A test for linkage and association in general pedigrees: the pedigree disequilibrium test

Family-based tests of linkage disequilibrium typically are based on nuclear-family data including affected individuals and their parents or their unaffected siblings. A limitation of such tests is that they generally are not valid tests of association when data from related nuclear families from larger pedigrees are used. Standard methods require selection of a single nuclear family from any extended pedigrees when testing for linkage disequilibrium. Often data are available for larger pedigrees, and it would be desirable to have a valid test of linkage disequilibrium that can use all potentially informative data. In this study, we present the pedigree disequilibrium test (PDT) for analysis of linkage disequilibrium in general pedigrees. The PDT can use data from related nuclear families from extended pedigrees and is valid even when there is population substructure. Using computer simulations, we demonstrated validity of the test when the asymptotic distribution is used to assess the significance, and examined statistical power. Power simulations demonstrate that, when extended pedigree data are available, substantial gains in power can be attained by use of the PDT rather than existing methods that use only a subset of the data. Furthermore, the PDT remains more powerful even when there is misclassification of unaffected individuals. Our simulations suggest that there may be advantages to using the PDT even if the data consist of independent families without extended family information. Thus, the PDT provides a general test of linkage disequilibrium that can be widely applied to different data structures.     

Insights from linked single nucleotide polymorphisms: what we can learn from linkage disequilibrium

New methods for analyzing sequence polymorphism data have uncovered some striking patterns of linkage disequilibrium in both humans and fruitflies. These methods have revealed examples where the observed amount of linkage disequilibrium is either much more or much less than expected, and have led to advances in our understanding of the forces that affect naturally occurring genetic variation. With the recent explosion of sequence polymorphism data, the prospects for further progress from these methods are quite promising.     

Inferring population parameters from single-feature polymorphism data

This article is concerned with a statistical modeling procedure to call single-feature polymorphisms from microarray experiments. We use this new type of polymorphism data to estimate the mutation and recombination parameters in a population. The mutation parameter can be estimated via the number of single-feature polymorphisms called in the sample. For the recombination parameter, a two-feature sampling distribution is derived in a way analogous to that for the two-locus sampling distribution with SNP data. The approximate-likelihood approach using the two-feature sampling distribution is examined and found to work well. A coalescent simulation study is used to investigate the accuracy and robustness of our method. Our approach allows the utilization of single-feature polymorphism data for inference in population genetics.     

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.     

Comparison of genetic models for analysing the effects of a PvuII polymorphism in the oestrogen receptor 1 (ESR1) gene on prolificacy in an Iberian x Meishan pig population

The effect of a previously reported PvuII polymorphism in oestrogen receptor 1 (ESR1) was analysed in an F(2) population of Iberian x Meishan pigs. We tested three hypotheses: (1) that a causal mutation was fixed in the parental populations, (2) that a causal mutation existed that was in complete linkage disequilibrium with the alleles of the PvuII polymorphism and (3) that a causal mutation existed in linkage disequilibrium within each parental population. The third model was the most plausible based on the available data. ESR1 alleles displayed different patterns of linkage disequilibrium with the causal mutation in each of the parental populations and the PvuII polymorphism was clearly not the causal mutation. As a consequence, the use of the ESR1 mutation for selection must be evaluated for a particular pig population before it is applied.     

Does probabilistic modelling of linkage disequilibrium evolution improve the accuracy of QTL location in animal pedigree?

Background

Since 2001, the use of more and more dense maps has made researchers aware that combining linkage and linkage disequilibrium enhances the feasibility of fine-mapping genes of interest. So, various method types have been derived to include concepts of population genetics in the analyses. One major drawback of many of these methods is their computational cost, which is very significant when many markers are considered. Recent advances in technology, such as SNP genotyping, have made it possible to deal with huge amount of data. Thus the challenge that remains is to find accurate and efficient methods that are not too time consuming. The study reported here specifically focuses on the half-sib family animal design. Our objective was to determine whether modelling of linkage disequilibrium evolution improved the mapping accuracy of a quantitative trait locus of agricultural interest in these populations. We compared two methods of fine-mapping. The first one was an association analysis. In this method, we did not model linkage disequilibrium evolution. Therefore, the modelling of the evolution of linkage disequilibrium was a deterministic process; it was complete at time 0 and remained complete during the following generations. In the second method, the modelling of the evolution of population allele frequencies was derived from a Wright-Fisher model. We simulated a wide range of scenarios adapted to animal populations and compared these two methods for each scenario.

Results

Our results indicated that the improvement produced by probabilistic modelling of linkage disequilibrium evolution was not significant. Both methods led to similar results concerning the location accuracy of quantitative trait loci which appeared to be mainly improved by using four flanking markers instead of two.

Conclusions

Therefore, in animal half-sib designs, modelling linkage disequilibrium evolution using a Wright-Fisher model does not significantly improve the accuracy of the QTL location when compared to a simpler method assuming complete and constant linkage between the QTL and the marker alleles. Finally, given the high marker density available nowadays, the simpler method should be preferred as it gives accurate results in a reasonable computing time.     

Power of association and linkage tests when the disease alleles are unobserved.

Genomewide association studies have been advocated as a promising alternative to genomewide linkage scans for detection of small-effect genes in complex diseases. Comparisons of power and sample size between the two strategies have shown considerable advantages for the association studies. These comparisons assume that the set of markers includes the exact disease-related polymorphism. A concern, however, is that the power of an association study decreases when this is not the case, because of discrepant allele frequencies and less-than-maximum disequilibrium between the disease-related polymorphism and its nearest marker. Here, we quantify this concern by comparing the sample sizes needed by the two strategies when the markers exclude the disease-related polymorphism. For affected sib pairs and their parents, we found that incomplete disequilibrium and differing allele frequencies can have substantial negative impact on the power of association studies, resulting, in some circumstances, in little gain and even in loss of power, compared with linkage analysis. We provide some guidelines for choosing between strategies, for the detection of genes for complex diseases.     

Modeling linkage disequilibrium between a polymorphic marker locus and a locus affecting complex dichotomous traits in natural populations

Linkage disequilibrium is an important topic in evolutionary and population genetics. An issue yet to be settled is the theory required to extend the linkage disequilibrium analysis to complex traits. In this study, we present theoretical analysis and methods for detecting or estimating linkage disequilibrium (LD) between a polymorphic marker locus and any one of the loci affecting a complex dichotomous trait on the basis of samples randomly or selectively collected from natural populations. Statistical properties of these methods were investigated and their powers were compared analytically or by use of Monte Carlo simulations. The results show that the disequilibrium may be detected with a power of 80% by using phenotypic records and marker genotype when both the trait and marker variants are common (30%) and the LD is relatively high (40-100% of the theoretical maximum). The maximum-likelihood approach provides accurate estimates of the model parameters as well as detection of linkage disequilibrium. The likelihood method is preferred for its higher power and reliability in parameter estimation. The approaches developed in this article are also compared to those for analyzing a continuously distributed quantitative trait. It is shown that a larger sample size is required for the dichotomous trait model to obtain the same level of power in detecting linkage disequilibrium as the continuous trait analysis. Potential use of these estimates in mapping the trait locus is also discussed.     

Combined linkage disequilibrium and linkage mapping: Bayesian multilocus approach

Quantitative trait loci (QTL) affecting the phenotype of interest can be detected using linkage analysis (LA), linkage disequilibrium (LD) mapping or a combination of both (LDLA). The LA approach uses information from recombination events within the observed pedigree and LD mapping from the historical recombinations within the unobserved pedigree. We propose the Bayesian variable selection approach for combined LDLA analysis for single-nucleotide polymorphism (SNP) data. The novel approach uses both sources of information simultaneously as is commonly done in plant and animal genetics, but it makes fewer assumptions about population demography than previous LDLA methods. This differs from approaches in human genetics, where LDLA methods use LA information conditional on LD information or the other way round. We argue that the multilocus LDLA model is more powerful for the detection of phenotype–genotype associations than single-locus LDLA analysis. To illustrate the performance of the Bayesian multilocus LDLA method, we analyzed simulation replicates based on real SNP genotype data from small three-generational CEPH families and compared the results with commonly used quantitative transmission disequilibrium test (QTDT). This paper is intended to be conceptual in the sense that it is not meant to be a practical method for analyzing high-density SNP data, which is more common. Our aim was to test whether this approach can function in principle.     

A powerful likelihood method for the analysis of linkage disequilibrium between trait loci and one or more polymorphic marker loci.

Historically, most methods for detecting linkage disequilibrium were designed for use with diallelic marker loci, for which the analysis is straightforward. With the advent of polymorphic markers with many alleles, the normal approach to their analysis has been either to extend the methodology for two-allele systems (leading to an increase in df and to a corresponding loss of power) or to select the allele believed to be associated and then collapse the other alleles, reducing, in a biased way, the locus to a diallelic system. I propose a likelihood-based approach to testing for linkage disequilibrium, an approach that becomes more conservative as the number of alleles increases, and as the number of markers considered jointly increases in a multipoint test for linkage disequilibrium, while maintaining high power. Properties of this method for detecting associations and fine mapping the location of disease traits are investigated. It is found to be, in general, more powerful than conventional methods, and it provides a tractable framework for the fine mapping of new disease loci. Application to the cystic fibrosis data of Kerem et al, is included to illustrate the method.     

Characterization of single nucleotide polymorphism markers for the green sea turtle (Chelonia mydas)

We present data on 29 new single nucleotide polymorphism assays for the green sea turtle, Chelonia mydas. DNA extracts from 39 green turtles were used for two methods of single nucleotide polymorphism discovery. The first approach employed an amplified fragment length polymorphism technique. The second technique screened a microsatellite library. Allele-specific amplification assays were developed for high-throughput single nucleotide polymorphism genotyping and tested on two Pacific C. mydas nesting populations. Observed heterozygosities ranged from 0 to 0.95 for a Hawaiian population and from 0 to 0.85 for a Galapagos population. Each of the populations had one locus out of Hardy-Weinberg equilibrium, SSCM2b and SSCM5 for Hawaii and Galapagos, respectively. No loci showed significant genotypic linkage disequilibrium across an expanded set of four Pacific nesting populations. However, two loci, SSCM4 and SSCM10b showed linkage disequilibrium across three populations indicating possible association.     

A sib-pair regression model of linkage disequilibrium for quantitative traits

A multiple-regression model is described for the detection of linkage disequilibrium in quantitative trait loci. The model is developed for application to large numbers of single nucleotide polymorphism (SNP) markers genotyped on small nuclear families. Parental data are not required by the method, although it provides a direct means to test quantitative trait locus-marker allele association and to determine whether any such association is attributable to linkage disequilibrium or population admixture. Analytical expectations for the regression coefficients are derived, allowing direct interpretation of the parameter estimates. Simulation studies indicate a substantial improvement in power over classical linkage studies of sibling pairs and show the effects of population admixture on the model outcomes.     

Detecting strong positive selection in the genome

New statistical tests have been developed in the past decade that enable us to infer evidence of recent strong positive selection from genome-wide data on single-nucleotide polymorphism and to localize the targets of selection in the genome. Based on these tests, past demographic events that led to distortions of the site-frequency spectrum of variation can be distinguished from selection, in particular if linkage disequilibrium is taken into account. These methods have been successfully applied to species from which complete sequence information and polymorphism data are available, including Drosophila melanogaster, humans, and several plant species. To make full use of the available data, however, the tests that were primarily designed for panmictic populations need to be extended to spatially structured populations.     

A haplotype-based 'haplotype relative risk' approach to detecting allelic associations.

A novel variation of the Haplotype Relative Risk (HRR) of Rubinstein et al. [Hum Immunol 1981;3:384] is proposed, in order to glean increased information about linkage disequilibrium or allelic associations by analyzing haplotype-based data rather than genotypic data. It is shown that statistical tests based on our design give much higher power than those based on the original HRR approach. Several additional nonparametric tests based on the same data are analyzed, and power is computed for each of them. Further, parametric likelihood methods are applied to testing linkage equilibrium, and estimating delta, the coefficient of linkage disequilibrium, from the same data.     

Fine-mapping chromosome 20 in 230 systemic lupus erythematosus sib pair and multiplex families: evidence for genetic epistasis with chromosome 16q12

The presence of systemic lupus erythematosus (SLE) susceptibility genes on chromosome 20 is suggested by the observation of genetic linkage in several independent SLE family collections. To further localize the genetic effects, we typed 59 microsatellites in the two best regions, as defined by genome screens. Genotypes were analyzed for statistical linkage and/or association with SLE, by use of a combination of nonparametric linkage methods, family-based tests of association (transmission/disequilibrium and pedigree disequilibrium tests), and haplotype-sharing statistics (haplotype runs test), in a set of 230 SLE pedigrees. Maximal evidence for linkage to SLE was to 20p12 (LOD = 2.84) and 20q13.1 (LOD = 1.64) in the white pedigrees. Subsetting families on the basis of evidence for linkage to 16q12 significantly improved the LOD scores at both chromosome 20 locations (20p12 LOD = 5.06 and 20q13 LOD = 3.65), consistent with epistasis. We then typed 162 single-nucleotide polymorphism markers across a 1.3-Mb candidate region on 20q13.1 and identified several SNPs that demonstrated significant evidence for association. These data provide additional support for linkage and association to 20p12 and 20q13.1 in SLE and further refine the intervals of interest. These data further suggest the possibility of epistatic relationships among loci within the 20q12, 20q13, and 16q12 regions in SLE families.     

Linkage disequilibrium testing when linkage phase is unknown

Linkage disequilibrium, the nonrandom association of alleles from different loci, can provide valuable information on the structure of haplotypes in the human genome and is often the basis for evaluating the association of genomic variation with human traits among unrelated subjects. But, linkage phase of genetic markers measured on unrelated subjects is typically unknown, and so measurement of linkage disequilibrium, and testing whether it differs significantly from the null value of zero, requires statistical methods that can account for the ambiguity of unobserved haplotypes. A common method to test whether linkage disequilibrium differs significantly from zero is the likelihood-ratio statistic, which assumes Hardy-Weinberg equilibrium of the marker phenotype proportions. We show, by simulations, that this approach can be grossly biased, with either extremely conservative or liberal type I error rates. In contrast, we use simulations to show that a composite statistic, proposed by Weir and Cockerham, maintains the correct type I error rates, and, when comparisons are appropriate, has similar power as the likelihood-ratio statistic. We extend the composite statistic to allow for more than two alleles per locus, providing a global composite statistic, which is a strong competitor to the usual likelihood-ratio statistic.     

Monte Carlo pedigree disequilibrium test for markers on the X chromosome

Because of the need for fine mapping of disease loci and the availability of dense single-nucleotide-polymorphism markers, many forms of association tests have been developed. Most of them are applicable only to triads, whereas some are amenable to nuclear families (sibships). Although there are a number of methods that can deal with extended families (e.g., the pedigree disequilibrium test [PDT]), most of them cannot accommodate incomplete data. Furthermore, despite a large body of literature on association mapping, only a very limited number of publications are applicable to X-chromosomal markers. In this report, we first extend the PDT to markers on the X chromosome for testing linkage disequilibrium in the presence of linkage. This method is applicable to any pedigree structure and is termed "X-chromosomal pedigree disequilibrium test" (XPDT). We then further extend the XPDT to accommodate pedigrees with missing genotypes in some of the individuals, especially founders. Monte Carlo (MC) samples of the missing genotypes are generated and used to calculate the XMCPDT (X-chromosomal MC PDT) statistic, which is defined as the conditional expectation of the XPDT statistic given the incomplete (observed) data. This MC version of the XPDT remains a valid test for association under linkage with the assumption that the pedigrees and their associated affection patterns are drawn randomly from a population of pedigrees with at least one affected offspring. This set of methods was compared with existing approaches through simulation, and substantial power gains were observed in all settings considered, with type I error rates closely tracking their nominal values.     

Theory of the effects of population structure and sampling on patterns of linkage disequilibrium applied to genomic data from humans

We develop predictions for the correlation of heterozygosity and for linkage disequilibrium between two loci using a simple model of population structure that includes migration among local populations, or demes. We compare the results for a sample of size two from the same deme (a single-deme sample) to those for a sample of size two from two different demes (a scattered sample). The correlation in heterozygosity for a scattered sample is surprisingly insensitive to both the migration rate and the number of demes. In contrast, the correlation in heterozygosity for a single-deme sample is sensitive to both, and the effect of an increase in the number of demes is qualitatively similar to that of a decrease in the migration rate: both increase the correlation in heterozygosity. These same conclusions hold for a commonly used measure of linkage disequilibrium (r(2)). We compare the predictions of the theory to genomic data from humans and show that subdivision might account for a substantial portion of the genetic associations observed within the human genome, even though migration rates among local populations of humans are relatively large. Because correlations due to subdivision rather than to physical linkage can be large even in a single-deme sample, then if long-term migration has been important in shaping patterns of human polymorphism, the common practice of disease mapping using linkage disequilibrium in "isolated" local populations may be subject to error.     

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.     

Inflammation, genetics, and ischemic heart disease: focus on the major histocompatibility complex (MHC) genes

BACKGROUND: Increasing data suggest that ischemic heart disease (IHD) shares several characteristics with common inflammatory diseases (such as rheumatoid arthritis), in which the pathogenetic role of inflammatory gene polymorphisms is well established. Variants in the genes for the major histocompatibility complex (MHC) molecules on the short arm of chromosome 6 show profound "linkage disequilibrium", leading to the formation of "haplotypes", i.e., frozen blocks of alleles travelling together through generations. DESIGN: We performed a review of published studies linking IHD with gene polymorphisms of the MHC molecules tumor necrosis factor (TNF)-alpha and -beta, the class II DR human leukocyte antigens, heat shock protein 70-1, hemochromatosis related gene, and complement C4. RESULTS: The emerging data are quite conflicting and do not provide definitive evidence for a role of these gene variants in the pathogenesis of IHD; a possible exception is the G252A and polymorphism in the TNF-beta gene (also known as lymphotoxin-alpha) which, in a comprehensive genome-scan linkage analysis of unrelated Japanese, but not in a smaller German population, was linked to myocardial infarction. However, some important biases appear, e.g. different study design and variable linkage disequilibrium among different populations. CONCLUSIONS: Preliminary positive results should encourage future studies to focus on clinical models of IHD with well-codified inflammatory components, using novel methods (such as haplotype analysis) to assess gene polymorphisms and their clinical effect.