Linkage analysis and association analysis in the presence of linkage using age at onset of COGA alcoholism data

Complex disease mapping usually involves a combination of linkage and association techniques. Linkage analysis can scan the entire genome in a few hundred tests. Association tests may involve an even greater number of tests. However, association tests can localize the susceptibility genes more accurately. Using a recently developed combined linkage and association strategy, we analyzed a subset of the Collaborative Study on the Genetics of Alcoholism (COGA) data for the Genetic Analysis Workshop 14 (GAW14). In this analysis, we first employed linkage analysis based on frailty models that take into account age of onset information to establish which regions along the chromosome are likely to harbor disease susceptibility genes for alcohol dependence. Second, we used an association analysis by exploiting linkage disequilibrium to narrow down the peak regions. We also compare the methods with mean identity-by-descent tests and transmission/disequilibrium tests that do not use age of onset information.     

Linkage analysis of "necessary" disease loci versus "susceptibility" loci.

The association of some diseases with specific alleles of certain genetic markers has been difficult to explain. Several explanations have been proposed for the phenomenon of association, e.g. the existence of multiple, interacting genes (epistasis) or a disease locus in linkage disequilibrium with the marker locus. One might suppose that when marker data from families with associated diseases are analyzed for linkage, the existence of the association would assure that linkage will be found, and found at a tight recombination fraction. In fact, however, linkage analyses of some diseases associated with HLA, as well as diseases associated with alleles at other loci located throughout the genome, show significant evidence against linkage, and others show loose linkage, to the puzzlement of many researchers. In part, the puzzlement arises because linkage analysis is ideal for looking for loci that are necessary, even if not sufficient, for disease expression but may be much less useful for finding loci that are neither necessary nor sufficient for disease expression (so-called susceptibility loci). This work explores what happens when one looks for linkage to susceptibility loci. A susceptibility locus in this case means that the allele increases risk but is neither necessary nor sufficient for disease expression. It might be either an allele at the marker locus itself that is increasing susceptibility or an allele at a locus in linkage disequilibrium with the marker. This work uses computer simulation to examine how linkage analyses behave when confronted with data from such a model.(ABSTRACT TRUNCATED AT 250 WORDS)     

Identification of Genetic Loci Associated with Quality Traits in Almond via Association Mapping

To design an appropriate association study, we need to understand population structure and the structure of linkage disequilibrium within and among populations as well as in different regions of the genome in an organism. In this study, we have used a total of 98 almond accessions, from five continents located and maintained at the Centro de Investigación y Tecnología Agroalimentaria de Aragón (CITA; Spain), and 40 microsatellite markers. Population structure analysis performed in ‘Structure’ grouped the accessions into two principal groups; the Mediterranean (Western-Europe) and the non-Mediterranean, with K = 3, being the best fit for our data. There was a strong subpopulation structure with linkage disequilibrium decaying with increasing genetic distance resulting in lower levels of linkage disequilibrium between more distant markers. A significant impact of population structure on linkage disequilibrium in the almond cultivar groups was observed. The mean r² value for all intra-chromosomal loci pairs was 0.040, whereas, the r² for the inter-chromosomal loci pairs was 0.036. For analysis of association between the markers and phenotypic traits, five models comprising both general linear models and mixed linear models were selected to test the marker trait associations. The mixed linear model (MLM) approach using co-ancestry values from population structure and kinship estimates (K model) as covariates identified a maximum of 16 significant associations for chemical traits and 12 for physical traits. This study reports for the first time the use of association mapping for determining marker-locus trait associations in a world-wide almond germplasm collection. It is likely that association mapping will have the most immediate and largest impact on the tier of crops such as almond with the greatest economic value.     

Candidate gene analysis for quantitative traits using the transmission disequilibrium test: the example of the melanocortin 4-receptor in pigs

Population-wide associations between loci due to linkage disequilibrium can be used to map quantitative trait loci (QTL) with high resolution. However, spurious associations between markers and QTL can also arise as a consequence of population stratification. Statistical methods that cannot differentiate between loci associations due to linkage disequilibria from those caused in other ways can render false-positive results. The transmission-disequilibrium test (TDT) is a robust test for detecting QTL. The TDT exploits within-family associations that are not affected by population stratification. However, some TDTs are formulated in a rigid form, with reduced potential applications. In this study we generalize TDT using mixed linear models to allow greater statistical flexibility. Allelic effects are estimated with two independent parameters: one exploiting the robust within-family information and the other the potentially biased between-family information. A significant difference between these two parameters can be used as evidence for spurious association. This methodology was then used to test the effects of the fourth melanocortin receptor (MC4R) on production traits in the pig. The new analyses supported the previously reported results; i.e., the studied polymorphism is either causal or in very strong linkage disequilibrium with the causal mutation, and provided no evidence for spurious association.     

On the utility of linkage disequilibrium as a statistic for identifying targets of positive selection in nonequilibrium populations

A critically important challenge in empirical population genetics is distinguishing neutral nonequilibrium processes from selective forces that produce similar patterns of variation. We here examine the extent to which linkage disequilibrium (i.e., nonrandom associations between markers) improves this discrimination. We show that patterns of linkage disequilibrium recently proposed to be unique to hitchhiking models are replicated under nonequilibrium neutral models. We also demonstrate that jointly considering spatial patterns of association among variants alongside the site-frequency spectrum is nonetheless of value. Through a comparison of models of equilibrium neutrality, nonequilibrium neutrality, equilibrium hitchhiking, nonequilibrium hitchhiking, and recurrent hitchhiking, we evaluate a linkage disequilibrium (LD) statistic (omega(max)) that appears to have power to identify regions recently shaped by positive selection. Most notably, for demographic parameters relevant to non-African populations of Drosophila melanogaster, we demonstrate that selected loci are distinguishable from neutral loci using this statistic.     

Association studies under general disease models

There is great expectation that the levels of association found between genetic markers and disease status will play a role in the location of disease genes. This expectation follows from regarding association as being proportional to linkage disequilibrium and therefore inversely related to recombination value. For disease genes with more than two alleles, the association measure is instead a weighted average of linkage disequilibria, with the weights depending on allele frequencies and genotype susceptibilities at the disease loci. There is no longer a simple relationship, even in expectation, with recombination. We adopt a general framework to examine association mapping methods which helps to clarify the nature of case-control and transmission/disequilibrium-type tests and reveals the relationship between measures of association and coefficients of linkage disequilibrium. In particular, we can show the consequences of additive and nonadditive effects at the trait locus on the behavior of these tests. These concepts have a natural extension to marker haplotypes. The association of two-locus marker haplotypes with disease phenotype depends on a weighted average of three-locus disequilibria (two markers with each disease locus). It is likely that these two-marker analyses will provide additional information in association mapping studies.     

Population structure in admixed populations: effect of admixture dynamics on the pattern of linkage disequilibrium

Gene flow between genetically distinct populations creates linkage disequilibrium (admixture linkage disequilibrium [ALD]) among all loci (linked and unlinked) that have different allele frequencies in the founding populations. We have explored the distribution of ALD by using computer simulation of two extreme models of admixture: the hybrid-isolation (HI) model, in which admixture occurs in a single generation, and the continuous-gene-flow (CGF) model, in which admixture occurs at a steady rate in every generation. Linkage disequilibrium patterns in African American population samples from Jackson, MS, and from coastal South Carolina resemble patterns observed in the simulated CGF populations, in two respects. First, significant association between two loci (FY and AT3) separated by 22 cM was detected in both samples. The retention of ALD over relatively large (>10 cM) chromosomal segments is characteristic of a CGF pattern of admixture but not of an HI pattern. Second, significant associations were also detected between many pairs of unlinked loci, as observed in the CGF simulation results but not in the simulated HI populations. Such a high rate of association between unlinked markers in these populations could result in false-positive linkage signals in an admixture-mapping study. However, we demonstrate that by conditioning on parental admixture, we can distinguish between true linkage and association resulting from shared ancestry. Therefore, populations with a CGF history of admixture not only are appropriate for admixture mapping but also have greater power for detection of linkage disequilibrium over large chromosomal regions than do populations that have experienced a pattern of admixture more similar to the HI model, if methods are employed that detect and adjust for disequilibrium caused by continuous admixture.     

The transmission/disequilibrium test: history, subdivision, and admixture.

Disease association with a genetic marker is often taken as a preliminary indication of linkage with disease susceptibility. However, population subdivision and admixture may lead to disease association even in the absence of linkage. In a previous paper, we described a test for linkage (and linkage disequilibrium) between a genetic marker and disease susceptibility; linkage is detected by this test only if association is also present. This transmission/disequilibrium test (TDT) is carried out with data on transmission of marker alleles from parents heterozygous for the marker to affected offspring. The TDT is a valid test for linkage and association, even when the association is caused by population subdivision and admixture. In the previous paper, we did not explicitly consider the effect of recent history on population structure. Here we extend the previous results by examining in detail the effects of subdivision and admixture, viewed as processes in population history. We describe two models for these processes. For both models, we analyze the properties of (a) the TDT as a test for linkage (and association) between marker and disease and (b) the conventional contingency statistic used with family data to test for population association. We show that the contingency test statistic does not have a chi 2 distribution if subdivision or admixture is present. In contrast, the TDT remains a valid chi 2 statistic for the linkage hypothesis, regardless of population history.     

A Discordant-Sibship Test for Disequilibrium and Linkage: No Need for Parental Data

The sibship disequilibrium test (SDT) is designed to detect both linkage in the presence of association and association in the presence of linkage (linkage disequilibrium). The test does not require parental data but requires discordant sibships with at least one affected and one unaffected sibling. The SDT has many desirable properties: it uses all the siblings in the sibship; it remains valid if there are misclassifications of the affectation status; it does not detect spurious associations due to population stratification; asymptotically it has a chi2 distribution under the null hypothesis; and exact P values can be easily computed for a biallelic marker. We show how to extend the SDT to markers with multiple alleles and how to combine families with parents and data from discordant sibships. We discuss the power of the test by presenting sample-size calculations involving a complex disease model, and we present formulas for the asymptotic relative efficiency (which is approximately the ratio of sample sizes) between SDT and the transmission/disequilibrium test (TDT) for special family structures. For sib pairs, we compare the SDT to a test proposed both by Curtis and, independently, by Spielman and Ewens. We show that, for discordant sib pairs, the SDT has good power for testing linkage disequilibrium relative both to Curtis''s tests and to the TDT using trios comprising an affected sib and its parents. With additional sibs, we show that the SDT can be more powerful than the TDT for testing linkage disequilibrium, especially for disease prevalence >.3.     

Towards linkage analysis with markers in linkage disequilibrium by graphical modelling

We review recent developments of MCMC integration methods for computations on graphical models for two applications in statistical genetics: modelling allelic association and pedigree based linkage analysis. We discuss and illustrate estimation of graphical models from haploid and diploid genotypes, and the importance of MCMC updating schemes beyond what is strictly necessary for irreducibility. We then outline an approach combining these methods to compute linkage statistics when alleles at the marker loci are in linkage disequilibrium. Other extensions suitable for analysis of SNP genotype data in pedigrees are also discussed and programs that implement these methods, and which are available from the author's web site, are described. We conclude with a discussion of how this still experimental approach might be further developed.     

The immunogenetics of multiple sclerosis

The discoveries in the 1970s of strong associations between various diseases and certain human leukocyte antigen (HLA) factors were a revolution within genetic epidemiology in the last century by demonstrating for the first time how genetic markers can help unravel the genetics of disorders with complex genetic backgrounds. HLA controls immune response genes and HLA associations indicate the involvement of autoimmunity. Multiple sclerosis (MS) was one of the first conditions proven to be HLA associated involving primarily HLA class II factors. We review how HLA studies give fundamental information on the genetics of the susceptibility to MS, on the importance of linkage disequilibrium in association studies, and on the pathogenesis of MS. The HLA-DRB1*1501 molecule may explain about 50% of MS cases and its role in the pathogenesis is supported by studies of transgenic mice. Studies of polymorphic non-HLA genetic markers are discussed based on linkage studies and candidate gene approaches including complete genome scans. No other markers have so far rivaled the importance of HLA in the genetic susceptibility to MS. Recently, large international collaborations provided strong evidence for the involvement of polymorphism of two cytokine receptor genes in the pathogenesis of MS: the interleukin 7 receptor alpha chain gene (IL7RA) on chromosome 5p13 and the interleukin 2 receptor alpha chain gene (IL2RA (=CD25)) on chromosome 10p15. It is estimated that the C allele of a single nucleotide polymorphism, rs6897932, within the alternative spliced exon 6 of IL7RA is involved in about 30% of MS cases.     

Genetics of sputum gene expression in chronic obstructive pulmonary disease

Previous expression quantitative trait loci (eQTL) studies have performed genetic association studies for gene expression, but most of these studies examined lymphoblastoid cell lines from non-diseased individuals. We examined the genetics of gene expression in a relevant disease tissue from chronic obstructive pulmonary disease (COPD) patients to identify functional effects of known susceptibility genes and to find novel disease genes. By combining gene expression profiling on induced sputum samples from 131 COPD cases from the ECLIPSE Study with genomewide single nucleotide polymorphism (SNP) data, we found 4315 significant cis-eQTL SNP-probe set associations (3309 unique SNPs). The 3309 SNPs were tested for association with COPD in a genomewide association study (GWAS) dataset, which included 2940 COPD cases and 1380 controls. Adjusting for 3309 tests (p<1.5e-5), the two SNPs which were significantly associated with COPD were located in two separate genes in a known COPD locus on chromosome 15: CHRNA5 and IREB2. Detailed analysis of chromosome 15 demonstrated additional eQTLs for IREB2 mapping to that gene. eQTL SNPs for CHRNA5 mapped to multiple linkage disequilibrium (LD) bins. The eQTLs for IREB2 and CHRNA5 were not in LD. Seventy-four additional eQTL SNPs were associated with COPD at p<0.01. These were genotyped in two COPD populations, finding replicated associations with a SNP in PSORS1C1, in the HLA-C region on chromosome 6. Integrative analysis of GWAS and gene expression data from relevant tissue from diseased subjects has located potential functional variants in two known COPD genes and has identified a novel COPD susceptibility locus.     

Analysis of the MTHFR gene linkage disequilibrium structure and association of polymorphic gene variants with coronary atherosclerosis

Analysis of the genome-specific linkage disequilibrium patterns in certain populations is a highly promising approach to the identification of functional variants that underlie susceptibility to complex diseases. In the present study, the linkage disequilibrium patterns of the methylenetetrahydrofolate reductase gene (MTHFR) were examined in a group of patients with coronary atherosclerosis (coronary artery disease, CAD) and in a control sample from the Russian population. It was demonstrated that in the samples from one population, which were differentiated by the presence or absence of CAD, the MTHFR linkage disequilibrium patterns had similar features. Association of the MTHFR rs7533315 and rs2066462 polymorphisms with CAD was demonstrated. In addition, the evolution of the haplotypes and their role in the formation of CAD in the Russian population was reconstructed. The data on the association between genetic variability in the MTHFR locus and pathogenetically important indices of lipid metabolism were obtained. The high informativeness of the haplotype approach in case-control tests for associations with CAD was demonstrated.     

A genealogical interpretation of linkage disequilibrium

The degree of association between alleles at different loci, or linkage disequilibrium, is widely used to infer details of evolutionary processes. Here I explore how associations between alleles relate to properties of the underlying genealogy of sequences. Under the neutral, infinite-sites assumption I show that there is a direct correspondence between the covariance in coalescence times at different parts of the genome and the degree of linkage disequilibrium. These covariances can be calculated exactly under the standard neutral model and by Monte Carlo simulation under different demographic models. I show that the effects of population growth, population bottlenecks, and population structure on linkage disequilibrium can be described through their effects on the covariance in coalescence times.     

Transmission test for linkage disequilibrium: the insulin gene region and insulin-dependent diabetes mellitus (IDDM).

A population association has consistently been observed between insulin-dependent diabetes mellitus (IDDM) and the "class 1" alleles of the region of tandem-repeat DNA (5'' flanking polymorphism [5''FP]) adjacent to the insulin gene on chromosome 11p. This finding suggests that the insulin gene region contains a gene or genes contributing to IDDM susceptibility. However, several studies that have sought to show linkage with IDDM by testing for cosegregation in affected sib pairs have failed to find evidence for linkage. As means for identifying genes for complex diseases, both the association and the affected-sib-pairs approaches have limitations. It is well known that population association between a disease and a genetic marker can arise as an artifact of population structure, even in the absence of linkage. On the other hand, linkage studies with modest numbers of affected sib pairs may fail to detect linkage, especially if there is linkage heterogeneity. We consider an alternative method to test for linkage with a genetic marker when population association has been found. Using data from families with at least one affected child, we evaluate the transmission of the associated marker allele from a heterozygous parent to an affected offspring. This approach has been used by several investigators, but the statistical properties of the method as a test for linkage have not been investigated. In the present paper we describe the statistical basis for this "transmission test for linkage disequilibrium" (transmission/disequilibrium test [TDT]). We then show the relationship of this test to tests of cosegregation that are based on the proportion of haplotypes or genes identical by descent in affected sibs. The TDT provides strong evidence for linkage between the 5''FP and susceptibility to IDDM. The conclusions from this analysis apply in general to the study of disease associations, where genetic markers are usually closely linked to candidate genes. When a disease is found to be associated with such a marker, the TDT may detect linkage even when haplotype-sharing tests do not.     

DNA haplotype analysis suggests linkage disequilibrium in the human insulin receptor gene

Summary Haplotypes of the insulin receptor gene were resolved in parents from Scandinavian nuclear families by studying the segregation of seven restriction fragment length polymorphisms (RFLPs). Of 97 unrelated parents, 41 had non-insulin-dependent diabetes mellitus (NIDDM). Considerable linkage disequilibrium in the region of the insulin receptor gene was found. Pairwise non-random associations were found between proximate RFLP sites, indicating the absence of recombinational hot spots between these sites. Thus, association studies between DNA polymorphisms at this locus and disease susceptibility genes could well be feasible in this population. Differences in the distribution of insulin receptor haplotypes were examined between NIDDM patients and healthy subjects. However, the differences observed were not statistically significant.     

Linkage disequilibrium clustering‐based approach for association mapping with tightly linked genomewide data

Genomewide association studies (GWAS) aim to identify genetic markers strongly associated with quantitative traits by utilizing linkage disequilibrium (LD) between candidate genes and markers. However, because of LD between nearby genetic markers, the standard GWAS approaches typically detect a number of correlated SNPs covering long genomic regions, making corrections for multiple testing overly conservative. Additionally, the high dimensionality of modern GWAS data poses considerable challenges for GWAS procedures such as permutation tests, which are computationally intensive. We propose a cluster‐based GWAS approach that first divides the genome into many large nonoverlapping windows and uses linkage disequilibrium network analysis in combination with principal component (PC) analysis as dimensional reduction tools to summarize the SNP data to independent PCs within clusters of loci connected by high LD. We then introduce single‐ and multilocus models that can efficiently conduct the association tests on such high‐dimensional data. The methods can be adapted to different model structures and used to analyse samples collected from the wild or from biparental F₂ populations, which are commonly used in ecological genetics mapping studies. We demonstrate the performance of our approaches with two publicly available data sets from a plant (Arabidopsis thaliana) and a fish (Pungitius pungitius), as well as with simulated data.     

Review and evaluation of methods correcting for population stratification with a focus on underlying statistical principles

When two or more populations have been separated by geographic or cultural boundaries for many generations, drift, spontaneous mutations, differential selection pressures and other factors may lead to allele frequency differences among populations. If these 'parental' populations subsequently come together and begin inter-mating, disequilibrium among linked markers may span a greater genetic distance than it typically does among populations under panmixia [see glossary]. This extended disequilibrium can make association studies highly effective and more economical than disequilibrium mapping in panmictic populations since less marker loci are needed to detect regions of the genome that harbor phenotype-influencing loci. However, under some circumstances, this process of intermating (as well as other processes) can produce disequilibrium between pairs of unlinked loci and thus create the possibility of confounding or spurious associations due to this population stratification. Accordingly, researchers are advised to employ valid statistical tests for linkage disequilibrium mapping allowing conduct of genetic association studies that control for such confounding. Many recent papers have addressed this need. We provide a comprehensive review of advances made in recent years in correcting for population stratification and then evaluate and synthesize these methods based on statistical principles such as (1) randomization, (2) conditioning on sufficient statistics, and (3) identifying whether the method is based on testing the genotype-phenotype covariance (conditional upon familial information) and/or testing departures of the marginal distribution from the expected genotypic frequencies.     

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.