Ignoring linkage disequilibrium among tightly linked markers induces false-positive evidence of linkage for affected sib pair analysis

Most multipoint linkage programs assume linkage equilibrium among the markers being studied. The assumption is appropriate for the study of sparsely spaced markers with intermarker distances exceeding a few centimorgans, because linkage equilibrium is expected over these intervals for almost all populations. However, with recent advancements in high-throughput genotyping technology, much denser markers are available, and linkage disequilibrium (LD) may exist among the markers. Applying linkage analyses that assume linkage equilibrium to dense markers may lead to bias. Here, we demonstrated that, when some or all of the parental genotypes are missing, assuming linkage equilibrium among tightly linked markers where strong LD exists can cause apparent oversharing of multipoint identity by descent (IBD) between sib pairs and false-positive evidence for multipoint model-free linkage analysis of affected sib pair data. LD can also mimic linkage between a disease locus and multiple tightly linked markers, thus causing false-positive evidence of linkage using parametric models, particularly when heterogeneity LOD score approaches are applied. Bias can be eliminated by inclusion of parental genotype data and can be reduced when additional unaffected siblings are included in the analysis.     

Transmission/disequilibrium tests using multiple tightly linked markers

Transmission/disequilibrium tests have attracted much attention in genetic studies of complex traits because (a) their power to detect genes having small to moderate effects may be greater than that of other linkage methods and (b) they are robust against population stratification. Highly polymorphic markers have become available throughout the human genome, and many such markers can be studied within short physical distances. Studies using multiple tightly linked markers are more informative than those using single markers. However, such information has not been fully utilized by existing statistical methods, resulting in possibly substantial loss of information in the identification of genes underlying complex traits. In this article, we propose novel statistical methods to analyze multiple tightly linked markers. Simulation studies comparing our methods versus existing methods suggest that our methods are more powerful. Finally, we apply the proposed methods to study genetic linkage between the dopamine D2 receptor locus and alcoholism.     

Transmission/disequilibrium test based on haplotype sharing for tightly linked markers

Studies using haplotypes of multiple tightly linked markers are more informative than those using a single marker. However, studies based on multimarker haplotypes have some difficulties. First, if we consider each haplotype as an allele and use the conventional single-marker transmission/disequilibrium test (TDT), then the rapid increase in the degrees of freedom with an increasing number of markers means that the statistical power of the conventional tests will be low. Second, the parental haplotypes cannot always be unambiguously reconstructed. In the present article, we propose a haplotype-sharing TDT (HS-TDT) for linkage or association between a disease-susceptibility locus and a chromosome region in which several tightly linked markers have been typed. This method is applicable to both quantitative traits and qualitative traits. It is applicable to any size of nuclear family, with or without ambiguous phase information, and it is applicable to any number of alleles at each of the markers. The degrees of freedom (in a broad sense) of the test increase linearly as the number of markers considered increases but do not increase as the number of alleles at the markers increases. Our simulation results show that the HS-TDT has the correct type I error rate in structured populations and that, in most cases, the power of HS-TDT is higher than the power of the existing single-marker TDTs and haplotype-based TDTs.     

Evaluation of linkage disequilibrium measures between multi-allelic markers as predictors of linkage disequilibrium between markers and QTL

Effectiveness of marker-assisted selection (MAS) and quantitative trait loci (QTL) mapping using population-wide linkage disequilibrium (LD) between markers and QTL depends on the extent of LD and how it declines with distance in a population. Because marker-QTL LD cannot be observed directly, the objective of this study was to evaluate alternative measures of observable LD between multi-allelic markers as predictors of usable LD of multi-allelic markers with presumed biallelic QTL. Observable LD between marker pairs was evaluated using eight existing measures and one new measure. These consisted of two pooled and standardized measures of LD between pairs of alleles at two markers based on Lewontin's LD measure, two pooled measures of squared correlations between alleles, one standardized measure using Hardy-Weinberg heterozygosities, and four measures based on the chi-square statistic for testing for association between alleles at two loci. In simulated populations with a range of LD generated by drift and a range of marker polymorphism, marker-marker LD measured by a standardized chi-square statistic (denoted chi(2')) was found to be the best predictor of useable marker-QTL LD for a group of multi-allelic markers. Estimates of the level and decline of marker-marker LD with distance obtained from chi(2') were linearly and highly correlated with usable LD of those markers with QTL across population structures and marker polymorphism. Corresponding relationships were poorer for the other marker-marker LD measures. Therefore, when LD is generated by drift, chi(2') is recommended to quantify the amount and extent of usable LD in a population for QTL mapping and MAS based on multi-allelic markers.     

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.     

Evaluation of linkage disequilibrium measures between multi-allelic markers as predictors of linkage disequilibrium between single nucleotide polymorphisms

Effectiveness of marker-assisted selection (MAS) and quantitative trait locus (QTL) mapping using population-wide linkage disequilibrium (LD) between markers and QTLs depends on the extent of LD and how it declines with distance between markers and QTLs in a population. Marker-QTL LD can be predicted from LD between markers. Our previous work evaluated LD measures between multi-allelic markers as predictors of usable LD of multi-allelic markers with QTLs. Since single nucleotide polymorphisms (SNPs) are the current marker of choice for high-density genotyping and LD-mapping of QTLs, the objective of this study was to use LD between multi-allelic markers to predict LD among biallelic SNPs or between SNPs and QTLs. Observable LD between multi-allelic markers was evaluated using nine measures. These included two pooled and standardized measures of LD between pairs of alleles at two markers based on Lewontin's LD measure, two pooled measures of squared correlations between alleles, one standardized measure using Hardy-Weinberg heterozygosities, and four measures based on the chi-square statistic for testing for association between alleles at two loci. The standardized chi-square measure that best predicted usable LD between multi-allelic markers and QTLs, based on our previous work, overestimated usable SNP-SNP or SNP-QTL LD. Instead, three other measures were found to be good predictors of usable SNP-SNP or SNP-QTL LD when LD is generated by drift. Therefore, the LD measure between multi-allelic markers that is best for predicting usable LD in a population depends on the type of markers (i.e. multi-allelic or biallelic) that will eventually be used for QTL mapping or MAS.     

The influence of gene conversion on linkage disequilibrium around a selective sweep

In a 2007 article, McVean studied the effect of recombination on linkage disequilibrium (LD) between two neutral loci located near a third locus that has undergone a selective sweep. The results demonstrated that two loci on the same side of a selected locus might show substantial LD, whereas the expected LD for two loci on opposite sides of a selected locus is zero. In this article, we extend McVean's model to include gene conversion. We show that one of the conclusions is strongly affected by gene conversion: when gene conversion is present, there may be substantial LD between two loci on opposite sides of a selective sweep.     

Distinguishing recombination and intragenic gene conversion by linkage disequilibrium patterns

Deterministic theory suggests that reciprocal recombination and intragenic, interallelic conversion have different effects on the linkage disequilibrium between a pair of genetic markers. Under a model of reciprocal recombination, the decay rate of linkage disequilibrium depends on the distance between the two markers, while under conversion the decay rate is independent of this distance, provided that conversion tracts are short. A population genetic three-locus model provides a function Q of two-locus linkage disequilibria. Viewed as a random variable, Q is the basis for a test of the relative impact of conversion and recombination. This test requires haplotype frequency data of a sufficiently variable three-locus system. One of the few examples currently available is data from the Human Leukocyte Antigen (HLA) class I genes of three Amerindian populations. We find that conversion may have played a dominant role in shaping haplotype patterns over short stretches of DNA, whereas reciprocal recombination may have played a greater role over longer stretches of DNA. However, in order to draw firm conclusions more independent data are necessary.     

The hitchhiking effect on linkage disequilibrium between linked neutral loci

We analyzed a three-locus model of genetic hitchhiking with one locus experiencing positive directional selection and two partially linked neutral loci. Following the original hitchhiking approach by Maynard Smith and Haigh, our analysis is purely deterministic. In the first half of the selected phase after a favored mutation has entered the population, hitchhiking may lead to a strong increase of linkage disequilibrium (LD) between the two neutral sites if both are <0.1 s away from the selected site (where s is the selection coefficient). In the second half of the selected phase, the main effect of hitchhiking is to destroy LD. This occurs very quickly (before the end of the selected phase) when the selected site is between both neutral loci. This pattern cannot be attributed to the well-known variation-reducing effect of hitchhiking but is a consequence of secondary hitchhiking effects on the recombinants created in the selected phase. When the selected site is outside the neutral loci (which are, say, <0.1s apart), however, a fast decay of LD is observed only if the selected site is in the immediate neighborhood of one of the neutral sites (i.e., if the recombination rate r between the selected site and one of the neutral sites satisfies r<0.1 s). If the selected site is far away from the neutral sites (say, r > 0.3 s), the decay rate of LD approaches that of neutrality. Averaging over a uniform distribution of initial gamete frequencies shows that the expected LD at the end of the hitchhiking phase is driven toward zero, while the variance is increased when the selected site is well outside the two neutral sites. When the direction of LD is polarized with respect to the more common allele at each neutral site, hitchhiking creates more positive than negative linkage disequilibrium. Thus, hitchhiking may have a distinctively patterned LD-reducing effect, in particular near the target of selection.     

Nonparametric disequilibrium mapping of functional sites using haplotypes of multiple tightly linked single-nucleotide polymorphism markers

As the speed and efficiency of genotyping single-nucleotide polymorphisms (SNPs) increase, using the SNP map, it becomes possible to evaluate the extent to which a common haplotype contributes to the risk of disease. In this study we propose a new procedure for mapping functional sites or regions of a candidate gene of interest using multiple linked SNPs. Based on a case-parent trio family design, we use expectation-maximization (EM) algorithm-derived haplotype frequency estimates of multiple tightly linked SNPs from both unambiguous and ambiguous families to construct a contingency statistic S for linkage disequilibrium (LD) analysis. In the procedure, a moving-window scan for functional SNP sites or regions can cover an unlimited number of loci except for the limitation of computer storage. Within a window, all possible widths of haplotypes are utilized to find the maximum statistic S* for each site (or locus). Furthermore, this method can be applied to regional or genome-wide scanning for determining linkage disequilibrium using SNPs. The sensitivity of the proposed procedure was examined on the simulated data set from the Genetic Analysis Workshop (GAW) 12. Compared with the conventional and generalized TDT methods, our procedure is more flexible and powerful.     

The detection of linkage disequilibrium between closely linked markers: RFLPs at the AI-CIII apolipoprotein genes.

Study of very closely linked DNA variants at various loci has frequently shown linkage disequilibrium. We studied three closely linked RFLPs at the apolipoprotein AI-CIII locus. Two variants detected by MspI and SstI were in strong linkage disequilibrium; but when conventional statistical tests were used, a third variant (PstI), located between the MspI and SstI markers, appeared to be in linkage equilibrium with these two "outside" markers. Similar discrepancies from the expected monotone relationship between physical distance and linkage disequilibrium have been reported by others. To investigate these discrepancies, the power to detect linkage disequilibrium was calculated. It could be shown that, for the gene frequencies encountered, very large sample sizes would be required to demonstrate negative (i.e., repulsion-phase) linkage disequilibrium. Such numbers are usually very difficult to attain in human studies. Failure to demonstrate linkage disequilibrium by conventional methods therefore does not imply its absence. Appropriate nomograms and tables are provided.     

The Friedreich ataxia gene is assigned to chromosome 9q13-q21 by mapping of tightly linked markers and shows linkage disequilibrium with D9S15.

Chamberlain et al. have assigned the gene for Friedreich ataxia (FA), a recessive neurodegenerative disorder, to chromosome 9, and have proposed a regional localization in the proximal short arm (9p22-cen), on the basis of linkage to D9S15 and to interferon-beta (IFNB), the latter being localized in 9p22. We confirmed more recently the close linkage to D9S15 in another set of families but found much looser linkage to IFNB. We also reported another closely linked marker, D9S5. Additional families have now been studied, and our updated lod scores are z = 14.30 at theta = .00 for D9S15-FA linkage and z = 6.30 at theta = .00 for D9S5-FA linkage. Together with the recent data of Chamberlain et al., this shows that D9S15 is very likely within 1 cM of the FA locus. We have found very significant linkage disequilibrium (delta Std = .28, chi 2 = 9.71, P less than .01) between FA and the D9S15 MspI RFLP in French families, which further supports the very close proximity of these two loci. No recombination between D9S5 and D9S15 was found in the FA families or Centre d'Etude du Polymorphisme Humain families (z = 9.30 at theta = .00). Thus D9S5, D9S15, and FA define a cluster of tightly linked loci. We have mapped D9S5 by in situ hybridization to 9q13-q21, and, accordingly, we assign the D9S5, D9S15, and FA cluster to the proximal part of chromosome 9 long arm, close to the heterochromatic region.     

A survey on haplotyping algorithms for tightly linked markers

Two grand challenges in the postgenomic era are to develop a detailed understanding of heritable variation in the human genome, and to develop robust strategies for identifying the genetic contribution to diseases and drug responses. Haplotypes of single nucleotide polymorphisms (SNPs) have been suggested as an effective representation of human variation, and various haplotype-based association mapping methods for complex traits have been proposed in the literature. However, humans are diploid and, in practice, genotype data instead of haplotype data are collected directly. Therefore, efficient and accurate computational methods for haplotype reconstruction are needed and have recently been investigated intensively, especially for tightly linked markers such as SNPs. This paper reviews statistical and combinatorial haplotyping algorithms using pedigree data, unrelated individuals, or pooled samples.     

Ethnic-difference markers for use in mapping by admixture linkage disequilibrium

Mapping by admixture linkage disequilibrium (MALD) is a potentially powerful technique for the mapping of complex genetic diseases. The practical requirements of this method include (a) a set of markers spanning the genome that have large allele-frequency differences between the parental ethnicities contributing to the admixed population and (b) an understanding of the extent of admixture in the study population. To this end, a DNA-pooling technique was used to screen microsatellite and diallelic insertion/deletion markers for allele-frequency differences between putative representatives of the parental populations of the admixed Mexican American (MA) and African American (AA) populations. Markers with promising pooled differences were then confirmed by individual genotyping in both the parental and admixed populations. For the MA population, screening of >600 markers identified 151 ethnic-difference markers (EDMs) with delta>0.30 (where delta is the absolute value of each allele-frequency difference between two populations, summed over all marker alleles and divided by two) that are likely to be useful for MALD analysis. For the AA population, analysis of >400 markers identified 97 EDMs. In addition, individual genotyping of these markers in Pima Amerindians, Yavapai Amerindians, European American (EA) individuals, Africans from Zimbabwe, MA individuals, and AA individuals, as well as comparison to the CEPH genotyping set, suggests that the differences between subpopulations of an ethnicity are small for many markers with large interethnic differences. Estimates of admixture that are based on individual genotyping of these markers are consistent with a 60% EA:40% Amerindian contribution to MA populations and with a 20% EA:80% African contribution to AA populations. Taken together, these data suggest that EDMs with large interpopulation and small intrapopulation differences can be readily identified for MALD studies in both AA and MA populations.     

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.     

Efficiency of typing unaffected relatives in an affected-sib-pair linkage study with single-locus and multiple tightly linked markers.

In an affected-sib-pair study, the parents are often unavailable for typing, particularly for diseases of late onset. In many cases, however, it is possible to sample unaffected siblings. It is therefore desirable to assess the contribution of such siblings to the power of such a study. The likelihood ratio introduced by Risch and improved by Holmans was extended to incorporate data from unaffected siblings. Tests based on two likelihoods were considered: the full likelihood of the data, based on the identity-by-descent (IBD) sharing states of the entire sibship, and a pseudolikelihood based on the IBD sharing states of the affected pair only, using the unaffected siblings to infer parental genotypes. The latter approach was found to be more powerful, except when penetrance was high. Typing an unaffected sibling, or just one parent, was found to give only a small increase in power except when the PIC of the marker was low. Even then, typing an unaffected relative increased the overall number of individuals that had to be typed to achieve a given power. If there is no highly informative marker locus in the area under study, it may be possible to "build" one by combining the alleles from two or more neighboring tightly linked loci into haplotypes. Typing two loci gave a sizeable power increase over a single locus, but typing further loci gave much smaller gains. Building haplotypes will introduce phase uncertainties, with the result that such a system will yield less power than will a single locus with the same number of alleles. This power loss was small, however, and did not affect the conclusions regarding the worth of typing unaffected relatives.     

The posterior probability of linkage allowing for linkage disequilibrium and a new estimate of disequilibrium between a trait and a marker

The posterior probability of linkage (PPL) statistic has been developed as a method for the rigorous accumulation of evidence for or against linkage allowing for both intra- and inter-sample heterogeneity. To date, the method has assumed linkage equilibrium between alleles at the trait locus and the marker locus. We now generalize the PPL to allow for linkage disequilibrium (LD), by incorporating variable phase probabilities into the underlying linkage likelihood. This enables us to recover the marginal posterior density of the recombination fraction, integrating out nuisance parameters of the trait model, including the locus heterogeneity (admixture) parameter, as well as a vector of LD parameters. The marginal posterior density can then be updated across data subsets or new data as they become available, while allowing parameters of the trait model to vary between data sets. The method applies immediately to general pedigree structures and to markers with multiple alleles. In the case of SNPs, the likelihood is parameterized in terms of the standard single LD parameter D'; and it therefore affords a mechanism for estimation of D' between the marker and the trait, again, without fixing the parameters of the trait model and allowing for updating across data sets. It is even possible to allow for a different associated allele in different populations, while accumulating information regarding the strength of LD. While a computationally efficient implementation for multi-allelic markers is still in progress, we have implemented a version of this new LD-PPL for SNPs and evaluated its performance in nuclear families. Our simulations show that LD-PPLs tend to be larger than PPLs (stronger evidence in favor of linkage/LD) with increased LD level, under a variety of generating models; while in the absence of linkage and LD, LD-PPLs tend to be smaller than PPLs (stronger evidence against linkage). The estimate of D' also behaves well even in relatively small, heterogeneous samples.     

Insights into recombination from patterns of linkage disequilibrium in humans

An ability to predict levels of linkage disequilibrium (LD) between linked markers would facilitate the design of association studies and help to distinguish between evolutionary models. Unfortunately, levels of LD depend crucially on the rate of recombination, a parameter that is difficult to measure. In humans, rates of genetic exchange between markers megabases apart can be estimated from a comparison of genetic and physical maps; these large-scale estimates can then be interpolated to predict LD at smaller ("local") scales. However, if there is extensive small-scale heterogeneity, as has been recently proposed, local rates of recombination could differ substantially from those averaged over much larger distances. We test this hypothesis by estimating local recombination rates indirectly from patterns of LD in 84 genomic regions surveyed by the SeattleSNPs project in a sample of individuals of European descent and of African-Americans. We find that LD-based estimates are significantly positively correlated with map-based estimates. This implies that large-scale, average rates are informative about local rates of recombination. Conversely, although LD-based estimates are based on a number of simplifying assumptions, it appears that they capture considerable information about the underlying recombination rate or at least about the ordering of regions by recombination rate. Using LD-based estimators, we also find evidence for homologous gene conversion in patterns of polymorphism. However, as we demonstrate by simulation, inferences about gene conversion are unreliable, even with extensive data from homogeneous regions of the genome, and are confounded by genotyping error.