Motivation: Imaging genetic studies typically focus on identifying single-nucleotide polymorphism (SNP) markers associated with imaging phenotypes. Few studies perform regression of SNP values on phenotypic measures for examining how the SNP values change when phenotypic measures are varied. This alternative approach may have a potential to help us discover important imaging genetic associations from a different perspective. In addition, the imaging markers are often measured over time, and this longitudinal profile may provide increased power for differentiating genotype groups. How to identify the longitudinal phenotypic markers associated to disease sensitive SNPs is an important and challenging research topic.Results: Taking into account the temporal structure of the longitudinal imaging data and the interrelatedness among the SNPs, we propose a novel ‘task-correlated longitudinal sparse regression’ model to study the association between the phenotypic imaging markers and the genotypes encoded by SNPs. In our new association model, we extend the widely used ℓ2,1-norm for matrices to tensors to jointly select imaging markers that have common effects across all the regression tasks and time points, and meanwhile impose the trace-norm regularization onto the unfolded coefficient tensor to achieve low rank such that the interrelationship among SNPs can be addressed. The effectiveness of our method is demonstrated by both clearly improved prediction performance in empirical evaluations and a compact set of selected imaging predictors relevant to disease sensitive SNPs.Availability: Software is publicly available at: http://ranger.uta.edu/%7eheng/Longitudinal/Contact:heng@uta.edu or shenli@inpui.edu Neuroimaging genetics is an emerging research field, where brain imaging is used as quantitative phenotypes to investigate the role of genetic variation in brain structure and function. It holds great promise for a systems biology of the brain to better understand complex neurobiological systems, from genetic determinants to cellular processes to the complex interplay of brain structure, function, behavior and cognition. Disorders of the nervous system are associated with complex neurobiological changes, which may lead to profound alterations at all levels of organization.www.alzgene.org).Genome-wide association studies (GWAS) have been increasingly performed to correlate high-throughput single-nucleotide polymorphism (SNP) data to large-scale imaging data. To facilitate such association analysis, many studies used a hypothesis-driven approach , and somSo far most studies focus on selecting and associating SNPs to AD status or imaging phenotypes. Very few studies have been done to directly examine how the SNP values change when phenotypic measures are varied, i.e. via regression of SNP values on phenotypic measures. This alternative approach may have a potential to help us discover important imaging genetic associations from a different perspective. In this study, we perform such an initial analysis for finding phenotypic imaging markers that are related to SNPs from or proximal to AlzGene candidates.Neuroimaging measures have been widely studied to predict disease status and/or cognitive performance  cohort  data used in the preparation of this article were obtained from the ADNI database (adni.loni.ucla.edu). One goal of ADNI has been to test whether serial MRI, positron emission tomography (PET), other biological markers and clinical and neuropsychological assessment can be combined to measure the progression of mild cognitive impairment (MCI) and early AD. For up-to-date information, we refer interested readers to www.alzgene.org) as of June 10, 2010, were selected after the standard quality control (QC) and imputation steps. The QC criteria for the SNP data include (i) call rate check per subject and per SNP marker, (ii) gender check, (iii) sibling pair identification, (iv) the Hardy–Weinberg equilibrium test, (v) marker removal by the minor allele frequency and (vi) population stratification. As the second pre-processing step, the quality-controlled SNPs were imputed using the MaCH software . Obviously, d imaging features, n subject samples and T time points. The output genetic variations described by c SNPs for the n subject samples forms a matrix Y = T ∈ ℝn×c, where the yi ∈ ℝn×c is the SNP values of the ith subject sample. Our goal is to learn from {Y} a model that can reveal the associations between the longitudinal imaging phenotypes Y.For the association study of longitudinal imaging phenotypes to the genotypes, the input imaging features are a set of matrices A straightforward method for relating imaging phenotypes and SNPs is to perform regression at each time point separately, which, though, does not take into account the valuable information conveyed by the longitudinal patterns of the phenotypic inputs. To overcome this limitation, different from previous studies that learned the regression coefficient matrix for each time point individually, we aim to learn a unified longitudinal regression model to find the genetic features that are associated to the longitudinal imaging patterns over all the measurement time points. To this end, we expect to learn a coefficient tensor (a stack of coefficient matrices) btk denotes the kth row of coefficient matrix tB at time t, and J0 in T groups of regression tasks at different time points should not be decoupled and have to be performed simultaneously. Thus, we introduce the structured sparse regularization j should have certain correlations, where (bt)j denotes the jth column of tB. Namely, the coefficient matrices tB(1 ≤ t ≤ T) should be of low rank. Given a general n-mode tensor kth mode. Then we can achieve our goal by minimizing the rank of B), the trace-norm of M is defined as J2 in J2 defined in To further take into account that many SNPs are interrelated together and their effects on brain structure or disease progression could overlap, we expect to further develop own that  the tracJ2 is non-smooth, the problem in J2 with rigorous proof of its global convergence.Because our new objective J2 w.r.t tB and set it to zeros, we have:D is a diagonal matrix with t changes from 1 to T, we can compute tB  problem, and Step 4 solves a system of linear equations, both of which, thereby the whole algorithm, are well studied in literature and can be solved very efficiently by existing numerical packages.In this section, we evaluate the proposed method by applying it to the ADNI cohort, where a wide range of imaging markers measured over a period of 2 years are examined and associated to SNPs that are relevant to AD. The goal is to discover a compact set of phenotypic imaging markers that are closely related to AD-sensitive genotypes encoded by SNPs.We first evaluate the proposed method by applying it to the ADNI cohort to predict the SNPs of the participants from each of their two types of imaging phenotypes, i.e. VBM markers and FreeSurfer markers, tracked over four different time points, including BL and M06/M12/M24. Because some subjects of the ADNI cohort do not have complete imaging marker measurements over all the four time points, in our experiments we use the subject samples that have both SNPs data and complete imaging measurements. As a result, two subsets of ADNI subjects are included in our experiments, one for each type of imaging phenotypes, as detailed in ℓ2-norm regularization in RR method by the ℓ1-norm regularization, from which sparse results can be achieved ’, which only makes use of the SNPs’ correlations, but does not select longitudinal imaging markers. Second, we implement the full version of the proposed method, denoted as ‘Ours’, which solves the problem in We compare the proposed method against its three close counterparts including multivariate linear regression (LR) method, ridge regression (RR) method and least absolute shrinkage and selection operator (Lasso)  method. achieved . DiffereAs can be seen from In addition, These results demonstrate the effectiveness of using longitudinal data for improved regression from imaging phenotypes to genotypes, especially by the proposed method, which has the capability to make use of the input data through longitudinal feature selection; and the integration of the interrelatedness among the SNPs.One primary goal of this study is to identify a subset of imaging phenotypes that are highly correlated to certain SNPs to capture important imaging genomic associations in AD research. Thus, we examine the phenotypic imaging markers identified by the proposed methods, which are relevant to the genotypes encoded by SNPs.Shown in A first glance at the association weigh maps shows that the selected imaging markers have clear patterns that span across all the four studied time points, which demonstrates that these phenotypic markers are longitudinally stable thus can serve as screening target over the course of AD progression. We also observe that hippocampal measures  are identified, which is in accordance with the fact that in the pathological pathway of AD, medial temporal lobe including hippocampus is firstly affected, followed by progressive neocortical damage CCF-0830780, CCF-0917274, DMS-0915228 and IIS-1117965 at UTA; and by NSFIIS-1117335, NIHUL1 RR025761, U01 AG024904, NIARC2 AG036535, NIAR01 AG19771 and NIAP30 AG10133-18S1 at IU.Foundation for the National Institutes of Health (www.fnih.org). The grantee organization is the Northern California Institute for Research and Education and the study is coordinated by the Alzheimer's Disease Cooperative Study at the University of California, San Diego. ADNI data are disseminated by the Laboratory for Neuro Imaging at the University of California, Los Angeles. This research was also supported by NIH grants P30 AG010129, K01 AG030514 and the Dana Foundation.Data collection and sharing for this project was funded by the ADNI . ADNI is funded by the National Institute on Aging, the National Institute of Biomedical Imaging and Bioengineering, and through generous contributions from the following: Abbott; Alzheimer's Association; Alzheimer's Drug Discovery Foundation; Amorfix Life Sciences Ltd.; AstraZeneca; Bayer HealthCare; BioClinica, Inc.; Biogen Idec Inc.; Bristol-Myers Squibb Company; Eisai Inc.; Elan Pharmaceuticals Inc.; Eli Lilly and Company; F. Hoffmann-La Roche Ltd and its affiliated company Genentech, Inc.; GE Healthcare; Innogenetics, N.V.; Janssen Alzheimer Immunotherapy Research & Development, LLC.; Johnson & Johnson Pharmaceutical Research & Development LLC.; Medpace, Inc.; Merck & Co., Inc.; Meso Scale Diagnostics, LLC.; Novartis Pharmaceuticals Corporation; Pfizer Inc.; Servier; Synarc Inc. and Takeda Pharmaceutical Company. The Canadian Institutes of Health Research is providing funds to support ADNI clinical sites in Canada. Private sector contributions are facilitated by the


The analysis of polygenic, phenotypic characteristics such as quantitative traits or inheritable diseases remains an important challenge. It requires reliable scoring of many genetic markers covering the entire genome. The advent of high-throughput sequencing technologies provides a new way to evaluate large numbers of single nucleotide polymorphisms (SNPs) as genetic markers. Combining the technologies with pooling of segregants, as performed in bulked segregant analysis (BSA), should, in principle, allow the simultaneous mapping of multiple genetic loci present throughout the genome. The gene mapping process, applied here, consists of three steps: First, a controlled crossing of parents with and without a trait. Second, selection based on phenotypic screening of the offspring, followed by the mapping of short offspring sequences against the parental reference. The final step aims at detecting genetic markers such as SNPs, insertions and deletions with next generation sequencing (NGS). Markers in close proximity of genomic loci that are associated to the trait have a higher probability to be inherited together. Hence, these markers are very useful for discovering the loci and the genetic mechanism underlying the characteristic of interest. Within this context, NGS produces binomial counts along the genome, i.e., the number of sequenced reads that matches with the SNP of the parental reference strain, which is a proxy for the number of individuals in the offspring that share the SNP with the parent. Genomic loci associated with the trait can thus be discovered by analyzing trends in the counts along the genome. We exploit the link between smoothing splines and generalized mixed models for estimating the underlying structure present in the SNP scatterplots. Saccharomyces cerevisiae, are phenotypic characteristics that vary and are controlled by multiple genetic elements that may contribute differently to the trait. A quantitative trait locus (QTL) is a region in the genome that is linked to the genes that contribute to a quantitative trait. QTL mapping aims at identifying gene loci that determine a specific polygenic trait. This method relies on the extent of co-segregation of genes, which are located in unknown QTLs and that contribute to a quantitative trait, and genetic markers with known chromosomal locations. During a cross between two organisms, the quantitative-trait gene and a genetic marker located on different chromosomes of the same organism will segregate independently and the recombination frequency will be 50%. However, if the marker is located on the same chromosome as the gene, then they could segregate together, depending on the distance between their loci. The closer they are, the lower the recombination frequency, which eventually reaches 0%. This deviation from random segregation, due to the inverse relation between distance and recombination frequency, can be used to identify QTLs.Quantitative traits, such as high ethanol tolerance in The advent of new high throughput screening techniques, such as next generation sequencing (NGS), provides a fast way to identify large numbers of single nucleotide polymorphisms (SNPs) on a genome-wide scale. When combined with a pooling of segregants, NGS allows for simultaneous mapping of QTLs throughout the whole genome.In this paper, we consider analysis of data coming from an experiment, in which the Illumina/Solexa NGS technique The scatterplot smoothers, Eqs.(1)–(2) and (5), were defined by using a cubic P-spline as basis and a fourth-order difference penalty on the coefficients For both pools, the confidence band indicates a broad region with mismatch frequencies larger than 50%. For pool 2, an additional region with frequencies lower than 50% can be also identified.MKT1, SWS2 and APJ1, has been confirmed by the combination of individual scoring of SNPs with a binomial test and introducing artificial markers at predetermined neutral positions in the genome of the parental strain without high ethanol tolerance The presence of three genes in chromosome XIV, i.e., The left panel of LYS2, was confirmed Note that the reference curve, which reflects the frequencies of the artificial markers, remains below 50% throughout almost the complete chromosome. This anomaly suggests that a SNP frequency of 50% might lead to incorrect results. We propose to conduct a sequencing run on an unselected pool of segregants to estimate the SNP frequency under random segregation. The SNP frequency in the control pool can than be compared with one or more selected segregant pools by using model (5).The right panel of In our contribution, we showed that scatterplot smoothers are valuable tools for discovering potential QTLs in NGS-BSA experiments. The techniques can be used to model experiments with single as well as multiple segregant pools.The selected chromosomes, used for validation, illustrate the three possible scenarios one can encounter during genetic mapping, i.e. presence of a major QTL (chromosome XIV), a minor QTL (chromosome II) and the absence of a QTL (chromosome IX). For each of these scenarios, the proposed method performs as expected. Additionally, the possibility to incorporate multiple segregant pools clearly shows to be an important feature. It not only allows investigating enrichment effects, it can also reduce the size of the identified chromosomal regions. Chromosome IX, which does not contain QTLs, also indicates that a control pool is required for estimating the baseline mismatch frequency under random segregation. In the examples, the discovered regions were relatively wide. The low resolution is inherent to the data. For the experiments used here, only the first offspring generation is considered. Hence, the QTLs in the selected segregants are likely to be surrounded by a relative large number of SNP markers. Backcrossing the selected segregants with the parent without the trait will increase the resolution, i.e., the region with flanking SNPs around the QTL will decrease due to the subsequent recombination events. Another possible way to improve the resolution would be to additionally include the information about the first-order derivative of the smoothed trend. The information would allow to identify locations at which the derivative is equal to 0. These would be the locations, at which the estimated SNP mismatch frequency would reach its local maximum or minimum and would thus deviate the most from the random-segregation frequency. This is a topic of further research.Saccharomyces cerevisiae is the most common yeast strain in industry such as winemaking, baking, and brewing. It is an intensively studied eukaryotic model organisms in molecular and cell biology and has become an important subject for studies in quantitative genetics. The aim of the experiment was to map various QTLs determining high ethanol tolerance in S. cerevisiae. For this purpose, a highly ethanol-tolerant yeast strain was crossed with a laboratory strain of a moderate ethanol tolerance. After sporulation, the resulting haploid offspring was screened for high ethanol tolerance, first in a medium with 16% ethanol, and subsequently in a medium with 17% ethanol. The first screening step returned 136 ethanol-tolerant segregants out of a total of 5974 viable haploid yeast cells. The second screening reduced this number further to 31. The difference between 16% and 17% ethanol tolerance is substantial, as 17% ethanol is very close to the maximum ethanol concentration of 18% that yeast cells can tolerate. Most of them will not or only very poorly grow in such a medium. The extent of this difference is also illustrated by the large reduction of viable yeast cells when shifting from a medium with 16% ethanol to the one with 17% ethanol.After screening, these two pools were subjected to a pooled-segregant genome-wide sequencing analysis by means of high-throughput NGS, as implemented in the Illumina/Solexa NGS technique The number of mapped reads that do not match with the parental reference sequence at the position Note that, Bulk Segregant Analysis The highly ethanol-tolerant yeast strain was also crossed with 28 partial artificial marked strains There are several issues that have to be taken into account prior to the analysis. The scatterplot of the mismatch SNP frequencies along chromosome XIV, shown in et al. (2008) To address these issues, one could try to correct the sequencing errors Trends in the mismatch frequencies for the selected segregants are useful for discovering potential QTLs  To avoid overfitting, the spline model is typically estimated by considering penalized maximum likelihood estimation, with a penalty term of the form The estimation of the model (3) is performed by means of penalized quasi-likelihood (PQL). Initial estimates for If multiple segregated pools are available, differences between the observed trends in these pools are useful for identifying potential loci associated with the trait. The scatterplot smoother, proposed in Eqs. (1)-(2), can be extended so as to identify the underlying trends in different pools as well as the pairwise differences between these trends. In particular, we proposeEstimating the underlying trends does not suffice for identifying chromosomal regions that might be linked to the trait. Therefore, we propose a more formal assessment to discover systematic deviations from random segregation for single pools and/or for discovering differences in trends between multiple pools. Our approach is based on confidence intervals or confidence bands for the estimated smoothers.et al. (2003) According to Ruppert Pointwise confidence bands, however, need to be corrected for multiplicity and ignore serial correlation. Therefore, we propose the use of simultaneous confidence bands, which allow to make joint statements on multiple locations of the fitted curve. A 100Click here for additional data file.


Twin studies have shown that anxiety in a general population sample of children involves both domain-general and trait-specific genetic effects. For this reason, in an attempt to identify genes responsible for these effects, we investigated domain-general and trait-specific genetic associations in the first genome-wide association (GWA) study on anxiety-related behaviours (ARBs) in childhood.The sample included 2810 7-year-olds drawn from the Twins Early Development Study (TEDS) with data available for parent-rated anxiety and genome-wide DNA markers. The measure was the Anxiety-Related Behaviours Questionnaire (ARBQ), which assesses four anxiety traits and also yields a general anxiety composite. Affymetrix GeneChip 6.0 DNA arrays were used to genotype nearly 700,000 single-nucleotide polymorphisms (SNPs), and IMPUTE v2 was used to impute more than 1 million SNPs. Several GWA associations from this discovery sample were followed up in another TEDS sample of 4804 children. In addition, Genome-wide Complex Trait Analysis (GCTA) was used on the discovery sample, to estimate the total amount of variance in ARBs that can be accounted for by SNPs on the array.−8). Attempts to replicate the top associations did not yield significant results. In contrast to the substantial twin study estimates of heritability which ranged from 0.50 (0.03) to 0.61 (0.01), the GCTA estimates of phenotypic variance accounted for by the SNPs were much lower 0.01 (0.11) to 0.19 (0.12).No SNP associations met the demanding criterion of genome-wide significance that corrects for multiple testing across the genome (p<5×10Taken together, these GWAS and GCTA results suggest that anxiety – similar to height, weight and intelligence − is affected by many genetic variants of small effect, but unlike these other prototypical polygenic traits, genetic influence on anxiety is not well tagged by common SNPs. Anxiety disorders are among the most common psychiatric disorders Twin studies have shown that childhood anxiety in representative samples, like other complex traits, is influenced genetically, e.g. Until recently, molecular genetic investigation into the aetiology of anxiety relied on linkage and candidate-gene designs. Linkage, which looks for co-inheritance between DNA variants and a disorder within families, is a systematic strategy for detecting genes of large effect size throughout the genome. However, linkage found few such large effects for common disorders like anxiety and lacks power to detect more modest effects In contrast, allelic association, which looks for correlations between an allele and a trait among unrelated individuals, is much more powerful than linkage, but until recently, association has been limited to the exploration of a few candidate genes and could not be used to conduct a systematic search of the genome. Candidate-gene association studies of anxiety-related traits reported many associations but few of these associations have stood the test of replication, similar to candidate-gene studies in other domains in the life sciences Association studies became systematic with the advent of genome-wide DNA arrays that genotype hundreds of thousands of DNA variants throughout the genome and resulted in a plethora of genome-wide association (GWA) studies Genomewide Complex Trait Analysis (GCTA), has been developed that allows estimation of the total genetic variance captured by SNPs on a genome-wide DNA array, even though it does not identify which SNPs are responsible for the genetic influence The current study presents the first GWA study of anxiety-related traits in children. The multivariate genetic results mentioned earlier led us to consider trait-specific as well as domain-general measures. Despite the success of GWA, reported associations are of small effect size and together account for only a modest proportion of the heritability of traits, known as the “missing heritability” problem Written parental consent was obtained prior to data collection and the project received approval from the Institute of Psychiatry ethics committee (05/Q0706/228).The sample was drawn from the Twins Early Development Study (TEDS), a multivariate longitudinal study which recruited over 11,000 twin pairs born in England and Wales in 1994, 1995 and 1996 3747 DNA samples from unrelated children in TEDS were sent for DNA array genotyping at the Wellcome Trust Sanger Institute, Hinxton, UK as part of the Wellcome Trust Case Control Consortium 2.3665 samples were successfully hybridized to Affymetrix GeneChip 6.0 SNP genotyping arrays using standard experimental protocols see . 3152 saThe replication sample was also drawn from TEDS children for whom DNA and anxiety data were available but for whom genome-wide genotyping was not available. After quality control, both anxiety data and SNP genotyping were available for 4804 additional individuals. Of these, 2625 were unrelated children who were also unrelated to children in the discovery sample; for 1742 children, their fraternal co-twin was in the discovery sample, and for 437 children their fraternal co-twin was also in the replication sample.Anxiety was rated by parents using the Anxiety-Related Behaviours Questionnaire (ARBQ) Genome-wide genotyping was done on AffymetrixGeneChip 6.0 SNP genotyping array with additional ∼2.5 million SNPs imputed from HapMap 2 and 3 and WTCCC controls Details about genotyping and quality control are included in the www.r-project.org) Linear regression analyses were conducted using SNPTEST v2.0 The strongest association results from the GWA were selected for genotyping in the replication sample. Where imputed SNPs were in LD with genotyped SNPs, the genotyped SNPs were preferred. However, one especially promising imputed SNP (rs1113313) was also selected. The SNPs were selected that were not in linkage disequilibrium (LD) with each other.Sequenom genotyping results for the replication sample were analysed using the same protocols and software as those in GWA analysis. We conducted analyses using the total replication sample as well as the subsample of individuals genetically unrelated to each other or to individuals in the discovery sample. Although this is somewhat unorthodox, power is crucial for replication and the total sample provides maximum power because it maximises sample size. If replication is found for the total sample, the replication may be biased because the sample is not completely independent of the discovery sample and more replication would be required for definitive proof of replication. However, if the results from the discovery sample do not replicate using the total sample, this is the strongest possible evidence of failure to replicate because our replication sample consists of a highly similar sample tested at exactly the same age using exactly the same measures.GCTA does not attempt to identify specific variants associated with traits. Instead, it uses chance genetic similarity among unrelated individuals across hundreds of thousands of SNPs to predict phenotypic similarity. We used the GCTA software package 10 p values against the –log10 p values expected on the basis of no association. Although there is some increase of observed p values against expected p values for the lowest p values, few of the associations fall outside the 95% confidence bands (the grey areas), which indicates that there is little evidence of significant deviation from the null hypothesis of no association.10 p values on the Y axis for the ∼1.7 million SNPs across the 22 autosomes on the X axis. The p values on the Y axis are the negative logarithms of the p values so that the highest points in the plot represent the strongest SNP associations. The dotted horizontal line represents suggestive significance (5×10−7), not genome-wide significance (5×10−8). Regions with the strongest associations were chosen for replication – for example, regions of chromosome 6 and 12 that reached suggestive significance (5×10−7) for the anxiety composite and negative cognition scale respectively. The association of the SNP on chromosome 6 with negative affect (−7), and rs1952500, which was associated with Negative Cognition (p = 4.12×10−7). The significance of the remaining SNPs varied from 10−4 to 8−10−7. The amount of variance explained in the discovery sample as indicated by the squared beta values varied from 0.09% to 1.0%. Visual inspection of the genotype-specific means suggested that none of the selected SNPs deviated from additivity.e affect  was not As described earlier, we used ∼1.7 million SNPs to estimate the GCTA Genetic Relatedness Matrix for our sample of 2810 individuals. Our sample included no known pairs related in the traditional sense, which was confirmed by finding that no pairs reached the standard GCTA relatedness cut-off threshold of 0.025 genetic relatedness. −8. As seen in missing heritability problemThis first genome-wide association study of anxiety-related traits in childhood indicates that no common genetic variants of large effect contribute to the heritability of these traits. Our sample of 2810 had 80% power to detect causal variants with effect sizes greater than 1.4% of the variance and none were detected. Power was calculated with the Genetic Power Calculator Dozens of papers have been published about possible solutions to the missing heritability problem Two hypotheses for explaining the gap between these anxiety-related GCTA estimates and twin-study estimates are that GCTA underestimates genetic influence or that twin studies overestimate genetic influence, although these are not mutually exclusive hypotheses. We know that GCTA underestimates genetic influence to some extent because it only captures causal variants that are in linkage disequilibrium with the common SNPs used in the analysis; it misses the effect of rarer DNA variants not tagged by these SNPs. In addition, GCTA only assesses additive genetic effects. So, one possibility is that anxiety is influenced by rarer DNA variants or nonadditive genetic effects to a greater extent than height and weight.On the other hand, our twin study heritability estimates for parental ratings may be inflated – most estimates of heritability of anxiety traits in childhood and adolescence using other assessment techniques are around 30% It is important to resolve this issue of the gap between GCTA and twin-study estimates of heritability in general and specifically in terms of the possibility that the gap might be larger for anxiety-related traits than for other complex traits. To the extent that GCTA estimates account for heritability, it should be possible to identify genes responsible for the heritability of anxiety using common SNPs alone if samples are sufficiently large. Larger samples could result in closing this gap by producing an increased number of significant SNP associations in GWA and by providing GCTA estimates with smaller error terms. That said, a recent study reported GCTA estimate of 0.06(0.03) for neuroticism in a sample of nearly 12,000 adults Our GWA results for anxiety-related traits suggest that, similar to other quantitative traits and common disorders, heritability is caused by many genes of small effect. Our GCTA results suggest that the genetic architecture of parent-rated anxiety-related traits may differ from previously published results in showing a greater gap between GCTA estimates of genetic influence and twin study estimates of heritability. One implication of knowing that there are no genes of large effect and that at least some of the genetic variance can be accounted for by the common SNPs on current DNA arrays is to increase sample sizes to detect associations of small effect size. Eventually, polygenic prediction, using composites of hundreds or thousands of DNA markers, may reach levels of predictive power useful at least for research if not for clinical practice.Text S1Genotyping protocol, quality control and statistical analysis.(DOC)Click here for additional data file.Table S1Lambda Inflation rates for all variables.(DOCX)Click here for additional data file.


The development of genotyping arrays containing hundreds of thousands of rare variants across the genome and advances in high-throughput sequencing technologies have made feasible empirical genetic association studies to search for rare disease susceptibility alleles. As single variant testing is underpowered to detect associations, the development of statistical methods to combine analysis across variants – so-called “burden tests” - is an area of active research interest. We previously developed a method, the admixture maximum likelihood test, to test multiple, common variants for association with a trait of interest. We have extended this method, called the rare admixture maximum likelihood test (RAML), for the analysis of rare variants. In this paper we compare the performance of RAML with six other burden tests designed to test for association of rare variants.We used simulation testing over a range of scenarios to test the power of RAML compared to the other rare variant association testing methods. These scenarios modelled differences in effect variability, the average direction of effect and the proportion of associated variants. We evaluated the power for all the different scenarios. RAML tended to have the greatest power for most scenarios where the proportion of associated variants was small, whereas SKAT-O performed a little better for the scenarios with a higher proportion of associated variants.The RAML method makes no assumptions about the proportion of variants that are associated with the phenotype of interest or the magnitude and direction of their effect. The method is flexible and can be applied to both dichotomous and quantitative traits and allows for the inclusion of covariates in the underlying regression model. The RAML method performed well compared to the other methods over a wide range of scenarios. Generally power was moderate in most of the scenarios, underlying the need for large sample sizes in any form of association testing. Genome-wide association studies (GWAS) have successfully identified common genetic variants, mainly common single nucleotide polymorphisms (SNP), with small to modest effects for many complex human diseases and traits . HoweverUntil recently a limited understanding of the architecture of rare genetic variation across the genome and limitations of genotyping technologies have restricted the search for rare disease-susceptibility alleles to the analysis of a small number of candidate genes for specific diseases. The development of genotyping arrays containing hundreds of thousands of rare variants across the genome and advances in high-throughput sequencing technologies have made feasible empirical genetic association studies to search for rare disease susceptibility alleles. Even so, standard methods used for association testing, in which association with the trait of interest is tested one variant at a time, are limited by statistical power. As a result there has been an increase in interest in alternative analytic methods in which the information across multiple variant sites is combined – for example all variants in a specified gene or genomic region. Depending on the underlying model of genetic association these “burden” tests can enhance statistical power. Examples of these include the cohort allelic sum test (CAST) ,3, the cThe CAST and CMC methods collapse information on all rare variants within a region into a single dichotomous variable for each subject and then apply a univariate test. Rare variants are defined by a fixed threshold for minor allele frequency. The WST is a non-parametric test in which rare variants are grouped according to function (e.g. gene) and each individual is scored by a sum of the mutation counts weighted by the variance under the null hypothesis. The VT approach selects an allele frequency threshold by maximising the test statistic over all thresholds and assesses statistical significance by permutation. The major limitation of these simple burden tests is that they do not account for the direction of effects of the functional alleles that are assumed to be the same. However, a gene harbouring phenotypically relevant variation could include a handful of rare Mendelian mutations that cause disease, some variants that moderately increase or decrease risk, along with numerous variants of no effect.The CAT contrasts the variance of each observed count with the expected variance. However, the method does not allow for covariate adjustment. SKAT is a score-based variance-component test that makes no assumption about directionality of effect by performing multiple regressions of a phenotype on genotype for all variants in a region . P-valueWe have previously developed an admixture maximum likelihood (AML) test to test for association of multiple common genetic variants with the trait of interest . The metThe RAML method provides an omnibus test for joint effects of multiple variants on a phenotype and formulates the alternative hypothesis in terms of the probability that a given variant is associated with disease (α), the average effect of the associated variants (η) and the expected standard error of this effect (σ). The effect of each variant is estimated as the signed z-statistic (Z) from the score test. To generate the omnibus test statistic the distribution of the effects under the alternative hypothesis need to be defined. It is desirable to use a distribution with a conjugate prior so that the likelihood will have a tractable computational form. We defined this as a normal distribution of the z-statistic. Using the z-statistic gives flexibility to incorporate covariates and the approach can be easily extended to quantitative trait and survival-time analyses. The average expected z-statistic can be positive or negative corresponding to an excess of deleterious or protective variants respectively. Given that a variant is associated with the phenotype the likelihood of observing the test statistic (Z)x ~ N and y ~ N. The likelihood of observing S = x + y can then be expressed asTo solve this equation we can think of it in terms of the sum of two normal distributions Z given μ is distributed as a N distribution so it can be seen that equations (1) and (2) are equivalent. Thus in the case that a variant is associated the test statistic Z is distributed as N. The log-likelihood is of the formThe distribution of L1i is the likelihood given the variant is associated  distribution) and L0i is the null likelihood  distribution). Thus the log-likelihood can be expressed aswhere which we maximised using the Bound Optimization BY Quadratic Approximation (BOBYQA) algorithm .2) greater than a specified threshold with at least one other variant in the same group. For each group a proxy variant is generated, where the proxy is the maximum number of rare alleles for any variant in the group  carried by each subject. The default r2 threshold is set to 0.9. This deals with perfectly correlated variants whilst still being able to test most variants individually.One major problem in testing multiple variants in the same region of the genome is correlation due to linkage disequilibrium (LD), although this may be less of an issue for rare genetic variation. A permutation test can account for type I error, but there is still a loss of power as variants in strong LD with each other have a disproportionate effect on the test statistic. To deal with this, the RAML groups variants using a single link cluster approach, such that every variant in a group has a squared correlation . In order to determine the risk associated with each haplotype the risk associated with each variant was based on seven different scenarios with risk distributions defined belowWe simulated population data using phased haplotypes from the 1000 Genome Project data 1. β ~ N, 20 per cent of risk variants β ~ N2. 80 per cent of risk variants β ~ N3. β ~ N, 20 per cent of risk variants β ~ N4. 80 per cent of risk variants β ~ N5. β ~ N, 20 per cent of risk variants β ~ N6. 80 per cent of risk variants β ~ N7. et al.[These scenarios are similar to the ones presented by Lee et al. with theTwo haplotypes were selected at random for each individual. The overall risk associated with any pair of haplotypes was calculated under a log-additive model by summing the risks from each causal variant carried. An individual in the population was assigned as a case or control at random based on this risk and a disease prevalence of 10 per cent. Two thousand cases and two thousand controls were then selected randomly from the population.For each risk distribution we tested three scenarios in which 5%, 10% or 20% of variants were causal. The effect was set as proportional to the log of the variant minor allele frequency (p). The standard error (σ) varied under the different distributions: For 5% of associated variants,k is 1 for distributions 1 and 2, 1.5 for distributions 3 and 4, 2 for distribution 5 and 6 and 2.5 for distribution 7; for 10% and 20% of associated variants the average effect was 0.7 and 0.5 times this respectively.where We sampled haplotypes from three different regions of the genome  in order to evaluate the influence of different local LD structure on the different tests. Two hundred replicate data sets were simulated under each of the 21 different scenarios. We derived the power of each test as the proportion of replicates for which the empirical significance level achieved P < 0.05, P < 0.01 and P < 0.001.We compared the RAML method to SKAT-O using the default weights and the five methods included in the program ScoreSeq. We also applied our tests to three different genes to evaluate the effects that varying genomic architecture has on the relative efficacy of the methods.In order to evaluate the power for a larger sample size and slightly stronger effects we repeated the simulations for four thousand cases and four thousand controls across the same genomic regions with the effect of associated variants being 25 per cent larger. This data set was used to compare the performance of RAML with SKAT-O.BRCA1 , 274 rare variants in BRCA2  and 193 rare variants in TERT . The power of the seven methods for 21 scenarios at the three thresholds for statistical significance are shown in Tables BRCA1, BRCA2 and TERT respectively. Generally, power was limited (< 50 per cent) for all methods across a wide range of plausible scenarios for the underlying genetic model. The RAML test had the greatest power for most scenarios for both BRCA2 and TERT. For BRCA1, RAML tended to have the greatest power for the scenarios with a small proportion of associated variants, whereas SKAT-O performed a little better for the scenarios with a higher proportion of associated variants. Whether 100% or 80% of variants are associated with effects in the same direction did not change the relative efficacy of the two methods.There were 145 rare variants (MAF < 0.04) in BRCA1 , 274 rare variants in BRCA2  and 193 rare variants in TERT . The power of the two methods for 21 scenarios at the three thresholds for statistical significance are shown in Tables BRCA1, BRCA2 and TERT respectively. As expected, the power of the both methods is improved. The RAML method was still more powerful than SKAT-O under most scenarios, but the difference was greater than for the smaller sample sizes.Given the limited power of all the methods for the analysis of 2,000 cases and 2,000 controls, we repeated the evaluation of RAML and SKAT-O using data simulated for 4,000 cases and 4,000 controls across the same genomic regions. There were 145 rare variants (MAF < 0.04) in  BRCA2 19, 22, 56 BRCA1 and the other two regions is related to the fact that SKAT-O does not use a fixed threshold for the minor allele frequency, but uses a weighting function based on the minor allele frequency [BRCA1 than in the other two genes.The apparent difference between RAML and SKAT-O for the requency . Thus thWe have described a new method for association testing of multiple rare variants that makes no assumptions about the proportion of variants that are associated with the phenotype of interest or the magnitude and direction of their effect. The method is flexible and can be applied to both dichotomous and quantitative traits and allows for the inclusion of covariates in the underlying regression model. We have compared the performance of RAML with six other similar methods using data simulated under 21 plausible scenarios for the underlying genetic model of association. Under most of these scenarios, RAML was found to have the greatest power, although SKAT-O performed better under some circumstances.Genome-wide association studies have been very successful in identifying common alleles associated with many disease and physiological traits. However, these alleles explain a small fraction of the genetic component of the variance for most traits. It is very likely that rare variants will contribute to some of the so-called missing heritability. A systematic search for disease associated rare variants has been made possible by the availability of high-throughput, affordable sequencing technologies and the development of genotyping arrays that include hundreds of thousands of rare variants. Given that the underlying genetic model for association between rare genetic variants and disease related phenotypes is not known – effect allele frequency, effect size and proportion of associated variants - it is not possible to provide a definitive guide to the situations in which RAML should be preferred to SKAT-O or other methods. Until empirical evidence emerges for association of multiple rare variants across a genomic region it would seem reasonable to use multiple methods for burden testing including both RAML and SKAT-O.http://ccge.medschl.cam.ac.uk/software/.The AML and RAML software are available from The authors declare that they have no competing interests.JPT and PDPP conceived the idea for the method. JPT, QG and DFE developed the statistical methodology. JPT and QG programmed the simulation studies. All authors helped draft and edit the final manuscript.


Asymmetry is a prominent feature of human brains with important functional consequences. Many asymmetric traits show population bias, but little is known about the genetic and environmental sources contributing to inter-individual variance. Anatomic asymmetry has been observed in Old World monkeys, but the evidence for the direction and extent of asymmetry is equivocal and only one study has estimated the genetic contributions to inter-individual variance. In this study we characterize a range of qualitative and quantitative asymmetry measures in structural brain MRIs acquired from an extended pedigree of Old World vervet monkeys (n = 357), and implement variance component methods to estimate the proportion of trait variance attributable to genetic and environmental sources. Four of six asymmetry measures show pedigree-level bias and one of the traits has a significant heritability estimate of about 30%. We also found that environmental variables more significantly influence the width of the right compared to the left prefrontal lobe. C. aethiops (commonly termed African green monkeys or vervets).The high degree of lateralization in the capacity for some behaviors has stimulated decades of investigation regarding anatomic brain asymmetry, much of which has focused on the evolution of regions hypothesized to relate to language. Comparative studies in primates have shown that the human tendency for leftward biased asymmetry of Broca's area and the planum temporale is present in chimpanzees and gorillas Several factors have contributed to the equivocal findings in previous studies of anatomic asymmetry in monkeys. With the notable exception of a large sample from the Cayo Santiago macaque colony per se, but showed a lateralized influence of genes and environment on the two hemispheres. To our knowledge no studies in humans have examined genetic and environmental contributions to global measures of anatomic asymmetry and only one study has been performed in NHPs, which used indirect measurements of brain asymmetry from post-mortem skulls in macaques and found a modest genetic contribution (∼30%) to prefrontal asymmetry An additional focus of asymmetry research has been the attempt to identify the underlying basis of inter-individual variation in anatomic asymmetry. Several studies in humans have used twin designs to show that genes and environment differentially affect the volumes of the left and right hemispheres In accordance with the recommendations of the Weatherall report, “The use of non-human primates in research” the following details are provided regarding animal welfare and steps taken to ameliorate suffering of the vervet monkeys. Studies were conducted as approved by the Animal Research Committee in the Office for Protection of Research Subjects at UCLA and the Institutional Animal Care and Use Committee at the Sepulveda Veterans Administration Medical Center. The vervet subjects scanned in this study are part of an extended pedigree of the UCLA/Wake Forest Vervet Research Colony (VRC) which has included more than 1000 individuals since its founding in the 1970's. The animals were housed in large outdoor/indoor enclosures, each with between nine and 41 animals in groups designed to model natural vervet social organization. Food and water is readily available and disruptions to the colony are minimized to the extent possible. The brain images use in this study were acquired non-invasively using MRI technology. The only invasive procedure performed was the establishment of a venous catheter for the administration of anesthetics during image acquisition. Catheter placement was performed under aseptic conditions, and animals were monitored continuously during anesthesia to assure maintenance of normal physiological parameters. Animals were fasted starting the night prior to the procedure to reduce risk of aspiration. After initial intramuscular administration of 15 mg/kg ketamine, an intravenous line was established and used to initiate anesthesia using midazolam (0.25 mg/kg) and ketamine (5 mg/kg). Each animal was also given 0.027 mg/kg atropine and intubated to protect the airway and reduce risk of aspiration. After intubation, respiratory rate was monitored frequently and used to maintain adequate anesthesia using midazolam and ketamine. After the MRI procedure, anesthesia was discontinued and all animals were directly observed until they recovered completely from the anesthesia and returned to normal functioning. All animals tolerated the procedure well and there were no adverse events associated with any of the experiments.Details of the image acquisition and pre-processing protocol have been described previously After removal of image regions corresponding to non-brain tissue, an affine population atlas was created from the individual MRI images using methods described by Woods A single transverse slice dorsal to the upward deflection of the cingulate sulcus was selected from each image that showed the relative positions of the ascending rami of the left and right cingulate sulcus at the midline of the cerebrum. The left-right orientation of each slice was randomized by reflecting half of the images across the x-axis (left-right mirroring). Each slice was then scored three times by an expert rater (R.P.W) on a scale between −2 and +2 based on the relative positions of the cingulate sulci at the midline; 0 = symmetric . The intThe registration procedure used to transform each brain into a common space ensured that the mid-sagittal plane of each image was located in the mid-line of the image matrix and allowed precise separation of the left and right hemispheres. This fact was empirically checked by repeating the image registration protocol using right-left reflected images to ensure that the hemispheric volumes were exactly reversed as expected. Hemispheric volumes determined in affine space were converted back to native space dimensions prior to analysis. An asymmetry quotient (AQ) was calculated by subtracting the value of the left side from the value of the right side and dividing the result by the average value of the two hemispheres:http://www.osirix-viewer.com/). Cerebral width was measured for each hemisphere at two locations . This count was divided by 100,000 to determine the p-value. A similar approach was used to determine the significance of the correlation coefficient estimates between phenotypes. The null distribution for each correlation estimate was generated by randomly shuffling each pair of phenotype vectors before estimating the coefficient. This process was repeated 100,000 times and p-values were calculated as above.h2) represents the proportion of total phenotypic variance (σ2Z) attributable to all genetic sources  can be determined from the heritability estimate (σE = 1−σG) and represents the proportion of variance that is due to all non-genetic sources. The large size of the VRC pedigree provided good power to obtain significant estimates of the genetic contribution to anatomic asymmetry. The SOLAR package ij) for each pair of individuals in the pedigree, where each entry represents the probability that two genes, sampled at a particular locus from each individual are identical and inherited from a common ancestor. A maximum likelihood approach is implemented to estimate σ2G from the phenotypic covariance: iz represents the phenotypic value for the ith individual and I is the identity matrix. SOLAR also implements bivariate polygenic analyses to estimate genetic (ρG) and environmental correlations (ρE) from total phenotypic correlation (ρP). Genetic correlation is an estimate of the proportion of the covariance of two phenotypes that is due to common genetic sources and is a direct measure of the pleiotropic contributions to two traits (i.e. genetic loci that influence both traits). Likewise, the estimate of environmental correlation represents the common sources of non-genetic causal influences contributing to the covariance between two phenotypes. The two correlations are estimated using the following model: 21h and 22h are the heritabilities of the two traits. Prior to genetic analysis, standard linear regression was used to model the effects of sex, age and their interaction using the R environment Additive genetic heritability . We tested whether the difference observed between males and females was simply related to the difference in brain size, using a linear model to regress total brain volume on the cingulate sulcus trait, but did not find a significant effect.Each brain image was scored three times for relative position of the ascending ramus of the cingulate sulcus in each hemisphere. The distribution of asymmetry scores for this trait, averaged across three ratings, is shown in The distribution of the AQ for hemispheric volume is shown in the top graph of the right panel in The AQ distributions for occipital and prefrontal widths are shown in the right panel of −5).The amount of skew in the transverse and coronal planes required to optimally register each brain image to a symmetric atlas template is a measure of left-right asymmetry. The distributions of the transverse and coronal skew are shown in Panel C of The correlation coefficients and p-values based on permutation distributions for the 15 pairs of asymmetry measures are shown in 2 = 0.54, se = 0.10) and left hemispheres . In contrast, the heritability estimates for the left and right prefrontal widths differed. Whereas the left prefrontal width was significantly heritable with an estimate of 0.40 (se = 0.11), the estimate for the right prefrontal width was lower  and did not reach our threshold for significance. Bivariate analysis was implemented to estimate the proportion of covariance for each pair of cerebral widths that was due to common genetic causes (i.e. genetic correlation) and environmental causes . The results are listed in Prior to estimating the genetic contributions to the AQs, we implemented variance component analysis to estimate the proportion of variance due to genetic (heritability estimate) and environmental influences on cerebral volume and width measurements from the left and right hemispheres  and dorsal-ventral (DV) axis. Compared to the left hemisphere, cerebral volume in the right hemisphere is shifted posteriorly along the AP axis and ventrally along the DV axis, whereas left hemisphere volume is shifted anteriorly and dorsally compared to the right. The transverse and coronal skews are moderately correlated with each other (r = 0.25) indicating that the differential distribution of volume along the two orthogonal axes tends to occur together, but is not tightly coupled. Besides the skew measures, the other two asymmetry traits that showed pedigree-level bias support the general pattern of asymmetry described above. The posterior shift of volume in the right hemisphere is reflected in the pedigree-level tendency toward a wider right occipital lobe and in the finding that the ascending ramus of the right cingulate sulcus was shifted posteriorly on the AP axis in a majority (91.5%) of the animals with asymmetric cingulate sulci. The methods implemented in this study are relatively general, and do not provide much information regarding asymmetry that may be localized to specific regions. Methods have been developed to measure the asymmetry quotient from gray-matter maps at a voxel-sized scale along the AP and DV axis (e.g. Barrick et al. a priori expectation of directional bias. Emerging evidence in comparative behavior suggest the possibility of a general trend across a broad range of species including fish, frogs, birds and mammals for right-hemisphere specialization for approach behaviors and left-hemisphere specialization for avoidance behaviors The pattern of asymmetry that we identified contrasts with the common pattern of anatomic asymmetry observed in humans, who have a population bias with volume shifted anteriorly in the right hemisphere and posteriorly in the left hemisphere. Most of the previous research on endocranial shapes has shown that chimpanzees and gorillas have a biased asymmetry similar to humans. However, a recent study using innovative three-dimensional methods to quantify asymmetry from endocasts found a majority of gorilla skulls in their sample demonstrated a rightward biased asymmetry in the occipital regions The functional significance of anatomic asymmetry in non-human primates is an important overarching question for the field. It is difficult to speculate about the functional significance of our findings. Even the cingulate sulcus trait, which is the most anatomically localized measure we employed, may represent a sensitive indicator of global volumetric shifts due to its central location at the midline. An additional limitation on functional hypotheses is the uncertainty regarding cytoarchitectonic similarities between vervets and macaques, for which detailed functional maps are available (see Woods et al. Among the asymmetry measures, only transverse skew showed statistically significant evidence of heritability. The estimate of heritability for the dichotomous cingulate sulcus measure was similar in magnitude, but with a higher standard error compared to the estimate for transverse skew. In part this finding may be due to the better power of a continuous trait using the variance-component analysis method that we employed. It may also reflect an advantage of atlas-based methods, which use voxel data from the entire cerebral volume to linearly deform each image to match a symmetric atlas template and provide measures of global features that complement regional or localized measures like volume and width. Although the heritability estimate for transverse skew was significant, it was much lower than that observed for other neuroimaging phenotypes in the VRC Although the genetic isolation and large complex pedigree structure of this sample adds power for genetic analysis, it must be emphasized that this dataset does not represent a population sample of independent individuals, and therefore the results cannot be generalized to other populations. The current work provides a rigorous investigation of anatomic asymmetry in a non-human primate genetic model system and demonstrates that it is possible for the primate brain to develop an asymmetry pattern quite different from that typically observed in humans. Although, the heritability estimates observed in this study cannot be extrapolated to study samples outside of the VRC pedigree, they provide the most conclusive evidence to date that genetic factors can contribute to inter-individual variance in anatomic asymmetry. Combined with growing evidence of anatomic asymmetry in other Old and New World monkeys


FGF16/ATRX/MAGT1, joint P-value = 2.71×10−9, and rs1751138 near ITM2A, P-value = 3.03×10−10) and one for fasting insulin . Further, we find that effect sizes for variants near ITM2A, a gene implicated in cartilage development, show evidence for a lack of dosage compensation. This observation is further supported by a sex-difference in ITM2A expression in whole blood , and is also in agreement with a previous report showing ITM2A escapes from X chromosome inactivation (XCI) in the majority of women. Hence, our results show one of the first links between phenotypic variation in a population sample and an XCI-escaping locus and pinpoint ITM2A as a potential contributor to the sexual dimorphism in height. In conclusion, our study provides a clear motivation for including chrX in large-scale genetic studies of complex diseases and traits.The X chromosome (chrX) represents one potential source for the “missing heritability” for complex phenotypes, which thus far has remained underanalyzed in genome-wide association studies (GWAS). Here we demonstrate the benefits of including chrX in GWAS by assessing the contribution of 404,862 chrX SNPs to levels of twelve commonly studied cardiometabolic and anthropometric traits in 19,697 Finnish and Swedish individuals with replication data on 5,032 additional Finns. By using a linear mixed model, we estimate that on average 2.6% of the additive genetic variance in these twelve traits is attributable to chrX, this being in proportion to the number of SNPs in the chromosome. In a chrX-wide association analysis, we identify three novel loci: two for height  analyses have often been neglected in large-scale genome-wide association studies. Given that chrX contains a considerable proportion of DNA, we wanted to examine how the variation in the chromosome contributes to commonly studied phenotypes. To this end, we studied the associations of over 400,000 chrX variants with twelve complex phenotypes, such as height, in almost 25,000 Northern European individuals. Demonstrating the value of assessing chrX associations, we found that as a whole the variation in the chromosome influences the levels of many of these phenotypes and further identified three new genomic regions where the variants associate with height or fasting insulin levels. In one of these three associated regions, the region near  Genome-wide association studies (GWAS) have discovered a wealth of loci associated with complex phenotypes with almost 5,800 significant associations for more than 500 different phenotypes reported in the NHGRI GWAS catalog A likely explanation for the dearth of association findings in chrX is that the chromosome is often neglected in GWAS: Wise et al. recently surveyed all published GWAS from 2010 and 2011 and found that only 33% of these studies had included chrX analyses While women carry two copies of chrX, men are hemizygous for the chromosome. The allele dosages between the sexes are balanced by random X chromosome inactivation (XCI) that silences one of the two chromosomes in women, hence requiring the allele coding for chrX markers to be adjusted accordingly for the analyses. However, XCI does not evenly cover the whole of chrX, but approximately 15% of the loci in the chromosome completely escape from XCI and in further 10% of the sites the silenced chrX is variably active in women, although the expression from the inactivated copy of chrX is often lower than from the active chrX Given the underutilization of chrX data in previous studies and hence the potential for novel biological discoveries, we aimed at surveying the contribution of the chromosome to complex traits. To this end, we expanded the marker set for chrX by imputing the non-pseudoautosomal region of chrX in almost 25,000 Finnish and Swedish individuals from seven discovery and one replication cohort  by utili−6) was observed for height, a highly heritable and polygenic phenotype. For the other phenotypes the statistical significance of the estimates was not overwhelming, a result of the available sample size and lower trait heritability, but also the estimates for SBP, HDL-C and fasting insulin were significantly different  from zero. In these four phenotypes, which showed non-zero X-linked variance, on average 4.0% (range 2.4%–6.0%) of the estimated whole-genome genetic variance was attributable to chrX while the corresponding value over all twelve traits was 2.6%.We first estimated the proportion of variance in each of the twelve phenotypes accountable jointly to the common and low-frequency  >1%) SNPs in chrX using a linear mixed model Following the work of Yang et al. −8): two for height (both in Xq21.1) and one for fasting insulin (in Xq23)  . We follq23)  are located approximately 35 kb upstream of ITM2A , a gene implicated in early cartilage development ITM2A in whole blood  is intronic within ATRX, a gene associated with the X-linked alpha thalassaemia mental retardation syndrome (ATR-X), a rare condition manifesting itself as profound developmental delay often accompanied by several other distinct characteristics including skeletal abnormalities in 90% and short stature in two thirds of the affected individuals ITM2A locus. The conditional analysis did not attenuate the height signal in the ATRX region, yet here the most associated SNP . The lead SNP maps to an apparent gene desert: the gene closest to the association, SLC6A14, a possible candidate gene for X-linked obesity (OMIM: 300444), lies more than 500 kb away.In the more strongly associated height locus the associated SNPs  and Xq23 (0.51% vs. 0.19% for fasting insulin) loci, as expected under the model of random XCI, but not for the ITM2A SNP (0.12% vs. 0.39% for height) , and 0.18 for rs182838724 near ATRX (height), but 0.99 for rs1751138 near ITM2A (height) (To verify the observation of lack of dosage compensation in the (height) .ITM2A locus in women should be reflected in the level of ITM2A expression, given the two actively transcribed X chromosomes, we evaluated the sex difference in the level of the ITM2A expression probe that had earlier showed a significant cis-effect with the lead SNP of the locus. The average level of ITM2A expression in whole blood was observed to be higher in women  ITM2A association discovered in our analyses (r2 = 0.728 between the lead SNPs), however, in that study the finding failed to replicate and thus never reached the formal threshold for significance.As thus far chrX has only infrequently been included in GWAS of the twelve traits studied, it is unsurprising that the three loci now discovered, one for fasting insulin and two for height, represent the first ones reported in chrX for these phenotypes in European populations. Two earlier GWAS conducted in individuals of African ancestry discovered a height locus in Xp22.3 FGF16, ATRX and MAGT1 in a gene rich region. Both ATRX and MAGT1 have been implicated in mental retardation syndromes, and interestingly the syndrome associated with mutations in ATRX is often accompanied with skeletal abnormalities and short stature in the affected individuals FGF16, which is a member of fibroblast growth factor family shown to play various roles in developmental processes including morphogenesis. Mouse studies proposed a crucial role for FGF16 in cardiac morphogenesis FGF16 were demonstrated to associate with congenital limb malformations ITM2A is a functional candidate: The association signal maps just 35 kb upstream of the transcription start site of ITM2A, a gene known to be involved in cartilage development ITM2A. Interestingly, high expression of ITM2A in adipose tissue stem cells has been proposed to inhibit the initiation of chondrogenesis in these cells ITM2A, this suggests the allelic effect to height could be mediated through the capacity to generate cartilage and bone.While further studies are required to elaborate the causative variants underlying the association with fasting insulin in Xq23, in both of the height loci there are plausible candidate genes that could be responsible for the observations. The first height association spans ITM2A, while for the other two associated loci there was no such evidence. A large-scale scan on 270,000 individuals for sexual dimorphisms in autosomal genetic effects for various anthropometric phenotypes identified significant sex differences only in associations for waist phenotypes and none was observed for height ITM2A locus here is likely the first demonstration of its kind and hence warrants the investigation for potential sex heterogeneity in associations for other X-linked loci.Given the unique nature of chrX compared to autosomes, i.e., males being hemizygous for the chromosome and the partly incomplete XCI, which could give rise to sexual dimorphisms, we analyzed our association data also by accounting for potential heterogeneity in genetic effects between sexes. This led to the discovery of considerable sex-difference in the genetic effects for height near ITM2A appeared fully consistent with no dosage compensation in this locus. While we cannot completely exclude the possibility that such a difference can also arise through some other type of sex-by-SNP interaction effect, we gained further confirmation for the lack of dosage compensation for height in ITM2A by quantifying the evidence for the two dosage compensation models in each of the associated loci using a new model comparison framework. Additionally, the gene expression data that showed higher expression of ITM2A in women, as expected if two X chromosomes are transcriptionally active in this locus. Similarly, expression of ITM2A was previously observed to be female-biased in monocytes and in the same study the cis-eQTL for ITM2A showed sex heterogeneity ITM2A was found to be among the 10% of chrX genes, which variably escape from inactivation, i.e., are expressed from the inactivated copy of X (Xi) in a majority of women ATRX and MAGT1 in the other height locus (FGF16 was not included in the survey) from Xi is fully silenced The difference in the genetic effects for males and females near ITM2A are due to incomplete dosage compensation in this locus. Therefore, our study likely provides, to the best of our knowledge, the first link between an XCI-escaping gene and phenotypic variation in non-syndromic individuals. This discovery has several plausible implications. As increased expression of ITM2A links with shorter stature, the greater dosage of ITM2A in women compared to men may explain some of the substantial sex difference observed in height. In addition to the sex differences in the overall expression levels, incomplete dosage compensation also causes the genetic variation in the population to have different effects on the trait distribution of males and females. Assuming that rs1751138, the ITM2A lead SNP, is the causal variant for the observed height association, we estimate that the observed 36% frequency of the height decreasing allele accounts for 1.5% of the current difference in mean height between men and women in the Finnish population, when compared to a population that was monomorphic for the major allele at this SNP , The Cardiovascular Risk in Young Finns Study (YFS), The COROGENE Study (COROGENE), Helsinki Birth Cohort Study (HBCS), the Health 2000 GenMets Study (GenMets), the Diabetes Genetics Initiative (DGI) and a prospective cardiovascular disease (CVD) case-control sample from the FINRISK collections (PredictCVD). In the replication stage a further subset of individuals from the FINRISK collections (FR) was included. A summary of the cohort characteristics is given in NFBC1966 is a birth cohort study of children born in 1966 in the two northernmost provinces of Finland originally designed to focus on factors affecting pre-term birth, low birth weight, and subsequent morbidity and mortality http://mathgen.stats.ox.ac.uk/impute/data_download_1000G_phase1_integrated.html). The data were split into genomic regions of ∼5 Mb (with 250 kb (DGI) or 1 Mb (other cohorts) buffer region), using effective population size of 20000 (DGI) or 11418 and k value of 80.The following genotyping arrays were used for genotyping the study cohorts: Illumina 370K array for NFBC1966, Illumina 610K array for COROGENE and GenMets, custom generated Illumina 670K array for YFS and HBCS, Illumina 770K array for PredictCVD, Illumina HumanCoreExome-12v1-0 for FR and Affymetrix GeneChip Human Mapping 500K Array set for DGI. The quality control procedures included removing closely related individuals (PI_HAT >0.1) by analyzing pairwise IBD relationships for all individuals in five Finnish discovery cohorts together and have been described previously in detail Within each cohort, all twelve phenotypes were adjusted for males and females separately using age (not in NFBC1966) and ten first principal components as covariates. Additionally, WHR and blood pressure measurements were adjusted for BMI. The residuals from the linear regression were inverse normal transformed to have mean 0 and standard deviation 1, and the normalized residuals were then used as phenotypes in the variance estimate and association analyses. In cohorts where the information was available, individuals on lipid-lowering medication were excluded prior the covariate adjustment for the blood lipids , blood-pressure medication was an exclusion criterion for systolic and diastolic blood pressure and diabetes medication for glucose and insulin. Non-fasting individuals were excluded from the analysis of glucose and insulin, and pregnant women were only included in the analysis of CRP and height. All phenotype adjustments and data normalization were done in STATA/SE 12.1 or R (version 2.11.1). The sample size for each phenotype in the discovery cohorts, i.e., the number of individuals with both genotype and phenotype information, are given in We estimated how much phenotypic variance a panel of 217,112 high quality SNPs from chrX  explain using the linear mixed model approach implemented in GCTA (v.1.13) For a comparison, we also estimated the genetic variances using 9,517 directly genotyped SNPs in chrX but did not find notable differences from the results with the imputed data . For anoAll mixed model analyses excluded individuals in such a way that none of the remaining pairs of individuals had an estimated relatedness coefficient r >0.05 and the same trait values were used as with the association analyses. For comparison, the analyses were also carried out by using r = 0.025 as the relatedness cut-off .The associations between variants and phenotypes were tested for all available genotyped or imputed SNPs in chrX separately for men and women in each cohort encoding genotypes {0,2} in men and {0,1,2} in women, i.e., assuming that one of the two X chromosomes in women is fully inactivated. In DGI the analysis was performed using a linear mixed model that can account for sample structure, as implemented in EMMAX −8, three loci showed significant associations in the discovery analysis. In these associated loci the lead SNPs were imputed with high quality (imputation info >0.80) in all cohorts.The cohorts and genders were combined in a fixed-effects (inverse variance weighted) meta-analysis and in a sex-differentiated meta-analysis, which combines the results allowing for the allelic effects to differ between men and women and also conducts a meta-analysis separately for the results from men and from women, both meta-analysis options implemented in GWAMA ITM2A and ATRX are present already in pre-puberty, the association of the chrX SNPs with childhood height was studied in a subset of individuals from NFBC1966 and YFS cohorts  = 1204 and N = 1189 in NFBC1966; N = 417 and N = 478 in YFS) who had height measurements available both from pre-puberty (ages 8–10 years for NFBC1966 and 9 years for YFS) and adulthood. The height measurements were adjusted for age (in NFBC1966) and ten first principal components, the residuals were inverse normal transformed and subsequently the association of the SNP dosage with the transformed residuals was studied in SNPTEST using an additive model of association. The SNP-phenotype associations for the two height measurements were studied in both cohorts, separately for the genders, and the results were combined in a fixed-effects and a sex-differentiated meta-analysis using GWAMA applying genomic control correction. The association results for the height lead SNPs with childhood and adulthood height in these individuals are given in To investigate whether the observed associations with height near ITM2A/ILMN_2076600) we further evaluated whether the level of expression was different between the sexes by comparing the unadjusted expression in males and females using Student's t-test in R.A subset of the COROGENE cohort (N = 513) had both genome-wide SNP data and gene expression data from whole blood, assayed using Illumina HumanHT-12v3 Expression BeadChips, available, as described previously 2P(1-P) for females and 4P(1-P) males, where P denotes the allele frequency of the SNP. Thus, the estimation of the variance explained from the meta-analysis summary statistics should be evaluated for the genders separately using the formulas F22P(1-P)b for women and M24P(1-P)b for men, where bF and bM denote the standardized effect sizes in women and men, respectively.As males carry only one copy of the X chromosome, the genotype variances of the SNPs in the non-pseudoautosomal region of chrX differ between women and men. Assuming the model of complete inactivation of one the X chromosomes in women, and hence coding the X-linked alleles {0,2} in men and {0,1,2} in women, the genotype variance in men is twice that in women: F  and bM  together with their standard errors to approximate the likelihood function as in We applied a Bayesian framework F∼N, bM∼N and cor = 1FDC: bF∼N, bM∼N and cor = 1NDC: b2, the variance of the prior effect size in females, depends on the allele frequency of the SNP and is chosen so that with 95% probability the studied SNP explains less than 1% of the variance of the trait. Intuitively, according to the FDC model bF = bM whereas according to the NDC model bF = 2bM. Bayes factors between the two models can be computed using the approximate likelihood approach a priori.Where sa) at a particular SNP on chrX causally affects the trait value by ‘b’ both in males and in females, i.e., there is no dosage compensation. To simplify notation, we assume that the mean trait value of males with genotype ‘A’ is the same as the mean trait value in females with genotype ‘AA’, and denote this mean by ‘m’. The overall mean trait values in males, ‘mM’, and in females, ‘mF’, areSuppose that each copy of the minor allele (‘a’ with frequency fM = (1−fa)•m + fa•(m+b) = m + fa•b, andmF = fAA•m + fAa•(m+b) + faa•(m+2b) = m + (fAa+2faa)•b = m + 2fa•bmThe difference in the sex-specific means isM − mF = m + fa•b − (m + 2fa•b) = − fa•bma•b|, compared to the situation where only allele ‘A’ was present in the population.So the effect of allele ‘a’ is either to increase (if b<0) or decrease (if b>0) the male-female difference in the mean trait value by |fITM2A:Application to rs1751138, the lead SNP of the association near b = −0.555 cm (se = 0.0734 cm). This is a fixed-effects estimate of the allelic effects in quantile normalized height in females −0.092559 (0.013934) and males −0.071802 (0.019274), multiplied by an estimate of the standard deviation of height in Finland, 6.5 cm.a = 0.36 in the population, the male-female difference in mean height increases by 0.36*0.555 cm = 0.20 cm. As the mean difference in height between the sexes in Finland is about 13.7 cm, the variation at this SNP accounts for 0.20 cm/13.7 cm = 0.0146≈1.5% of that difference.Thus by introducing the minor allele (A) with frequency fFigure S1ITM2A height locus. A: The region near FGF16, ATRX and MAGT1. The lead associated SNP in this analysis, rs34979608, is highlighted with diamonds, the yellow diamond indicating the association in the discovery analysis and the purple diamond and text the association in the joint analysis of discovery and replication cohorts. The yellow × indicates the association of the SNP that was most associated with height in this region in the discovery meta-analysis, i.e., before the conditional analysis . B: The region near ITM2A. No association with height remains in this region in the conditional analysis. Each circle in the plots indicates a SNP and the color of the circle shows the linkage disequilibrium, r2, of the SNP to the lead associated SNP in each region, rs34979608 in A and rs1751138 in B: dark blue (r2<0.2), light blue (r2>0.2), green (r2>0.4), orange (r2>0.6) and red (r2>0.8). The correlation structure between the SNPs was calculated from Finnish data using the genotypes from the COROGENE cohort. The light blue line in the background and the right hand y-axis show the recombination rate in the region as calculated from HapMap CEU data.Regional association plots of the associations in the two height loci after conditioning the association analysis on rs1751138, the lead associated SNP in the (PDF)Click here for additional data file.Figure S2ITM2A expression in men and women. The levels of whole blood ITM2A expression visualized using boxplots separately for men (blue) and women (orange) in the individuals of COROGENE cohort (N = 513) for whom expression data was available. The mean expression level is higher in women  providing support for incomplete dosage compensation between men and women in the ITM2A locus.Boxplots of (PDF)Click here for additional data file.Figure S3Comparison of the phenotypic variances attributable to chromosome X variants (y-axis) and autosomal variants (x-axis). The dashed line is y = 0.03x and shows the region of the expected values of the points under the assumption that the genetic effects are small and uniformly distributed across the genome and that the X chromosome contains about 3% of all genetic variation. The dotted lines show the standard errors of the estimates. The traits are TC: total cholesterol; LDL-C: low-density lipoprotein cholesterol; HDL-C: high-density lipoprotein cholesterol; TG: total triglycerides; CRP: C-reactive protein; BMI: body-mass-index; WHR: waist-hip-ratio; SBP: systolic blood pressure; DBP: diastolic blood pressure; HGT: height; GLK: fasting glucose; INS: fasting insulin.(PNG)Click here for additional data file.Table S1Estimates of the phenotypic variance attributable to 217,112 imputed and genotyped chrX SNPs using three different dosage compensation models.(XLS)Click here for additional data file.Table S2ITM2A and rs182838724 near FGF16, ATRX and MAGT1 for height and rs139163435 in Xq23 for fasting insulin).Association results in each discovery cohort for the lead SNPs in the three associated loci (rs1751138 near (XLS)Click here for additional data file.Table S3FGF16, ATRX and MAGT1 after conditioning the association analysis on the lead SNP of the ITM2A locus, rs1751138.Lead associations in the height locus near (XLS)Click here for additional data file.Table S4Associations of the most associated SNPs in the two height loci with height in childhood (age 8–10) and adulthood in a subset of the study subjects from two cohorts (NFBC1966 and YFS) for whom childhood height measurements were available.(XLS)Click here for additional data file.Table S5Sample sizes for the twelve phenotypes in the discovery cohorts.(XLS)Click here for additional data file.Table S6Estimates of the phenotypic variance attributable to 9,517 directly genotyped chrX SNPs using three different dosage compensation models.(XLS)Click here for additional data file.Table S7Estimates of the phenotypic variance attributable to 217,112 imputed and genotyped chrX SNPs using three different dosage compensation models using a threshold of 0.025 to remove related individuals.(XLS)Click here for additional data file.Table S8Genomic control lambdas for the twelve phenotypes in the X chromosome-wide meta-analyses of the discovery cohorts. In cases where lambda >1, the meta-analysis results were corrected using the lambda statistic.(XLS)Click here for additional data file.