Combined high resolution linkage and association mapping of quantitative trait loci

In this paper, we investigate variance component models of both linkage analysis and high resolution linkage disequilibrium (LD) mapping for quantitative trait loci (QTL). The models are based on both family pedigree and population data. We consider likelihoods which utilize flanking marker information, and carry out an analysis of model building and parameter estimations. The likelihoods jointly include recombination fractions, LD coefficients, the average allele substitution effect and allele dominant effect as parameters. Hence, the model simultaneously takes care of the linkage, LD or association and the effects of the putative trait locus. The models clearly demonstrate that linkage analysis and LD mapping are complementary, not exclusive, methods for QTL mapping. By power calculations and comparisons, we show the advantages of the proposed method: (1) population data can provide information for LD mapping, and family pedigree data can provide information for both linkage analysis and LD mapping; (2) using family pedigree data and a sparse marker map, one may investigate the prior suggestive linkage between trait locus and markers to obtain low resolution of the trait loci, because linkage analysis can locate a broad candidate region; (3) with the prior knowledge of suggestive linkage from linkage analysis, both population and family pedigree data can be used simultaneously in high resolution LD mapping based on a dense marker map, since LD mapping can increase the resolution for candidate regions; (4) models of high resolution LD mappings using two flanking markers have higher power than that of models of using only one marker in the analysis; (5) excluding the dominant variance from the analysis when it does exist would lose power; (6) by performing linkage interval mappings, one may get higher power than by using only one marker in the analysis.     

Haplotypes vs single marker linkage disequilibrium tests: what do we gain?

The genetic dissection of complex diseases represents a formidable challenge for modern human genetics. Recently, it has been suggested that linkage disequilibrium (LD) based methods will be a powerful approach for delineating complex disease genes. Most proposed LD test statistics search for association between a single marker and a putative trait locus. However, the power of a single marker association test may suffer because LD information contained in flanking markers is ignored. Intuitively, haplotypes (which can be regarded as a collection of ordered markers) may be more powerful than individual, unorganised markers. In this study, we derive the analytical tools based on standard chi-square statistics to directly investigate and compare the power between multilocus haplotypes and single marker LD tests. More specifically, novel formulas are obtained in order to calculate expected haplotype frequencies of unlimited size. This study demonstrates that the use of haplotypes can significantly improve the power and robustness of mapping disease genes. Additionally, we detail how the power of haplotype based association tests are affected by important population genetic parameters such as the genetic distance between markers and disease locus, mode of disease inheritance, age of trait causing mutation, frequency of associated marker allele, and level of initial LD. Finally, published data from the Hereditary Hemochromatosis disease region is used to illustrate the utility of haplotypes.     

High resolution mapping of quantitative trait loci by linkage disequilibrium analysis

Two methods, linkage analysis and linkage disequilibrium (LD) mapping or association study, are usually utilised for mapping quantitative trait loci (QTL). Linkage mapping is appropriate for low resolution mapping to localise trait loci to broad chromosome regions within a few cM (<10 cM), and is based on family data. Linkage disequilibrium mapping, on the other hand, is useful in high resolution or fine mapping, and is based on both population and family data. Using only one marker, one may carry out single-point linkage analysis and linkage disequilibrium mapping. Using two or more markers, it is possible to flank the QTL by multipoint analysis. The development and thus availability of dense marker maps, such as single nucleotide polymorphisms (SNP) in human genome, presents a tremendous opportunity for multipoint fine mapping. In this article, we propose a regression approach of mapping QTL by linkage disequilibrium mapping based on population data. Assuming that two marker loci flank one quantitative trait locus, a two-point linear regression is proposed to analyse population data. We derive analytical formulas of parameter estimations, and non-centrality parameters of appropriate tests of genetic effects and linkage disequilibrium coefficients. The merit of the method is shown by the power calculation and comparison. The two-point regression model can capture much more linkage and linkage disequilibrium information than that derived when only one marker is used. For a complex disease with heritability h(2)> or =0.15, a study with sample size of 250 can provide high power for QTL detection under moderate linkage disequilibria.     

定位人类复杂性状位点的连锁不平衡指数研究进展

随着遗传领域中快速增长的单核苷酸多态性(single nucleotide polymorphism,SNP)和详细的人类单体型数据的获得,群体水平上的连锁不平衡(linkage disequilibrium,LD)定位或关联研究被广泛用来精细定位人类复杂性状位点.一个简单的LD定位方法的关键是选取一个优良的指数来有效地度量性状基因与它紧密相连的遗传标记之间的连锁不平衡程度.本文就精细定位人类复杂性状位点的连锁不平衡指数作一综述.     

Trans-ethnic fine mapping of a quantitative trait locus for circulating angiotensin I-converting enzyme (ACE)

Circulating angiotensin I-converting enzyme (ACE) levels are influenced by a major quantitative trait locus (QTL) that maps to the ACE gene. Phylogenetic and measured haplotype analyses have suggested that the ACE-linked QTL lies downstream of a putative ancestral breakpoint located near to position 6435. However, strong linkage disequilibrium between markers in the 3' portion of the gene has prevented further resolution of the QTL in Caucasian subjects. We have examined 10 ACE gene polymorphisms in Afro-Caribbean families recruited in JAMAICA: Variance components analyses showed strong evidence of linkage and association to circulating ACE levels. When the linkage results were contrasted with those from a set of British Caucasian families, there was no evidence for heterogeneity between the samples. However, patterns of allelic association between the markers and circulating ACE levels differed significantly in the two data sets. In the British families, three markers [G2215A, Alu insertion/deletion and G2350A] were in complete disequilibrium with the ACE-linked QTL. In the Jamaican families, only marker G2350A showed strong but incomplete disequilibrium with the ACE-linked QTL. These results suggest that additional unobserved polymorphisms have an effect on circulating ACE levels in Jamaican families. Furthermore, our results show that a variance components approach combined with structured, quantitative comparisons between families from different ethnic groups may be a useful strategy for helping to determine which, if any, variants in a small genomic region directly influence a quantitative trait.     

Combined Linkage and Association Mapping of Quantitative Trait Loci with Missing Completely at Random Genotype Data

In genetics study, the genotypes or phenotypes can be missing due to various reasons. In this paper, the impact of missing genotypes is investigated for high resolution combined linkage and association mapping of quantitative trait loci (QTL). We assume that the genotype data are missing completely at random (MCAR). Two regression models, “genotype effect model” and “additive effect model”, are proposed to model the association between the markers and the trait locus. If the marker genotype is not missing, the model is exactly the same as those of our previous study, i.e., the number of genotype or allele is used as weight to model the effect of the genotype or allele in single marker case. If the marker genotype is missing, the expected number of genotype or allele is used as weight to model the effect of the genotype or allele. By analytical formulae, we show that the “genotype effect model” can be used to model the additive and dominance effects simultaneously, and the “additive effect model” can only be used to model the additive effect. Based on the two models, F-test statistics are proposed to test association between the QTL and markers. The non-centrality parameter approximations of F-test statistics are derived to calculate power and to compare power, which show that the power of the F-tests is reduced due to the missingness. By simulation study, we show that the two models have reasonable type I error rates for a dataset of moderate sample size. However, the type I error rates can be very slightly inflated if all individuals with missing genotypes are removed from analysis. Hence, the proposed method can help to get correct type I error rates although it does not improve power. As a practical example, the method is applied to analyze the angiotensin-1 converting enzyme (ACE) data. Edited by Pak Sham.     

Power of Linkage Disequilibrium Mapping to Detect a Quantitative Trait Locus (QTL) in Selected Samples of Unrelated Individuals

We considered a strategy to map quantitative trait loci (QTLs) using linkage disequilibrium (LD) when the QTL and marker locus were multiallelic. The strategy involved phenotyping a large number of unrelated individuals and genotyping only selected individuals from the two tails of the trait distribution. Power to detect trait‐marker association was assessed as a function of the number of QTL and marker alleles. Two patterns of LD were used to study their influence on power. When the frequency of the QTL allele with the largest effect and that of the marker allele linked in coupling were equal, power was maximum. In this case, increasing the number of QTL alleles reduced the power. The maximum difference in power between the two LD patterns studied was ～30%. For low QTL heritabilities (h²_QTL < 0.1) and single trait studies we recommend selecting around 5% of the upper and lower tails of the trait distribution.     

Investigation of the Ability of Haplotype Association and Logistic Regression to Identify Associated Susceptibility Loci

While finely spaced markers are increasingly being used in case‐control association studies in attempts to identify susceptibility loci, not enough is yet known as to the optimal spacing of such markers, their likely power to detect association, the relative merits of single marker versus multimarker analysis, or which methods of analysis may be optimal. Some investigations of these issues have used markers simulated under different theoretical models of population evolution. However the HapMap project and other sources provide real datasets which can be used to obtain a more realistic view of the performance of these approaches. SNPs around APOE and from two HapMap regions were used to obtain information regarding linkage disequilibrium (LD) relationships between polymorphisms, and these real patterns of LD were used to simulate datasets such as would be obtained in case‐control studies were these SNPs to influence susceptibility to disease. The datasets obtained were analysed using tests for heterogeneity of estimated haplotype frequencies and using logistic regression analyses in which only main effects from each marker were considered. All markers surrounding the putative susceptibility locus were analysed, using sets of either 1, 2, 3 or 4 markers at a time. Some markers within 150 kb of the susceptibility locus were able to detect association. At distances less than 100 kb there was no correlation between the distance from the susceptibility locus and the strength of evidence for association. When the average inter‐locus spacing is 25 kb many loci would not be detected, while when the spacing is as low as 2 kb one can be fairly confident that at least one marker will be in strong enough LD with the susceptibility locus to enable association to be detected, if the susceptibility locus has a strong enough effect relative to the sample size. With an inter‐locus spacing of 4 kb some susceptibility loci did not have a marker locus in strong LD, potentially undermining the ability to detect association. There was little difference in the performance of haplotype‐based analysis compared with logistic regression considering effects of each marker as separate. Multimarker analysis on occasion produced results which were much more highly significant than single marker analysis, but only very rarely. Our results support the view that if markers are randomly selected then a spacing as low as 2 kb is desirable. Multimarker analysis can sometimes be more powerful than single marker analysis so both should be performed. However, because it is rare for multimarker analysis to be much more highly significant than single marker analysis one should strongly suspect that when such results occur they may be due to mistakes in genotyping or through some other artefact. Haplotype analysis may be more prone to such problems than logistic regression, suggesting that the latter method might be preferred.     

Complex haplotypic structure of the central MHC region flanking TNF in a West African population

TNF polymorphisms have been associated with susceptibility to malaria and other infectious and inflammatory conditions. We investigated a sample of 150 West African chromosomes to determine linkage disequilibrium (LD) between 25 SNP markers located in an 80 kb segment of the MHC Class III region encompassing TNF and eight neighbouring genes. We observed 45 haplotypes, and 22 of them comprise 80% of the sample. The pattern of LD is remarkably patchy, such that many markers show no LD with adjacent markers but high LD with markers that are much further away. We introduce a method of examining the implications of LD data for disease association studies based on sample size considerations: this shows that certain TNF polymorphisms would be likely to yield positive associations if the true disease allele resided in LTA or BAT1. We conclude that detailed marker maps are needed to resolve the causal origin of disease associations observed at the TNF locus.     

Can long-range microsatellite data be used to predict short-range linkage disequilibrium?

The distribution of linkage disequilibrium (LD) across the genome is highly complex. Little is known about the relationship between long-range and short-range LD in a genomic region. We assessed whether a dense set of microsatellite data could be used to predict short-range LD in family samples. We analyzed intermarker LD in data derived from chromosomal regions 18q22 and 10q25-26, densely genotyped with microsatellite markers. The pattern of LD was highly heterogeneous within and between both chromosomal regions. On 10q25-26, very little LD was detected. On 18q22, where marker density was higher, many marker pairs were in LD. We modeled the decay of LD over distance in this region. A classical model accounted for most of the relationship between LD and distance (R (2)=63%). We used this model to predict the proportion of markers expected to show useful levels of LD at short distances. This prediction agreed with estimates based on single-nucleotide polymorphism (SNP) marker genotypes in the region. Both microsatellite and SNP data predict that about 80% of marker pairs would display levels of LD that are useful for association studies at distances of up to 15 kb in this region. These projections also agree with levels of LD directly measured in a 10 kb set of SNP genotypes generated in a nearby region of finished sequence. Our results suggest that existing sets of microsatellite data, if sufficiently dense, may be used to develop good initial estimates of the density of additional markers needed to screen a region for disease alleles by association analysis.     

Further Investigation of Linkage Disequilibrium SNPs and their Ability to Identify Associated Susceptibility Loci

There is currently considerable interest in the use of single‐nucleotide polymorphisms (SNPs) to map disease susceptibility genes. The success of this method will depend on a number of factors including the strength of linkage disequilibrium (LD) between marker and disease loci. We used a data set of SNP genotypings in the region of the APOE disease susceptibility locus to investigate the likely usefulness of SNPs in case‐control studies. Using the estimated haplotype structure surrounding and including the APOE locus, and assuming a codominant disease model, we treated each SNP in turn as if it were a disease susceptibility locus and obtained, for each disease locus and markers, the expected likelihood ratio test (LRT) to assess disease association.We were particularly interested in the power to detect association with the susceptibility polymorphism itself, the power of nearby markers to detect association, and the ability to distinguish between the susceptibility polymorphism and marker loci also showing association. We found that the expected LRT depended critically on disease allele frequencies. For disease loci with a reasonably common allele we were usually able to detect association. However, for only a subset of markers in the close neighbourhood of the disease locus was association detectable. In these cases we were usually, but not always, able to distinguish the disease locus from nearby associated marker loci. For some disease loci, no other loci demonstrated detectable association with the disease phenotype. We conclude that one may need to use very dense SNP maps in order to avoid overlooking polymorphisms affecting susceptibility to a common phenotype.     

Allele association studies with SSR and SNP markers at known physical distances within a 1 Mb region embracing the ALDH2 locus in the Japanese, demonstrates linkage disequilibrium extending up to 400 kb

There has been considerable recent debate concerning the distances over which levels of allelic association useful for genomic quantitative trait locus (QTL) scans can be detected. We have examined simple sequence repeat (SSR) polymorphisms and two single nucleotide polymorphisms (SNPs) in the region flanking the aldehyde dehydrogenase 2 locus, ALDH2, in populations of Japanese alcoholics and controls. These groups differ significantly in the allele frequencies for the functional SNP in exon XII of this gene located on chromosome 12. The results obtained with SSR markers complement recent investigations with SNPs over similar distances at the TCR alpha/delta locus. Significant allelic association with this marker could be detected for SSRs over distances up to 400 kb and over 37 kb for the SNP thereby extending the distance over which LD at this locus could be detected by an order of magnitude. Furthermore, as a proof of principle, we show that comparisons of allele frequency differences for the SSR markers in the case (alcoholics) and control populations would have detected the ALDH2 marker as a putative QTL. Extending the tests to include alleles at two or three flanking loci suggests that the power to detect QTLs through association can be enhanced significantly.     

The prior probability of autosomal linkage

An expression is derived for the prior probability of linkage between a random trait locus and any one of m random marker loci, and this probability is computed form=1, 10, 20, 30, 50 and 100. A similar expression is derived for two trait loci, and computed for m=1, 10, 20 and 30. When one trait locus and 30 marker loci are being studied, a priori there is over a three-quarter probability that the trait locus should be syntenic with at least one of the markers, and about a one-half probability that there should be a linkage mappable from recombination frequencies. If two traits are studied, then the prior probability that at least one should be syntenic with one of the 30 markers is 0-94, and there is a three-quarter probability that such a linkage should be mappable.     

Linkage of multilocus components of variance to polymorphic markers

Haseman & Elston (1972) introduced a sib pair method using classical regression analysis to detect linkage between a polymorphic marker locus and any quantitative trait locus. Most of the diseases mapped to date follow simple Mendelian, single locus transmission. But there are many familial diseases that do not follow simple Mendelian segregation, for example diabetes, several forms of cancer, etc. In this paper, we extend Haseman and Elston's sib pair method to two unlinked quantitative trait loci each linked to one of two unlinked polymorphic marker loci. For the two-locus epistatic model, we give a general formulation of the complete regression model and details of the regression coefficients in terms of variance components.     

Finding disease genes: a fast and flexible approach for analyzing high-throughput data

Linkage disequilibrium (LD) is the non-random distribution of alleles across the genome, and it can create serious problems for modern linkage studies. In particular, computational feasibility is often obtained at the expense of power, precision, and/or accuracy. In our new approach, we combine linkage results over multiple marker subsets to provide fast, efficient, and robust analyses, without compromising power, precision, or accuracy. Allele frequencies and LD in the densely spaced markers are used to construct subsamples that are highly informative for linkage. We have tested our approach extensively, and implemented it in the software package EAGLET (Efficient Analysis of Genetic Linkage: Estimation and Testing). Relative to several commonly used methods we show that EAGLET has increased power to detect disease genes across a range of trait models, LD patterns, and family structures using both simulated and real data. In particular, when the underlying LD pattern is derived from real data, we find that EAGLET outperforms several commonly used linkage methods. In-depth analysis of family data, simulated with linkage and under the real-data derived LD pattern, showed that EAGLET had 78.1% power to detect a dominant disease with incomplete penetrance, whereas the method that uses one marker per cM had 69.7% power, and the cluster-based approach implemented in MERLIN had 76.7% power. In this same setting, EAGLET was three times faster than MERLIN, and it narrowed the MERLIN-based confidence interval for trait location by 29%. Overall, EAGLET gives researchers a fast, accurate, and powerful new tool for analyzing high-throughput linkage data, and large extended families are easily accommodated.     

Extent and distribution of linkage disequilibrium around the SLC11A1 locus

The SLC11A1 (or NRAMP1) locus on human chromosome 2q35 encodes for the protein solute carrier family 11, member 1. It is expressed in macrophages and involved in the early stages of macrophage priming and activation. Different association studies have shown that the SLC11A1 gene affects susceptibility to infectious diseases and autoimmune inflammatory diseases. Although functional SLC11A1 polymorphisms may account for its role in affecting the susceptibility to these diseases, the positive association can also be because of flanking polymorphisms showing linkage disequilibrium (LD) with this locus. This is the first systematic study to investigate the LD pattern within and around the gene. LD was investigated by genotyping 17 genetic markers in a Chinese population (n=360). The results indicate that LD is maintained at least 110 kb both upstream and downstream of the locus. The complex LD pattern demands that association studies with SLC11A1 should be carried out with both 5' and 3' markers. The strong LD between IL8RB and the 5' SLC11A1 markers also dictates that IL8RB be tested for association with these diseases. Thus, positive association with SLC11A1 should be interpreted cautiously, and IL8RB should also be considered as a potential candidate susceptibility gene unless proven otherwise.     

Confirmation of the DRB1-DQB1 loci as the major component of IDDM1 in the isolated founder population of Sardinia

There is considerable uncertainty and debate concerning the application of linkage disequilibrium (LD) mapping in common multifactorial diseases, including the choice of population and the density of the marker map. Previously, it has been shown that, in the large cosmopolitan population of the UK, the established type 1 diabetes IDDM1 locus in the HLA region could be mapped with high resolution by LD. The LD curve peaked at marker D6S2444, 85 kb from the HLA class II gene DQB1, which is known to be a major determinant of IDDM1. However, given the many unknown parameters underlying LD, a validation of the approach in a genetically distinct population is necessary. In the present report we have achieved this by the LD mapping of IDDM1 in the isolated founder population of Sardinia. Using a dense map of microsatellite markers, we determined the peak of LD to be located at marker D6S2447, which is only 6.5 kb from DQB1. Next, we typed a large number of SNPs defining allelic variation at functional candidate genes within the critical region. The association curve, with both classes of marker, peaked at the loci DRB1-DQB1. These results, while representing conclusive evidence that the class II loci DRB1-DQB1 dominate the association of the HLA region to type 1 diabetes, provide empirical support for LD mapping.     

Long-range sequence composition mirrors linkage disequilibrium pattern in a 1.13 Mb region of human chromosome 22.

Association studies, the most powerful tool for the identification of genes underlying complex traits, depend on the observation of linkage disequilibrium (LD) between marker alleles and the trait. The LD pattern of the human genome which determines the regional density of required markers is non-uniform, with regions of long-range LD over several hundred kilobases and regions where LD extends only over a few kilobases. Studying LD in the NF1 gene region we encountered a transition from long-range to short-range LD which coincides with a switch in the isochore pattern. This observation prompted us to investigate the regional variation in the extent of LD more systematically and we selected an isochore transition within the MN1/PITPNB gene region on chromosome 22q12.1. Long-range LD characterizes the GC-poor (40% GC) parts of the sequences. No LD can be observed between closely spaced markers throughout the whole range of the GC-rich (50% GC) parts. In both cases, the NF1 and the MN1/PITPNB gene region, a clear-cut transition of the long-range GC content precisely coincides with a change in the extent of observable LD. The results can be explained by a 72-fold lower recombination frequency in the GC-poor, compared to the GC-rich isochores. Although recombination is not the only factor governing LD, our findings can help to predict levels of LD and marker densities required for association studies on the basis of regional GC content.     

Clustering of haplotypes based on phylogeny: how good a strategy for association testing?

Haplotypes are now widely used in association studies between markers and disease susceptibility locus. However, when a large number of markers are considered, the number of possible haplotypes increases leading to two problems: an increased number of degrees of freedom that may result in a lack of power and the existence of rare haplotypes that may be difficult to take into account in the statistical analysis. In a recent paper, Durrant et al proposed a method, CLADHC, to group haplotypes based on distance matrices and showed that this could considerably increase the power of the association test as compared to either single-locus analysis or haplotype analysis without prior grouping. Although the authors considered different one-disease-locus susceptibility models in their simulations, they did not study the impact of the linkage disequilibrium (LD) pattern and of the susceptibility allele frequency on their conclusions. Here, we show, using haplotype data from five regions of the genome of different lengths and with different LD patterns, that, when a single disease susceptibility locus is simulated, the prior grouping of haplotypes based on the algorithm of Durrant et al does not increase the power of association testing except in very particular situations of LD patterns and allele frequencies.