Assessing whether an allele can account in part for a linkage signal: the Genotype-IBD Sharing Test (GIST)

To fine map genes, investigators often test for disease-marker association in chromosomal regions with evidence for linkage. Given a marker allele tentatively associated with disease, one would ask if this allele, or one in linkage disequilibrium (LD) with it, could account in part for the observed linkage signal. This question can be addressed by determining if families selected on the basis of the presence of the tentatively associated allele show stronger evidence of linkage as measured by increased allele sharing identical by descent (IBD) by affected family members. However, common selection strategies can be biased for or against linkage in the marker region, even given no disease-marker association. We define unbiased selection schemes and extend the definition to allow weighted selection on the basis of all genotyped family members. For affected-sibship data, we describe three genotype-based weight variables, corresponding to dominant, recessive, and additive models. We then introduce a test for association of a family weight variable with excess IBD sharing. This test allows us to determine if the linkage signal in a region can be attributed in part to the presence of a marker allele, either because of direct involvement in disease etiology or because of LD with a predisposing genetic variant. For samples of 500 affected sib pairs, the tests are powerful in detection of genotype-IBD sharing association, even for disease models with sib relative risk as low as lambda S=1.1, or when evidence for linkage is absent because of sampling variation. This makes our method a new tool for detecting linkage as well as association, especially in regions harboring a candidate gene. We have implemented these methods in the software package GIST (Genotype-IBD Sharing Test).     

Detecting genome wide haplotype sharing using SNP or microsatellite haplotype data

Genome wide association studies using high throughput technology are already being conducted despite the significant hurdles that need to be overcome (Nat Rev Genet 6:95–108, 2005; Nat Rev Genet 6:109–118, 2005). Methods for detecting haplotype association signals in genome wide haplotype datasets are as yet very limited. Much methodological research has already been devoted to linkage disequilibrium (LD) fine mapping where the focus is the identification of the disease locus rather than the detection of a disease signal. Applications of these approaches to genome wide scanning are limited by the strong model assumptions of the sharing process, which lead to computational complexity. We describe a new algorithm for the initial identification of disease susceptibility loci in genome wide haplotype association studies. Excess sharing of ancestral haplotypes, which indicates the presence of a disease locus, is detected with a simple, easy to interpret, χ ² based statistic. The method allows genome wide scanning for qualitative traits within reasonable computational timeframes and can serve as a first pass analysis prior to the usage of likelihood based methods, providing candidate regions and inferred susceptibility haplotypes. Our method makes no assumptions regarding the population history or the pattern of background LD. Statistical significance is evaluated with permutation tests. The method is illustrated on simulated and real data where it is applied to simple (cystic fibrosis) and complex disease (multiple sclerosis) examples. The statistic has low type I error and greater power to map disease loci over conventional single marker tests for low to moderate levels of LD.     

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。     

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

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

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.     

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

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

Family-based tests of association in the presence of linkage

Linkage analysis may not provide the necessary resolution for identification of the genes underlying phenotypic variation. This is especially true for gene-mapping studies that focus on complex diseases that do not exhibit Mendelian inheritance patterns. One positional genomic strategy involves application of association methodology to areas of identified linkage. Detection of association in the presence of linkage localizes the gene(s) of interest to more-refined regions in the genome than is possible through linkage analysis alone. This strategy introduces a statistical complexity when family-based association tests are used: the marker genotypes among siblings are correlated in linked regions. Ignoring this correlation will compromise the size of the statistical hypothesis test, thus clouding the interpretation of test results. We present a method for computing the expectation of a wide range of association test statistics under the null hypothesis that there is linkage but no association. To standardize the test statistic, an empirical variance-covariance estimator that is robust to the sibling marker-genotype correlation is used. This method is widely applicable: any type of phenotypic measure or family configuration can be used. For example, we analyze a deletion in the A2M gene at the 5' splice site of "exon II" of the bait region in Alzheimer disease (AD) discordant sibships. Since the A2M gene lies in a chromosomal region (chromosome 12p) that consistently has been linked to AD, association tests should be conducted under the null hypothesis that there is linkage but no association.     

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.     

Construction of a confidence set of markers for the location of a disease gene using affected sib pair data

We have previously proposed a confidence set approach for finding tightly linked genomic regions under the setting of parametric linkage analysis. In this article, we extend the confidence set approach to nonparametric linkage analysis of affected sib pair (ASP) data based on their identity-by-descent (IBD) information. Two well-known statistics in nonparametric linkage analysis, the Two-IBD test (proportion of ASPs sharing two alleles IBD), and the Mean test (average number of alleles shared IBD in the ASPs), are used for constructing confidence sets. Some numerical analyses as well as a simulation study were carried out to demonstrate the utility of the methods. Our results show that the fundamental advantages of the confidence set approach in parametric linkage analysis are retained when the method is generalized to nonparametric analysis. Our study on the accuracy of confidence sets, in terms of choice of tests, underlying disease incidence data, and amount of data available, leads us to conclude, among other things, that the Mean test outperforms the Two-IBD test in most situations, with the reverse being true only for traits with small additive variance. Although we describe how to construct confidence sets based on only two familiar tests, one can construct confidence sets similarly using other allele sharing statistics.     

Power calculations for a general class of tests of linkage and association that use nuclear families with affected and unaffected sibs

Family-based tests of association are now often used when trying to fine-map a disease susceptibility locus. Recently, several tests of linkage and association have been proposed that use nuclear families with multiple affected and unaffected sibs rather than just case-parent triads. In this paper we propose a test that generalizes these previous tests. Formulae are derived to calculate the power of the test for a randomly mating population. These power calculations are used to determine conditions under which it is advantageous to include unaffected sibs in the analysis.     

Linkage analysis versus association analysis: distinguishing between two models that explain disease-marker associations.

Human genetics researchers have been intrigued for many years by weak-to-moderate associations between markers and diseases. However, in most cases of association, the cause of this phenomenon is still not known. Recently, interest has grown in pursuing association studies for complex diseases, either instead of or in addition to linkage studies. Hence, it is timely to reconsider what a disease-marker association, particularly in the weak-to-moderate range (relative risk < 10), can tell us about disease etiology. To this end, this study accomplishes three aims: (1) It formulates two different models explaining weak-to-moderate associations and derives the relationship between them. One is a linkage disequilibrium model, and the other is a "susceptibility," or pure association, model. The importance of drawing the distinction between these two models and the implications for our understanding of the genetics of human disease will also be discussed. It will be argued that the linkage disequilibrium model represents true linkage but that the susceptibility model does not. (2) It examines two family-based association tests proposed recently by Parsian et al. and Spielman et al. and derives formulas for their behavior under the two models described above. It demonstrates that these tests yield almost identical results under these two models. It shows that, whereas these tests can confirm an association, they cannot determine whether the association is caused by the linkage disequilibrium model or the susceptibility model. The study also characterizes the probabilities yielded by the family association tests in the presence of weak-to-moderate associations, which will aid researchers using these tests. (3) It proposes two approaches, both based on linkage analysis, which can distinguish between the two models described above. One approach involves a straightforward linkage analysis of the data; the other involves a partitioned association-linkage (PAL) test, as suggested by Greenberg. Formulas are derived for testing identity by descent in affected sib pairs by using both approaches. (4) Finally, the formulas and arguments are illustrated with two examples from the literature and one computer-simulated data set.     

Multipoint linkage analysis of the pseudoautosomal regions, using affected sibling pairs

Affected sibling pairs are often the design of choice in linkage-analysis studies with the goal of identifying the genes that increase susceptibility to complex diseases. Methods for multipoint analysis based on sibling amount of sharing that is identical by descent are widely available, for both autosomal and X-linked markers. Such methods have the advantage of making few assumptions about the mode of inheritance of the disease. However, with this approach, data from the pseudoautosomal regions on the X chromosome pose special challenges. Same-sex sibling pairs will share, in that region of the genome, more genetic material identical by descent, with and without the presence of a disease-susceptibility gene. This increased sharing will be more pronounced for markers closely linked to the sex-specific region. For the same reason, opposite-sex sibling pairs will share fewer alleles identical by descent. Failure to take this inequality in sharing into account may result in a false declaration of linkage if the study sample contains an excess of sex-concordant pairs, or a linkage may be missed when an excess of sex-discordant pairs is present. We propose a method to take into account this expected increase/decrease in sharing when markers in the pseudoautosomal region are analyzed. For quantitative traits, we demonstrate, using the Haseman-Elston method, (1) the same inflation in type I error, in the absence of an appropriate correction, and (2) the inadequacy of permutation tests to estimate levels of significance when all phenotypic values are permuted, irrespective of gender. The proposed method is illustrated with a genome screen on 350 sibling pairs affected with type I diabetes.     

A Statistical Method for Identification of Polymorphisms That Explain a Linkage Result

Suppose that many polymorphic sites have been identified and genotyped in a region showing strong linkage with a trait. A key question of interest is which site (or combination of sites) in the region influences susceptibility to the trait. We have developed a novel statistical approach to this problem, in the context of qualitative-trait mapping, in which we use linkage data to identify the polymorphic sites whose genotypes could fully explain the observed linkage to the region. The information provided by this analysis is different from that provided by tests of either linkage or association. Our approach is based on the observation that if a particular site is the only site in the region that influences the trait, then-conditional on the genotypes at that site for the affected relatives-there should be no unexplained oversharing in the region among affected individuals. We focus on the affected sib-pair study design and develop test statistics that are variations on the usual allele-sharing methods used in linkage studies. We perform hypothesis tests and derive a confidence set for the true causal polymorphic site, under the assumption that there is only one site in the region influencing the trait. Our method is appropriate under a very general model for how the site influences the trait, including epistasis with unlinked loci, correlated environmental effects within families, and gene-environment interaction. We extend our method to larger sibships and apply it to an NIDDM1 data set.     

Genetic association mapping based on discordant sib pairs: the discordant-alleles test.

Family-based tests of association provide the opportunity to test for an association between a disease and a genetic marker. Such tests avoid false-positive results produced by population stratification, so that evidence for association may be interpreted as evidence for linkage or causation. Several methods that use family-based controls have been proposed, including the haplotype relative risk, the transmission-disequilibrium test, and affected family-based controls. However, because these methods require genotypes on affected individuals and their parents, they are not ideally suited to the study of late-onset diseases. In this paper, we develop several family-based tests of association that use discordant sib pairs (DSPs) in which one sib is affected with a disease and the other sib is not. These tests are based on statistics that compare counts of alleles or genotypes or that test for symmetry in tables of alleles or genotypes. We describe the use of a permutation framework to assess the significance of these statistics. These DSP-based tests provide the same general advantages as parent-offspring trio-based tests, while being applicable to essentially any disease; they may also be tailored to particular hypotheses regarding the genetic model. We compare the statistical properties of our DSP-based tests by computer simulation and illustrate their use with an application to Alzheimer disease and the apolipoprotein E polymorphism. Our results suggest that the discordant-alleles test, which compares the numbers of nonmatching alleles in DSPs, is the most powerful of the tests we considered, for a wide class of disease models and marker types. Finally, we discuss advantages and disadvantages of the DSP design for genetic association mapping.     

Statistical properties of affected sib-pair linkage tests

Genetic linkage analysis is a powerful tool for the identification of disease susceptibility loci. Among the most commonly applied genetic linkage strategies are affected sib-pair tests, but the statistical properties of these tests have not been well characterized. Here, we present a study of the distribution of affected sib-pair tests comparing the type I error rate and the power of the mean test and the proportion test, which are the most commonly used, along with a novel exact test. In contrast to existing literature, our findings showed that the mean and proportion tests have inflated type I error rates, especially when used with small samples. We developed and applied corrections to the tests which provide an excellent adjustment to the type I error rate for both small and large samples. We also developed a novel approach to identify the areas of higher power for the mean test versus the proportion test, providing a wider and simpler comparison with fewer assumptions about parameter values than existing approaches require.     

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.     

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

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

Score tests of genetic association in the presence of linkage based on the additive genetic gamma frailty model

Nuclear families with multiple affected sibs are often collected for genetic linkage analysis of complex diseases. Once linkage evidence is established, dense markers are often typed in the linked region for genetic association analysis based on linkage disequilibrium (LD). Detection of association in the presence of linkage localizes disease genes more accurately than the methods that rely on linkage alone. However, test of association due to LD in the linked region needs to account for dependency of the allele transmissions to different sibs within a family. In this paper, we define a joint model for genetic linkage and association and derive the corresponding joint survival function of age of onset for the sibs within a sibship. The joint survival function is a function of both the inheritance vector and the genotypes at the candidate marker locus. Based on this joint survival function, we derive score tests for genetic association. The proposed methods utilize the phenotype data of all the sibs and have the advantages of family-based designs which can avoid the potential spurious association caused by population admixture. In addition, the methods can account for variable age of onset or age at censoring and possible covariate effects, and therefore provide important tools for modelling disease heterogeneity. Simulation studies and application to the data sets from the 12th Genetic Analysis Workshop indicate that the proposed methods have correct type 1 error rates and increased power over other existing methods for testing allelic association.     

Combined linkage and association mapping of quantitative trait loci by multiple markers

Using multiple diallelic markers, variance component models are proposed for high-resolution combined linkage and association mapping of quantitative trait loci (QTL) based on nuclear families. The objective is to build a model that may fully use marker information for fine association mapping of QTL in the presence of prior linkage. The measures of linkage disequilibrium and the genetic effects are incorporated in the mean coefficients and are decomposed into orthogonal additive and dominance effects. The linkage information is modeled in variance-covariance matrices. Hence, the proposed methods model both association and linkage in a unified model. On the basis of marker information, a multipoint interval mapping method is provided to estimate the proportion of allele sharing identical by descent (IBD) and the probability of sharing two alleles IBD at a putative QTL for a sib-pair. To test the association between the trait locus and the markers, both likelihood-ratio tests and F-tests can be constructed on the basis of the proposed models. In addition, analytical formulas of noncentrality parameter approximations of the F-test statistics are provided. Type I error rates of the proposed test statistics are calculated to show their robustness. After comparing with the association between-family and association within-family (AbAw) approach by Abecasis and Fulker et al., it is found that the method proposed in this article is more powerful and advantageous based on simulation study and power calculation. By power and sample size comparison, it is shown that models that use more markers may have higher power than models that use fewer markers. The multiple-marker analysis can be more advantageous and has higher power in fine mapping QTL. As an application, the Genetic Analysis Workshop 12 German asthma data are analyzed using the proposed methods.     

Association testing in a linked region using large pedigrees

This report describes computer implementation of a scheme for joint linkage and association analysis. The model implemented in the computer package Mendel estimates both recombination and linkage-disequilibrium parameters and conducts likelihood-ratio tests for (1) linkage alone, (2) linkage and association simultaneously, and (3) association in the presence of linkage. Application of the method to data from Finnish pedigrees with familial combined hyperlipidemia illustrates its potential for identification of associated SNP haplotypes in the presence of linkage. For the test results to be valid, good estimates of haplotype frequencies must be used in the analysis.