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.     

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.     

General Framework for Meta-analysis of Rare Variants in Sequencing Association Studies

We propose a general statistical framework for meta-analysis of gene- or region-based multimarker rare variant association tests in sequencing association studies. In genome-wide association studies, single-marker meta-analysis has been widely used to increase statistical power by combining results via regression coefficients and standard errors from different studies. In analysis of rare variants in sequencing studies, region-based multimarker tests are often used to increase power. We propose meta-analysis methods for commonly used gene- or region-based rare variants tests, such as burden tests and variance component tests. Because estimation of regression coefficients of individual rare variants is often unstable or not feasible, the proposed method avoids this difficulty by calculating score statistics instead that only require fitting the null model for each study and then aggregating these score statistics across studies. Our proposed meta-analysis rare variant association tests are conducted based on study-specific summary statistics, specifically score statistics for each variant and between-variant covariance-type (linkage disequilibrium) relationship statistics for each gene or region. The proposed methods are able to incorporate different levels of heterogeneity of genetic effects across studies and are applicable to meta-analysis of multiple ancestry groups. We show that the proposed methods are essentially as powerful as joint analysis by directly pooling individual level genotype data. We conduct extensive simulations to evaluate the performance of our methods by varying levels of heterogeneity across studies, and we apply the proposed methods to meta-analysis of rare variant effects in a multicohort study of the genetics of blood lipid levels.     

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.     

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.     

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).     

Analysis of binary traits: testing association in the presence of linkage

Most methods for testing association in the presence of linkage, using family-based studies, have been developed for continuous traits. FBAT (family-based association tests) is one of few methods appropriate for discrete outcomes. In this article we describe a new test of association in the presence of linkage for binary traits. We use a gamma random effects model in which association and linkage are modelled as fixed effects and random effects, respectively. We have compared the gamma random effects model to an FBAT and a generalized estimating equation-based alternative, using two regions in the Genetic Analysis Workshop 14 simulated data. One of these regions contained haplotypes associated with disease, and the other did not.     

Family-based designs for genome-wide association studies

Association mapping has successfully identified common SNPs associated with many diseases. However, the inability of this class of variation to account for most of the supposed heritability has led to a renewed interest in methods - primarily linkage analysis - to detect rare variants. Family designs allow for control of population stratification, investigations of questions such as parent-of-origin effects and other applications that are imperfectly or not readily addressed in case-control association studies. This article guides readers through the interface between linkage and association analysis, reviews the new methodologies and provides useful guidelines for applications. Just as effective SNP-genotyping tools helped to realize the potential of association studies, next-generation sequencing tools will benefit genetic studies by improving the power of family-based approaches.     

Family-based approaches: design,imputation, analysis,and beyond

Participants in the family-based analysis group at Genetic Analysis Workshop 19 addressed diverse topics, all of which used the family data. Topics addressed included questions of study design and data quality control (QC), genotype imputation to augment available sequence data, and linkage and/or association analyses. Results show that pedigree-based tests that are sensitive to genotype error may be useful for QC. Imputation quality improved with inclusion of small amounts of pedigree information used to phase the data in evaluation of 5 commonly used approaches for imputation in samples of (typically) unrelated subjects. It improved still further when pedigree-based imputation using larger pedigrees was also added. An important distinction was made between methods that do versus do not make use of Mendelian transmission in pedigrees, because this serves as a key difference between underlying models and assumptions. Methods that model relatedness generally had higher power in association testing than did analyses that carry out testing in the presence of a transmission model, but this may reflect details of implementation and/or ability of more general methods to jointly include data from larger pedigrees. In either case, for single nucleotide polymorphism–set approaches, weights that incorporate information on functional effects may be more useful than those that are based only on allele frequencies. The overall results demonstrate that family data continue to provide important information in the search for trait loci.     

Linkage disequilibrium--understanding the evolutionary past and mapping the medical future

Linkage disequilibrium--the nonrandom association of alleles at different loci--is a sensitive indicator of the population genetic forces that structure a genome. Because of the explosive growth of methods for assessing genetic variation at a fine scale, evolutionary biologists and human geneticists are increasingly exploiting linkage disequilibrium in order to understand past evolutionary and demographic events, to map genes that are associated with quantitative characters and inherited diseases, and to understand the joint evolution of linked sets of genes. This article introduces linkage disequilibrium, reviews the population genetic processes that affect it and describes some of its uses. At present, linkage disequilibrium is used much more extensively in the study of humans than in non-humans, but that is changing as technological advances make extensive genomic studies feasible in other species.     

Models and tests of linkage and association studies of quantitative trait locus for multi-allele marker Loci

In this paper, we explore models and tests for association and linkage studies of a quantitative trait locus (QTL) linked to a multi-allele marker locus. Based on the difference between an offspring's conditional trait means of receiving and not receiving an allele from a parent at marker locus, we propose three statistics T(m), T(m,row) and T(m,col) to test association or linkage disequilibrium between the marker locus and the QTL. These tests are composite tests, and use the offspring marginal sample means including offspring data of both homozygous and heterozygous parents. For the linkage study, we calculate the offspring's conditional trait mean given the allele transmission status of a heterozygous parent at the marker locus. Based on the difference between the conditional means of a transmitted and a nontransmitted allele from a heterozygous parent, we propose statistics T(parsi), T(satur), T(gen) and T(m,het) to perform composite tests of linkage between the marker locus and the quantitative trait locus in the presence of association. These tests only use the offspring data that are related to the heterozygous parents at the marker locus. T(parsi) is a parsimonious or allele-wise statistic, T(satur) and T(gen )are satured or genotype-wise statistics, and T(m,het) compares the row and column sample means for offspring data of heterozygous parents. After comparing the powers and the sample sizes, we conclude that T(parsi) has higher power than those of the bi-allele tests, T(satur), T(gen), and T(m,het). If there is tight linkage between the marker and the trait locus, T(parsi) is powerful in detecting linkage between the marker and the trait locus in the presence of association. By investigating the goodness-of-fit of T(parsi), we find that T(satur) does not gain much power compared to that of T(parsi). Moreover, T(parsi) takes into account the pattern of the data that is consistent with linkage and linkage disequilibrium. As the number of alleles at the marker locus increases, T(parsi) is very conservative, and can be useful even for sparse data. To illustrate the usefulness and the power of the methods proposed in this paper, we analyze the chromosome 6 data of the Oxford asthma data, Genetic Analysis Workshop 12.     

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 studies under general disease models

There is great expectation that the levels of association found between genetic markers and disease status will play a role in the location of disease genes. This expectation follows from regarding association as being proportional to linkage disequilibrium and therefore inversely related to recombination value. For disease genes with more than two alleles, the association measure is instead a weighted average of linkage disequilibria, with the weights depending on allele frequencies and genotype susceptibilities at the disease loci. There is no longer a simple relationship, even in expectation, with recombination. We adopt a general framework to examine association mapping methods which helps to clarify the nature of case-control and transmission/disequilibrium-type tests and reveals the relationship between measures of association and coefficients of linkage disequilibrium. In particular, we can show the consequences of additive and nonadditive effects at the trait locus on the behavior of these tests. These concepts have a natural extension to marker haplotypes. The association of two-locus marker haplotypes with disease phenotype depends on a weighted average of three-locus disequilibria (two markers with each disease locus). It is likely that these two-marker analyses will provide additional information in association mapping studies.     

A Statistical Approach for Rare-Variant Association Testing in Affected Sibships

Sequencing and exome-chip technologies have motivated development of novel statistical tests to identify rare genetic variation that influences complex diseases. Although many rare-variant association tests exist for case-control or cross-sectional studies, far fewer methods exist for testing association in families. This is unfortunate, because cosegregation of rare variation and disease status in families can amplify association signals for rare variants. Many researchers have begun sequencing (or genotyping via exome chips) familial samples that were either recently collected or previously collected for linkage studies. Because many linkage studies of complex diseases sampled affected sibships, we propose a strategy for association testing of rare variants for use in this study design. The logic behind our approach is that rare susceptibility variants should be found more often on regions shared identical by descent by affected sibling pairs than on regions not shared identical by descent. We propose both burden and variance-component tests of rare variation that are applicable to affected sibships of arbitrary size and that do not require genotype information from unaffected siblings or independent controls. Our approaches are robust to population stratification and produce analytic p values, thereby enabling our approach to scale easily to genome-wide studies of rare variation. We illustrate our methods by using simulated data and exome chip data from sibships ascertained for hypertension collected as part of the Genetic Epidemiology Network of Arteriopathy (GENOA) study.     

Sibling-based tests of linkage and association for quantitative traits.

The transmission/disequilibrium test (TDT) developed by Spielman et al. can be a powerful family-based test of linkage and, in some cases, a test of association as well as linkage. It has recently been extended in several ways; these include allowance for implementation with quantitative traits, allowance for multiple alleles, and, in the case of dichotomous traits, allowance for testing in the absence of parental data. In this article, these three extensions are combined, and two procedures are developed that offer valid joint tests of linkage and (in the case of certain sibling configurations) association with quantitative traits, with use of data from siblings only, and that can accommodate biallelic or multiallelic loci. The first procedure uses a mixed-effects (i.e., random and fixed effects) analysis of variance in which sibship is the random factor, marker genotype is the fixed factor, and the continuous phenotype is the dependent variable. Covariates can easily be accommodated, and the procedure can be implemented in commonly available statistical software. The second procedure is a permutation-based procedure. Selected power studies are conducted to illustrate the relative power of each test under a variety of circumstances.     

Accounting for linkage in family-based tests of association with missing parental genotypes

In studies of complex diseases, a common paradigm is to conduct association analysis at markers in regions identified by linkage analysis, to attempt to narrow the region of interest. Family-based tests for association based on parental transmissions to affected offspring are often used in fine-mapping studies. However, for diseases with late onset, parental genotypes are often missing. Without parental genotypes, family-based tests either compare allele frequencies in affected individuals with those in their unaffected siblings or use siblings to infer missing parental genotypes. An example of the latter approach is the score test implemented in the computer program TRANSMIT. The inference of missing parental genotypes in TRANSMIT assumes that transmissions from parents to affected siblings are independent, which is appropriate when there is no linkage. However, using computer simulations, we show that, when the marker and disease locus are linked and the data set consists of families with multiple affected siblings, this assumption leads to a bias in the score statistic under the null hypothesis of no association between the marker and disease alleles. This bias leads to an inflated type I error rate for the score test in regions of linkage. We present a novel test for association in the presence of linkage (APL) that correctly infers missing parental genotypes in regions of linkage by estimating identity-by-descent parameters, to adjust for correlation between parental transmissions to affected siblings. In simulated data, we demonstrate the validity of the APL test under the null hypothesis of no association and show that the test can be more powerful than the pedigree disequilibrium test and family-based association test. As an example, we compare the performance of the tests in a candidate-gene study in families with Parkinson disease.     

X-APL: an improved family-based test of association in the presence of linkage for the X chromosome

Family-based association methods have been developed primarily for autosomal markers. The X-linked sibling transmission/disequilibrium test (XS-TDT) and the reconstruction-combined TDT for X-chromosome markers (XRC-TDT) are the first association-based methods for testing markers on the X chromosome in family data sets. These are valid tests of association in family triads or discordant sib pairs but are not theoretically valid in multiplex families when linkage is present. Recently, XPDT and XMCPDT, modified versions of the pedigree disequilibrium test (PDT), were proposed. Like the PDT, XPDT compares genotype transmissions from parents to affected offspring or genotypes of discordant siblings; however, the XPDT can have low power if there are many missing parental genotypes. XMCPDT uses a Monte Carlo sampling approach to infer missing parental genotypes on the basis of true or estimated population allele frequencies. Although the XMCPDT was shown to be more powerful than the XPDT, variability in the statistic due to the use of an estimate of allele frequency is not properly accounted for. Here, we present a novel family-based test of association, X-APL, a modification of the test for association in the presence of linkage (APL) test. Like the APL, X-APL can use singleton or multiplex families and properly infers missing parental genotypes in linkage regions by considering identity-by-descent parameters for affected siblings. Sampling variability of parameter estimates is accounted for through a bootstrap procedure. X-APL can test individual marker loci or X-chromosome haplotypes. To allow for different penetrances in males and females, separate sex-specific tests are provided. Using simulated data, we demonstrated validity and showed that the X-APL is more powerful than alternative tests. To show its utility and to discuss interpretation in real-data analysis, we also applied the X-APL to candidate-gene data in a sample of families with Parkinson disease.     

Transmission/Disequilibrium Tests Incorporating Unaffected Offspring

We propose a new method for family-based tests of association and linkage called transmission/disequilibrium tests incorporating unaffected offspring (TDTU). This new approach, constructed based on transmission/disequilibrium tests for quantitative traits (QTDT), provides a natural extension of the transmission/disequilibrium test (TDT) to utilize transmission information from heterozygous parents to their unaffected offspring as well as the affected offspring from ascertained nuclear families. TDTU can be used in various study designs and can accommodate all types of independent nuclear families with at least one affected offspring. When the study sample contains only case-parent trios, the TDTU is equivalent to TDT. Informative-transmission disequilibrium test (i-TDT) and generalized disequilibrium test(GDT) are another two methods that can use information of both unaffected offspring and affected offspring. In contract to i-TDT and GDT, the test statistic of TDTU is simpler and more explicit, and can be implemented more easily. Through computer simulations, we demonstrate that power of the TDTU is slightly higher compared to i-TDT and GDT. All the three methods are more powerful than method that uses affected offspring only, suggesting that unaffected siblings also provide information about linkage and association.     

The transmission/disequilibrium test and parental-genotype reconstruction for X-chromosomal markers

Family-based association methods have recently been introduced that allow testing for linkage in the presence of linkage disequilibrium between a marker and a disease even if there is only incomplete parental-marker information. No such tests are currently available for X-linked markers. This report fills this methodological gap by presenting the X-linked sibling transmission/disequilibrium test (XS-TDT) and the X-linked reconstruction-combination transmission/disequilibrium test (XRC-TDT). As do their autosomal counterparts (S-TDT and RC-TDT), these tests make no assumption about the mode of inheritance of the disease and the ascertainment of the sample. They protect against spurious association due to population stratification. The two tests were compared by simulations, which show that (1) the X-linked RC-TDT is, in general, considerably more powerful than the X-linked S-TDT and (2) the lack of parental-genotype information can be offset by the typing of a sufficient number of sibling controls. A freely available SAS implementation of these tests allows the calculation of exact P values.     

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.