A Novel Generalized Ridge Regression Method for Quantitative Genetics

As the molecular marker density grows, there is a strong need in both genome-wide association studies and genomic selection to fit models with a large number of parameters. Here we present a computationally efficient generalized ridge regression (RR) algorithm for situations in which the number of parameters largely exceeds the number of observations. The computationally demanding parts of the method depend mainly on the number of observations and not the number of parameters. The algorithm was implemented in the R package bigRR based on the previously developed package hglm. Using such an approach, a heteroscedastic effects model (HEM) was also developed, implemented, and tested. The efficiency for different data sizes were evaluated via simulation. The method was tested for a bacteria-hypersensitive trait in a publicly available Arabidopsis data set including 84 inbred lines and 216,130 SNPs. The computation of all the SNP effects required <10 sec using a single 2.7-GHz core. The advantage in run time makes permutation test feasible for such a whole-genome model, so that a genome-wide significance threshold can be obtained. HEM was found to be more robust than ordinary RR (a.k.a. SNP-best linear unbiased prediction) in terms of QTL mapping, because SNP-specific shrinkage was applied instead of a common shrinkage. The proposed algorithm was also assessed for genomic evaluation and was shown to give better predictions than ordinary RR.     

Screening and replication using the same data set: testing strategies for family-based studies in which all probands are affected

For genome-wide association studies in family-based designs, we propose a powerful two-stage testing strategy that can be applied in situations in which parent-offspring trio data are available and all offspring are affected with the trait or disease under study. In the first step of the testing strategy, we construct estimators of genetic effect size in the completely ascertained sample of affected offspring and their parents that are statistically independent of the family-based association/transmission disequilibrium tests (FBATs/TDTs) that are calculated in the second step of the testing strategy. For each marker, the genetic effect is estimated (without requiring an estimate of the SNP allele frequency) and the conditional power of the corresponding FBAT/TDT is computed. Based on the power estimates, a weighted Bonferroni procedure assigns an individually adjusted significance level to each SNP. In the second stage, the SNPs are tested with the FBAT/TDT statistic at the individually adjusted significance levels. Using simulation studies for scenarios with up to 1,000,000 SNPs, varying allele frequencies and genetic effect sizes, the power of the strategy is compared with standard methodology (e.g., FBATs/TDTs with Bonferroni correction). In all considered situations, the proposed testing strategy demonstrates substantial power increases over the standard approach, even when the true genetic model is unknown and must be selected based on the conditional power estimates. The practical relevance of our methodology is illustrated by an application to a genome-wide association study for childhood asthma, in which we detect two markers meeting genome-wide significance that would not have been detected using standard methodology.     

Results of a “GWAS Plus:” General Cognitive Ability Is Substantially Heritable and Massively Polygenic

We carried out a genome-wide association study (GWAS) for general cognitive ability (GCA) plus three other analyses of GWAS data that aggregate the effects of multiple single-nucleotide polymorphisms (SNPs) in various ways. Our multigenerational sample comprised 7,100 Caucasian participants, drawn from two longitudinal family studies, who had been assessed with an age-appropriate IQ test and had provided DNA samples passing quality screens. We conducted the GWAS across ∼2.5 million SNPs (both typed and imputed), using a generalized least-squares method appropriate for the different family structures present in our sample, and subsequently conducted gene-based association tests. We also conducted polygenic prediction analyses under five-fold cross-validation, using two different schemes of weighting SNPs. Using parametric bootstrapping, we assessed the performance of this prediction procedure under the null. Finally, we estimated the proportion of variance attributable to all genotyped SNPs as random effects with software GCTA. The study is limited chiefly by its power to detect realistic single-SNP or single-gene effects, none of which reached genome-wide significance, though some genomic inflation was evident from the GWAS. Unit SNP weights performed about as well as least-squares regression weights under cross-validation, but the performance of both increased as more SNPs were included in calculating the polygenic score. Estimates from GCTA were 35% of phenotypic variance at the recommended biological-relatedness ceiling. Taken together, our results concur with other recent studies: they support a substantial heritability of GCA, arising from a very large number of causal SNPs, each of very small effect. We place our study in the context of the literature–both contemporary and historical–and provide accessible explication of our statistical methods.     

Association between Expression Quantitative Trait Loci and Metabolic Traits in Two Korean Populations

Most genome-wide association studies consider genes that are located closest to single nucleotide polymorphisms (SNPs) that are highly significant for those studies. However, the significance of the associations between SNPs and candidate genes has not been fully determined. An alternative approach that used SNPs in expression quantitative trait loci (eQTL) was reported previously for Crohn’s disease; it was shown that eQTL-based preselection for follow-up studies was a useful approach for identifying risk loci from the results of moderately sized GWAS. In this study, we propose an approach that uses eQTL SNPs to support the functional relationships between an SNP and a candidate gene in a genome-wide association study. The genome-wide SNP genotypes and 10 biochemical measures (fasting glucose levels, BUN, serum albumin levels, AST, ALT, gamma GTP, total cholesterol, HDL cholesterol, triglycerides, and LDL cholesterol) were obtained from the Korean Association Resource (KARE) consortium. The eQTL SNPs were isolated from the SNP dataset based on the RegulomeDB eQTL-SNP data from the ENCODE projects and two recent eQTL reports. A total of 25,658 eQTL SNPs were tested for their association with the 10 metabolic traits in 2 Korean populations (Ansung and Ansan). The proportion of phenotypic variance explained by eQTL and non-eQTL SNPs showed that eQTL SNPs were more likely to be associated with the metabolic traits genetically compared with non-eQTL SNPs. Finally, via a meta-analysis of the two Korean populations, we identified 14 eQTL SNPs that were significantly associated with metabolic traits. These results suggest that our approach can be expanded to other genome-wide association studies.     

Improving the Power of GWAS and Avoiding Confounding from Population Stratification with PC-Select

Using a reduced subset of SNPs in a linear mixed model can improve power for genome-wide association studies, yet this can result in insufficient correction for population stratification. We propose a hybrid approach using principal components that does not inflate statistics in the presence of population stratification and improves power over standard linear mixed models.     

Pathways-Driven Sparse Regression Identifies Pathways and Genes Associated with High-Density Lipoprotein Cholesterol in Two Asian Cohorts

Standard approaches to data analysis in genome-wide association studies (GWAS) ignore any potential functional relationships between gene variants. In contrast gene pathways analysis uses prior information on functional structure within the genome to identify pathways associated with a trait of interest. In a second step, important single nucleotide polymorphisms (SNPs) or genes may be identified within associated pathways. The pathways approach is motivated by the fact that genes do not act alone, but instead have effects that are likely to be mediated through their interaction in gene pathways. Where this is the case, pathways approaches may reveal aspects of a trait''s genetic architecture that would otherwise be missed when considering SNPs in isolation. Most pathways methods begin by testing SNPs one at a time, and so fail to capitalise on the potential advantages inherent in a multi-SNP, joint modelling approach. Here, we describe a dual-level, sparse regression model for the simultaneous identification of pathways and genes associated with a quantitative trait. Our method takes account of various factors specific to the joint modelling of pathways with genome-wide data, including widespread correlation between genetic predictors, and the fact that variants may overlap multiple pathways. We use a resampling strategy that exploits finite sample variability to provide robust rankings for pathways and genes. We test our method through simulation, and use it to perform pathways-driven gene selection in a search for pathways and genes associated with variation in serum high-density lipoprotein cholesterol levels in two separate GWAS cohorts of Asian adults. By comparing results from both cohorts we identify a number of candidate pathways including those associated with cardiomyopathy, and T cell receptor and PPAR signalling. Highlighted genes include those associated with the L-type calcium channel, adenylate cyclase, integrin, laminin, MAPK signalling and immune function.     

GCTA: a tool for genome-wide complex trait analysis

For most human complex diseases and traits, SNPs identified by genome-wide association studies (GWAS) explain only a small fraction of the heritability. Here we report a user-friendly software tool called genome-wide complex trait analysis (GCTA), which was developed based on a method we recently developed to address the "missing heritability" problem. GCTA estimates the variance explained by all the SNPs on a chromosome or on the whole genome for a complex trait rather than testing the association of any particular SNP to the trait. We introduce GCTA's five main functions: data management, estimation of the genetic relationships from SNPs, mixed linear model analysis of variance explained by the SNPs, estimation of the linkage disequilibrium structure, and GWAS simulation. We focus on the function of estimating the variance explained by all the SNPs on the X chromosome and testing the hypotheses of dosage compensation. The GCTA software is a versatile tool to estimate and partition complex trait variation with large GWAS data sets.     

Genome-wide association study of body weight in Wenshang Barred chicken based on the SLAF-seq technology

Chicken body weight (BW) is an economically important trait, and many studies have been conducted on genetic selection for BW. However, previous studies have detected functional chromosome mutations or regions using gene chips. The present study used the specific-locus amplified fragment sequencing (SLAF-seq) technology to perform a genome-wide association study (GWAS) on purebred Wengshang Barred chicken. A total of 1,286,715 single-nucleotide polymorphisms (SNPs) were detected, and 175,211 SNPs were selected as candidate SNPs for genome-wide association analysis using TASSEL general linear models. Six SNP markers reached genome-wide significance. Of these, rs732048524, rs735522839, rs738991545, and rs15837818 were significantly associated with body weight at 28 days (BW28), while rs314086457 and rs315694878 were significantly associated with BW120. These SNPs are close to seven genes (PRSS23, ME3, FAM181B, NABP1, SDPR, TSSK6L2, and RBBP8). Moreover, 24 BW-associated SNPs reached “suggestive” genome-wide significance. Of these, 6, 13, 1, and 4 SNPs were associated with BW28, BW56, BW80, and BW120, respectively. These results would enrich the studies on BW and promote the use of Chinese chicken, especially the Wenshang Barred chicken.     

On Quality Control Measures in Genome-Wide Association Studies: A Test to Assess the Genotyping Quality of Individual Probands in Family-Based Association Studies and an Application to the HapMap Data

Allele transmissions in pedigrees provide a natural way of evaluating the genotyping quality of a particular proband in a family-based, genome-wide association study. We propose a transmission test that is based on this feature and that can be used for quality control filtering of genome-wide genotype data for individual probands. The test has one degree of freedom and assesses the average genotyping error rate of the genotyped SNPs for a particular proband. As we show in simulation studies, the test is sufficiently powerful to identify probands with an unreliable genotyping quality that cannot be detected with standard quality control filters. This feature of the test is further exemplified by an application to the third release of the HapMap data. The test is ideally suited as the final layer of quality control filters in the cleaning process of genome-wide association studies. It identifies probands with insufficient genotyping quality that were not removed by standard quality control filtering.     

Genome-wide association and genomic selection in animal breeding

Results from genome-wide association studies in livestock, and humans, has lead to the conclusion that the effect of individual quantitative trait loci (QTL) on complex traits, such as yield, are likely to be small; therefore, a large number of QTL are necessary to explain genetic variation in these traits. Given this genetic architecture, gains from marker-assisted selection (MAS) programs using only a small number of DNA markers to trace a limited number of QTL is likely to be small. This has lead to the development of alternative technology for using the available dense single nucleotide polymorphism (SNP) information, called genomic selection. Genomic selection uses a genome-wide panel of dense markers so that all QTL are likely to be in linkage disequilibrium with at least one SNP. The genomic breeding values are predicted to be the sum of the effect of these SNPs across the entire genome. In dairy cattle breeding, the accuracy of genomic estimated breeding values (GEBV) that can be achieved and the fact that these are available early in life have lead to rapid adoption of the technology. Here, we discuss the design of experiments necessary to achieve accurate prediction of GEBV in future generations in terms of the number of markers necessary and the size of the reference population where marker effects are estimated. We also present a simple method for implementing genomic selection using a genomic relationship matrix. Future challenges discussed include using whole genome sequence data to improve the accuracy of genomic selection and management of inbreeding through genomic relationships.     

基于DNA变异在亚欧混合人群中预测男性型脱发

男性型脱发(male pattern baldness,MPB)是一种雄激素依赖性的遗传性脱发疾病,对个人形象、心理产生较大的消极影响.近期欧美人群中进行的大样本全基因组关联分析(genome wide association studies,GWAS)已报道大量与MPB相关的遗传易感性单核苷酸多态性(single nucleotide polymorphisms,SNPs)位点,但这些位点在东亚人群中的遗传效应尚不清楚.本研究基于我国684个亚欧混合人群(Eurasian)样本,对在英国生物样本库(UK Biobank) 205 327个欧洲男性GWAS分析发现的624个与MPB相关的SNPs进行人群异质性分析,基于多基因风险打分(polygenic risk scores,PRS)建立预测模型,并对预测因子数量与模型预测性能的关系进行了研究.通过质控的467个SNPs中6.9%与MPB显著相关(P0.05).结合年龄、体质指数(body mass index,BMI)和25个SNPs建立的线性回归和逻辑回归模型,效果较好(R~2=28.9%,AUC=0.82).年龄对模型效果影响较大(R~2=22.9%,AUC=0.77),结合BMI及68个SNPs时AUC达到最大(约0.89).本研究表明MPB在欧洲和东亚人群中存在较强的遗传异质性,选取SNPs子集能达到与全集相近的预测准确性,预测模型有助于东亚人群MPB遗传机制的理解及疾病的早期诊断和预防.     

Novel rank-based approaches for discovery and replication in genome-wide association studies

In recent years, genome-wide association studies (GWAS) have uncovered a large number of susceptibility variants. Nevertheless, GWAS findings provide only tentative evidence of association, and replication studies are required to establish their validity. Due to this uncertainty, researchers often focus on top-ranking SNPs, instead of considering strict significance thresholds to guide replication efforts. The number of SNPs for replication is often determined ad hoc. We show how the rank-based approach can be used for sample size allocation in GWAS as well as for deciding on a number of SNPs for replication. The basis of this approach is the "ranking probability": chances that at least j true associations will rank among top u SNPs, when SNPs are sorted by P-value. By employing simple but accurate approximations for ranking probabilities, we accommodate linkage disequilibrium (LD) and evaluate consequences of ignoring LD. Further, we relate ranking probabilities to the proportion of false discoveries among top u SNPs. A study-specific proportion can be estimated from P-values, and its expected value can be predicted for study design applications.     

A Powerful Pathway-Based Adaptive Test for Genetic Association with Common or Rare Variants

In spite of the success of genome-wide association studies (GWASs), only a small proportion of heritability for each complex trait has been explained by identified genetic variants, mainly SNPs. Likely reasons include genetic heterogeneity (i.e., multiple causal genetic variants) and small effect sizes of causal variants, for which pathway analysis has been proposed as a promising alternative to the standard single-SNP-based analysis. A pathway contains a set of functionally related genes, each of which includes multiple SNPs. Here we propose a pathway-based test that is adaptive at both the gene and SNP levels, thus maintaining high power across a wide range of situations with varying numbers of the genes and SNPs associated with a trait. The proposed method is applicable to both common variants and rare variants and can incorporate biological knowledge on SNPs and genes to boost statistical power. We use extensively simulated data and a WTCCC GWAS dataset to compare our proposal with several existing pathway-based and SNP-set-based tests, demonstrating its promising performance and its potential use in practice.     

Beyond missing heritability: prediction of complex traits

Despite rapid advances in genomic technology, our ability to account for phenotypic variation using genetic information remains limited for many traits. This has unfortunately resulted in limited application of genetic data towards preventive and personalized medicine, one of the primary impetuses of genome-wide association studies. Recently, a large proportion of the "missing heritability" for human height was statistically explained by modeling thousands of single nucleotide polymorphisms concurrently. However, it is currently unclear how gains in explained genetic variance will translate to the prediction of yet-to-be observed phenotypes. Using data from the Framingham Heart Study, we explore the genomic prediction of human height in training and validation samples while varying the statistical approach used, the number of SNPs included in the model, the validation scheme, and the number of subjects used to train the model. In our training datasets, we are able to explain a large proportion of the variation in height (h(2) up to 0.83, R(2) up to 0.96). However, the proportion of variance accounted for in validation samples is much smaller (ranging from 0.15 to 0.36 depending on the degree of familial information used in the training dataset). While such R(2) values vastly exceed what has been previously reported using a reduced number of pre-selected markers (<0.10), given the heritability of the trait (～ 0.80), substantial room for improvement remains.     

Genomics and genome-wide association studies: an integrative approach to expression QTL mapping

Expression QTL mapping by integrating genome-wide gene expression and genotype data is a promising approach to identifying functional genetic variation, but is hampered by the large number of multiple comparisons inherent in such studies. A novel approach to addressing multiple testing problems in genome-wide family-based association studies is screening candidate markers using heritability or conditional power. We apply these methods in settings in which microarray gene expression data are used as phenotypes, screening for SNPs near the expressed genes. We perform association analyses for phenotypes using a univariate approach. We also perform simulations on trios with large numbers of causal SNPs to determine the optimal number of markers to use in a screen. We demonstrate that our family-based screening approach performs well in the analysis of integrative genomic datasets and that screening using either heritability or conditional power produces similar, though not identical, results.     

On the meta-analysis of genome-wide association studies: a robust and efficient approach to combine population and family-based studies

For the meta-analysis of genome-wide association studies, we propose a new method to adjust for the population stratification and a linear mixed approach that combines family-based and unrelated samples. The proposed approach achieves similar power levels as a standard meta-analysis which combines the different test statistics or p values across studies. However, by virtue of its design, the proposed approach is robust against population admixture and stratification, and no adjustments for population admixture and stratification, even in unrelated samples, are required. Using simulation studies, we examine the power of the proposed method and compare it to standard approaches in the meta-analysis of genome-wide association studies. The practical features of the approach are illustrated with a meta-analysis of three genome-wide association studies for Alzheimer's disease. We identify three single nucleotide polymorphisms showing significant genome-wide association with affection status. Two single nucleotide polymorphisms are novel and will be verified in other populations in our follow-up study.     

On the Analysis of Genome-Wide Association Studies in Family-Based Designs: A Universal,Robust Analysis Approach and an Application to Four Genome-Wide Association Studies

For genome-wide association studies in family-based designs, we propose a new, universally applicable approach. The new test statistic exploits all available information about the association, while, by virtue of its design, it maintains the same robustness against population admixture as traditional family-based approaches that are based exclusively on the within-family information. The approach is suitable for the analysis of almost any trait type, e.g. binary, continuous, time-to-onset, multivariate, etc., and combinations of those. We use simulation studies to verify all theoretically derived properties of the approach, estimate its power, and compare it with other standard approaches. We illustrate the practical implications of the new analysis method by an application to a lung-function phenotype, forced expiratory volume in one second (FEV1) in 4 genome-wide association studies.     

A study of CNVs as trait-associated polymorphisms and as expression quantitative trait loci

We conducted a comprehensive study of copy number variants (CNVs) well-tagged by SNPs (r(2)≥ 0.8) by analyzing their effect on gene expression and their association with disease susceptibility and other complex human traits. We tested whether these CNVs were more likely to be functional than frequency-matched SNPs as trait-associated loci or as expression quantitative trait loci (eQTLs) influencing phenotype by altering gene regulation. Our study found that CNV-tagging SNPs are significantly enriched for cis eQTLs; furthermore, we observed that trait associations from the NHGRI catalog show an overrepresentation of SNPs tagging CNVs relative to frequency-matched SNPs. We found that these SNPs tagging CNVs are more likely to affect multiple expression traits than frequency-matched variants. Given these findings on the functional relevance of CNVs, we created an online resource of expression-associated CNVs (eCNVs) using the most comprehensive population-based map of CNVs to inform future studies of complex traits. Although previous studies of common CNVs that can be typed on existing platforms and/or interrogated by SNPs in genome-wide association studies concluded that such CNVs appear unlikely to have a major role in the genetic basis of several complex diseases examined, our findings indicate that it would be premature to dismiss the possibility that even common CNVs may contribute to complex phenotypes and at least some common diseases.     

Meta-analysis of Dense Genecentric Association Studies Reveals Common and Uncommon Variants Associated with Height

Height is a classic complex trait with common variants in a growing list of genes known to contribute to the phenotype. Using a genecentric genotyping array targeted toward cardiovascular-related loci, comprising 49,320 SNPs across approximately 2000 loci, we evaluated the association of common and uncommon SNPs with adult height in 114,223 individuals from 47 studies and six ethnicities. A total of 64 loci contained a SNP associated with height at array-wide significance (p < 2.4 × 10⁻⁶), with 42 loci surpassing the conventional genome-wide significance threshold (p < 5 × 10⁻⁸). Common variants with minor allele frequencies greater than 5% were observed to be associated with height in 37 previously reported loci. In individuals of European ancestry, uncommon SNPs in IL11 and SMAD3, which would not be genotyped with the use of standard genome-wide genotyping arrays, were strongly associated with height (p < 3 × 10⁻¹¹). Conditional analysis within associated regions revealed five additional variants associated with height independent of lead SNPs within the locus, suggesting allelic heterogeneity. Although underpowered to replicate findings from individuals of European ancestry, the direction of effect of associated variants was largely consistent in African American, South Asian, and Hispanic populations. Overall, we show that dense coverage of genes for uncommon SNPs, coupled with large-scale meta-analysis, can successfully identify additional variants associated with a common complex trait.     

Insights into Colon Cancer Etiology via a Regularized Approach to Gene Set Analysis of GWAS Data

Genome-wide association studies (GWAS) have successfully identified susceptibility loci from marginal association analysis of SNPs. Valuable insight into genetic variation underlying complex diseases will likely be gained by considering functionally related sets of genes simultaneously. One approach is to further develop gene set enrichment analysis methods, which are initiated in gene expression studies, to account for the distinctive features of GWAS data. These features include the large number of SNPs per gene, the modest and sparse SNP associations, and the additional information provided by linkage disequilibrium (LD) patterns within genes. We propose a “gene set ridge regression in association studies (GRASS)” algorithm. GRASS summarizes the genetic structure for each gene as eigenSNPs and uses a novel form of regularized regression technique, termed group ridge regression, to select representative eigenSNPs for each gene and assess their joint association with disease risk. Compared with existing methods, the proposed algorithm greatly reduces the high dimensionality of GWAS data while still accounting for multiple hits and/or LD in the same gene. We show by simulation that this algorithm performs well in situations in which there are a large number of predictors compared to sample size. We applied the GRASS algorithm to a genome-wide association study of colon cancer and identified nicotinate and nicotinamide metabolism and transforming growth factor beta signaling as the top two significantly enriched pathways. Elucidating the role of variation in these pathways may enhance our understanding of colon cancer etiology.