Linear mixed models have attracted considerable attention recently as a powerful and effective tool for accounting for population stratification and relatedness in genetic association tests. However, existing methods for exact computation of standard test statistics are computationally impractical for even moderate-sized genome-wide association studies. To address this issue, several approximate methods have been proposed. Here, we present an efficient exact method, which we refer to as genome-wide efficient mixed-model association (GEMMA), that makes approximations unnecessary in many contexts. This method is approximately n times faster than the widely used exact method known as efficient mixed-model association (EMMA), where n is the sample size, making exact genome-wide association analysis computationally practical for large numbers of individuals.

Genome-wide efficient mixed-model analysis for association studies.

Although genome-wide association studies (GWASs) have identified numerous loci associated with complex traits, imprecise modeling of the genetic relatedness within study samples may cause substantial inflation of test statistics and possibly spurious associations. Variance component approaches, such as efficient mixed-model association (EMMA), can correct for a wide range of sample structures by explicitly accounting for pairwise relatedness between individuals, using high-density markers to model the phenotype distribution; but such approaches are computationally impractical. We report here a variance component approach implemented in publicly available software, EMMA eXpedited (EMMAX), that reduces the computational time for analyzing large GWAS data sets from years to hours. We apply this method to two human GWAS data sets, performing association analysis for ten quantitative traits from the Northern Finland Birth Cohort and seven common diseases from the Wellcome Trust Case Control Consortium. We find that EMMAX outperforms both principal component analysis and genomic control in correcting for sample structure.

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Variance component model to account for sample structure in genome-wide association studies

Motivation: Genome-wide association studies (GWASs) have been widely used to map loci contributing to variation in complex traits and risk of diseases in humans. Accurate specification of familial relationships is crucial for family-based GWAS, as well as in population-based GWAS with unknown (or unrecognized) family structure. The family structure in a GWAS should be routinely investigated using the SNP data prior to the analysis of population structure or phenotype. Existing algorithms for relationship inference have a major weakness of estimating allele frequencies at each SNP from the entire sample, under a strong assumption of homogeneous population structure. This assumption is often untenable.

Results: Here, we present a rapid algorithm for relationship inference using high-throughput genotype data typical of GWAS that allows the presence of unknown population substructure. The relationship of any pair of individuals can be precisely inferred by robust estimation of their kinship coefficient, independent of sample composition or population structure (sample invariance). We present simulation experiments to demonstrate that the algorithm has sufficient power to provide reliable inference on millions of unrelated pairs and thousands of relative pairs (up to 3rd-degree relationships). Application of our robust algorithm to HapMap and GWAS datasets demonstrates that it performs properly even under extreme population stratification, while algorithms assuming a homogeneous population give systematically biased results. Our extremely efficient implementation performs relationship inference on millions of pairs of individuals in a matter of minutes, dozens of times faster than the most efficient existing algorithm known to us.

Availability: Our robust relationship inference algorithm is implemented in a freely available software package, KING, available for download at http://people.virginia.edu/~wc9c/KING.

Contact: wmchen@virginia.edu

Supplementary information:Supplementary data are available at Bioinformatics online.

Robust relationship inference in genome-wide association studies

Medical genetics was revolutionized during the 1980s by the application of genetic mapping to locate the genes responsible for simple Mendelian diseases. Most diseases and traits, however, do not follow simple inheritance patterns. Geneticists have thus begun taking up the even greater challenge of the genetic dissection of complex traits. Four major approaches have been developed: linkage analysis, allele-sharing methods, association studies, and polygenic analysis of experimental crosses. This article synthesizes the current state of the genetic dissection of complex traits—describing the methods, limitations, and recent applications to biological problems.

Genetic Dissection of Complex Traits

The Alzheimer Disease Genetics Consortium (ADGC) performed a genome-wide association study of late-onset Alzheimer disease using a three-stage design consisting of a discovery stage (stage 1) and two replication stages (stages 2 and 3). Both joint analysis and meta-analysis approaches were used. We obtained genome-wide significant results at MS4A4A (rs4938933; stages 1 and 2, meta-analysis P (P(M)) = 1.7 × 10(-9), joint analysis P (P(J)) = 1.7 × 10(-9); stages 1, 2 and 3, P(M) = 8.2 × 10(-12)), CD2AP (rs9349407; stages 1, 2 and 3, P(M) = 8.6 × 10(-9)), EPHA1 (rs11767557; stages 1, 2 and 3, P(M) = 6.0 × 10(-10)) and CD33 (rs3865444; stages 1, 2 and 3, P(M) = 1.6 × 10(-9)). We also replicated previous associations at CR1 (rs6701713; P(M) = 4.6 × 10(-10), P(J) = 5.2 × 10(-11)), CLU (rs1532278; P(M) = 8.3 × 10(-8), P(J) = 1.9 × 10(-8)), BIN1 (rs7561528; P(M) = 4.0 × 10(-14), P(J) = 5.2 × 10(-14)) and PICALM (rs561655; P(M) = 7.0 × 10(-11), P(J) = 1.0 × 10(-10)), but not at EXOC3L2, to late-onset Alzheimer's disease susceptibility.

/pdf/common-variants-at-ms4a4-ms4a6e-cd2ap-cd33-and-epha1-are-12f3izd2c2.pdf

Common variants at MS4A4/MS4A6E, CD2AP, CD33 and EPHA1 are associated with late-onset Alzheimer's disease.

Misspecified relationships can have serious consequences for linkage studies, resulting in either reduced power or false-positive evidence for linkage. If some individuals in the pedigree are untyped, then Mendelian errors may not be observed. Previous approaches to detection of misspecified relationships by use of genotype data were developed for sib and half-sib pairs. We extend the likelihood calculations of Goring and Ott and Boehnke and Cox to more-general relative pairs, for which identity-by-descent (IBD) status is no longer a Markov chain, and we propose a likelihood-ratio test. We also extend the identity-by-state (IBS)–based test of Ehm and Wagner to nonsib relative pairs. The likelihood-ratio test has high power, but its drawbacks include the need to construct and apply a separate Markov chain for each possible alternative relationship and the need for simulation to assess significance. The IBS-based test is simpler but has lower power. We propose two new test statistics—conditional expected IBD (EIBD) and adjusted IBS (AIBS)—designed to retain the simplicity of IBS while increasing power by taking into account chance sharing. In simulations, the power of EIBD is generally close to that of the likelihood-ratio test. The power of AIBS is higher than that of IBS, in all cases considered. We suggest a strategy of initial screening by use of EIBD and AIBS, followed by application of the likelihood-ratio test to only a subset of relative pairs, identified by use of EIBD and AIBS. We apply the methods to a Genetic Analysis Workshop 11 data set from the Collaborative Study on the Genetics of Alcoholism.

https://www.cell.com/ajhg/pdf/S0002-9297(07)64031-2.pdf

Statistical Tests for Detection of Misspecified Relationships by Use of Genome-Screen Data

Linkage disequilibrium (LD) is of great interest for gene mapping and the study of population history. We propose a multilocus model for LD, based on the decay of haplotype sharing (DHS). The DHS model is most appropriate when the LD in which one is interested is due to the introduction of a variant on an ancestral haplotype, with recombinations in succeeding generations resulting in preservation of only a small region of the ancestral haplotype around the variant. This is generally the scenario of interest for gene mapping by LD. The DHS parameter is a measure of LD that can be interpreted as the expected genetic distance to which the ancestral haplotype is preserved, or, equivalently, 1/(time in generations to the ancestral haplotype). The method allows for multiple origins of alleles and for mutations, and it takes into account missing observations and ambiguities in haplotype determination, via a hidden Markov model. Whereas most commonly used measures of LD apply to pairs of loci, the DHS measure is designed for application to the densely mapped haplotype data that are increasingly available. The DHS method explicitly models the dependence among multiple tightly linked loci on a chromosome. When the assumptions about population structure are sufficiently tractable, the estimate of LD is obtained by maximum likelihood. For more-complicated models of population history, we find means and covariances based on the model and solve a quasi-score estimating equation. Simulations show that this approach works extremely well both for estimation of LD and for fine mapping. We apply the DHS method to published data sets for cystic fibrosis and progressive myoclonus epilepsy.

https://www.cell.com/ajhg/pdf/S0002-9297(07)62337-4.pdf

Assessment of Linkage Disequilibrium by the Decay of Haplotype Sharing, with Application to Fine-Scale Genetic Mapping

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 M QLS 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 M QLS 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 M QLS detects genomewide significant association (after Bonferroni correction) with an alcoholism-related phenotype for four different single-nucleotide polymorphisms: tsc1177811 ( P =5.9×10 −7 ), tsc1750530 ( P =4.0×10 −7 ), tsc0046696 ( P =4.7×10 −7 ), and tsc0057290 ( P =5.2×10 −7 ) on chromosomes 1, 16, 18, and 18, respectively. Three of these four significant associations were not detected in previous studies analyzing these data.

http://www.downstate.edu/hbnl/documents/2007-Thornton-Case-ControlAssociationTestingwithRelatedIndividuals_AMorePowerfulQuasi-Likeli.pdf

Case-Control Association Testing with Related Individuals: A More Powerful Quasi-Likelihood Score Test

We estimated broad heritabilities (H 2 ) and narrow heritabilities (h 2 ) and conducted genomewide screens, using a novel association-based mapping approach for 20 quantitative trait loci (QTLs) among the Hutterites, a founder population that practices a communal lifestyle. Heritability estimates ranged from .21 for diastolic blood pressure (DBP) to .99 for whole-blood serotonin levels. Using a multipoint method to detect association under a recessive model we found evidence of major QTLs for six traits: low-density lipoprotein (LDL), triglycerides, lipoprotein (a) (Lp[a]), systolic blood pressure (SBP), serum cortisol, and whole-blood serotonin. Second major QTLs for Lp(a) and for cortisol were identified using a single-point method to detect association under a general two-allele model. The heritabilities for these six traits ranged from .37 for triglycerides to .99 for serotonin, and three traits (LDL, SBP, and serotonin) had significant dominance variances (i.e., H 2 1 h 2 ). Surprisingly, there was little correlation between measures of heritability and the strength of association on a genomewide screen ( ), suggesting that P 1 .50 heritability estimates per se do not identify phenotypes that are influenced by genes with major effects. The present study demonstrates the feasibility of genomewide association studies for QTL mapping. However, even in this young founder population that has extensive linkage disequilibrium, map densities !!5 cM may be required to detect all major QTLs.

https://www.cell.com/ajhg/pdf/S0002-9297(07)61323-8.pdf

The Genetic Dissection of Complex Traits in a Founder Population

Genome-wide association studies are routinely conducted to identify genetic variants that influence complex disorders. It is well known that failure to properly account for population or pedigree structure can lead to spurious association as well as reduced power. We propose a method, ROADTRIPS, for case-control association testing in samples with partially or completely unknown population and pedigree structure. ROADTRIPS uses a covariance matrix estimated from genome-screen data to correct for unknown population and pedigree structure while maintaining high power by taking advantage of known pedigree information when it is available. ROADTRIPS can incorporate data on arbitrary combinations of related and unrelated individuals and is computationally feasible for the analysis of genetic studies with millions of markers. In simulations with related individuals and population structure, including admixture, we demonstrate that ROADTRIPS provides a substantial improvement over existing methods in terms of power and type 1 error. The ROADTRIPS method can be used across a variety of study designs, ranging from studies that have a combination of unrelated individuals and small pedigrees to studies of isolated founder populations with partially known or completely unknown pedigrees. We apply the method to analyze two data sets: a study of rheumatoid arthritis in small UK pedigrees, from Genetic Analysis Workshop 15, and data from the Collaborative Study of the Genetics of Alcoholism on alcohol dependence in a sample of moderate-size pedigrees of European descent, from Genetic Analysis Workshop 14. We detect genome-wide significant association, after Bonferroni correction, in both studies.

http://www.downstate.edu/hbnl/documents/2010-Thornton-ROADTRIPScase-controlassociationtestingwithpartiallyorcompletelyunknownpopulat.pdf

Mary Sara McPeek

Papers

Statistical Tests for Detection of Misspecified Relationships by Use of Genome-Screen Data

Assessment of Linkage Disequilibrium by the Decay of Haplotype Sharing, with Application to Fine-Scale Genetic Mapping

Case-Control Association Testing with Related Individuals: A More Powerful Quasi-Likelihood Score Test

The Genetic Dissection of Complex Traits in a Founder Population

ROADTRIPS: Case-Control Association Testing with Partially or Completely Unknown Population and Pedigree Structure