Linkage detection adaptive to linkage disequilibrium: the disequilibrium maximum-likelihood-binomial test for affected-sibship data

It has been demonstrated in the literature that the transmission/disequilibrium test (TDT) has higher power than the affected-sib-pair (ASP) mean test when linkage disequilibrium (LD) is strong but that the mean test has higher power when LD is weak. Thus, for ASP data, it seems clear that the TDT should be used when LD is strong but that the mean test or other linkage tests should be used when LD is weak or absent. However, in practice, it may be difficult to follow such a guideline, because the extent of LD is often unknown. Even with a highly dense genetic-marker map, in which some markers should be located near the disease-predisposing mutation, strong LD is not inevitable. Besides the genetic distance, LD is also affected by many factors, such as the allelic heterogeneity at the disease locus, the initial LD, the allelic frequencies at both disease locus and marker locus, and the age of the mutation. Therefore, it is of interest to develop methods that are adaptive to the extent of LD. In this report, we propose a disequilibrium maximum-binomial-likelihood (DMLB) test that incorporates LD in the maximum-binomial-likelihood (MLB) test. Examination of the corresponding score statistics shows that this method adaptively combines two sources of information: (a) the identity-by-descent (IBD) sharing score, which is informative for linkage regardless of the existence of LD, and (b) the contrast between allele-specific IBD sharing score, which is informative for linkage only in the presence of LD. For ASP data, the proposed test has higher power than either the TDT or the mean test when the extent of LD ranges from moderate to strong. Only when LD is very weak or absent is the DMLB slightly less powerful than the mean test; in such cases, the TDT has essentially no power to detect linkage. Therefore, the DMLB test is an interesting approach to linkage detection when the extent of LD is unknown.     

Joint modeling of linkage and association: identifying SNPs responsible for a linkage signal

Once genetic linkage has been identified for a complex disease, the next step is often association analysis, in which single-nucleotide polymorphisms (SNPs) within the linkage region are genotyped and tested for association with the disease. If a SNP shows evidence of association, it is useful to know whether the linkage result can be explained, in part or in full, by the candidate SNP. We propose a novel approach that quantifies the degree of linkage disequilibrium (LD) between the candidate SNP and the putative disease locus through joint modeling of linkage and association. We describe a simple likelihood of the marker data conditional on the trait data for a sample of affected sib pairs, with disease penetrances and disease-SNP haplotype frequencies as parameters. We estimate model parameters by maximum likelihood and propose two likelihood-ratio tests to characterize the relationship of the candidate SNP and the disease locus. The first test assesses whether the candidate SNP and the disease locus are in linkage equilibrium so that the SNP plays no causal role in the linkage signal. The second test assesses whether the candidate SNP and the disease locus are in complete LD so that the SNP or a marker in complete LD with it may account fully for the linkage signal. Our method also yields a genetic model that includes parameter estimates for disease-SNP haplotype frequencies and the degree of disease-SNP LD. Our method provides a new tool for detecting linkage and association and can be extended to study designs that include unaffected family members.     

Positional cloning of disease genes: advantages of genetic isolates.

Genetic isolates with a history of a small founder population, long-lasting isolation and population bottlenecks represent exceptional resources in the identification of disease genes. Specific rare, monogenic diseases become enriched, and families with multiple affected individuals occur frequently enough to be used in linkage analyses for locus identification. Further, the vast majority of cases are caused by the same mutation, and disease alleles reveal linkage disequilibrium (LD) with markers over significant genetic intervals; this facilitates disease locus identification by similarity search for a shared genotype or haplotype in small study samples consisting of few affected individuals. LD observed in disease alleles adds power to linkage analyses and helps to define the exact location of disease loci on the genetic map. Typically, based on the linkage disequilibrium and the ancient haplotype, the critical DNA region can be defined from the original 1- to 2-cM resolution obtained in linkage analysis to 50-200 kb, greatly facilitating the targeting of physical cloning and sequencing efforts. These advantages have been well demonstrated in the positional cloning of several rare monogenic diseases enriched in population isolates like the example of Finland used here. How useful genetic isolates will prove to be in the identification of complex disease genes is dependent on the genealogical history of the isolate, including the size of the founding population and the expansion rate during the history of the population.     

PSEUDOMARKER: a powerful program for joint linkage and/or linkage disequilibrium analysis on mixtures of singletons and related individuals

A decade ago, there was widespread enthusiasm for the prospects of genome-wide association studies to identify common variants related to common chronic diseases using samples of unrelated individuals from populations. Although technological advancements allow us to query more than a million SNPs across the genome at low cost, a disappointingly small fraction of the genetic portion of common disease etiology has been uncovered. This has led to the hypothesis that less frequent variants might be involved, stimulating a renaissance of the traditional approach of seeking genes using multiplex families from less diverse populations. However, by using the modern genotyping and sequencing technology, we can now look not just at linkage, but jointly at linkage and linkage disequilibrium (LD) in such samples. Software methods that can look simultaneously at linkage and LD in a powerful and robust manner have been lacking. Most algorithms cannot jointly analyze datasets involving families of varying structures in a statistically or computationally efficient manner. We have implemented previously proposed statistical algorithms in a user-friendly software package, PSEUDOMARKER. This paper is an announcement of this software package. We describe the motivation behind the approach, the statistical methods, and software, and we briefly demonstrate PSEUDOMARKER's advantages over other packages by example.     

Investigation of altering single-nucleotide polymorphism density on the power to detect trait loci and frequency of false positive in nonparametric linkage analyses of qualitative traits

Genome-wide linkage analysis using microsatellite markers has been successful in the identification of numerous Mendelian and complex disease loci. The recent availability of high-density single-nucleotide polymorphism (SNP) maps provides a potentially more powerful option. Using the simulated and Collaborative Study on the Genetics of Alcoholism (COGA) datasets from the Genetics Analysis Workshop 14 (GAW14), we examined how altering the density of SNP marker sets impacted the overall information content, the power to detect trait loci, and the number of false positive results. For the simulated data we used SNP maps with density of 0.3 cM, 1 cM, 2 cM, and 3 cM. For the COGA data we combined the marker sets from Illumina and Affymetrix to create a map with average density of 0.25 cM and then, using a sub-sample of these markers, created maps with density of 0.3 cM, 0.6 cM, 1 cM, 2 cM, and 3 cM. For each marker set, multipoint linkage analysis using MERLIN was performed for both dominant and recessive traits derived from marker loci. Our results showed that information content increased with increased map density. For the homogeneous, completely penetrant traits we created, there was only a modest difference in ability to detect trait loci. Additionally, as map density increased there was only a slight increase in the number of false positive results when there was linkage disequilibrium (LD) between markers. The presence of LD between markers may have led to an increased number of false positive regions but no clear relationship between regions of high LD and locations of false positive linkage signals was observed.     

High-resolution joint linkage disequilibrium and linkage mapping of quantitative trait loci based on sibship data

This paper proposes variance component models for high resolution joint linkage disequilibrium (LD) and linkage mapping of quantitative trait loci (QTL) based on sibship data; this can include population data if independent individuals are treated as single sibships. One application of these models is late onset complex disease gene mapping, when parental data are not available. The models simultaneously incorporate both LD and linkage information. The LD information is contained in mean coefficients of sibship data. The linkage information is contained in the variance-covariance matrices of trait values for sibships with at least two siblings. We derive formulas for calculating the probability of sharing two trait alleles identical by descent (IBD) for sibpairs in interval mapping of QTL; this is the coefficient of dominant variance of the trait covariance of sibpairs on major QTL. To investigate the performance of the formulas, we calculate the numerical values via the formulas and get satisfactory approximations. We compare the power and sample sizes for both LD and linkage mapping. By simulation and theoretical analysis, we compare the results with those of Fulker and Abecasis "AbAw" approach. It is well known that the resolution of linkage analysis can be low for complex disease gene mapping. LD mapping, on the other hand, can increase mapping precision and is useful in high resolution mapping. Linkage analysis is less sensitive to population subdivisions and admixtures. The level of LD is sensitive to population stratification which may easily lead to spurious association. Performing a joint analysis of LD and linkage mapping can help to overcome the limits of both approaches. Moreover, the advantages of the two complementary strategies can be utilized maximally. In practice, linkage analysis may be performed using pedigree data to identify suggestive linkage between markers and trait loci based on a sparse marker map. In the presence of linkage, joint LD and linkage mapping can be carried out to do fine gene mapping based on a dense genetic map using both pedigree and population data. Population and pedigree data of any type can be combined to perform a joint analysis of high resolution LD and linkage mapping of QTL by generalizing the method.     

Increased gene coverage and Alu frequency in large linkage disequilibrium blocks of the human genome

The human genome has linkage disequilibrium (LD) blocks, within which single-nucleotide polymorphisms show strong association with each other. We examined data from the International HapMap Project to define LD blocks and to detect DNA sequence features inside of them. We used permutation tests to determine the empirical significance of the association of LD blocks with genes and Alu repeats. Very large LD blocks (>200 kb) have significantly higher gene coverage and Alu frequency than the outcome obtained from permutation-based simulation, whereas there was no significant positive correlation between gene density and block size. We also observed a reduced frequency of Alu repeats at the gaps between large LD blocks, indicating that their enrichment in large LD blocks does not introduce recombination hotspots that would cause these gaps.     

Linkage disequilibrium for different scales and applications

Assessing the patterns of linkage disequilibrium (LD) has become an important issue in both evolutionary biology and medical genetics since the rapid accumulation of densely spaced DNA sequence variation data in several organisms. LD deals with the correlation of genetic variation at two or more loci or sites in the genome within a given population. There are a variety of LD measures which range from traditional pairwise LD measures such as D' or r2 to entropy-based multi-locus measures or haplotype-specific approaches. Understanding the evolutionary forces (in particular recombination) that generate the observed variation of LD patterns across genomic regions is addressed by model-based LD analysis. Marker type and its allelic composition also influence the observed LD pattern, microsatellites having a greater power to detect LD in population isolates than SNPs. This review aims to explain basic LD measures and their application properties.     

Comparison of linkage disequilibrium patterns between the HapMap CEPH samples and a family-based cohort of Northern European descent

The International HapMap Consortium has determined the linkage disequilibrium (LD) patterns of four major human populations. The aim of our investigation was to compare the LD patterns of the HapMap CEPH (Centre d'Etude du Polymorphisme Humain) samples with a family-based cohort of similar ancestry to determine its usefulness as a reference population for disease association studies. We examined four genomic regions on chromosomes 7q, 12p, and 14q totaling 14.3 Mb, initially identified in our linkage study of obesity and the metabolic syndrome. Near identical patterns of LD were detected in both populations. Furthermore, tagSNPs selected based on the HapMap CEPH cohort data capture over 98% of the variants at an r2 > 0.8 in the disease cohort. This confirms the usefulness of the CEPH cohort of the HapMap as a reference sample for further investigations into the genomic variation of populations of Northern European descent.     

Complex high-resolution linkage disequilibrium and haplotype patterns of single-nucleotide polymorphisms in 2.5 Mb of sequence on human chromosome 21.

One approach to identify potentially important segments of the human genome is to search for DNA regions with nonrandom patterns of human sequence variation. Previous studies have investigated these patterns primarily in and around candidate gene regions. Here, we determined patterns of DNA sequence variation in 2.5 Mb of finished sequence from five regions on human chromosome 21. By sequencing 13 individual chromosomes, we identified 1460 single-nucleotide polymorphisms (SNPs) and obtained unambiguous haplotypes for all chromosomes. For all five chromosomal regions, we observed segments with high linkage disequilibrium (LD), extending from 1.7 to>81 kb (average 21.7 kb), disrupted by segments of similar or larger size with no significant LD between SNPs. At least 25% of the contig sequences consisted of segments with high LD between SNPs. Each of these segments was characterized by a restricted number of observed haplotypes,with the major haplotype found in over 60% of all chromosomes. In contrast, the interspersed segments with low LD showed significantly more haplotype patterns. The position and extent of the segments of high LD with restricted haplotype variability did not coincide with the location of coding sequences. Our results indicate that LD and haplotype patterns need to be investigated with closely spaced SNPs throughout the human genome, independent of the location of coding sequences, to reliably identify regions with significant LD useful for disease association studies.     

一种有效的复杂疾病基因定位的检测法

连锁不平衡（LD）应用于某些复杂疾病基因的定位,近年来发展了许多LD定位方法,除TDT外,大多数LD定位方法须先假定无人群混和,人群混合可增大在疾病基因定位时犯Ⅰ类错误的机率,产生无效结果。此方法利用LD来检测标记位点和疾病敏感位点（DSL）的连锁（有连锁不平衡）相关（有连锁）。分析时采用不相关样本,已知其父母基因型和至少父母之一为杂合子,再将随机样本依基因型不同分类,然后对来自不同类的数据应用有力的统计方法进行单独和联合分析。此LD定位法不仅适用于患病和正常个体,而且有效消除据父母基因分类的样本定位时人群混合的影响,分析结果和模拟结果也表明此方法解决了在检测标记位点和疾病敏感位点之间的连锁和相关时人群混和的问题,但与TDT比,此法在检测的位点为DSL时丙能有效和充分地利用矫正数据,检测位点不是DSL时,此法和TDT法可相互补充更有效地检测连锁的DSL。     

Mapping genes for common diseases: the case for genetic (LD) maps

We examine the current effort to develop a haplotype map of the human genome and suggest an alternative approach which represents linkage disequilibrium patterns in the form of a metric LD map. LD maps have some of the useful properties of genetic linkage maps but have a much higher resolution which is optimal for SNP-based association mapping of common diseases. The studies that have been undertaken to date suggest that LD and recombination maps show some close similarities because of abundant, narrow, recombination hot spots. These hot spots are co-localised in all populations but, unlike linkage maps, LD maps differ in scale for different populations because of differences in population history. The prospects for developing optimized panels of SNPs and the use of linkage disequilibrium maps in disease gene localisation are assessed in the light of recent evidence.     

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.     

Accounting for linkage disequilibrium among markers in linkage analysis: impact of haplotype frequency estimation and molecular haplotypes for a gene in a candidate region for Alzheimer's disease

OBJECTIVES: Linkage disequilibrium (LD) between closely spaced SNPs can be accommodated in linkage analysis by specifying the multi-SNP haplotype frequencies, if known. Phased haplotypes in candidate regions can provide gold standard haplotype frequency estimates, and may be of inherent interest as markers. We evaluated the effects of different methods of haplotype frequency estimation, and the use of marker phase information, on linkage analysis of a multi-SNP cluster in a candidate region for Alzheimer's disease (AD). METHODS: We performed parametric linkage analysis of a five-SNP cluster in extended pedigrees to compare the use of: (1) haplotype frequencies estimated by molecular phase determination, maximum likelihood estimation, or by assuming linkage equilibrium (LE); (2) AD families or controls as the frequency source; and (3) unphased or molecularly phased SNP data. RESULTS: There was moderate to strong pairwise LD among the five SNPs. Falsely assuming LE substantially inflated the LOD score, but the method of haplotype frequency estimation and particular sample used made little difference provided that LD was accommodated. Use of phased haplotypes produced a modest increase in the LOD score over unphased SNPs. CONCLUSIONS: Ignoring LD between markers can lead to substantially inflated evidence for linkage in LOD score analysis of extended pedigrees with missing data. Use of marker phase information in linkage analysis may be important in disease studies where the costs of family recruitment and phenotyping greatly exceed the costs of phase determination.     

Patterns of linkage disequilibrium in the human genome

Particular alleles at neighbouring loci tend to be co-inherited. For tightly linked loci, this might lead to associations between alleles in the population a property known as linkage disequilibrium (LD). LD has recently become the focus of intense study in the hope that it might facilitate the mapping of complex disease loci through whole-genome association studies. This approach depends crucially on the patterns of LD in the human genome. In this review, we draw on empirical studies in humans and Drosophila, as well as simulation studies, to assess the current state of knowledge about patterns of LD, and consider the implications for the use of LD as a mapping tool.     

Multiple DNA Variant Association Analysis: Application to the Insulin Gene Region in Type 1 Diabetes

Association and linkage studies have shown that at least one of the genetic factors involved in susceptibility to insulin-dependent diabetes mellitus (IDDM) is contained within a 4.1-kb region of the insulin gene. Sequence analysis has led to the identification of 10 DNA variants in this region that are associated with increased risk for IDDM. These variants are in strong linkage disequilibrium with each other, and previous studies have failed to distinguish between the variant(s) that cause increased susceptibility to IDDM and others that are associated with the disease because of linkage disequilibrium. To address this problem, we have undertaken a large population study of French diabetics and controls and have analyzed genotype patterns for several of the variant sites simultaneously. This has led to the identification of a subset consisting of four variants (−2733AC, −23HphI, −365VNTR, and +1140AC), at least one of which appears to be directly implicated in disease susceptibility. The multiple-DNA-variant association-analysis approach that is applied here to the problem of identifying potential susceptibility variants in IDDM is likely to be important in studies of many other multifactorial diseases.     

GOLDsurfer: three dimensional display of linkage disequilibrium

GOLDsurfer is a java-based analysis and graphics program for three-dimensional plotting of linkage disequilibrium (LD). Simultaneous presentation of LD measures, including recombination rate estimates and disease association statistics, helps to clarify LD patterns and facilitates interpretations based on multiple indices of local genetic data.     

Genome-wide association filtering using a highly locus-specific transmission/disequilibrium test

Multimarker transmission/disequilibrium tests (TDTs) are powerful association and linkage tests used to perform genome-wide filtering in the search for disease susceptibility loci. In contrast to case/control studies, they have a low rate of false positives for population stratification and admixture. However, the length of a region found in association with a disease is usually very large because of linkage disequilibrium (LD). Here, we define a multimarker proportional TDT (mTDT _P ) designed to improve locus specificity in complex diseases that has good power compared to the most powerful multimarker TDTs. The test is a simple generalization of a multimarker TDT in which haplotype frequencies are used to weight the effect that each haplotype has on the whole measure. Two concepts underlie the features of the metric: the ‘common disease, common variant’ hypothesis and the decrease in LD with chromosomal distance. Because of this decrease, the frequency of haplotypes in strong LD with common disease variants decreases with increasing distance from the disease susceptibility locus. Thus, our haplotype proportional test has higher locus specificity than common multimarker TDTs that assume a uniform distribution of haplotype probabilities. Because of the common variant hypothesis, risk haplotypes at a given locus are relatively frequent and a metric that weights partial results for each haplotype by its frequency will be as powerful as the most powerful multimarker TDTs. Simulations and real data sets demonstrate that the test has good power compared with the best tests but has remarkably higher locus specificity, so that the association rate decreases at a higher rate with distance from a disease susceptibility or disease protective locus.     

Identifying disease polymorphisms from case–control genetic association data

In case-control association studies, it is typical to observe several associated polymorphisms in a gene region. Often the most significantly associated polymorphism is considered to be the disease polymorphism; however, it is not clear whether it is the disease polymorphism or there is more than one disease polymorphism in the gene region. Currently, there is no method that can handle these problems based on the linkage disequilibrium (LD) relationship between polymorphisms. To distinguish real disease polymorphisms from markers in LD, a method that can detect disease polymorphisms in a gene region has been developed. Relying on the LD between polymorphisms in controls, the proposed method utilizes model-based likelihood ratio tests to find disease polymorphisms. This method shows reliable Type I and Type II error rates when sample sizes are large enough, and works better with re-sequenced data. Applying this method to fine mapping using re-sequencing or dense genotyping data would provide important information regarding the genetic architecture of complex traits.     

Prospects for whole genome linkage disequilibrium mapping in domestic dog breeds

Linkage disequilibrium (LD) mapping is commonly used as a fine mapping tool in human genome mapping and has been used with some success for initial disease gene isolation in certain isolated inbred human populations. An understanding of the population history of domestic dog breeds suggests that LD mapping could be routinely utilized in this species for initial genome-wide scans. Such an approach offers significant advantages over traditional linkage analysis. Here, we demonstrate, using canine copper toxicosis in the Bedlington terrier as the model, that LD mapping could be reasonably expected to be a useful strategy in low-resolution, genome-wide scans in pure-bred dogs. Significant LD was demonstrated over distances up to 33.3 cM. It is very unlikely, for a number of reasons discussed, that this result could be extrapolated to the rest of the genome. It is, however, consistent with the expectation given the population structure of canine breeds and, in this breed at least, with the hypothesis that it may be possible to utilize LD in a genome-wide scan. In this study, LD mapping confirmed the location of the copper toxicosis in Bedlington terrier gene (CT-BT) and was able to do so in a population that was refractory to traditional linkage analysis.