A genomic background based method for association analysis in related individuals

Background

Feasibility of genotyping of hundreds and thousands of single nucleotide polymorphisms (SNPs) in thousands of study subjects have triggered the need for fast, powerful, and reliable methods for genome-wide association analysis. Here we consider a situation when study participants are genetically related (e.g. due to systematic sampling of families or because a study was performed in a genetically isolated population). Of the available methods that account for relatedness, the Measured Genotype (MG) approach is considered the ‘gold standard’. However, MG is not efficient with respect to time taken for the analysis of genome-wide data. In this context we proposed a fast two-step method called Genome-wide Association using Mixed Model and Regression (GRAMMAR) for the analysis of pedigree-based quantitative traits. This method certainly overcomes the drawback of time limitation of the measured genotype (MG) approach, but pays in power. One of the major drawbacks of both MG and GRAMMAR, is that they crucially depend on the availability of complete and correct pedigree data, which is rarely available.

Methodology

In this study we first explore type 1 error and relative power of MG, GRAMMAR, and Genomic Control (GC) approaches for genetic association analysis. Secondly, we propose an extension to GRAMMAR i.e. GRAMMAR-GC. Finally, we propose application of GRAMMAR-GC using the kinship matrix estimated through genomic marker data, instead of (possibly missing and/or incorrect) genealogy.

Conclusion

Through simulations we show that MG approach maintains high power across a range of heritabilities and possible pedigree structures, and always outperforms other contemporary methods. We also show that the power of our proposed GRAMMAR-GC approaches to that of the ‘gold standard’ MG for all models and pedigrees studied. We show that this method is both feasible and powerful and has correct type 1 error in the context of genome-wide association analysis in related individuals.     

Case-control association testing with related individuals: a more powerful quasi-likelihood score test

We consider the problem of genomewide association testing of a binary trait when some sampled individuals are related, with known relationships. This commonly arises when families sampled for a linkage study are included in an association study. Furthermore, power to detect association with complex traits can be increased when affected individuals with affected relatives are sampled, because they are more likely to carry disease alleles than are randomly sampled affected individuals. With related individuals, correlations among relatives must be taken into account, to ensure validity of the test, and consideration of these correlations can also improve power. We provide new insight into the use of pedigree-based weights to improve power, and we propose a novel test, the MQLS test, which, as we demonstrate, represents an overall, and in many cases, substantial, improvement in power over previous tests, while retaining a computational simplicity that makes it useful in genomewide association studies in arbitrary pedigrees. Other features of the MQLS are as follows: (1) it is applicable to completely general combinations of family and case-control designs, (2) it can incorporate both unaffected controls and controls of unknown phenotype into the same analysis, and (3) it can incorporate phenotype data about relatives with missing genotype data. The methods are applied to data from the Genetic Analysis Workshop 14 Collaborative Study of the Genetics of Alcoholism, where the MQLS detects genomewide significant association (after Bonferroni correction) with an alcoholism-related phenotype for four different single-nucleotide polymorphisms: tsc1177811 (P=5.9x10(-7)), tsc1750530 (P=4.0x10(-7)), tsc0046696 (P=4.7x10(-7)), and tsc0057290 (P=5.2x10(-7)) on chromosomes 1, 16, 18, and 18, respectively. Three of these four significant associations were not detected in previous studies analyzing these data.     

Combined linkage and association mapping of quantitative trait loci by multiple markers

Using multiple diallelic markers, variance component models are proposed for high-resolution combined linkage and association mapping of quantitative trait loci (QTL) based on nuclear families. The objective is to build a model that may fully use marker information for fine association mapping of QTL in the presence of prior linkage. The measures of linkage disequilibrium and the genetic effects are incorporated in the mean coefficients and are decomposed into orthogonal additive and dominance effects. The linkage information is modeled in variance-covariance matrices. Hence, the proposed methods model both association and linkage in a unified model. On the basis of marker information, a multipoint interval mapping method is provided to estimate the proportion of allele sharing identical by descent (IBD) and the probability of sharing two alleles IBD at a putative QTL for a sib-pair. To test the association between the trait locus and the markers, both likelihood-ratio tests and F-tests can be constructed on the basis of the proposed models. In addition, analytical formulas of noncentrality parameter approximations of the F-test statistics are provided. Type I error rates of the proposed test statistics are calculated to show their robustness. After comparing with the association between-family and association within-family (AbAw) approach by Abecasis and Fulker et al., it is found that the method proposed in this article is more powerful and advantageous based on simulation study and power calculation. By power and sample size comparison, it is shown that models that use more markers may have higher power than models that use fewer markers. The multiple-marker analysis can be more advantageous and has higher power in fine mapping QTL. As an application, the Genetic Analysis Workshop 12 German asthma data are analyzed using the proposed methods.     

Region-Based Association Analysis of Human Quantitative Traits in Related Individuals

Regional-based association analysis instead of individual testing of each SNP was introduced in genome-wide association studies to increase the power of gene mapping, especially for rare genetic variants. For regional association tests, the kernel machine-based regression approach was recently proposed as a more powerful alternative to collapsing-based methods. However, the vast majority of existing algorithms and software for the kernel machine-based regression are applicable only to unrelated samples. In this paper, we present a new method for the kernel machine-based regression association analysis of quantitative traits in samples of related individuals. The method is based on the GRAMMAR+ transformation of phenotypes of related individuals, followed by use of existing kernel machine-based regression software for unrelated samples. We compared the performance of kernel-based association analysis on the material of the Genetic Analysis Workshop 17 family sample and real human data by using our transformation, the original untransformed trait, and environmental residuals. We demonstrated that only the GRAMMAR+ transformation produced type I errors close to the nominal value and that this method had the highest empirical power. The new method can be applied to analysis of related samples by using existing software for kernel-based association analysis developed for unrelated samples.     

Approximating identity-by-descent matrices using multiple haplotype configurations on pedigrees

Identity-by-descent (IBD) matrix calculation is an important step in quantitative trait loci (QTL) analysis using variance component models. To calculate IBD matrices efficiently for large pedigrees with large numbers of loci, an approximation method based on the reconstruction of haplotype configurations for the pedigrees is proposed. The method uses a subset of haplotype configurations with high likelihoods identified by a haplotyping method. The new method is compared with a Markov chain Monte Carlo (MCMC) method (Loki) in terms of QTL mapping performance on simulated pedigrees. Both methods yield almost identical results for the estimation of QTL positions and variance parameters, while the new method is much more computationally efficient than the MCMC approach for large pedigrees and large numbers of loci. The proposed method is also compared with an exact method (Merlin) in small simulated pedigrees, where both methods produce nearly identical estimates of position-specific kinship coefficients. The new method can be used for fine mapping with joint linkage disequilibrium and linkage analysis, which improves the power and accuracy of QTL mapping.     

Family-based association tests for genomewide association scans

With millions of single-nucleotide polymorphisms (SNPs) identified and characterized, genomewide association studies have begun to identify susceptibility genes for complex traits and diseases. These studies involve the characterization and analysis of very-high-resolution SNP genotype data for hundreds or thousands of individuals. We describe a computationally efficient approach to testing association between SNPs and quantitative phenotypes, which can be applied to whole-genome association scans. In addition to observed genotypes, our approach allows estimation of missing genotypes, resulting in substantial increases in power when genotyping resources are limited. We estimate missing genotypes probabilistically using the Lander-Green or Elston-Stewart algorithms and combine high-resolution SNP genotypes for a subset of individuals in each pedigree with sparser marker data for the remaining individuals. We show that power is increased whenever phenotype information for ungenotyped individuals is included in analyses and that high-density genotyping of just three carefully selected individuals in a nuclear family can recover >90% of the information available if every individual were genotyped, for a fraction of the cost and experimental effort. To aid in study design, we evaluate the power of strategies that genotype different subsets of individuals in each pedigree and make recommendations about which individuals should be genotyped at a high density. To illustrate our method, we performed genomewide association analysis for 27 gene-expression phenotypes in 3-generation families (Centre d'Etude du Polymorphisme Humain pedigrees), in which genotypes for ~860,000 SNPs in 90 grandparents and parents are complemented by genotypes for ~6,700 SNPs in a total of 168 individuals. In addition to increasing the evidence of association at 15 previously identified cis-acting associated alleles, our genotype-inference algorithm allowed us to identify associated alleles at 4 cis-acting loci that were missed when analysis was restricted to individuals with the high-density SNP data. Our genotype-inference algorithm and the proposed association tests are implemented in software that is available for free.     

Statistical distributions of test statistics used for quantitative trait association mapping in structured populations

Background

Spurious associations between single nucleotide polymorphisms and phenotypes are a major issue in genome-wide association studies and have led to underestimation of type 1 error rate and overestimation of the number of quantitative trait loci found. Many authors have investigated the influence of population structure on the robustness of methods by simulation. This paper is aimed at developing further the algebraic formalization of power and type 1 error rate for some of the classical statistical methods used: simple regression, two approximate methods of mixed models involving the effect of a single nucleotide polymorphism (SNP) and a random polygenic effect (GRAMMAR and FASTA) and the transmission/disequilibrium test for quantitative traits and nuclear families. Analytical formulae were derived using matrix algebra for the first and second moments of the statistical tests, assuming a true mixed model with a polygenic effect and SNP effects.

Results

The expectation and variance of the test statistics and their marginal expectations and variances according to the distribution of genotypes and estimators of variance components are given as a function of the relationship matrix and of the heritability of the polygenic effect. These formulae were used to compute type 1 error rate and power for any kind of relationship matrix between phenotyped and genotyped individuals for any level of heritability. For the regression method, type 1 error rate increased with the variability of relationships and with heritability, but decreased with the GRAMMAR method and was not affected with the FASTA and quantitative transmission/disequilibrium test methods.

Conclusions

The formulae can be easily used to provide the correct threshold of type 1 error rate and to calculate the power when designing experiments or data collection protocols. The results concerning the efficacy of each method agree with simulation results in the literature but were generalized in this work. The power of the GRAMMAR method was equal to the power of the FASTA method at the same type 1 error rate. The power of the quantitative transmission/disequilibrium test was low. In conclusion, the FASTA method, which is very close to the full mixed model, is recommended in association mapping studies.     

An improved method for quantitative trait loci detection and identification of within-line segregation in F2 intercross designs

We present a new flexible, simple, and powerful genome-scan method (flexible intercross analysis, FIA) for detecting quantitative trait loci (QTL) in experimental line crosses. The method is based on a pure random-effects model that simultaneously models between- and within-line QTL variation for single as well as epistatic QTL. It utilizes the score statistic and thereby facilitates computationally efficient significance testing based on empirical significance thresholds obtained by means of permutations. The properties of the method are explored using simulations and analyses of experimental data. The simulations showed that the power of FIA was as good as, or better than, Haley-Knott regression and that FIA was rather insensitive to the level of allelic fixation in the founders, especially for pedigrees with few founders. A chromosome scan was conducted for a meat quality trait in an F(2) intercross in pigs where a mutation in the halothane (Ryanodine receptor, RYR1) gene with a large effect on meat quality was known to segregate in one founder line. FIA obtained significant support for the halothane-associated QTL and identified the base generation allele with the mutated allele. A genome scan was also performed in a previously analyzed chicken F(2) intercross. In the chicken intercross analysis, four previously detected QTL were confirmed at a 5% genomewide significance level, and FIA gave strong evidence (P < 0.01) for two of these QTL to be segregating within the founder lines. FIA was also extended to account for epistasis and using simulations we show that the method provides good estimates of epistatic QTL variance even for segregating QTL. Extensions of FIA and its applications on other intercross populations including backcrosses, advanced intercross lines, and heterogeneous stocks are also discussed.     

Haplotype-based association analysis via variance-components score test

Haplotypes provide a more informative format of polymorphisms for genetic association analysis than do individual single-nucleotide polymorphisms. However, the practical efficacy of haplotype-based association analysis is challenged by a trade-off between the benefits of modeling abundant variation and the cost of the extra degrees of freedom. To reduce the degrees of freedom, several strategies have been considered in the literature. They include (1) clustering evolutionarily close haplotypes, (2) modeling the level of haplotype sharing, and (3) smoothing haplotype effects by introducing a correlation structure for haplotype effects and studying the variance components (VC) for association. Although the first two strategies enjoy a fair extent of power gain, empirical evidence showed that VC methods may exhibit only similar or less power than the standard haplotype regression method, even in cases of many haplotypes. In this study, we report possible reasons that cause the underpowered phenomenon and show how the power of the VC strategy can be improved. We construct a score test based on the restricted maximum likelihood or the marginal likelihood function of the VC and identify its nontypical limiting distribution. Through simulation, we demonstrate the validity of the test and investigate the power performance of the VC approach and that of the standard haplotype regression approach. With suitable choices for the correlation structure, the proposed method can be directly applied to unphased genotypic data. Our method is applicable to a wide-ranging class of models and is computationally efficient and easy to implement. The broad coverage and the fast and easy implementation of this method make the VC strategy an effective tool for haplotype analysis, even in modern genomewide association studies.     

Relevance of genetic relationship in GWAS and genomic prediction

The objective of this study was to analyze the relevance of relationship information on the identification of low heritability quantitative trait loci (QTLs) from a genome-wide association study (GWAS) and on the genomic prediction of complex traits in human, animal and cross-pollinating populations. The simulation-based data sets included 50 samples of 1000 individuals of seven populations derived from a common population with linkage disequilibrium. The populations had non-inbred and inbred progeny structure (50 to 200) with varying number of members (5 to 20). The individuals were genotyped for 10,000 single nucleotide polymorphisms (SNPs) and phenotyped for a quantitative trait controlled by 10 QTLs and 90 minor genes showing dominance. The SNP density was 0.1 cM and the narrow sense heritability was 25%. The QTL heritabilities ranged from 1.1 to 2.9%. We applied mixed model approaches for both GWAS and genomic prediction using pedigree-based and genomic relationship matrices. For GWAS, the observed false discovery rate was kept below the significance level of 5%, the power of detection for the low heritability QTLs ranged from 14 to 50%, and the average bias between significant SNPs and a QTL ranged from less than 0.01 to 0.23 cM. The QTL detection power was consistently higher using genomic relationship matrix. Regardless of population and training set size, genomic prediction provided higher prediction accuracy of complex trait when compared to pedigree-based prediction. The accuracy of genomic prediction when there is relatedness between individuals in the training set and the reference population is much higher than the value for unrelated individuals.     

Family-based approaches: design,imputation, analysis,and beyond

Participants in the family-based analysis group at Genetic Analysis Workshop 19 addressed diverse topics, all of which used the family data. Topics addressed included questions of study design and data quality control (QC), genotype imputation to augment available sequence data, and linkage and/or association analyses. Results show that pedigree-based tests that are sensitive to genotype error may be useful for QC. Imputation quality improved with inclusion of small amounts of pedigree information used to phase the data in evaluation of 5 commonly used approaches for imputation in samples of (typically) unrelated subjects. It improved still further when pedigree-based imputation using larger pedigrees was also added. An important distinction was made between methods that do versus do not make use of Mendelian transmission in pedigrees, because this serves as a key difference between underlying models and assumptions. Methods that model relatedness generally had higher power in association testing than did analyses that carry out testing in the presence of a transmission model, but this may reflect details of implementation and/or ability of more general methods to jointly include data from larger pedigrees. In either case, for single nucleotide polymorphism–set approaches, weights that incorporate information on functional effects may be more useful than those that are based only on allele frequencies. The overall results demonstrate that family data continue to provide important information in the search for trait loci.     

Coverage and power in genomewide association studies

The ability of genomewide association studies to decipher genetic traits is driven in part by how well the measured single-nucleotide polymorphisms "cover" the unmeasured causal variants. Estimates of coverage based on standard linkage-disequilibrium measures, such as the average maximum squared correlation coefficient (r2), can lead to inaccurate and inflated estimates of the power of genomewide association studies. In contrast, use of the "cumulative r2 adjusted power" measure presented here gives more-accurate estimates of power for genomewide association studies.     

Association of the heart fatty acid-binding protein (FABP3) gene with milk traits in Manchega breed sheep

The ovine fatty acid-binding protein type 3 gene has been chosen as a functional candidate gene for milk traits. Two different single nucleotide polymorphisms (SNPs) of ovine FABP3 gene have been tested in a daughter design comprising 13 families. No association was found between estimated breeding values for milk yield, protein and fat contents (FC) and genotypes across families using anova and transmission disequilibrium test (TDT). In within-family analysis, one family showed a significant effect for FC. These results could indicate linkage disequilibrium between the FABP3 gene and a quantitative trait loci (QTL) for FC, with the heterozygous genotype associated with a positive effect in this trait.     

A variant in XPNPEP2 is associated with angioedema induced by angiotensin I-converting enzyme inhibitors

Angiotensin I-converting enzyme inhibitors (ACEi), which are used to treat common cardiovascular diseases, are associated with a potentially life-threatening adverse reaction known as angioedema (AE-ACEi). We have previously documented a significant association between AE-ACEi and low plasma aminopeptidase P (APP) activity. With eight large pedigrees, we hereby demonstrate that this quantitative trait is partially regulated by genetic factors. We tested APP activity using a variance-component QTL analysis of a 10-cM genomewide microsatellite scan enriched with seven markers over two candidate regions. We found significant linkage (LOD = 3.75) to a locus that includes the XPNPEP2 candidate gene encoding membrane-bound APP. Mutation screening of this QTL identified a large coding deletion segregating in one pedigree and an upstream single-nucleotide polymorphism (C-2399A SNP), which segregates in the remaining seven pedigrees. Measured genotype analysis strongly suggests that the linkage signal for APP activity at this locus is accounted for predominantly by the SNP association. In a separate case-control study (20 cases and 60 controls), we found significant association of this SNP to ACEi-induced AE (P=.0364). In conclusion, our findings provide supporting evidence that the C-2399A variant in XPNPEP2 is associated with reduced APP activity and a higher incidence of AE-ACEi.     

Linear models for joint association and linkage QTL mapping

Background

Populational linkage disequilibrium and within-family linkage are commonly used for QTL mapping and marker assisted selection. The combination of both results in more robust and accurate locations of the QTL, but models proposed so far have been either single marker, complex in practice or well fit to a particular family structure.

Results

We herein present linear model theory to come up with additive effects of the QTL alleles in any member of a general pedigree, conditional to observed markers and pedigree, accounting for possible linkage disequilibrium among QTLs and markers. The model is based on association analysis in the founders; further, the additive effect of the QTLs transmitted to the descendants is a weighted (by the probabilities of transmission) average of the substitution effects of founders'' haplotypes. The model allows for non-complete linkage disequilibrium QTL-markers in the founders. Two submodels are presented: a simple and easy to implement Haley-Knott type regression for half-sib families, and a general mixed (variance component) model for general pedigrees. The model can use information from all markers. The performance of the regression method is compared by simulation with a more complex IBD method by Meuwissen and Goddard. Numerical examples are provided.

Conclusion

The linear model theory provides a useful framework for QTL mapping with dense marker maps. Results show similar accuracies but a bias of the IBD method towards the center of the region. Computations for the linear regression model are extremely simple, in contrast with IBD methods. Extensions of the model to genomic selection and multi-QTL mapping are straightforward.     

Genome‐wide association study identifies quantitative trait loci affecting hematological traits in an F2 intercross between Landrace and Korean native pigs

Changes affecting the status of health and robustness can bring about physiological alterations including hematological parameters in swine. To identify quantitative trait loci (QTL) associated with eight hematological traits (one leukocyte trait, six erythrocyte traits and one platelet trait), we conducted a genome‐wide association study using the PorcineSNP60K BeadChip in a resource population derived from an intercross between Landrace and Korean native pigs. A total of 36 740 SNPs from 816 F₂ progeny were analyzed for each blood‐related trait after filtering for quality control. Data were analyzed by the genome‐wide rapid association using mixed model and regression (GRAMMAR) approach. A total of 257 significant SNPs (P < 1.36 × 10^?6) on SSC3, 6, 8, 13 and 17 were identified for blood‐related traits in this study. Interestingly, the genomic region between 17.9 and 130 Mb on SSC8 was found to be significantly associated with red blood cell, mean corpuscular volume and mean corpuscular hemoglobin. Our results include the identification of five significant SNPs within five candidate genes (KIT, IL15, TXK, ARAP2 and ERG) for hematopoiesis. Further validation of these identified SNPs could give valuable information for understanding the variation of hematological traits in pigs.     

Evaluation of multi-locus models for genome-wide association studies: a case study in sugar beet

Association mapping has become a widely applied genomic approach to dissect the genetic architecture of complex traits. A major issue for association mapping is the need to control for the confounding effects of population structure, which is commonly done by mixed models incorporating kinship information. In this case study, we employed experimental data from a large sugar beet population to evaluate multi-locus models for association mapping. As in linkage mapping, markers are selected as cofactors to control for population structure and genetic background variation. We compared different biometric models with regard to important quantitative trait locus (QTL) mapping parameters like the false-positive rate, the QTL detection power and the predictive power for the proportion of explained genotypic variance. Employing different approaches we show that the multi-locus model, that is, incorporating cofactors, outperforms the other models, including the mixed model used as a reference model. Thus, multi-locus models are an attractive alternative for association mapping to efficiently detect QTL for knowledge-based breeding.     

Efficient mapping of plant height quantitative trait loci in a sorghum association population with introgressed dwarfing genes

Of the four major dwarfing genes described in sorghum, only Dw3 has been cloned. We used association mapping to characterize the phenotypic effects of the dw3 mutation and to fine map a second, epistatic dwarfing QTL on sorghum chromosome 9 (Sb-HT9.1). Our panel of 378 sorghum inbreds includes 230 sorghum conversion (SC) lines, which are exotic lines that have been introgressed with dwarfing quantitative trait loci (QTL) from a common parent. The causal mutation in dw3 associates with reduced lower internode length and an elongation of the apex, consistent with its role as an auxin efflux carrier. Lines carrying the dw3 mutation display high haplotype homozygosity over several megabases in the Dw3 region, but most markers linked to Dw3 do not associate significantly with plant height due to allele sharing between Dw3 and dw3 individuals. Using markers with a high mutation rate and the dw3 mutation as an interaction term, significant trait associations were detected across a 7-Mb region around Sb-HT9.1, largely due to higher detection power in the SC lines. Conversely, the likely QTL interval for Sb-HT9.1 was reduced to approximately 100 kb, demonstrating that the unique structure of this association panel provides both power and resolution for a genomewide scan.