title: The future of fMRI and genetics research

paper_content:

Abstract I provide a brief and subjective view of where the field of imaging genetics is heading. After recapitulating early debates between imagers and geneticists revolving around the topic of candidate gene studies, I point out the importance of genome-wide significant, rare and common variants. I propose that the next stages will be dominated by large-scale multi-site studies that will enable the examination of rare-high penetrance variants and methodological developments that will be required to properly assess the effects of pleiotropy, epistasis, and gene-by environment interactions. The incorporation of new sources of biological information such as whole genome sequencing, proteomic, lipidomic and expression profiles and cellular models derived from induced pluripotent stem cells opens new vistas for imaging genetics in a translational enterprise that is ultimately hoped to improve and create therapeutic options for psychiatric disorders.
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paper_title: False positives in imaging genetics

paper_content:

Abstract Imaging genetics provides an enormous amount of functional–structural data on gene effects in living brain, but the sheer quantity of potential phenotypes raises concerns about false discovery. Here, we provide the first empirical results on false positive rates in imaging genetics. We analyzed 720 frequent coding SNPs without significant association with schizophrenia and a subset of 492 of these without association with cognitive function. Effects on brain structure (using voxel-based morphometry, VBM) and brain function, using two archival imaging tasks, the n-back working memory task and an emotional face matching task, were studied in whole brain and regions of interest and corrected for multiple comparisons using standard neuroimaging procedures. Since these variants are unlikely to impact relevant brain function, positives obtained provide an upper empirical estimate of the false positive association rate. In a separate analysis, we randomly permuted genotype labels across subjects, removing any true genotype–phenotype association in the data, to derive a lower empirical estimate. At a set correction level of 0.05, in each region of interest and data set used, the rate of positive findings was well below 5% (0.2–4.1%). There was no relationship between the region of interest and the false positive rate. Permutation results were in the same range as empirically derived rates. The observed low rates of positives provide empirical evidence that the type I error rate is well controlled by current commonly used correction procedures in imaging genetics, at least in the context of the imaging paradigms we have used. In fact, our observations indicate that these statistical thresholds are conservative.
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paper_title: The Endophenotype Concept in Psychiatry: Etymology and Strategic Intentions

paper_content:

Endophenotypes, measurable components unseen by the unaided eye along the pathway between disease and distal genotype, have emerged as an important concept in the study of complex neuropsychiatric diseases. An endophenotype may be neurophysiological, biochemical, endocrinological, neuroanatomical, cognitive, or neuropsychological (including configured self-report data) in nature. Endophenotypes represent simpler clues to genetic underpinnings than the disease syndrome itself, promoting the view that psychiatric diagnoses can be decomposed or deconstructed, which can result in more straightforward—and successful—genetic analysis. However, to be most useful, endophenotypes for psychiatric disorders must meet certain criteria, including association with a candidate gene or gene region, heritability that is inferred from relative risk for the disorder in relatives, and disease association parameters. In addition to furthering genetic analysis, endophenotypes can clarify classification and diagnosis and foster...
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paper_title: Identification of risk loci with shared effects on five major psychiatric disorders: a genome-wide analysis

paper_content:

BACKGROUND ::: Findings from family and twin studies suggest that genetic contributions to psychiatric disorders do not in all cases map to present diagnostic categories. We aimed to identify specific variants underlying genetic effects shared between the five disorders in the Psychiatric Genomics Consortium: autism spectrum disorder, attention deficit-hyperactivity disorder, bipolar disorder, major depressive disorder, and schizophrenia. ::: ::: ::: METHODS ::: We analysed genome-wide single-nucleotide polymorphism (SNP) data for the five disorders in 33,332 cases and 27,888 controls of European ancestory. To characterise allelic effects on each disorder, we applied a multinomial logistic regression procedure with model selection to identify the best-fitting model of relations between genotype and phenotype. We examined cross-disorder effects of genome-wide significant loci previously identified for bipolar disorder and schizophrenia, and used polygenic risk-score analysis to examine such effects from a broader set of common variants. We undertook pathway analyses to establish the biological associations underlying genetic overlap for the five disorders. We used enrichment analysis of expression quantitative trait loci (eQTL) data to assess whether SNPs with cross-disorder association were enriched for regulatory SNPs in post-mortem brain-tissue samples. ::: ::: ::: FINDINGS ::: SNPs at four loci surpassed the cutoff for genome-wide significance (p<5×10(-8)) in the primary analysis: regions on chromosomes 3p21 and 10q24, and SNPs within two L-type voltage-gated calcium channel subunits, CACNA1C and CACNB2. Model selection analysis supported effects of these loci for several disorders. Loci previously associated with bipolar disorder or schizophrenia had variable diagnostic specificity. Polygenic risk scores showed cross-disorder associations, notably between adult-onset disorders. Pathway analysis supported a role for calcium channel signalling genes for all five disorders. Finally, SNPs with evidence of cross-disorder association were enriched for brain eQTL markers. ::: ::: ::: INTERPRETATION ::: Our findings show that specific SNPs are associated with a range of psychiatric disorders of childhood onset or adult onset. In particular, variation in calcium-channel activity genes seems to have pleiotropic effects on psychopathology. These results provide evidence relevant to the goal of moving beyond descriptive syndromes in psychiatry, and towards a nosology informed by disease cause. ::: ::: ::: FUNDING ::: National Institute of Mental Health.
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paper_title: Discovering genetic associations with high-dimensional neuroimaging phenotypes: A sparse reduced-rank regression approach

paper_content:

Abstract There is growing interest in performing genome-wide searches for associations between genetic variants and brain imaging phenotypes. While much work has focused on single scalar valued summaries of brain phenotype, accounting for the richness of imaging data requires a brain-wide, genome-wide search. In particular, the standard approach based on mass-univariate linear modelling (MULM) does not account for the structured patterns of correlations present in each domain. In this work, we propose sparse reduced rank regression (sRRR), a strategy for multivariate modelling of high-dimensional imaging responses (measurements taken over regions of interest or individual voxels) and genetic covariates (single nucleotide polymorphisms or copy number variations), which enforces sparsity in the regression coefficients. Such sparsity constraints ensure that the model performs simultaneous genotype and phenotype selection. Using simulation procedures that accurately reflect realistic human genetic variation and imaging correlations, we present detailed evaluations of the sRRR method in comparison with the more traditional MULM approach. In all settings considered, sRRR has better power to detect deleterious genetic variants compared to MULM. Important issues concerning model selection and connections to existing latent variable models are also discussed. This work shows that sRRR offers a promising alternative for detecting brain-wide, genome-wide associations.
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paper_title: Intermediate phenotypes and genetic mechanisms of psychiatric disorders

paper_content:

Genes are major contributors to many psychiatric diseases, but their mechanisms of action have long seemed elusive. The intermediate phenotype concept represents a strategy for characterizing the neural systems affected by risk gene variants to elucidate quantitative, mechanistic aspects of brain function implicated in psychiatric disease. Using imaging genetics as an example, we illustrate recent advances, challenges and implications of linking genes to structural and functional variation in brain systems related to cognition and emotion.
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paper_title: Neuroimaging-Genetic Paradigms: A New Approach to Investigate the Pathophysiology and Treatment of Cognitive Deficits in Schizophrenia

paper_content:

Cognitive impairment is a prominent and debilitating feature of schizophrenia. Genetic predisposition likely accounts for a large proportion of these cognitive deficits. Direct associations between candidate genes and cognitive dysfunction have been difficult to establish, however, largely due to the subtle effects of these genes on observable behavior. Neuroimaging techniques can provide a sensitive means to bridge the neurobiology of genes and behavior. Here we illustrate the use of neuroimaging-genetics paradigms to elaborate the relationship between genes and cognitive dysfunction in schizophrenia. After reviewing principles important for the selection of genes, neuroimaging techniques, and subjects, we describe how imaging-genetics investigations have helped clarify the contribution of five candidate genes (COMT, GRM3, G72, DISC1, and BDNF) to cognitive deficits in schizophrenia. The potential of this approach for improving patient care will depend on its ability to predict outcomes with greater accu...
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paper_title: The influence of polygenic risk for bipolar disorder on neural activation assessed using fMRI

paper_content:

Genome-wide association studies (GWAS) have demonstrated a significant polygenic contribution to bipolar disorder (BD) where disease risk is determined by the summation of many alleles of small individual magnitude. Modelling polygenic risk scores may be a powerful way of identifying disrupted brain regions whose genetic architecture is related to that of BD. We determined the extent to which common genetic variation underlying risk to BD affected neural activation during an executive processing/language task in individuals at familial risk of BD and healthy controls. Polygenic risk scores were calculated for each individual based on GWAS data from the Psychiatric GWAS Consortium Bipolar Disorder Working Group (PGC-BD) of over 16 000 subjects. The familial group had a significantly higher polygene score than the control group (P=0.04). There were no significant group by polygene interaction effects in terms of association with brain activation. However, we did find that an increasing polygenic risk allele load for BD was associated with increased activation in limbic regions previously implicated in BD, including the anterior cingulate cortex and amygdala, across both groups. The findings suggest that this novel polygenic approach to examine brain-imaging data may be a useful means of identifying genetically mediated traits mechanistically linked to the aetiology of BD.
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paper_title: Signi fi cant correlation between a set of genetic polymorphisms and a functional brain network revealed by feature selection and sparse Partial Least Squares

paper_content:

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.
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paper_title: Intermediate phenotypes in psychiatric disorders.

paper_content:

The small effect size of most individual risk factors for psychiatric disorders likely reflects biological heterogeneity and diagnostic imprecision, which has encouraged genetic studies of intermediate biological phenotypes that are closer to the molecular effects of risk genes than are the clinical symptoms. Neuroimaging-based intermediate phenotypes have emerged as particularly promising because they map risk associated gene effects onto physiological processes in brain that are altered in patients and in their healthy relatives. Recent evidence using this approach has elucidated discrete, dissociable biological mechanisms of risk genes at the level of neural circuitries, and their related cognitive functions. This approach may greatly contribute to our understanding of the genetics and pathophysiology of psychiatric disorders.
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paper_title: Cerebral metabolic and cognitive decline in persons at genetic risk for Alzheimer's disease

paper_content:

The major known genetic risk for Alzheimer's disease (AD), apolipoprotein E-4 (APOE-4), is associated with lowered parietal, temporal, and posterior cingulate cerebral glucose metabolism in patients with a clinical diagnosis of AD. To determine cognitive and metabolic decline patterns according to genetic risk, we investigated cerebral metabolic rates by using positron emission tomography in middle-aged and older nondemented persons with normal memory performance. A single copy of the APOE-4 allele was associated with lowered inferior parietal, lateral temporal, and posterior cingulate metabolism, which predicted cognitive decline after 2 years of longitudinal follow-up. For the 20 nondemented subjects followed longitudinally, memory performance scores did not decline significantly, but cortical metabolic rates did. In APOE-4 carriers, a 4% left posterior cingulate metabolic decline was observed, and inferior parietal and lateral temporal regions demonstrated the greatest magnitude (5%) of metabolic decline after 2 years. These results indicate that the combination of cerebral metabolic rates and genetic risk factors provides a means for preclinical AD detection that will assist in response monitoring during experimental treatments.
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paper_title: Cumulative Genetic Risk and Prefrontal Activity in Patients With Schizophrenia

paper_content:

The lack of consistency of genetic associations in highly heritable mental illnesses, such as schizophrenia, remains a challenge in molecular psychiatry. Because clinical phenotypes for psychiatric disorders are often ill defined, considerable effort has been made to relate genetic polymorphisms to underlying physiological aspects of schizophrenia (so called intermediate phenotypes), that may be more reliable. Given the polygenic etiology of schizophrenia, the aim of this work was to form a measure of cumulative genetic risk and study its effect on neural activity during working memory (WM) using functional magnetic resonance imaging. Neural activity during the Sternberg Item Recognition Paradigm was measured in 79 schizophrenia patients and 99 healthy controls. Participants were genotyped, and a genetic risk score (GRS), which combined the additive effects of 41 single-nucleotide polymorphisms (SNPs) from 34 risk genes for schizophrenia, was calculated. These risk SNPs were chosen according to the continuously updated meta-analysis of genetic studies on schizophrenia available at www.schizophreniaresearchforum.org. We found a positive relationship between GRS and left dorsolateral prefrontal cortex inefficiency during WM processing. GRS was not correlated with age, performance, intelligence, or medication effects and did not differ between acquisition sites, gender, or diagnostic groups. Our study suggests that cumulative genetic risk, combining the impact of many genes with small effects, is associated with a known brain-based intermediate phenotype for schizophrenia. The GRS approach could provide an advantage over studying single genes in studies focusing on the genetic basis of polygenic conditions such as neuropsychiatric disorders.
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paper_title: Hippocampal Atrophy as a Quantitative Trait in a Genome-Wide Association Study Identifying Novel Susceptibility Genes for Alzheimer's Disease

paper_content:

BACKGROUND ::: With the exception of APOE epsilon4 allele, the common genetic risk factors for sporadic Alzheimer's Disease (AD) are unknown. ::: ::: ::: METHODS AND FINDINGS ::: We completed a genome-wide association study on 381 participants in the ADNI (Alzheimer's Disease Neuroimaging Initiative) study. Samples were genotyped using the Illumina Human610-Quad BeadChip. 516,645 unique Single Nucleotide Polymorphisms (SNPs) were included in the analysis following quality control measures. The genotype data and raw genetic data are freely available for download (LONI, http://www.loni.ucla.edu/ADNI/Data/). Two analyses were completed: a standard case-control analysis, and a novel approach using hippocampal atrophy measured on MRI as an objectively defined, quantitative phenotype. A General Linear Model was applied to identify SNPs for which there was an interaction between the genotype and diagnosis on the quantitative trait. The case-control analysis identified APOE and a new risk gene, TOMM40 (translocase of outer mitochondrial membrane 40), at a genome-wide significance level of < or =10(-6) (10(-11) for a haplotype). TOMM40 risk alleles were approximately twice as frequent in AD subjects as controls. The quantitative trait analysis identified 21 genes or chromosomal areas with at least one SNP with a p-value < or =10(-6), which can be considered potential "new" candidate loci to explore in the etiology of sporadic AD. These candidates included EFNA5, CAND1, MAGI2, ARSB, and PRUNE2, genes involved in the regulation of protein degradation, apoptosis, neuronal loss and neurodevelopment. Thus, we identified common genetic variants associated with the increased risk of developing AD in the ADNI cohort, and present publicly available genome-wide data. Supportive evidence based on case-control studies and biological plausibility by gene annotation is provided. Currently no available sample with both imaging and genetic data is available for replication. ::: ::: ::: CONCLUSIONS ::: Using hippocampal atrophy as a quantitative phenotype in a genome-wide scan, we have identified candidate risk genes for sporadic Alzheimer's disease that merit further investigation.
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paper_title: The Endophenotype Concept in Psychiatry: Etymology and Strategic Intentions

paper_content:

Endophenotypes, measurable components unseen by the unaided eye along the pathway between disease and distal genotype, have emerged as an important concept in the study of complex neuropsychiatric diseases. An endophenotype may be neurophysiological, biochemical, endocrinological, neuroanatomical, cognitive, or neuropsychological (including configured self-report data) in nature. Endophenotypes represent simpler clues to genetic underpinnings than the disease syndrome itself, promoting the view that psychiatric diagnoses can be decomposed or deconstructed, which can result in more straightforward—and successful—genetic analysis. However, to be most useful, endophenotypes for psychiatric disorders must meet certain criteria, including association with a candidate gene or gene region, heritability that is inferred from relative risk for the disorder in relatives, and disease association parameters. In addition to furthering genetic analysis, endophenotypes can clarify classification and diagnosis and foster...
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paper_title: A versatile gene-based test for genome-wide association studies.

paper_content:

We have derived a versatile gene-based test for genome-wide association studies (GWAS). Our approach, called VEGAS (versatile gene-based association study), is applicable to all GWAS designs, including family-based GWAS, meta-analyses of GWAS on the basis of summary data, and DNA-pooling-based GWAS, where existing approaches based on permutation are not possible, as well as singleton data, where they are. The test incorporates information from a full set of markers (or a defined subset) within a gene and accounts for linkage disequilibrium between markers by using simulations from the multivariate normal distribution. We show that for an association study using singletons, our approach produces results equivalent to those obtained via permutation in a fraction of the computation time. We demonstrate proof-of-principle by using the gene-based test to replicate several genes known to be associated on the basis of results from a family-based GWAS for height in 11,536 individuals and a DNA-pooling-based GWAS for melanoma in approximately 1300 cases and controls. Our method has the potential to identify novel associated genes; provide a basis for selecting SNPs for replication; and be directly used in network (pathway) approaches that require per-gene association test statistics. We have implemented the approach in both an easy-to-use web interface, which only requires the uploading of markers with their association p-values, and a separate downloadable application.
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paper_title: Discovering genetic associations with high-dimensional neuroimaging phenotypes: A sparse reduced-rank regression approach

paper_content:

Abstract There is growing interest in performing genome-wide searches for associations between genetic variants and brain imaging phenotypes. While much work has focused on single scalar valued summaries of brain phenotype, accounting for the richness of imaging data requires a brain-wide, genome-wide search. In particular, the standard approach based on mass-univariate linear modelling (MULM) does not account for the structured patterns of correlations present in each domain. In this work, we propose sparse reduced rank regression (sRRR), a strategy for multivariate modelling of high-dimensional imaging responses (measurements taken over regions of interest or individual voxels) and genetic covariates (single nucleotide polymorphisms or copy number variations), which enforces sparsity in the regression coefficients. Such sparsity constraints ensure that the model performs simultaneous genotype and phenotype selection. Using simulation procedures that accurately reflect realistic human genetic variation and imaging correlations, we present detailed evaluations of the sRRR method in comparison with the more traditional MULM approach. In all settings considered, sRRR has better power to detect deleterious genetic variants compared to MULM. Important issues concerning model selection and connections to existing latent variable models are also discussed. This work shows that sRRR offers a promising alternative for detecting brain-wide, genome-wide associations.
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paper_title: Signi fi cant correlation between a set of genetic polymorphisms and a functional brain network revealed by feature selection and sparse Partial Least Squares

paper_content:

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.
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paper_title: Voxelwise Genome-Wide Association Study ( vGWAS )

paper_content:

Abstract The structure of the human brain is highly heritable, and is thought to be influenced by many common genetic variants, many of which are currently unknown. Recent advances in neuroimaging and genetics have allowed collection of both highly detailed structural brain scans and genome-wide genotype information. This wealth of information presents a new opportunity to find the genes influencing brain structure. Here we explore the relation between 448,293 single nucleotide polymorphisms in each of 31,622 voxels of the entire brain across 740 elderly subjects (mean age ± s.d.: 75.52 ± 6.82 years; 438 male) including subjects with Alzheimer's disease, Mild Cognitive Impairment, and healthy elderly controls from the Alzheimer's Disease Neuroimaging Initiative (ADNI). We used tensor-based morphometry to measure individual differences in brain structure at the voxel level relative to a study-specific template based on healthy elderly subjects. We then conducted a genome-wide association at each voxel to identify genetic variants of interest. By studying only the most associated variant at each voxel, we developed a novel method to address the multiple comparisons problem and computational burden associated with the unprecedented amount of data. No variant survived the strict significance criterion, but several genes worthy of further exploration were identified, including CSMD2 and CADPS2. These genes have high relevance to brain structure. This is the first voxelwise genome wide association study to our knowledge, and offers a novel method to discover genetic influences on brain structure.
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paper_title: Gene Size Matters

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In this work we show that in genome-wide association studies (GWAS) there is a strong bias favoring of genes covered by larger numbers of SNPs. Thus, we state here that there is a need for correction for such bias when performing downstream gene-level analysis, e.g. pathway analysis and gene-set analysis. We investigate several methods of obtaining gene level statistical significance in GWAS, and compare their effectiveness in correcting such bias. We also propose a simple algorithm based on first order statistic that corrects such bias.
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paper_title: Cumulative Genetic Risk and Prefrontal Activity in Patients With Schizophrenia

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The lack of consistency of genetic associations in highly heritable mental illnesses, such as schizophrenia, remains a challenge in molecular psychiatry. Because clinical phenotypes for psychiatric disorders are often ill defined, considerable effort has been made to relate genetic polymorphisms to underlying physiological aspects of schizophrenia (so called intermediate phenotypes), that may be more reliable. Given the polygenic etiology of schizophrenia, the aim of this work was to form a measure of cumulative genetic risk and study its effect on neural activity during working memory (WM) using functional magnetic resonance imaging. Neural activity during the Sternberg Item Recognition Paradigm was measured in 79 schizophrenia patients and 99 healthy controls. Participants were genotyped, and a genetic risk score (GRS), which combined the additive effects of 41 single-nucleotide polymorphisms (SNPs) from 34 risk genes for schizophrenia, was calculated. These risk SNPs were chosen according to the continuously updated meta-analysis of genetic studies on schizophrenia available at www.schizophreniaresearchforum.org. We found a positive relationship between GRS and left dorsolateral prefrontal cortex inefficiency during WM processing. GRS was not correlated with age, performance, intelligence, or medication effects and did not differ between acquisition sites, gender, or diagnostic groups. Our study suggests that cumulative genetic risk, combining the impact of many genes with small effects, is associated with a known brain-based intermediate phenotype for schizophrenia. The GRS approach could provide an advantage over studying single genes in studies focusing on the genetic basis of polygenic conditions such as neuropsychiatric disorders.
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paper_title: Comparative study of gene set enrichment methods

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BackgroundThe analysis of high-throughput gene expression data with respect to sets of genes rather than individual genes has many advantages. A variety of methods have been developed for assessing the enrichment of sets of genes with respect to differential expression. In this paper we provide a comparative study of four of these methods: Fisher's exact test, Gene Set Enrichment Analysis (GSEA), Random-Sets (RS), and Gene List Analysis with Prediction Accuracy (GLAPA). The first three methods use associative statistics, while the fourth uses predictive statistics. We first compare all four methods on simulated data sets to verify that Fisher's exact test is markedly worse than the other three approaches. We then validate the other three methods on seven real data sets with known genetic perturbations and then compare the methods on two cancer data sets where our a priori knowledge is limited.ResultsThe simulation study highlights that none of the three method outperforms all others consistently. GSEA and RS are able to detect weak signals of deregulation and they perform differently when genes in a gene set are both differentially up and down regulated. GLAPA is more conservative and large differences between the two phenotypes are required to allow the method to detect differential deregulation in gene sets. This is due to the fact that the enrichment statistic in GLAPA is prediction error which is a stronger criteria than classical two sample statistic as used in RS and GSEA. This was reflected in the analysis on real data sets as GSEA and RS were seen to be significant for particular gene sets while GLAPA was not, suggesting a small effect size. We find that the rank of gene set enrichment induced by GLAPA is more similar to RS than GSEA. More importantly, the rankings of the three methods share significant overlap.ConclusionThe three methods considered in our study recover relevant gene sets known to be deregulated in the experimental conditions and pathologies analyzed. There are differences between the three methods and GSEA seems to be more consistent in finding enriched gene sets, although no method uniformly dominates over all data sets. Our analysis highlights the deep difference existing between associative and predictive methods for detecting enrichment and the use of both to better interpret results of pathway analysis. We close with suggestions for users of gene set methods.
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paper_title: SNP-based pathway enrichment analysis for genome-wide association studies

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BackgroundRecently we have witnessed a surge of interest in using genome-wide association studies (GWAS) to discover the genetic basis of complex diseases. Many genetic variations, mostly in the form of single nucleotide polymorphisms (SNPs), have been identified in a wide spectrum of diseases, including diabetes, cancer, and psychiatric diseases. A common theme arising from these studies is that the genetic variations discovered by GWAS can only explain a small fraction of the genetic risks associated with the complex diseases. New strategies and statistical approaches are needed to address this lack of explanation. One such approach is the pathway analysis, which considers the genetic variations underlying a biological pathway, rather than separately as in the traditional GWAS studies. A critical challenge in the pathway analysis is how to combine evidences of association over multiple SNPs within a gene and multiple genes within a pathway. Most current methods choose the most significant SNP from each gene as a representative, ignoring the joint action of multiple SNPs within a gene. This approach leads to preferential identification of genes with a greater number of SNPs.ResultsWe describe a SNP-based pathway enrichment method for GWAS studies. The method consists of the following two main steps: 1) for a given pathway, using an adaptive truncated product statistic to identify all representative (potentially more than one) SNPs of each gene, calculating the average number of representative SNPs for the genes, then re-selecting the representative SNPs of genes in the pathway based on this number; and 2) ranking all selected SNPs by the significance of their statistical association with a trait of interest, and testing if the set of SNPs from a particular pathway is significantly enriched with high ranks using a weighted Kolmogorov-Smirnov test. We applied our method to two large genetically distinct GWAS data sets of schizophrenia, one from European-American (EA) and the other from African-American (AA). In the EA data set, we found 22 pathways with nominal P-value less than or equal to 0.001 and corresponding false discovery rate (FDR) less than 5%. In the AA data set, we found 11 pathways by controlling the same nominal P-value and FDR threshold. Interestingly, 8 of these pathways overlap with those found in the EA sample. We have implemented our method in a JAVA software package, called SNP Set Enrichment Analysis (SSEA), which contains a user-friendly interface and is freely available at http://cbcl.ics.uci.edu/SSEA.ConclusionsThe SNP-based pathway enrichment method described here offers a new alternative approach for analysing GWAS data. By applying it to schizophrenia GWAS studies, we show that our method is able to identify statistically significant pathways, and importantly, pathways that can be replicated in large genetically distinct samples.
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paper_title: Comparison of Invariant NKT Cells with Conventional T Cells by Using Gene Set Enrichment Analysis (GSEA)

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Invariant Natural killer T (iNKT) cells, a distinct subset of CD1d-restricted T cells with invariant Vαβ TCR, functionally bridge innate and adaptive immunity. While iNKT cells share features with conventional T cells in some functional aspects, they simultaneously produce large amount of Th1 and Th2 cytokines upon T-cell receptor (TCR) ligation. However, gene expression pattern in two types of cells has not been well characterized. Methods: we performed comparative microarray analyses of gene expression in murine iNKT cells and conventional CD4 + CD25^- γδTCR^- T cells by using Gene Set Enrichment Analysis (GSEA) method. Results: Here, we describe profound differences in gene expression pattern between iNKT cells and conventional CD4 + CD25^- γδTCR^- T cells. Conclusion: Our results provide new insights into the functional competence of iNKT cells and a better understanding of their various roles during immune responses.
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paper_title: PGC-1α-responsive genes involved in oxidative phosphorylation are coordinately downregulated in human diabetes

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DNA microarrays can be used to identify gene expression changes characteristic of human disease. This is challenging, however, when relevant differences are subtle at the level of individual genes. We introduce an analytical strategy, Gene Set Enrichment Analysis, designed to detect modest but coordinate changes in the expression of groups of functionally related genes. Using this approach, we identify a set of genes involved in oxidative phosphorylation whose expression is coordinately decreased in human diabetic muscle. Expression of these genes is high at sites of insulin-mediated glucose disposal, activated by PGC-1alpha and correlated with total-body aerobic capacity. Our results associate this gene set with clinically important variation in human metabolism and illustrate the value of pathway relationships in the analysis of genomic profiling experiments.
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paper_title: GATES: a rapid and powerful gene-based association test using extended Simes procedure.

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The gene has been proposed as an attractive unit of analysis for association studies, but a simple yet valid, powerful, and sufficiently fast method of evaluating the statistical significance of all genes in large, genome-wide datasets has been lacking. Here we propose the use of an extended Simes test that integrates functional information and association evidence to combine the p values of the single nucleotide polymorphisms within a gene to obtain an overall p value for the association of the entire gene. Our computer simulations demonstrate that this test is more powerful than the SNP-based test, offers effective control of the type 1 error rate regardless of gene size and linkage-disequilibrium pattern among markers, and does not need permutation or simulation to evaluate empirical significance. Its statistical power in simulated data is at least comparable, and often superior, to that of several alternative gene-based tests. When applied to real genome-wide association study (GWAS) datasets on Crohn disease, the test detected more significant genes than SNP-based tests and alternative gene-based tests. The proposed test, implemented in an open-source package, has the potential to identify additional novel disease-susceptibility genes for complex diseases from large GWAS datasets.
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paper_title: A versatile gene-based test for genome-wide association studies.

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We have derived a versatile gene-based test for genome-wide association studies (GWAS). Our approach, called VEGAS (versatile gene-based association study), is applicable to all GWAS designs, including family-based GWAS, meta-analyses of GWAS on the basis of summary data, and DNA-pooling-based GWAS, where existing approaches based on permutation are not possible, as well as singleton data, where they are. The test incorporates information from a full set of markers (or a defined subset) within a gene and accounts for linkage disequilibrium between markers by using simulations from the multivariate normal distribution. We show that for an association study using singletons, our approach produces results equivalent to those obtained via permutation in a fraction of the computation time. We demonstrate proof-of-principle by using the gene-based test to replicate several genes known to be associated on the basis of results from a family-based GWAS for height in 11,536 individuals and a DNA-pooling-based GWAS for melanoma in approximately 1300 cases and controls. Our method has the potential to identify novel associated genes; provide a basis for selecting SNPs for replication; and be directly used in network (pathway) approaches that require per-gene association test statistics. We have implemented the approach in both an easy-to-use web interface, which only requires the uploading of markers with their association p-values, and a separate downloadable application.
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paper_title: Identification of risk loci with shared effects on five major psychiatric disorders: a genome-wide analysis

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BACKGROUND ::: Findings from family and twin studies suggest that genetic contributions to psychiatric disorders do not in all cases map to present diagnostic categories. We aimed to identify specific variants underlying genetic effects shared between the five disorders in the Psychiatric Genomics Consortium: autism spectrum disorder, attention deficit-hyperactivity disorder, bipolar disorder, major depressive disorder, and schizophrenia. ::: ::: ::: METHODS ::: We analysed genome-wide single-nucleotide polymorphism (SNP) data for the five disorders in 33,332 cases and 27,888 controls of European ancestory. To characterise allelic effects on each disorder, we applied a multinomial logistic regression procedure with model selection to identify the best-fitting model of relations between genotype and phenotype. We examined cross-disorder effects of genome-wide significant loci previously identified for bipolar disorder and schizophrenia, and used polygenic risk-score analysis to examine such effects from a broader set of common variants. We undertook pathway analyses to establish the biological associations underlying genetic overlap for the five disorders. We used enrichment analysis of expression quantitative trait loci (eQTL) data to assess whether SNPs with cross-disorder association were enriched for regulatory SNPs in post-mortem brain-tissue samples. ::: ::: ::: FINDINGS ::: SNPs at four loci surpassed the cutoff for genome-wide significance (p<5×10(-8)) in the primary analysis: regions on chromosomes 3p21 and 10q24, and SNPs within two L-type voltage-gated calcium channel subunits, CACNA1C and CACNB2. Model selection analysis supported effects of these loci for several disorders. Loci previously associated with bipolar disorder or schizophrenia had variable diagnostic specificity. Polygenic risk scores showed cross-disorder associations, notably between adult-onset disorders. Pathway analysis supported a role for calcium channel signalling genes for all five disorders. Finally, SNPs with evidence of cross-disorder association were enriched for brain eQTL markers. ::: ::: ::: INTERPRETATION ::: Our findings show that specific SNPs are associated with a range of psychiatric disorders of childhood onset or adult onset. In particular, variation in calcium-channel activity genes seems to have pleiotropic effects on psychopathology. These results provide evidence relevant to the goal of moving beyond descriptive syndromes in psychiatry, and towards a nosology informed by disease cause. ::: ::: ::: FUNDING ::: National Institute of Mental Health.
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paper_title: The influence of polygenic risk for bipolar disorder on neural activation assessed using fMRI

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Genome-wide association studies (GWAS) have demonstrated a significant polygenic contribution to bipolar disorder (BD) where disease risk is determined by the summation of many alleles of small individual magnitude. Modelling polygenic risk scores may be a powerful way of identifying disrupted brain regions whose genetic architecture is related to that of BD. We determined the extent to which common genetic variation underlying risk to BD affected neural activation during an executive processing/language task in individuals at familial risk of BD and healthy controls. Polygenic risk scores were calculated for each individual based on GWAS data from the Psychiatric GWAS Consortium Bipolar Disorder Working Group (PGC-BD) of over 16 000 subjects. The familial group had a significantly higher polygene score than the control group (P=0.04). There were no significant group by polygene interaction effects in terms of association with brain activation. However, we did find that an increasing polygenic risk allele load for BD was associated with increased activation in limbic regions previously implicated in BD, including the anterior cingulate cortex and amygdala, across both groups. The findings suggest that this novel polygenic approach to examine brain-imaging data may be a useful means of identifying genetically mediated traits mechanistically linked to the aetiology of BD.
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paper_title: Evaluation of the Psoriasis Transcriptome across Different Studies by Gene Set Enrichment Analysis (GSEA)

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Background: Our objective was to develop a consistent molecular definition of psoriasis. There have been several published microarray studies of psoriasis, and we compared disease-related genes identified across these different studies of psoriasis with our own in order to establish a consensus. Methodology/Principal Findings: We present a psoriasis transcriptome from a group of 15 patients enrolled in a clinical study, and assessed its biological validity using a set of important pathways known to be involved in psoriasis. We also identified a key set of cytokines that are now strongly implicated in driving disease-related pathology, but which are not detected well on gene array platforms and require more sensitive methods to measure mRNA levels in skin tissues. Comparison of our transcriptome with three other published lists of psoriasis genes showed apparent inconsistencies based on the number of overlapping genes. We extended the well-established approach of Gene Set Enrichment Analysis (GSEA) to compare a new study with these other published list of differentially expressed genes (DEG) in a more comprehensive manner. We applied our method to these three published psoriasis transcriptomes and found them to be in good agreement with our study. Conclusions/Significance: Due to wide variability in clinical protocols, platform and sample handling, and subtle diseaserelated signals, intersection of published DEG lists was unable to establish consensus between studies. In order to leverage the power of multiple transcriptomes reported by several laboratories using different patients and protocols, more sophisticated methods like the extension of GSEA presented here, should be used in order to overcome the shortcomings of overlapping individual DEG approach.
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paper_title: GSEA-SNP: applying gene set enrichment analysis to SNP data from genome-wide association studies

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The power of genome-wide SNP association studies is limited, among others, by the large number of false positive test results. To provide a remedy, we combined SNP association analysis with the pathway-driven gene set enrichment analysis (GSEA), recently developed to facilitate handling of genome-wide gene expression data. The resulting GSEA-SNP method rests on the assumption that SNPs underlying a disease phenotype are enriched in genes constituting a signaling pathway or those with a common regulation. Besides improving power for association mapping, GSEA-SNP may facilitate the identification of disease-associated SNPs and pathways, as well as the understanding of the underlying biological mechanisms. GSEA-SNP may also help to identify markers with weak effects, undetectable in association studies without pathway consideration. The program is freely available and can be downloaded from our website.
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paper_title: Gene set enrichment analysis: A knowledge-based approach for interpreting genome-wide expression profiles

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Although genomewide RNA expression analysis has become a routine tool in biomedical research, extracting biological insight from such information remains a major challenge. Here, we describe a powerful analytical method called Gene Set Enrichment Analysis (GSEA) for interpreting gene expression data. The method derives its power by focusing on gene sets, that is, groups of genes that share common biological function, chromosomal location, or regulation. We demonstrate how GSEA yields insights into several cancer-related data sets, including leukemia and lung cancer. Notably, where single-gene analysis finds little similarity between two independent studies of patient survival in lung cancer, GSEA reveals many biological pathways in common. The GSEA method is embodied in a freely available software package, together with an initial database of 1,325 biologically defined gene sets.
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paper_title: Cluster analysis for gene expression data: a survey

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DNA microarray technology has now made it possible to simultaneously monitor the expression levels of thousands of genes during important biological processes and across collections of related samples. Elucidating the patterns hidden in gene expression data offers a tremendous opportunity for an enhanced understanding of functional genomics. However, the large number of genes and the complexity of biological networks greatly increases the challenges of comprehending and interpreting the resulting mass of data, which often consists of millions of measurements. A first step toward addressing this challenge is the use of clustering techniques, which is essential in the data mining process to reveal natural structures and identify interesting patterns in the underlying data. Cluster analysis seeks to partition a given data set into groups based on specified features so that the data points within a group are more similar to each other than the points in different groups. A very rich literature on cluster analysis has developed over the past three decades. Many conventional clustering algorithms have been adapted or directly applied to gene expression data, and also new algorithms have recently been proposed specifically aiming at gene expression data. These clustering algorithms have been proven useful for identifying biologically relevant groups of genes and samples. In this paper, we first briefly introduce the concepts of microarray technology and discuss the basic elements of clustering on gene expression data. In particular, we divide cluster analysis for gene expression data into three categories. Then, we present specific challenges pertinent to each clustering category and introduce several representative approaches. We also discuss the problem of cluster validation in three aspects and review various methods to assess the quality and reliability of clustering results. Finally, we conclude this paper and suggest the promising trends in this field.
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paper_title: Multifactor-Dimensionality Reduction Reveals High-Order Interactions among Estrogen-Metabolism Genes in Sporadic Breast Cancer

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One of the greatest challenges facing human geneticists is the identification and characterization of susceptibility genes for common complex multifactorial human diseases. This challenge is partly due to the limitations of parametric-statistical methods for detection of gene effects that are dependent solely or partially on interactions with other genes and with environmental exposures. We introduce multifactor-dimensionality reduction (MDR) as a method for reducing the dimensionality of multilocus information, to improve the identification of polymorphism combinations associated with disease risk. The MDR method is nonparametric (i.e., no hypothesis about the value of a statistical parameter is made), is model-free (i.e., it assumes no particular inheritance model), and is directly applicable to case-control and discordant-sib-pair studies. Using simulated case-control data, we demonstrate that MDR has reasonable power to identify interactions among two or more loci in relatively small samples. When it was applied to a sporadic breast cancer case-control data set, in the absence of any statistically significant independent main effects, MDR identified a statistically significant high-order interaction among four polymorphisms from three different estrogen-metabolism genes. To our knowledge, this is the first report of a four-locus interaction associated with a common complex multifactorial disease.
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paper_title: New strategies for identifying gene-gene interactions in hypertension

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Essential hypertension is a common disease that has complex multifactorial etiology. For this reason, it is not surprising that studies of the effects of single genes on hypertension have often failed to replicate the original findings. We propose, as a working hypothesis, that the failure to replicate some single locus results is because the impact of single alleles on the risk of hypertension is dependent on genetic variations at other loci (i.e. gene-gene interactions) and on environmental factors (i.e. gene-environment interactions). Thus, studies that do not consider the appropriate genetic and/or environmental contexts may not identify important susceptibility loci. The identification and characterization of such gene-gene and gene-environment interactions have been limited by lack of powerful statistical methods and/or a lack of large enough sample sizes. Here, we review the general problem of identifying gene-gene interactions and describe several traditional and several newer methods that are bei...
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paper_title: A computationally efficient hypothesis testing method for epistasis analysis using multifactor dimensionality reduction

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Multifactor dimensionality reduction (MDR) was developed as a nonparametric and model-free data mining method for detecting, characterizing, and interpreting epistasis in the absence of significant main effects in genetic and epidemiologic studies of complex traits such as disease susceptibility. The goal of MDR is to change the representation of the data using a constructive induction algorithm to make nonadditive interactions easier to detect using any classification method such as naïve Bayes or logistic regression. Traditionally, MDR constructed variables have been evaluated with a naïve Bayes classifier that is combined with 10-fold cross validation to obtain an estimate of predictive accuracy or generalizability of epistasis models. Traditionally, we have used permutation testing to statistically evaluate the significance of models obtained through MDR. The advantage of permutation testing is that it controls for false positives due to multiple testing. The disadvantage is that permutation testing is computationally expensive. This is an important issue that arises in the context of detecting epistasis on a genome-wide scale. The goal of the present study was to develop and evaluate several alternatives to large-scale permutation testing for assessing the statistical significance of MDR models. Using data simulated from 70 different epistasis models, we compared the power and type I error rate of MDR using a 1,000-fold permutation test with hypothesis testing using an extreme value distribution (EVD). We find that this new hypothesis testing method provides a reasonable alternative to the computationally expensive 1,000-fold permutation test and is 50 times faster. We then demonstrate this new method by applying it to a genetic epidemiology study of bladder cancer susceptibility that was previously analyzed using MDR and assessed using a 1,000-fold permutation test.
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paper_title: Genetic pathway-based hierarchical clustering analysis of older adults with cognitive complaints and amnestic mild cognitive impairment using clinical and neuroimaging phenotypes.

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Hierarchical clustering is frequently used for grouping results in expression or haplotype analyses. These methods can elucidate patterns between measures that can then be applied to discerning their validity in discriminating between experimental conditions. Here a hierarchical clustering method is used to analyze the results of an imaging genetics study using multiple brain morphology and cognitive testing endpoints for older adults with amnestic mild cognitive impairment (MCI) or cognitive complaints (CC) compared to healthy controls (HC). The single nucleotide polymorphisms (SNPs) are a subset of those included on a larger array that are found in a reported Alzheimer's disease (AD) and neurodegeneration pathway. The results indicate that genetic models within the endpoints cluster together, while there are 4 distinct sets of SNPs that differentiate between the endpoints, with most significant results associated with morphology endpoints rather than cognitive testing of patients' reported symptoms. The genes found in at least one cluster are ABCB1, APBA1, BACE1, BACE2, BCL2, BCL2L1, CASP7, CHAT, CST3, DRD3, DRD5, IL6, LRP1, NAT1, and PSEN2. The greater associations with morphology endpoints suggests that changes in brain structure can be influenced by an individual's genetic background in the absence of dementia and in some cases (Cognitive Complaints group) even without those effects necessarily being detectable on commonly used clinical tests of cognition. The results are consistent with polygenic influences on early neurodegenerative changes and demonstrate the effectiveness of hierarchical clustering in identifying genetic associations among multiple related phenotypic endpoints.
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paper_title: A novel method to identify high order gene-gene interactions in genome-wide association studies: Gene-based MDR

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BackgroundBecause common complex diseases are affected by multiple genes and environmental factors, it is essential to investigate gene-gene and/or gene-environment interactions to understand genetic architecture of complex diseases. After the great success of large scale genome-wide association (GWA) studies using the high density single nucleotide polymorphism (SNP) chips, the study of gene-gene interaction becomes a next challenge. Multifactor dimensionality reduction (MDR) analysis has been widely used for the gene-gene interaction analysis. In practice, however, it is not easy to perform high order gene-gene interaction analyses via MDR in genome-wide level because it requires exploring a huge search space and suffers from a computational burden due to high dimensionality.ResultsWe propose dimensional reduction analysis, Gene-MDR analysis for the fast and efficient high order gene-gene interaction analysis. The proposed Gene-MDR method is composed of two-step applications of MDR: within- and between-gene MDR analyses. First, within-gene MDR analysis summarizes each gene effect via MDR analysis by combining multiple SNPs from the same gene. Second, between-gene MDR analysis then performs interaction analysis using the summarized gene effects from within-gene MDR analysis. We apply the Gene-MDR method to bipolar disorder (BD) GWA data from Wellcome Trust Case Control Consortium (WTCCC). The results demonstrate that Gene-MDR is capable of detecting high order gene-gene interactions associated with BD.ConclusionBy reducing the dimension of genome-wide data from SNP level to gene level, Gene-MDR efficiently identifies high order gene-gene interactions. Therefore, Gene-MDR can provide the key to understand complex disease etiology.
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paper_title: Epistasis, Complexity, and Multifactor Dimensionality Reduction

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Genome-wide association studies (GWASs) and other high-throughput initiatives have led to an information explosion in human genetics and genetic epidemiology. Conversion of this wealth of new information about genomic variation to knowledge about public health and human biology will depend critically on the complexity of the genotype to phenotype mapping relationship. We review here computational approaches to genetic analysis that embrace, rather than ignore, the complexity of human health. We focus on multifactor dimensionality reduction (MDR) as an approach for modeling one of these complexities: epistasis or gene–gene interaction.
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paper_title: Bioinformatics challenges for genome-wide association studies

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MOTIVATION ::: The sequencing of the human genome has made it possible to identify an informative set of >1 million single nucleotide polymorphisms (SNPs) across the genome that can be used to carry out genome-wide association studies (GWASs). The availability of massive amounts of GWAS data has necessitated the development of new biostatistical methods for quality control, imputation and analysis issues including multiple testing. This work has been successful and has enabled the discovery of new associations that have been replicated in multiple studies. However, it is now recognized that most SNPs discovered via GWAS have small effects on disease susceptibility and thus may not be suitable for improving health care through genetic testing. One likely explanation for the mixed results of GWAS is that the current biostatistical analysis paradigm is by design agnostic or unbiased in that it ignores all prior knowledge about disease pathobiology. Further, the linear modeling framework that is employed in GWAS often considers only one SNP at a time thus ignoring their genomic and environmental context. There is now a shift away from the biostatistical approach toward a more holistic approach that recognizes the complexity of the genotype-phenotype relationship that is characterized by significant heterogeneity and gene-gene and gene-environment interaction. We argue here that bioinformatics has an important role to play in addressing the complexity of the underlying genetic basis of common human diseases. The goal of this review is to identify and discuss those GWAS challenges that will require computational methods.
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paper_title: Integrated Analysis of Gene Expression and Copy Number Data on Gene Shaving Using Independent Component Analysis

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DNA microarray gene expression and microarray-based comparative genomic hybridization (aCGH) have been widely used for biomedical discovery. Because of the large number of genes and the complex nature of biological networks, various analysis methods have been proposed. One such method is "gene shaving,” a procedure which identifies subsets of the genes with coherent expression patterns and large variation across samples. Since combining genomic information from multiple sources can improve classification and prediction of diseases, in this paper we proposed a new method, "ICA gene shaving” (ICA, independent component analysis), for jointly analyzing gene expression and copy number data. First we used ICA to analyze joint measurements, gene expression and copy number, of a biological system and project the data onto statistically independent biological processes. Next, we used these results to identify patterns of variation in the data and then applied an iterative shaving method. We investigated the properties of our proposed method by analyzing both simulated and real data. We demonstrated that the robustness of our method to noise using simulated data. Using breast cancer data, we showed that our method is superior to the Generalized Singular Value Decomposition (GSVD) gene shaving method for identifying genes associated with breast cancer.
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paper_title: Identification of Genetic and Epigenetic Marks Involved in Population Structure

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Population structure is well known as a prevalent and important factor in genetic studies, but its relevance in epigenetics is unclear. Very little is known about the affected epigenetic markers and their connections with genetics. In this study we assessed the impact of population diversity on genome wide single nucleotide polymorphisms (SNPs) and DNA methylation levels in 196 participants from five ethnic groups, using principle and independent component analyses. Three population stratification factors (PSFs) were identified in the genomic SNP dataset, accounting for a relatively large portion of total variance (6%). In contrast, only one PSF was identified in genomic methylation dataset accounting for 0.2% of total variance. This methylation PSF, however, was significantly correlated with the largest SNP PSF (r = 0.72, p<1E-23). We then investigated the top contributing markers in these two linked PSFs. The SNP PSF predominantly consists of 8 SNPs from three genes, SLC45A2, HERC2 and CTNNA2, known to encode skin/hair/eye color. The methylation PSF includes 48 methylated sites in 44 genes coding for basic molecular functions, including transcription regulation, DNA binding, cytokine, and transferase activity. Among them, 8 sites are either hypo- or hyper-methylated correlating to minor alleles of SNPs in the SNP PSF. We found that the genes in SNP and methylation PSFs share common biological processes including sexual/multicellular organism reproduction, cell-cell signaling and cytoskeleton organization. We further investigated the transcription regulatory network operating at these genes and identified that most of genes closely interact with ID2, which encodes for a helix-loop-helix inhibitor of DNA binding. Overall, our results show a significant correlation between genetic and epigenetic population stratification, and suggest that the interrelationship between genetic and epigenetic population structure is mediated via complex multiple gene interactions in shared biological processes, through possibly, SNP-dependent modulation and ID2 repressor function.
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paper_title: Identification of Significant Association and Gene-Gene Interaction of GABA Receptor Subunit Genes in Autism

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Autism is a common neurodevelopmental disorder with a significant genetic component. Existing research suggests that multiple genes contribute to autism and that epigenetic effects or gene-gene interactions are likely contributors to autism risk. However, these effects have not yet been identified. Gamma-aminobutyric acid (GABA), the primary inhibitory neurotransmitter in the adult brain, has been implicated in autism etiology. Fourteen known autosomal GABA receptor subunit genes were studied to look for the genes associated with autism and their possible interactions. Single-nucleotide polymorphisms (SNPs) were screened in the following genes: GABRG1, GABRA2, GABRA4, and GABRB1 on chromosome 4p12; GABRB2, GABRA6, GABRA1, GABRG2, and GABRP on 5q34q35.1; GABRR1 and GABRR2 on 6q15; and GABRA5, GABRB3, and GABRG3 on 15q12. Intronic and/or silent mutation SNPs within each gene were analyzed in 470 white families with autism. Initially, SNPs were used in a family-based study for allelic association analysis—with the pedigree disequilibrium test and the family-based association test—and for genotypic and haplotypic association analysis—with the genotype-pedigree disequilibrium test (geno-PDT), the association in the presence of linkage (APL) test, and the haplotype family-based association test. Next, with the use of five refined independent marker sets, extended multifactor-dimensionality reduction (EMDR) analysis was employed to identify the models with locus joint effects, and interaction was further verified by conditional logistic regression. Significant allelic association was found for markers RS1912960 (in GABRA4; P p .01) and HCV9866022 (in GABRR2; P p .04). The geno-PDT found significant genotypic association for HCV8262334 (in GABRA2), RS1912960 and RS2280073 (in GABRA4), and RS2617503 and RS12187676 (in GABRB2). Consistent with the allelic and genotypic association results, EMDR confirmed the main effect at RS1912960 (in GABRA4). EMDR also identified a significant two-locus gene-gene effect model involving RS1912960 in GABRA4 and RS2351299 in GABRB1. Further support for this two-locus model came from both the multilocus geno-PDT and the APL test, which indicated a common genotype and haplotype combination positively associated with disease. Finally, these results were also consistent with the results from the conditional logistic regression, which confirmed the interaction between GABRA4 and GABRB1 (odds ratio p 2.9 for interaction term; P p .002). Through the convergence of all analyses, we conclude that GABRA4 is involved in the etiology of autism and potentially increases autism risk through interaction with GABRB1. These results support the hypothesis that GABA receptor subunit genes are involved in autism, most likely via complex gene-gene interactions.
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paper_title: Significance testing in ridge regression for genetic data

paper_content:

BackgroundTechnological developments have increased the feasibility of large scale genetic association studies. Densely typed genetic markers are obtained using SNP arrays, next-generation sequencing technologies and imputation. However, SNPs typed using these methods can be highly correlated due to linkage disequilibrium among them, and standard multiple regression techniques fail with these data sets due to their high dimensionality and correlation structure. There has been increasing interest in using penalised regression in the analysis of high dimensional data. Ridge regression is one such penalised regression technique which does not perform variable selection, instead estimating a regression coefficient for each predictor variable. It is therefore desirable to obtain an estimate of the significance of each ridge regression coefficient.ResultsWe develop and evaluate a test of significance for ridge regression coefficients. Using simulation studies, we demonstrate that the performance of the test is comparable to that of a permutation test, with the advantage of a much-reduced computational cost. We introduce the p-value trace, a plot of the negative logarithm of the p-values of ridge regression coefficients with increasing shrinkage parameter, which enables the visualisation of the change in p-value of the regression coefficients with increasing penalisation. We apply the proposed method to a lung cancer case-control data set from EPIC, the European Prospective Investigation into Cancer and Nutrition.ConclusionsThe proposed test is a useful alternative to a permutation test for the estimation of the significance of ridge regression coefficients, at a much-reduced computational cost. The p-value trace is an informative graphical tool for evaluating the results of a test of significance of ridge regression coefficients as the shrinkage parameter increases, and the proposed test makes its production computationally feasible.
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paper_title: Sparse reduced-rank regression detects genetic associations with voxel-wise longitudinal phenotypes in Alzheimer's disease

paper_content:

Abstract 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.
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paper_title: Independent component analysis: Mining microarray data for fundamental human gene expression modules

paper_content:

As public microarray repositories rapidly accumulate gene expression data, these resources contain increasingly valuable information about cellular processes in human biology. This presents a unique opportunity for intelligent data mining methods to extract information about the transcriptional modules underlying these biological processes. Modeling cellular gene expression as a combination of functional modules, we use independent component analysis (ICA) to derive 423 fundamental components of human biology from a 9395-array compendium of heterogeneous expression data. Annotation using the Gene Ontology (GO) suggests that while some of these components represent known biological modules, others may describe biology not well characterized by existing manually-curated ontologies. In order to understand the biological functions represented by these modules, we investigate the mechanism of the preclinical anti-cancer drug parthenolide (PTL) by analyzing the differential expression of our fundamental components. Our method correctly identifies known pathways and predicts that N-glycan biosynthesis and T-cell receptor signaling may contribute to PTL response. The fundamental gene modules we describe have the potential to provide pathway-level insight into new gene expression datasets.
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paper_title: A Simple and Computationally Efficient Approach to Multifactor Dimensionality Reduction Analysis of Gene-Gene Interactions for Quantitative Traits

paper_content:

We present an extension of the two-class multifactor dimensionality reduction (MDR) algorithm that enables detection and characterization of epistatic SNP-SNP interactions in the context of a quantitative trait. The proposed Quantitative MDR (QMDR) method handles continuous data by modifying MDR’s constructive induction algorithm to use a T-test. QMDR replaces the balanced accuracy metric with a T-test statistic as the score to determine the best interaction model. We used a simulation to identify the empirical distribution of QMDR’s testing score. We then applied QMDR to genetic data from the ongoing prospective Prevention of Renal and Vascular End-Stage Disease (PREVEND) study.
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paper_title: Characterizing genetic interactions in human disease association studies using statistical epistasis networks

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BackgroundEpistasis is recognized ubiquitous in the genetic architecture of complex traits such as disease susceptibility. Experimental studies in model organisms have revealed extensive evidence of biological interactions among genes. Meanwhile, statistical and computational studies in human populations have suggested non-additive effects of genetic variation on complex traits. Although these studies form a baseline for understanding the genetic architecture of complex traits, to date they have only considered interactions among a small number of genetic variants. Our goal here is to use network science to determine the extent to which non-additive interactions exist beyond small subsets of genetic variants. We infer statistical epistasis networks to characterize the global space of pairwise interactions among approximately 1500 Single Nucleotide Polymorphisms (SNPs) spanning nearly 500 cancer susceptibility genes in a large population-based study of bladder cancer.ResultsThe statistical epistasis network was built by linking pairs of SNPs if their pairwise interactions were stronger than a systematically derived threshold. Its topology clearly differentiated this real-data network from networks obtained from permutations of the same data under the null hypothesis that no association exists between genotype and phenotype. The network had a significantly higher number of hub SNPs and, interestingly, these hub SNPs were not necessarily with high main effects. The network had a largest connected component of 39 SNPs that was absent in any other permuted-data networks. In addition, the vertex degrees of this network were distinctively found following an approximate power-law distribution and its topology appeared scale-free.ConclusionsIn contrast to many existing techniques focusing on high main-effect SNPs or models of several interacting SNPs, our network approach characterized a global picture of gene-gene interactions in a population-based genetic data. The network was built using pairwise interactions, and its distinctive network topology and large connected components indicated joint effects in a large set of SNPs. Our observations suggested that this particular statistical epistasis network captured important features of the genetic architecture of bladder cancer that have not been described previously.
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paper_title: Model-based multifactor dimensionality reduction for detecting epistasis in case-control data in the presence of noise.

paper_content:

Analyzing the combined effects of genes and/or environmental factors on the development of complex diseases is a great challenge from both the statistical and computational perspective, even using a relatively small number of genetic and nongenetic exposures. Several data-mining methods have been proposed for interaction analysis, among them, the Multifactor Dimensionality Reduction Method (MDR) has proven its utility in a variety of theoretical and practical settings. Model-Based Multifactor Dimensionality Reduction (MB-MDR), a relatively new MDR-based technique that is able to unify the best of both nonparametric and parametric worlds, was developed to address some of the remaining concerns that go along with an MDR analysis. These include the restriction to univariate, dichotomous traits, the absence of flexible ways to adjust for lower order effects and important confounders, and the difficulty in highlighting epistatic effects when too many multilocus genotype cells are pooled into two new genotype groups. We investigate the empirical power of MB-MDR to detect gene-gene interactions in the absence of any noise and in the presence of genotyping error, missing data, phenocopy, and genetic heterogeneity. Power is generally higher for MB-MDR than for MDR, in particular in the presence of genetic heterogeneity, phenocopy, or low minor allele frequencies.
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paper_title: Principal components analysis corrects for stratification in genome-wide association studies

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Population stratification--allele frequency differences between cases and controls due to systematic ancestry differences-can cause spurious associations in disease studies. We describe a method that enables explicit detection and correction of population stratification on a genome-wide scale. Our method uses principal components analysis to explicitly model ancestry differences between cases and controls. The resulting correction is specific to a candidate marker's variation in frequency across ancestral populations, minimizing spurious associations while maximizing power to detect true associations. Our simple, efficient approach can easily be applied to disease studies with hundreds of thousands of markers.
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paper_title: A robust multifactor dimensionality reduction method for detecting gene-gene interactions with application to the genetic analysis of bladder cancer susceptibility.

paper_content:

A central goal of human genetics is to identify susceptibility genes for common human diseases. An important challenge is modelling gene-gene interaction or epistasis that can result in nonadditivity of genetic effects. The multifactor dimensionality reduction (MDR) method was developed as a machine learning alternative to parametric logistic regression for detecting interactions in the absence of significant marginal effects. The goal of MDR is to reduce the dimensionality inherent in modelling combinations of polymorphisms using a computational approach called constructive induction. Here, we propose a Robust Multifactor Dimensionality Reduction (RMDR) method that performs constructive induction using a Fisher's Exact Test rather than a predetermined threshold. The advantage of this approach is that only statistically significant genotype combinations are considered in the MDR analysis. We use simulation studies to demonstrate that this approach will increase the success rate of MDR when there are only a few genotype combinations that are significantly associated with case-control status. We show that there is no loss of success rate when this is not the case. We then apply the RMDR method to the detection of gene-gene interactions in genotype data from a population-based study of bladder cancer in New Hampshire.
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paper_title: Applications of Multifactor Dimensionality Reduction to Genome-Wide Data Using the R Package ‘MDR’

paper_content:

This chapter describes how to use the R package 'MDR' to search and identify gene-gene interactions in high-dimensional data and illustrates applications for exploratory analysis of multi-locus models by providing specific examples.
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paper_title: ARTICLE A Generalized Combinatorial Approach for Detecting Gene-by-Gene and Gene-by-Environment Interactions with Application to Nicotine Dependence

paper_content:

The determination of gene-by-gene and gene-by-environment interactions has long been one of the greatest challenges in genetics. The traditional methods are typically inadequate because of the problem referred to as the "curse of dimensionality." Recent combinatorial approaches, such as the multifactor dimensionality reduction (MDR) method, the combinatorial partitioning method, and the restricted partition method, have a straightforward correspondence to the concept of the phenotypic landscape that unifies biological, statistical genetics, and evolutionary theories. However, the existing approaches have several limitations, such as not allowing for covariates, that restrict their practical use. In this study, we report a generalized MDR (GMDR) method that permits adjustment for discrete and quantitative covariates and is applicable to both dichotomous and continuous phenotypes in various population-based study designs. Computer simulations indicated that the GMDR method has superior performance in its ability to identify epistatic loci, compared with current methods in the literature. We applied our proposed method to a genetics study of four genes that were reported to be associated with nicotine dependence and found significant joint action between CHRNB4 and NTRK2. Moreover, our example illustrates that the newly proposed GMDR approach can increase prediction ability, suggesting that its use is justified in practice. In summary, GMDR serves the purpose of identifying contributors to population variation better than do the other existing methods.
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paper_title: Genetics of human episodic memory: dealing with complexity

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Episodic memory is a polygenic behavioral trait with substantial heritability estimates. Despite its complexity, recent empirical evidence supports the notion that behavioral genetic studies of episodic memory might successfully identify trait-associated molecules and pathways. The development of high-throughput genotyping methods, of elaborated statistical analyses and of phenotypic assessment methods at the neural systems level will facilitate the reliable identification of novel memory-related genes. Importantly, a necessary crosstalk between behavioral genetic studies and investigation of causality by molecular genetic studies will ultimately pave the way towards the identification of biologically important, and hopefully druggable, genes and molecular pathways related to human episodic memory.
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paper_title: Independent component analysis of microarray data in the study of endometrial cancer

paper_content:

Gene microarray technology is highly effective in screening for differential gene expression and has hence become a popular tool in the molecular investigation of cancer. When applied to tumours, molecular characteristics may be correlated with clinical features such as response to chemotherapy. Exploitation of the huge amount of data generated by microarrays is difficult, however, and constitutes a major challenge in the advancement of this methodology. Independent component analysis (ICA), a modern statistical method, allows us to better understand data in such complex and noisy measurement environments. The technique has the potential to significantly increase the quality of the resulting data and improve the biological validity of subsequent analysis. We performed microarray experiments on 31 postmenopausal endometrial biopsies, comprising 11 benign and 20 malignant samples. We compared ICA to the established methods of principal component analysis (PCA), Cyber-T, and SAM. We show that ICA generated patterns that clearly characterized the malignant samples studied, in contrast to PCA. Moreover, ICA improved the biological validity of the genes identified as differentially expressed in endometrial carcinoma, compared to those found by Cyber-T and SAM. In particular, several genes involved in lipid metabolism that are differentially expressed in endometrial carcinoma were only found using this method. This report highlights the potential of ICA in the analysis of microarray data.
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paper_title: A principal components regression approach to multilocus genetic association studies.

paper_content:

With the rapid development of modern genotyping technology, it is becoming commonplace to genotype densely spaced genetic markers such as single nucleotide polymorphisms (SNPs) along the genome. This development has inspired a strong interest in using multiple markers located in the target region for the detection of association. We introduce a principal components (PCs) regression method for candidate gene association studies where multiple SNPs from the candidate region tend to be correlated. In this approach, the total variance in the original genotype scores is decomposed into parts that correspond to uncorrelated PCs. The PCs with the largest variances are then used as regressors in a multiple regression. Simulation studies suggest that this approach can have higher power than some popular methods. An application to CHI3L2 gene expression data confirms a significant association between CHI3L2 gene expression level and SNPs from this gene that has been previously reported by others.
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paper_title: Tensorial extensions of independent component analysis for multisubject FMRI analysis.

paper_content:

Abstract We discuss model-free analysis of multisubject or multisession FMRI data by extending the single-session probabilistic independent component analysis model (PICA; Beckmann and Smith, 2004. IEEE Trans. on Medical Imaging, 23 (2) 137–152) to higher dimensions. This results in a three-way decomposition that represents the different signals and artefacts present in the data in terms of their temporal, spatial, and subject-dependent variations. The technique is derived from and compared with parallel factor analysis (PARAFAC; Harshman and Lundy, 1984. In Research methods for multimode data analysis, chapter 5, pages 122–215. Praeger, New York). Using simulated data as well as data from multisession and multisubject FMRI studies we demonstrate that the tensor PICA approach is able to efficiently and accurately extract signals of interest in the spatial, temporal, and subject/session domain. The final decompositions improve upon PARAFAC results in terms of greater accuracy, reduced interference between the different estimated sources (reduced cross-talk), robustness (against deviations of the data from modeling assumptions and against overfitting), and computational speed. On real FMRI ‘activation’ data, the tensor PICA approach is able to extract plausible activation maps, time courses, and session/subject modes as well as provide a rich description of additional processes of interest such as image artefacts or secondary activation patterns. The resulting data decomposition gives simple and useful representations of multisubject/multisession FMRI data that can aid the interpretation and optimization of group FMRI studies beyond what can be achieved using model-based analysis techniques.
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paper_title: Source density-driven independent component analysis approach for fMRI data

paper_content:

Independent component analysis (ICA) has become a popular tool for functional magnetic resonance imaging (fMRI) data analysis. Conventional ICA algorithms including Infomax and FAST-ICA algorithms employ the underlying assumption that data can be decomposed into statistically independent sources and implicitly model the probability density functions of the underlying sources as highly kurtotic or symmetric. When source data violate these assumptions (e.g., are asymmetric), however, conventional ICA methods might not work well. As a result, modeling of the underlying sources becomes an important issue for ICA applications. We propose a source density-driven ICA (SD-ICA) method. The SD-ICA algorithm involves a two-step procedure. It uses a conventional ICA algorithm to obtain initial independent source estimates for the first-step and then, using a kernel estimator technique, the source density is calculated. A refitted nonlinear function is used for each source at the second step. We show that the proposed SD-ICA algorithm provides flexible source adaptivity and improves ICA performance. On SD-ICA application to fMRI signals, the physiologic meaningful components (e.g., activated regions) of fMRI signals are governed typically by a small percentage of the whole-brain map on a task-related activation. Extra prior information (using a skewed-weighted distribution transformation) is thus additionally applied to the algorithm for the regions of interest of data (e.g., visual activated regions) to emphasize the importance of the tail part of the distribution. Our experimental results show that the source density-driven ICA method can improve performance further by incorporating some a priori information into ICA analysis of fMRI signals.
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paper_title: Analysis of Multimodal Neuroimaging Data

paper_content:

Each method for imaging brain activity has technical or physiological limits. Thus, combinations of neuroimaging modalities that can alleviate these limitations such as simultaneous recordings of neurophysiological and hemodynamic activity have become increasingly popular. Multimodal imaging setups can take advantage of complementary views on neural activity and enhance our understanding about how neural information processing is reflected in each modality. However, dedicated analysis methods are needed to exploit the potential of multimodal methods. Many solutions to this data integration problem have been proposed, which often renders both comparisons of results and the choice of the right method for the data at hand difficult. In this review we will discuss different multimodal neuroimaging setups, the advances achieved in basic research and clinical application and the methods used. We will provide a comprehensive overview of mathematical tools reoccurring in multimodal neuroimaging studies for artifact removal, data-driven and model-driven analyses, enabling the practitioner to try established or new combinations from these algorithmic building blocks.
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paper_title: Semiblind Spatial ICA of fMRI Using Spatial Constraints

paper_content:

Independent component analysis (ICA) utilizing prior information, also called semiblind ICA, has demonstrated considerable promise in the analysis of functional magnetic resonance imaging (fMRI). So far, temporal information about fMRI has been used in temporal ICA or spatial ICA as additional con- straints to improve estimation of task-related components. Considering that prior information about spa- tial patterns is also available, a semiblind spatial ICA algorithm utilizing the spatial information was proposed within the framework of constrained ICA with fixed-point learning. The proposed approach was first tested with synthetic fMRI-like data, and then was applied to real fMRI data from 11 subjects perform- ing a visuomotor task. Three components of interest including two task-related components and the ''default mode'' component were automatically extracted, and atlas-defined masks were used as the spatial constraints. The default mode network, a set of regions that appear correlated in particular in the absence of tasks or external stimuli and is of increasing interest in fMRI studies, was found to be greatly improved when incorporating spatial prior information. Results from simulation and real fMRI data demonstrate that the proposed algorithm can improve ICA performance compared to a different semiblind ICA algo- rithm and a standard blind ICA algorithm. Hum Brain Mapp 31:1076-1088, 2010. V C 2009 Wiley-Liss, Inc.
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paper_title: A review of multivariate methods for multimodal fusion of brain imaging data

paper_content:

Abstract The development of various neuroimaging techniques is rapidly improving the measurements of brain function/structure. However, despite improvements in individual modalities, it is becoming increasingly clear that the most effective research approaches will utilize multi-modal fusion, which takes advantage of the fact that each modality provides a limited view of the brain. The goal of multi-modal fusion is to capitalize on the strength of each modality in a joint analysis, rather than a separate analysis of each. This is a more complicated endeavor that must be approached more carefully and efficient methods should be developed to draw generalized and valid conclusions from high dimensional data with a limited number of subjects. Numerous research efforts have been reported in the field based on various statistical approaches, e.g. independent component analysis (ICA), canonical correlation analysis (CCA) and partial least squares (PLS). In this review paper, we survey a number of multivariate methods appearing in previous multimodal fusion reports, mostly fMRI with other modality, which were performed with or without prior information. A table for comparing optimization assumptions, purpose of the analysis, the need of priors, dimension reduction strategies and input data types is provided, which may serve as a valuable reference that helps readers understand the trade-offs of the 7 methods comprehensively. Finally, we evaluate 3 representative methods via simulation and give some suggestions on how to select an appropriate method based on a given research.
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paper_title: Probabilistic independent component analysis for functional magnetic resonance imaging

paper_content:

We present an integrated approach to probabilistic independent component analysis (ICA) for functional MRI (FMRI) data that allows for nonsquare mixing in the presence of Gaussian noise. In order to avoid overfitting, we employ objective estimation of the amount of Gaussian noise through Bayesian analysis of the true dimensionality of the data, i.e., the number of activation and non-Gaussian noise sources. This enables us to carry out probabilistic modeling and achieves an asymptotically unique decomposition of the data. It reduces problems of interpretation, as each final independent component is now much more likely to be due to only one physical or physiological process. We also describe other improvements to standard ICA, such as temporal prewhitening and variance normalization of timeseries, the latter being particularly useful in the context of dimensionality reduction when weak activation is present. We discuss the use of prior information about the spatiotemporal nature of the source processes, and an alternative-hypothesis testing approach for inference, using Gaussian mixture models. The performance of our approach is illustrated and evaluated on real and artificial FMRI data, and compared to the spatio-temporal accuracy of results obtained from classical ICA and GLM analyses.
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paper_title: Semi-supervised pattern classification of medical images: Application to mild cognitive impairment (MCI)

paper_content:

Many progressive disorders are characterized by unclear or transient diagnoses for specific subgroups of patients. Commonly used supervised pattern recognition methodology may not be the most suitable approach to deriving image-based biomarkers in such cases, as it relies on the availability of categorically labeled data (e.g., patients and controls). In this paper, we explore the potential of semi-supervised pattern classification to provide image-based biomarkers in the absence of precise diagnostic information for some individuals. We employ semi-supervised support vector machines (SVM) and apply them to the problem of classifying MR brain images of patients with uncertain diagnoses. We examine patterns in serial scans of ADNI participants with mild cognitive impairment (MCI), and propose that in the absence of sufficient follow-up evaluations of individuals with MCI, semi-supervised strategy is potentially more appropriate than the fully-supervised paradigm employed up to date.
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paper_title: A fast fixed - point algorithm for independent component analysis

paper_content:

An apparatus for hydrolytic degradation of plastics in which plastic material is deposited into a tubular housing via a feed hopper. An elongated screw shaft has a first section in the form of a high pitch screw thread disposed below the feed hopper to receive and advance the material to a second section. The second section of the screw shaft is in the form of a lower pitch thread for compressing the plastic material and transferring it to a longer, third section in the form of kneading discs, from which material passes through an outlet nozzle section to a cyclone separator where trapped gases and liquid may be withdrawn. The tubular housing is vented upstream of the feed hopper and a water inlet pipe is disposed adjacent to the second section of the screw shaft, downstream of the feed hopper. The outlet nozzle section is provided with pressure measuring and regulating means and a liquid level measuring and regulating device.
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paper_title: IVA for multi-subject FMRI analysis: A comparative study using a new simulation toolbox

paper_content:

Joint blind source separation (JBSS) techniques have proven to be a natural solution for achieving source separation of multiple data sets. JBSS algorithms, such as independent vector analysis (IVA), are a promising alternative to independent component analysis (ICA) based approaches for the analysis of multi-subject functional magnetic resonance imaging (fMRI) data. Unlike ICA, little is known about the effectiveness of JBSS methods for fMRI analysis. In this paper, a new fMRI simulation toolbox (SimTB) is used to simulate multi-subject realistic fMRI datasets that include inter-subject variability. We study the performance of two JBSS algorithms representing two different approaches to the problem: (1) a recently proposed IVA algorithm combining second-order and higher-order statistics denoted by IVA-GL; and (2) a JBSS solution found by jointly diagonalizing cross-cumulant matrices denoted IVA-GJD. We compare these two JBSS algorithms with similar ICA algorithms implemented in the widely used group ICA for fMRI toolbox (GIFT). The results show that in addition to offering an effective solution for making group inferences, IVA algorithms provide superior performance in terms of capturing spatial inter-subject variability.
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paper_title: Infomax and maximum likelihood for blind source separation

paper_content:

Algorithms for the blind separation of sources can be derived from several different principles. This article shows that the infomax (information-maximization) principle is equivalent to the maximum likelihood. The application of the infomax principle to source separation consists of maximizing an output entropy.
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paper_title: Kernel independent component analysis

paper_content:

We present a class of algorithms for independent component analysis (ICA) which use contrast functions based on canonical correlations in a reproducing kernel Hilbert space. On the one hand, we show that our contrast functions are related to mutual information and have desirable mathematical properties as measures of statistical dependence. On the other hand, building on recent developments in kernel methods, we show that these criteria can be computed efficiently. Minimizing these criteria leads to flexible and robust algorithms for ICA. We illustrate with simulations involving a wide variety of source distributions, showing that our algorithms outperform many of the presently known algorithms.
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paper_title: Independent Vector Analysis: Definition and Algorithms

paper_content:

We present a new approach to independent component analysis (ICA) by extending the formulation of univariate source signals to multivariate source signals. The new approach is termed independent vector analysis (IVA). In the model, we assume that linear mixing model exists in each dimension separately, and the latent sources are independent of the others. In contrast to ICA, the sources are random vectors, not just single variables, which means the elements of a random vector are closely related to the others. Thus, we assume the dependency between the elements of a source vector. In this manner, we define dependence between vectors as Kullback-Leibler divergence between the total joint probability of vectors and the product of marginal probabilities of vectors. Then, the model allows independence between multivariate source signals represented as random vectors, and dependence between the source signals within the vector representation. The proposed vector density model can for example capture variance dependencies within a vector source signal. There are several applications of this new formulation. In the separation of acoustic sources, the algorithm mitigates the permutation problem, i.e. the usual ICA algorithms applied in to the frequency domain mixture data suffer from the unknown permutation of the output signals. Although there are several engineering solutions to fix this problem after the ICA stage, the proposed method provides a natural solution to the problem by capturing the inherent dependencies of the acoustic signals. It therefore avoids the permutation problem and allows the separation of sources in very challenging environments for many sound sources.
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paper_title: Independent component analysis of functional MRI: what is signal and what is noise?

paper_content:

Many sources of fluctuation contribute to the functional magnetic resonance imaging (fMRI) signal, complicating attempts to infer those changes that are truly related to brain activation. Unlike methods of analysis of fMRI data that test the time course of each voxel against a hypothesized waveform, data-driven methods, such as independent component analysis and clustering, attempt to find common features within the data. This exploratory approach can be revealing when the brain activation is difficult to predict beforehand, such as with complex stimuli and internal shifts of activation that are not time-locked to an easily specified sensory or motor event. These methods can be further improved by incorporating prior knowledge regarding the temporal and spatial extent of brain activation.
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paper_title: Comparison of three methods for generating group statistical inferences from independent component analysis of functional magnetic resonance imaging data.

paper_content:

PURPOSE ::: To evaluate the relative effectiveness of three previously proposed methods of performing group independent component analysis (ICA) of functional magnetic resonance imaging (fMRI) data. ::: ::: ::: MATERIALS AND METHODS ::: Data were generated via computer simulation. Components were added to a varying number of subjects between 1 and 20, and intersubject variability was simulated for both the added sources and their associated time courses. Three methods of group ICA analyses were performed: across-subject averaging, subject-wise concatenation, and row-wise concatenation (e.g., across time courses). ::: ::: ::: RESULTS ::: Concatenating across subjects provided the best overall performance in terms of accurate estimation of the sources and associated time courses. Averaging across subjects provided accurate estimation (R > 0.9) of the time courses when the sources were present in a sufficient fraction (about 15%) of 100 subjects. Concatenating across time courses was shown not to be a feasible method when unique sources were added to the data from each subject, simulating the effects of motion and susceptibility artifacts. ::: ::: ::: CONCLUSION ::: Subject-wise concatenation should be used when computationally feasible. For studies involving a large number of subjects, across-subject averaging provides an acceptable alternative and reduces the computational load.
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paper_title: A projection pursuit algorithm to classify individuals using fMRI data: Application to schizophrenia

paper_content:

Abstract Schizophrenia is diagnosed based largely upon behavioral symptoms. Currently, no quantitative, biologically based diagnostic technique has yet been developed to identify patients with schizophrenia. Classification of individuals into patient with schizophrenia and healthy control groups based on quantitative biologically based data is of great interest to support and refine psychiatric diagnoses. We applied a novel projection pursuit technique on various components obtained with independent component analysis (ICA) of 70 subjects’ fMRI activation maps obtained during an auditory oddball task. The validity of the technique was tested with a leave-one-out method and the detection performance varied between 80% and 90%. The findings suggest that the proposed data reduction algorithm is effective in classifying individuals into schizophrenia and healthy control groups and may eventually prove useful as a diagnostic tool.
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paper_title: Semi-blind ICA of FMRI: a method for utilizing hypothesis-derived time courses in a spatial ICA analysis

paper_content:

Independent component analysis (ICA), a data-driven approach utilizing high-order statistical moments to find maximally independent sources, has found fruitful application in functional magnetic resonance imaging (fMRI). ICA, being a blind source separation technique, does not require any explicit constraints upon the fMRI time courses. In some cases, such as for the analysis of a rapid event-related paradigm, it would be useful to incorporate paradigm information into the ICA analysis in a flexible way. In this paper, we present an approach for constrained or semi-blind ICA (sbICA) analysis of fMRI data. We demonstrate the performance of our approach using simulations and fMRI data of an auditory oddball paradigm. Simulation results suggest that 1) a regression approach slightly outperforms ICA when prior information is accurate and ICA outperforms the general linear modeling (GLM) approach when prior information is not completely accurate, 2) prior information improves the robustness of ICA in the presence of noise, and 3) and ICA analysis using prior information with weak constraints can outperform a regression approach when the prior information is not completely accurate
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paper_title: Comparison of multi-subject ICA methods for analysis of fMRI data.

paper_content:

Here, we provide extensive comparisons of three data reduction methods and four multi-subject ICA approaches using simulated and fMRI task data. We compare subject-specific, spatial concatenation, and group data mean subject-level reduction strategies using PCA and probabilistic PCA (PPCA). We compare three direct back-reconstruction group ICA approaches (GICA1-GICA3) and an indirect back-reconstruction approach, spatio-temporal regression (STR, or dual regression). All are in GIFT for Matlab (http://icatb.sourceforge.net/). Methods: Subject-level PCA methods: Subject-specific reduces each subject; spatial concatenation obtains a PCA reducing matrix on the spatially-concatenated data, then applies that reduction to each subject separately; group data mean obtains a PCA reducing matrix on the mean data matrix, applies that reduction to each subject separately, then additional subjectspecific PCA rotation. Finally, the subject-reduced data are time-concatenated and a PCA and ICA is performed on this group data.
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paper_title: Independent vector analysis (IVA): Multivariate approach for fMRI group study

paper_content:

Abstract Independent component analysis (ICA) of fMRI data generates session/individual specific brain activation maps without a priori assumptions regarding the timing or pattern of the blood-oxygenation-level-dependent (BOLD) signal responses. However, because of a random permutation among output components, ICA does not offer a straightforward solution for the inference of group-level activation. In this study, we present an independent vector analysis (IVA) method to address the permutation problem during fMRI group data analysis. In comparison to ICA, IVA offers an analysis of additional dependent components, which were assigned for use in the automated grouping of dependent activation patterns across subjects. Upon testing using simulated trial-based fMRI data, our proposed method was applied to real fMRI data employing both a single-trial task-paradigm (right hand motor clenching and internal speech generation tasks) and a three-trial task-paradigm (right hand motor imagery task). A generalized linear model (GLM) and the group ICA of the fMRI toolbox (GIFT) were also applied to the same data set for comparison to IVA. Compared to GLM, IVA successfully captured activation patterns even when the functional areas showed variable hemodynamic responses that deviated from a hypothesized response. We also showed that IVA effectively inferred group-activation patterns of unknown origins without the requirement for a pre-processing stage (such as data concatenation in ICA-based GIFT). IVA can be used as a potential alternative or an adjunct to current ICA-based fMRI group processing methods.
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paper_title: Independent component analysis of fMRI group studies by self-organizing clustering

paper_content:

Abstract Independent component analysis (ICA) is a valuable technique for the multivariate data-driven analysis of functional magnetic resonance imaging (fMRI) data sets. Applications of ICA have been developed mainly for single subject studies, although different solutions for group studies have been proposed. These approaches combine data sets from multiple subjects into a single aggregate data set before ICA estimation and, thus, require some additional assumptions about the separability across subjects of group independent components. Here, we exploit the application of similarity measures and a related visual tool to study the natural self-organizing clustering of many independent components from multiple individual data sets in the subject space. Our proposed framework flexibly enables multiple criteria for the generation of group independent components and their random-effects evaluation. We present real visual activation fMRI data from two experiments, with different spatiotemporal structures, and demonstrate the validity of this framework for a blind extraction and selection of meaningful activity and functional connectivity group patterns. Our approach is either alternative or complementary to the group ICA of aggregated data sets in that it exploits commonalities across multiple subject-specific patterns, while addressing as much as possible of the intersubject variability of the measured responses. This property is particularly of interest for a blind group and subgroup pattern extraction and selection.
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paper_title: Multisubject Independent Component Analysis of fMRI: A Decade of Intrinsic Networks, Default Mode, and Neurodiagnostic Discovery

paper_content:

Since the discovery of functional connectivity in fMRI data (i.e., temporal correlations between spatially distinct regions of the brain) there has been a considerable amount of work in this field. One important focus has been on the analysis of brain connectivity using the concept of networks instead of regions. Approximately ten years ago, two important research areas grew out of this concept. First, a network proposed to be “a default mode of brain function” since dubbed the default mode network was proposed by Raichle. Secondly, multisubject or group independent component analysis (ICA) provided a data-driven approach to study properties of brain networks, including the default mode network. In this paper, we provide a focused review of how ICA has contributed to the study of intrinsic networks. We discuss some methodological considerations for group ICA and highlight multiple analytic approaches for studying brain networks. We also show examples of some of the differences observed in the default mode and resting networks in the diseased brain. In summary, we are in exciting times and still just beginning to reap the benefits of the richness of functional brain networks as well as available analytic approaches.
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paper_title: A new look at the statistical model identification

paper_content:

The history of the development of statistical hypothesis testing in time series analysis is reviewed briefly and it is pointed out that the hypothesis testing procedure is not adequately defined as the procedure for statistical model identification. The classical maximum likelihood estimation procedure is reviewed and a new estimate minimum information theoretical criterion (AIC) estimate (MAICE) which is designed for the purpose of statistical identification is introduced. When there are several competing models the MAICE is defined by the model and the maximum likelihood estimates of the parameters which give the minimum of AIC defined by AIC = (-2)log-(maximum likelihood) + 2(number of independently adjusted parameters within the model). MAICE provides a versatile procedure for statistical model identification which is free from the ambiguities inherent in the application of conventional hypothesis testing procedure. The practical utility of MAICE in time series analysis is demonstrated with some numerical examples.
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paper_title: Identifying disease sensitive and quantitative trait-relevant biomarkers from multidimensional heterogeneous imaging genetics data via sparse multimodal multitask learning

paper_content:

Motivation: Recent advances in brain imaging and high-throughput genotyping techniques enable new approaches to study the influence of genetic and anatomical variations on brain functions and disorders. Traditional association studies typically perform independent and pairwise analysis among neuroimaging measures, cognitive scores and disease status, and ignore the important underlying interacting relationships between these units. ::: ::: Results: To overcome this limitation, in this article, we propose a new sparse multimodal multitask learning method to reveal complex relationships from gene to brain to symptom. Our main contributions are three-fold: (i) introducing combined structured sparsity regularizations into multimodal multitask learning to integrate multidimensional heterogeneous imaging genetics data and identify multimodal biomarkers; (ii) utilizing a joint classification and regression learning model to identify disease-sensitive and cognition-relevant biomarkers; (iii) deriving a new efficient optimization algorithm to solve our non-smooth objective function and providing rigorous theoretical analysis on the global optimum convergency. Using the imaging genetics data from the Alzheimer's Disease Neuroimaging Initiative database, the effectiveness of the proposed method is demonstrated by clearly improved performance on predicting both cognitive scores and disease status. The identified multimodal biomarkers could predict not only disease status but also cognitive function to help elucidate the biological pathway from gene to brain structure and function, and to cognition and disease. ::: ::: Availability: Software is publicly available at: http://ranger.uta.edu/%7eheng/multimodal/ ::: ::: Contact:heng@uta.edu; shenli@iupui.edu
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paper_title: Estimating the number of independent components for functional magnetic resonance imaging data

paper_content:

Multivariate analysis methods such as independent component analysis (ICA) have been applied to the analysis of functional magnetic resonance imaging (fMRI) data to study brain function. Because of the high dimensionality and high noise level of the fMRI data, order selection, i.e., estimation of the number of informative components, is critical to reduce over/underfitting in such methods. De- pendence among fMRI data samples in the spatial and temporal domain limits the usefulness of the practical formulations of information-theoretic criteria (ITC) for order selection, since they are based on likelihood of independent and identically distributed (i.i.d.) data samples. To address this issue, we pro- pose a subsampling scheme to obtain a set of effectively i.i.d. samples from the dependent data samples and apply the ITC formulas to the effectively i.i.d. sample set for order selection. We apply the proposed method on the simulated data and show that it significantly improves the accuracy of order selection from dependent data. We also perform order selection on fMRI data from a visuomotor task and show that the proposed method alleviates the over-estimation on the number of brain sources due to the intrin- sic smoothness and the smooth preprocessing of fMRI data. We use the software package ICASSO (Him- berg et al. (2004): Neuroimage 22:1214-1222) to analyze the independent component (IC) estimates at dif- ferent orders and show that, when ICA is performed at overestimated orders, the stability of the IC esti- mates decreases and the estimation of task related brain activations show degradation. Hum Brain Mapp
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paper_title: A Parallel Independent Component Analysis Approach to Investigate Genomic Influence on Brain Function

paper_content:

Relationships between genomic data and functional brain images are of great interest but require new analysis approaches to integrate the high-dimensional data types. This letter presents an extension of a technique called parallel independent component analysis (paraICA), which enables the joint analysis of multiple modalities including interconnections between them. We extend our earlier work by allowing for multiple interconnections and by providing important overfitting controls. Performance was assessed by simulations under different conditions, and indicated reliable results can be extracted by properly balancing overfitting and underfitting. An application to functional magnetic resonance images and single nucleotide polymorphism array produced interesting findings.
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paper_title: Correlation-based multivariate analysis of genetic influence on brain volume

paper_content:

Considerable research effort has focused on achieving a better understanding of the genetic correlates of individual differences in volumetric and morphological brain measures. The importance of these efforts is underlined by evidence suggesting that brain changes in a number of neuropsychiatric disorders are at least partly genetic in origin. The currently used methods to study these relationships are mostly based on single-genotype univariate analysis techniques. These methods are limited as multiple genes are likely to interact with each other in their influences on brain structure and function. In this paper we present a feasibility study where we show that by using kernel correlation analysis, with a new genotypes representation, it is possible to analyse the relative associations of several genetic polymorphisms with brain structure. The implementation of the method is demonstrated on genetic and structural magnetic resonance imaging (MRI) data acquired from a group of 16 healthy subjects by showing the multivariate genetic influence on grey and white matter.
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paper_title: Parallel independent component analysis using an optimized neurovascular coupling for concurrent EEG-fMRI sources

paper_content:

The complexity of the human brain and the limitation of any one imaging approach motivates the need for multimodal measurements to better understand cerebral processing. A very natural goal is to integrate electrophysiological and hemodynamic activity. Among them, concurrent EEG-fMRI studies have shown great promise for understanding intrinsic brain properties yet analyzing such data presents a significant methodological challenge. Here, we propose a multivariate parallel ICA decomposition incorporating dynamic neurovascular coupling for concurrent EEG-fMRI recordings. The goal of our algorithm is to fuse multimodal EEG-fMRI information and detect/interpret the relationship between electrophysiological and hemodynamic sources via a temporal neurovascular connection enhancement. We analyze the performance of the algorithm on a valid simulation based on real EEG and fMRI components (sources) from our previous works and a neurovascular coupling built from an extended ‘balloon model’. The results from our simulations yield an accurate source tracking and linkage for concurrent EEG-fMRI, and provide a novel and efficient way to combine EEG and hemodynamic responses.
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paper_title: Projection regression models for multivariate imaging phenotype.

paper_content:

This paper presents a projection regression model (PRM) to assess the relationship between a multivariate phenotype and a set of covariates, such as a genetic marker, age, and gender. In the existing literature, a standard statistical approach to this problem is to fit a multivariate linear model to the multivariate phenotype and then use Hotelling's T(2) to test hypotheses of interest. An alternative approach is to fit a simple linear model and test hypotheses for each individual phenotype and then correct for multiplicity. However, even when the dimension of the multivariate phenotype is relatively small, say 5, such standard approaches can suffer from the issue of low statistical power in detecting the association between the multivariate phenotype and the covariates. The PRM generalizes a statistical method based on the principal component of heritability for association analysis in genetic studies of complex multivariate phenotypes. The key components of the PRM include an estimation procedure for extracting several principal directions of multivariate phenotypes relating to covariates and a test procedure based on wild-bootstrap method for testing the association between the weighted multivariate phenotype and explanatory variables. Simulation studies and an imaging genetic dataset are used to examine the finite sample performance of the PRM.
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paper_title: A Hybrid Machine Learning Method for Fusing fMRI and Genetic Data: Combining both Improves Classification of Schizophrenia

paper_content:

We demonstrate a hybrid machine learning method to classify schizophrenia patients and healthy controls, using functional magnetic resonance imaging (fMRI) and single nucleotide polymorphism (SNP) data. The method consists of four stages: (1) SNPs with the most discriminating information between the healthy controls and schizophrenia patients are selected to construct a support vector machine ensemble (SNP-SVME). (2) Voxels in the fMRI map contributing to classification are selected to build another SVME (Voxel-SVME). (3) Components of fMRI activation obtained with independent component analysis (ICA) are used to construct a single SVM classifier (ICA-SVMC). (4) The above three models are combined into a single module using a majority voting approach to make a final decision (Combined SNP-fMRI). The method was evaluated by a fully validated leave-one-out method using 40 subjects (20 patients and 20 controls). The classification accuracy was: 0.74 for SNP-SVME, 0.82 for Voxel-SVME, 0.83 for ICA-SVMC, and 0.87 for Combined SNP-fMRI. Experimental results show that better classification accuracy was achieved by combining genetic and fMRI data than using either alone, indicating that genetic and brain function representing different, but partially complementary aspects, of schizophrenia etiopathology. This study suggests an effective way to reassess biological classification of individuals with schizophrenia, which is also potentially useful for identifying diagnostically important markers for the disorder.
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paper_title: Multifaceted genomic risk for brain function in schizophrenia

paper_content:

Abstract Recently, deriving candidate endophenotypes from brain imaging data has become a valuable approach to study genetic influences on schizophrenia (SZ), whose pathophysiology remains unclear. In this work we utilized a multivariate approach, parallel independent component analysis, to identify genomic risk components associated with brain function abnormalities in SZ. 5157 candidate single nucleotide polymorphisms (SNPs) were derived from genome-wide array based on their possible connections with SZ and further investigated for their associations with brain activations captured with functional magnetic resonance imaging (fMRI) during a sensorimotor task. Using data from 92 SZ patients and 116 healthy controls, we detected a significant correlation (r = 0.29; p = 2.41 × 10 − 5 ) between one fMRI component and one SNP component, both of which significantly differentiated patients from controls. The fMRI component mainly consisted of precentral and postcentral gyri, the major activated regions in the motor task. On average, higher activation in these regions was observed in participants with higher loadings of the linked SNP component, predominantly contributed to by 253 SNPs. 138 identified SNPs were from known coding regions of 100 unique genes. 31 identified SNPs did not differ between groups, but moderately correlated with some other group-discriminating SNPs, indicating interactions among alleles contributing toward elevated SZ susceptibility. The genes associated with the identified SNPs participated in four neurotransmitter pathways: GABA receptor signaling, dopamine receptor signaling, neuregulin signaling and glutamate receptor signaling. In summary, our work provides further evidence for the complexity of genomic risk to the functional brain abnormality in SZ and suggests a pathological role of interactions between SNPs, genes and multiple neurotransmitter pathways.
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paper_title: Guided exploration of genomic risk for gray matter abnormalities in schizophrenia using parallel independent component analysis with reference

paper_content:

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

paper_content:

Abstract 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.
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paper_title: PARALLEL INDEPENDENT COMPONENT ANALYSIS FOR MULTIMODAL ANALYSIS: APPLICATION TO FMRI AND EEG DATA

paper_content:

This paper presents the technique of parallel independent component analysis (paraICA) with adaptive dynamic constraints applied to two datasets simultaneously. As a framework to investigate the integration of data from two imaging modalities, this method is dedicated to identify components of both modalities and connections between them through enhancing intrinsic interrelationships. The performance is assessed by simulations under different conditions of signal to noise ratio, connection strength and estimation of component order. An application to functional magnetic resonance images and electroencephalography data is conducted to illustrate the usage of paraICA. Results show that paraICA provides stable results and can identify the linked components with a relatively high accuracy. The application exhibits the ability to discover the connection between brain maps and event related potential time courses, and suggests a new way to investigate the coupling between hemodynamics and neural activity.
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paper_title: A multimodality ICA study - integrating genomic single nucleotide polymorphisms with functional neuroimaging data

paper_content:

Genomic experiments encapsulate such rich information that specific analysis tools are needed to take full advantage of the available data. Recently, more attention has been devoted to developing tools to identify the association between genomic variations and phenotypic traits. This paper focuses on understanding an approach called parallel independent component analysis (ICA), while applied to massive microarray data. Parallel ICA is a multivariate approach which can process genotypic and phenotypic data in parallel while emphasizing the relationship between data types. We simulated single nucleotide polymorphism (SNP) array data and functional magnetic resonance imaging data, generating hidden connections between the two modalities. The performance of parallel ICA was compared with a correlation test for a single hypothesis. Our evaluation shows that parallel ICA, in general, is able to extract more accurately the components and connections than the correlation test, in particular for weak linkages. Results also indicate that the ratio of sample size to SNP size should be at least 0.02. However, when the data have a low odds ratio or cases vs. controls ratio, the correlation test provides results reliably, though with lower accuracy.
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paper_title: Genome-wide association study identifies five new schizophrenia loci

paper_content:

We examined the role of common genetic variation in schizophrenia in a genome-wide association study of substantial size: a stage 1 discovery sample of 21,856 individuals of European ancestry and a stage 2 replication sample of 29,839 independent subjects. The combined stage 1 and 2 analysis yielded genome-wide significant associations with schizophrenia for seven loci, five of which are new (1p21.3, 2q32.3, 8p23.2, 8q21.3 and 10q24.32-q24.33) and two of which have been previously implicated (6p21.32-p22.1 and 18q21.2). The strongest new finding (P = 1.6 × 10 -11) was with rs1625579 within an intron of a putative primary transcript for MIR137 (microRNA 137), a known regulator of neuronal development. Four other schizophrenia loci achieving genome-wide significance contain predicted targets of MIR137, suggesting MIR137-mediated dysregulation as a previously unknown etiologic mechanism in schizophrenia. In a joint analysis with a bipolar disorder sample (16,374 affected individuals and 14,044 controls), three loci reached genome-wide significance: CACNA1C (rs4765905, P = 7.0 × 10 -9), ANK3 (rs10994359, P = 2.5 × 10 -8) and the ITIH3-ITIH4 region (rs2239547, P = 7.8 × 10 -9).
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paper_title: Random forests on distance matrices for imaging genetics studies

paper_content:

We propose a non-parametric regression methodology, Random Forests on Distance Matrices (RFDM), for detecting genetic variants associated to quantitative phenotypes representing the human brain's structure or function, and obtained using neuroimaging techniques. RFDM, which is an extension of decision forests, requires a distance matrix as response that encodes all pair-wise phenotypic distances in the random sample. We discuss ways to learn such distances directly from the data using manifold learning techniques, and how to define such distances when the phenotypes are non-vectorial objects such as brain connectivity networks. We also describe an extension of RFDM to detect espistatic effects while keeping the computational complexity low. Extensive simulation results and an application to an imaging genetics study of Alzheimer's Disease are presented and discussed.
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paper_title: An Information-Maximization Approach to Blind Separation and Blind Deconvolution

paper_content:

We derive a new self-organizing learning algorithm that maximizes the information transferred in a network of nonlinear units. The algorithm does not assume any knowledge of the input distributions, and is defined here for the zero-noise limit. Under these conditions, information maximization has extra properties not found in the linear case (Linsker 1989). The nonlinearities in the transfer function are able to pick up higher-order moments of the input distributions and perform something akin to true redundancy reduction between units in the output representation. This enables the network to separate statistically independent components in the inputs: a higher-order generalization of principal components analysis. We apply the network to the source separation (or cocktail party) problem, successfully separating unknown mixtures of up to 10 speakers. We also show that a variant on the network architecture is able to perform blind deconvolution (cancellation of unknown echoes and reverberation in a speech signal). Finally, we derive dependencies of information transfer on time delays. We suggest that information maximization provides a unifying framework for problems in "blind" signal processing.
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paper_title: Discovering genetic associations with high-dimensional neuroimaging phenotypes: A sparse reduced-rank regression approach

paper_content:

Abstract There is growing interest in performing genome-wide searches for associations between genetic variants and brain imaging phenotypes. While much work has focused on single scalar valued summaries of brain phenotype, accounting for the richness of imaging data requires a brain-wide, genome-wide search. In particular, the standard approach based on mass-univariate linear modelling (MULM) does not account for the structured patterns of correlations present in each domain. In this work, we propose sparse reduced rank regression (sRRR), a strategy for multivariate modelling of high-dimensional imaging responses (measurements taken over regions of interest or individual voxels) and genetic covariates (single nucleotide polymorphisms or copy number variations), which enforces sparsity in the regression coefficients. Such sparsity constraints ensure that the model performs simultaneous genotype and phenotype selection. Using simulation procedures that accurately reflect realistic human genetic variation and imaging correlations, we present detailed evaluations of the sRRR method in comparison with the more traditional MULM approach. In all settings considered, sRRR has better power to detect deleterious genetic variants compared to MULM. Important issues concerning model selection and connections to existing latent variable models are also discussed. This work shows that sRRR offers a promising alternative for detecting brain-wide, genome-wide associations.
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paper_title: A pilot multivariate parallel ICA study to investigate differential linkage between neural networks and genetic profiles in schizophrenia

paper_content:

Abstract Understanding genetic influences on both healthy and disordered brain function is a major focus in psychiatric neuroimaging. We utilized task-related imaging findings from an fMRI auditory oddball task known to be robustly associated with abnormal activation in schizophrenia, to investigate genomic factors derived from multiple single nucleotide polymorphisms (SNPs) from genes previously shown to be associated with schizophrenia. Our major aim was to investigate the relationship of these genomic factors to normal/abnormal brain functionality between controls and schizophrenia patients. We studied a Caucasian-only sample of 35 healthy controls and 31 schizophrenia patients. All subjects performed an auditory oddball task, which consists of detecting an infrequent sound within a series of frequent sounds. Each subject was characterized on 24 different SNP markers spanning multiple risk genes previously associated with schizophrenia. We used a recently developed technique named parallel independent component analysis (para-ICA) to analyze this multimodal data set (Liu et al., 2008). The method aims to identify simultaneously independent components of each modality (functional imaging, genetics) and the relationships between them. We detected three fMRI components significantly correlated with two distinct gene components. The fMRI components, along with their significant genetic profile (dominant SNP) correlations were as follows: (1) Inferior frontal–anterior/posterior cingulate–thalamus–caudate with SNPs from Brain derived neurotropic factor (BDNF) and dopamine transporter (DAT) [r = -0.51; p
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paper_title: Identification of gene pathways implicated in Alzheimer's disease using longitudinal imaging phenotypes with sparse regression

paper_content:

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 464 subjects in the Alzheimer's Disease Neuroimaging Initiative (ADNI) database. 66,182 SNPs are mapped to 185 gene pathways from the KEGG pathways 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 chemokine, Jak-stat and insulin signalling pathways, and tight junction interactions. 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, and identify a number of previously validated AD genes including CR1, APOE and TOMM40.
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paper_title: Signi fi cant correlation between a set of genetic polymorphisms and a functional brain network revealed by feature selection and sparse Partial Least Squares

paper_content:

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.
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paper_title: High-Order Contrasts for Independent Component Analysis

paper_content:

This article considers high-order measures of independence for the independent component analysis problem and discusses the class of Jacobi algorithms for their optimization. Several implementations are discussed. We compare the proposed approaches with gradient-based techniques from the algorithmic point of view and also on a set of biomedical data.
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paper_title: A large scale multivariate parallel ICA method reveals novel imaging–genetic relationships for Alzheimer's disease in the ADNI cohort

paper_content:

The underlying genetic etiology of late onset Alzheimer’s disease (LOAD) remains largely unknown, likely due to its polygenic architecture and a lack of sophisticated analytic methods to evaluate complex genotype-phenotype models. The aim of the current study was to overcome these limitations in a bi-multivariate fashion by linking intermediate magnetic resonance imaging (MRI) phenotypes with a genome-wide sample of common single nucleotide polymorphism (SNP) variants. We compared associations between 94 different brain regions of interest derived from structural MRI scans and 533,872 genome-wide SNPs using a novel multivariate statistical procedure, parallel-independent component analysis, in a large, national multi-center subject cohort. The study included 209 elderly healthy controls, 367 subjects with amnestic mild cognitive impairment and 181 with mild, early-stage LOAD, Caucasian adults, from the Alzheimer’s Disease Neuroimaging Initiative cohort. Imaging was performed on comparable 1.5T scanners at over 50 sites in the USA/Canada. Four primary “genetic components” were associated significantly with a single structural network including all regions involved neuropathologically in LOAD. Pathway analysis suggested that each component included several genes already known to contribute to LOAD risk (e.g. APOE4) or involved in pathologic processes contributing to the disorder, including inflammation, diabetes, obesity and cardiovascular disease. In addition significant novel genes identified included ZNF673, VPS13, SLC9A7, ATP5G2 and SHROOM2. Unlike conventional analyses, this multivariate approach identified distinct groups of genes that are plausibly linked in physiologic pathways, perhaps epistatically. Further, the study exemplifies the value of this novel approach to explore large-scale data sets involving high-dimensional gene and endophenotype data.
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paper_title: Parallel ICA identifies sub-components of resting state networks that covary with behavioral indices

paper_content:

Parallel Independent Component Analysis (para-ICA) is a multivariate method that can identify complex relationships between different data modalities by simultaneously performing Independent Component Analysis on each data set while finding mutual information between the two data sets. We use para-ICA to test the hypothesis that spatial sub-components of common resting state networks (RSNs) covary with specific behavioral measures. Resting state scans and a battery of behavioral indices were collected from 24 younger adults. Group ICA was performed and common RSNs were identified by spatial correlation to publically available templates. Nine RSNs were identified and para-ICA was run on each network with a matrix of behavioral measures serving as the second data type. Five networks had spatial sub-components that significantly correlated with behavioral components. These included a sub-component of the temporo-parietal attention network that differentially covaried with different trial-types of a sustained attention task, sub-components of default mode networks that covaried with attention and working memory tasks, and a sub-component of the bilateral frontal network that split the left inferior frontal gyrus into three clusters according to its cytoarchitecture that differentially covaried with working memory performance. Additionally, we demonstrate the validity of para-ICA in cases with unbalanced dimensions using simulated data.
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paper_title: Genetic determinants of target and novelty-related event-related potentials in the auditory oddball response

paper_content:

Processing of novel and target stimuli in the auditory target detection or ‘oddball’ task encompasses the chronometry of perception, attention and working memory and is reflected in scalp recorded event-related potentials (ERPs). A variety of ERP components related to target and novelty processing have been described and extensively studied, and linked to deficits of cognitive processing. However, little is known about associations of genotypes with ERP endophenotypes. Here we sought to elucidate the genetic underpinnings of auditory oddball ERP components using a novel data analysis technique. A parallel independent component analysis of the electrophysiology and single nucleotide polymorphism (SNP) data was used to extract relations between patterns of ERP components and SNP associations purely based on an analysis incorporating higher order statistics. The method allows for broader associations of genotypes with phenotypes than traditional hypothesis-driven univariate correlational analyses. We show that target detection and processing of novel stimuli are both associated with a shared cluster of genes linked to the adrenergic and dopaminergic pathways. These results provide evidence of genetic influences on normal patterns of ERP generation during auditory target detection and novelty processing at the SNP association level.
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paper_title: Imaging genetics via sparse canonical correlation analysis

paper_content:

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.
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paper_title: Sparse canonical correlation analysis applied to fMRI and genetic data fusion

paper_content:

Fusion of functional magnetic resonance imaging (fMRI) and genetic information is becoming increasingly important in biomarker discovery. These studies can contain vastly different types of information occupying different measurement spaces and in order to draw significant inferences and make meaningful predictions about genetic influence on brain activity; methodologies need to be developed that can accommodate the acute differences in data structures. One powerful, and occasionally overlooked, method of data fusion is canonical correlation analysis (CCA). Since the data modalities in question potentially contain millions of variables in each measurement, conventional CCA is not suitable for this task. This paper explores applying a sparse CCA algorithm to fMRI and genetic data fusion.
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paper_title: A proteome analysis of the anterior cingulate cortex gray matter in schizophrenia

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The Anterior Cingulate Cortex (ACC, Brodmans Area 24) is implicated in the pathogenesis of schizophrenia due to its normal functions and connectivity together with reports of structural, morphological and neurotransmitter aberrations within this brain area in the disease state. Two-dimensional gel electrophoresis (2DE) was employed to scan and compare the ACC gray matter proteomes between schizophrenia (n=10) and control (n=10) post-mortem human tissue. This proteomic approach has detected 42 protein spots with altered levels in the schizophrenia cohort, which to our knowledge is the first proteomic analysis of the ACC in schizophrenia. Thirty nine of these proteins were subsequently identified using mass spectrometry and functionally classified into metabolism and oxidative stress, cytoskeletal, synaptic, signalling, trafficking and glial-specific groups. Some of the identified proteins have previously been implicated in the disease pathogenesis and some offer new insights into schizophrenia. Investigating these proteins, the genes encoding these proteins, their functions and interactions may shed light on the molecular mechanisms underlying the heterogeneous symptoms characteristic of schizophrenia.
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paper_title: The ENIGMA Consortium: large-scale collaborative analyses of neuroimaging and genetic data

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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.
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paper_title: Copy-number variation and association studies of human disease

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The central goal of human genetics is to understand the inherited basis of human variation in phenotypes, elucidating human physiology, evolution and disease. Rare mutations have been found underlying two thousand mendelian diseases; more recently, it has become possible to assess systematically the contribution of common SNPs to complex disease. The known role of copy-number alterations in sporadic genomic disorders, combined with emerging information about inherited copy-number variation, indicate the importance of systematically assessing copy-number variants (CNVs), including common copy-number polymorphisms (CNPs), in disease. Here we discuss evidence that CNVs affect phenotypes, directions for basic knowledge to support clinical study of CNVs, the challenge of genotyping CNPs in clinical cohorts, the use of SNPs as markers for CNPs and statistical challenges in testing CNVs for association with disease. Critical needs are high-resolution maps of common CNPs and techniques that accurately determine the allelic state of affected individuals.
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paper_title: Rare Copy Number Deletions Predict Individual Variation in Human Brain Metabolite Concentrations in Individuals with Alcohol Use Disorders

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Background Although variations in neurometabolite concentrations occur in diverse neuropsychiatric and neurodegenerative disorders, little is known about the nature of underlying genetic influences. The current study investigated the importance of a specific type of genetic mutation, copy number variation (CNV), for neurometabolite concentrations in a bilateral anterior cingulate voxel. Methods These neurometabolic signals were quantified using proton magnetic resonance spectroscopy ( 1 H-MRS): N-acetylaspartate (NAA), creatine-phosphocreatine (Cre), glutamate/glutamine (Glx), myoinositol (mI), and phosphorylcholine-glycerol phosphorylcholine (Cho). Genetic data were collected using the Illumina 1MDuoBeadChip Array from a sample adults with alcohol use disorders ( n = 146). Results The number of base pairs lost through rare copy number deletions (occurring in less than 5% of our sample) predicted lower NAA, Cre, mI, and Glx. More total rare deletions also predicted lower NAA, Cre, and Glx. Principal components analyses of the five neurometabolites identified two correlated components, the first comprised of NAA, Glx, and Cre, and the second comprised of Cho, mI, and to a lesser extent, Cre. The number and length of rare deletions were correlated with the first component, capturing approximately 10% of phenotypic variance, but not the second component. Conclusions These results suggest that mutation load affects neurometabolite concentrations, potentially increasing risk for neuropsychiatric disorders. The greater effect of CVNs on NAA, Glx, and Cre may reflect a greater sensitivity to the effects of mutations (i.e., reduced canalization) for neurometabolites related to metabolic activity and cellular energetics, due to extensive recent selection pressure on these phenotypes in the human lineage.
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paper_title: The IMAGEN study: reinforcement-related behaviour in normal brain function and psychopathology

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The IMAGEN study: reinforcement-related behaviour in normal brain function and psychopathology
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paper_title: Methylation Patterns in Whole Blood Correlate With Symptoms in Schizophrenia Patients

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DNA methylation, one of the main epigenetic mechanisms to regulate gene expression, appears to be involved in the development of schizophrenia (SZ). In this study, we investigated 7562 DNA methylation markers in blood from 98 SZ patients and 108 healthy controls. A linear regression model including age, gender, race, alcohol, nicotine and cannabis use status, and diagnosis was implemented to identify C-phosphate-G (CpG) sites significantly associated with diagnosis. These CpG sites were further validated using an independent data set. Sixteen CpG sites were identified with hyper- or hypomethylation in patients. A further verification of expression of the corresponding genes identified 7 genes whose expression levels were also significantly altered in patients. While such altered methylation patterns showed no correlation with disorganized symptoms and negative symptoms in patients, 11 CpG sites significantly correlated with reality distortion symptoms. The direction of the correlations indicates that methylation changes possibly play a protective mechanism to lessen delusion and hallucination symptoms in patients. Pathway analyses showed that the most significant biological function of the differentially methylated CpGs is inflammatory response with CD224, LAX1, TXK, PRF1, CD7, MPG, and MPO genes directly involved in activations of T cells, B cells, and natural killer cells or in cytotoxic reaction. Our results suggest that such methylation changes may modulate aspects of the immune response and hence protect against the neurobiological substrate of reality distortion symptoms in SZ patients.
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paper_title: A Pilot Study on Collective Effects of 22q13.31 Deletions on Gray Matter Concentration in Schizophrenia

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The association of copy number variation (CNV) with schizophrenia has been reported with evidence of increased frequency of both rare and large CNVs. Yet, little is known about the impact of CNVs in brain structure. In this pilot study, we explored collective effects of all CNVs in each cytogenetic band on the risk of schizophrenia and gray matter variation measured in structural magnetic resonance imaging. With 324 participants' CNV profiles (151 schizophrenia patients and 173 healthy controls), we first extracted specific CNV features that differ between patients and controls using a two sample t-test, and then tested their associations with gray matter concentration using a linear regression model in a subset of 301 participants. Our data first provided evidence of population structure in CNV features where elevated rare CNV burden in schizophrenia patients was confounded by the levels associated with African American subjects. We considered this ethnic group difference in the following cytoband analyses. Deletions in one cytoband 22q13.31 were observed significantly (p<0.05) more in patients than controls from all samples after controlling ethnicity, and the deletion load was also significantly (p = 1.44×10⁻⁴) associated with reduced gray matter concentration of a brain network mainly comprised of the cingulate gyrus and insula. Since 80% deletion carriers were patients, patients with deletions also showed reduced gray matter concentration compared with patients without deletions (p = 3.36×10⁻⁴). Our findings indicate that regional CNVs at 22q13.31, no matter the size, may influence the risk of schizophrenia with a remarkably increased mutation rate and with reduced gray matter concentration in the peri-limbic cortex. This proof-of-concept study suggests that the CNVs occurring at some 'hotspots' may in fact cause biological downstream effects and larger studies are important for confirming our initial results.
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paper_title: Recurrent rearrangements in synaptic and neurodevelopmental genes and shared biologic pathways in schizophrenia , autism , and mental retardation

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CONTEXT: Results of comparative genomic hybridization studies have suggested that rare copy number variations (CNVs) at numerous loci are involved in the cause of mental retardation, autism spectrum disorders, and schizophrenia. OBJECTIVES: To provide an estimate of the collective frequency of a set of recurrent or overlapping CNVs in 3 different groups of cases compared with healthy control subjects and to assess whether each CNV is present in more than 1 clinical category. DESIGN: Case-control study. SETTING: Academic research. PARTICIPANTS: We investigated 28 candidate loci previously identified by comparative genomic hybridization studies for gene dosage alteration in 247 cases with mental retardation, in 260 cases with autism spectrum disorders, in 236 cases with schizophrenia or schizoaffective disorder, and in 236 controls. MAIN OUTCOME MEASURES: Collective and individual frequencies of the analyzed CNVs in cases compared with controls. RESULTS: Recurrent or overlapping CNVs were found in cases at 39.3% of the selected loci. The collective frequency of CNVs at these loci is significantly increased in cases with autism, in cases with schizophrenia, and in cases with mental retardation compared with controls (P < .001, P = .01, and P = .001, respectively, Fisher exact test). Individual significance (P = .02 without correction for multiple testing) was reached for the association between autism and a 350-kilobase deletion located at 22q11 and spanning the PRODH and DGCR6 genes. CONCLUSIONS: Weakly to moderately recurrent CNVs (transmitted or occurring de novo) seem to be causative or contributory factors for these diseases. Most of these CNVs (which contain genes involved in neurotransmission or in synapse formation and maintenance) are present in the 3 pathologic conditions (schizophrenia, autism, and mental retardation), supporting the existence of shared biologic pathways in these neurodevelopmental disorders.
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paper_title: Association of genetic copy number variations at 11 q14.2 with brain regional volume differences in an alcohol use disorder population

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This study investigates the relationship between genetic copy number variations and brain volume differences in an alcohol use disorder (AUD) population. We hypothesized that copy number variations may influence subject’s risk for alcohol use disorders through variations in regional gray and white matter brain volumes. Since genetic influences upon behavior are the result of many complicated interactions we focus on differences in brain volume as a putative intermediate phenotype between genetic variation and behavior. Copy number variation, alcohol use assessments and brain structural magnetic resonance images from 283 subjects, 199 male and 84 females who were enrolled in two AUD studies were obtained and analyzed using a combination of the Freesurfer image analysis suite and independent component analysis. Because brain volume varies by age we compared participant’s volume variation with that derived from a control cohort of 75 subjects. In addition we also regressed out the possible brain volume changes induced by long term alcohol consumption. Small cerebral cortex, cerebellar and caudate along with large cerebral white matter and 5th ventricle volumes are shown to be significantly associated with increased AUD severity. When these volume variations are compared with control subject volumes; the variations seen in subjects with AUD are markedly different from normal aging effects. CNVs at 11 q14.2 are marginally (p < 0.05 uncorrected) correlated with such brain volume variations and the correlation holds true after controlling for long-term alcohol consumption; deletion carriers have smaller cerebral cortex, cerebellar, caudate and larger cerebral white matter and 5th ventricle volumes than insertion carriers or subjects with no variation in this region. Similarly, deletion carriers also demonstrate higher AUD severity scores than insertion carriers or subjects with no variation. The results presented here suggest that copy number variation and in particular the variation at chromosome 11 q14.2 may have an impact in brain volume variation, potentially influencing AUD behavior.
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paper_title: Three-way (N-way) fusion of brain imaging data based on mCCA+jICA and its application to discriminating schizophrenia

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Abstract Multimodal fusion is an effective approach to better understand brain diseases. However, most such instances have been limited to pair-wise fusion; because there are often more than two imaging modalities available per subject, there is a need for approaches that can combine multiple datasets optimally. In this paper, we extended our previous two-way fusion model called “multimodal CCA + joint ICA”, to three or N-way fusion, that enables robust identification of correspondence among N data types and allows one to investigate the important question of whether certain disease risk factors are shared or distinct across multiple modalities. We compared “mCCA + jICA” with its alternatives in a 3-way fusion simulation and verified its advantages in both decomposition accuracy and modal linkage detection. We also applied it to real functional Magnetic Resonance Imaging (fMRI)–Diffusion Tensor Imaging (DTI) and structural MRI fusion to elucidate the abnormal architecture underlying schizophrenia (n = 97) relative to healthy controls (n = 116). Both modality-common and modality-unique abnormal regions were identified in schizophrenia. Specifically, the visual cortex in fMRI, the anterior thalamic radiation (ATR) and forceps minor in DTI, and the parietal lobule, cuneus and thalamus in sMRI were linked and discriminated between patients and controls. One fMRI component with regions of activity in motor cortex and superior temporal gyrus individually discriminated schizophrenia from controls. Finally, three components showed significant correlation with duration of illness (DOI), suggesting that lower gray matter volumes in parietal, frontal, and temporal lobes and cerebellum are associated with increased DOI, along with white matter disruption in ATR and cortico-spinal tracts. Findings suggest that the identified fractional anisotropy changes may relate to the corresponding functional/structural changes in the brain that are thought to play a role in the clinical expression of schizophrenia. The proposed “mCCA + jICA” method showed promise for elucidating the joint or coupled neuronal abnormalities underlying mental illnesses and improves our understanding of the disease process.
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paper_title: Genetics of Alzheimer's disease. A rapidly evolving field.

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Genetic factors have a variable impact on Alzheimer's Disease (AD), ranging from familial forms that are transmitted in an autosomal dominant fashion to sporadic AD, where a polygenic component is present. Most genes conferring susceptibility to AD are related to amyloid-beta deposition (APP; PS1; PS2; APOE; Cystatin-C; ubiquilin-1), oxidative stress (NOS2; NOS3) and inflammatory response (IL-1 alpha; IL-1 beta; IL-6; TNF-alpha). Genome-wide analyses, transcriptomics and proteomics approaches have pointed also to proapoptotic genes as increasing AD liability. Depression and psychotic symptoms that occur in a large proportion of AD patients have been associated with monoamine genes coding for metabolic enzymes (COMT), transporters (5-HTTLPR) and receptors (DRD1; DRD3). Genetic testing may be useful to confirm the diagnosis of AD in individuals with clinical signs of dementia, while it is generally not recommended as a predictive testing for AD in asymptomatic individuals. Drugs currently in use to treat AD are effective in only 20% of patients; their therapeutic effect is predominantly under genetic control (CYP26 gene; APOE). Environmental factors have been shown to moderate the effects of genes on psychiatric disorders such as depression, schizophrenia and ADHD. The study of gene-environment interactions in AD, that are still poorly understood, is essential to predict disease-risk in asymptomatic individuals. Genomics will provide a dynamic picture of biological processes in AD and new targets for the forthcoming anti-AD drugs.
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paper_title: Copy number variations and risk for schizophrenia in 22q11.2 deletion syndrome

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22q11.2 Deletion Syndrome (22q11.2DS) is a common microdeletion syndrome with congenital and late-onset features. Testing for the genomic content of copy number variations (CNVs) may help elucidate the 22q11.2 deletion mechanism and the variable clinical expression of the syndrome including the high (25%) risk for schizophrenia. We used genome-wide microarrays to assess CNV content and the parental origin of 22q11.2 deletions in a cohort of 100 adults with 22q11.2DS (44 with schizophrenia) and controls. 22q11.2DS subjects with schizophrenia failed to exhibit de novo CNVs or any excess of novel inherited CNVs outside the 22q11.2 region. There were no significant effects of parental origin of the 22q11.2 deletion, deletion length, parental age or family history on expression of schizophrenia. There was no evidence for a general increase of de novo CNVs in 22q11.2DS. A novel finding was the relative paucity of males with de novo 22q11.2 deletions of paternal origin (P = 0.019). The Y chromosome may play a mediating role in the mechanism of 22q11.2 deletion events during spermatogenesis, resulting in the previously observed excess of maternal de novo 22q11.2 deletions. Hemizygosity of the 22q11.2 region appears to be the major CNV-related risk factor for schizophrenia in 22q11.2DS. The results reinforce the need for further efforts to identify specific molecular mechanisms underlying this expression and to identify the 1% of patients with schizophrenia who carry 22q11.2 deletions.
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Title: A Review of Multivariate Analyses in Imaging Genetics

Section 1: INTRODUCTION
Description 1: Introduce the concept of imaging genetics, its growth, challenges, and the need for multivariate analysis methods in the field.

Section 2: OVERVIEW OF ANALYSIS STRATEGIES IN IMAGING GENETICS
Description 2: Discuss the different strategies and considerations for designing and performing imaging genetic studies, including the selection of intermediate phenotypes and preprocessing of genetic and imaging data.

Section 3: A priori BASED MULTIVARIATE ANALYSES ON GENETIC/GENOMIC DATA (CATEGORY 2)
Description 3: Explain the methods that use a priori information for multivariate analyses on genetic data, such as Gene Set Enrichment Analysis (GSEA).

Section 4: DATA DRIVEN MULTIVARIATE ANALYSES ON GENETIC/GENOMIC DATA (CATEGORY 2)
Description 4: Describe the data-driven multivariate methods used in genetic studies, including Multifactor Dimensionality Reduction (MDR) and various regression techniques.

Section 5: COMPONENT-BASED ANALYSES ON IMAGING DATA (CATEGORY 3)
Description 5: Summarize component-based multivariate analysis methods applied to imaging data, such as Independent Component Analysis (ICA) and its extensions.

Section 6: MULTIVARIATE ANALYSES BRIDGING IMAGING AND GENETICS (CATEGORY 4)
Description 6: Discuss methods that simultaneously analyze genetic and imaging data, including Partial Least Squares (PLS), Canonical Correlation Analysis (CCA), and Independent Component Analysis (ICA).

Section 7: CHALLENGE AND FUTURE DEVELOPMENTS
Description 7: Highlight the challenges faced by current methods, the need for integrating additional types of data, and the future direction of imaging genetics research including multi-site and multi-modal studies.