Haplotype-sharing analysis using Mantel statistics for combined genetic effects

We applied a new approach based on Mantel statistics to analyze the Genetic Analysis Workshop 14 simulated data with prior knowledge of the answers. The method was developed in order to improve the power of a haplotype sharing analysis for gene mapping in complex disease. The new statistic correlates genetic similarity and phenotypic similarity across pairs of haplotypes from case-control studies. The genetic similarity is measured as the shared length between haplotype pairs around a genetic marker. The phenotypic similarity is measured as the mean corrected cross-product based on the respective phenotypes. Cases with phenotype P1 and unrelated controls were drawn from the population of Danacaa. Power to detect main effects was compared to the X2-test for association based on 3-marker haplotypes and a global permutation test for haplotype association to test for main effects. Power to detect gene x gene interaction was compared to unconditional logistic regression. The results suggest that the Mantel statistics might be more powerful than alternative tests.     

Composite statistics for QTL mapping with moderately discordant sibling pairs

Extreme discordant sibling-pair (EDSP) designs have been shown in theory to be very powerful for mapping quantitative-trait loci (QTLs) in humans. However, their practical applicability has been somewhat limited by the need to phenotype very large populations to find enough pairs that are extremely discordant. In this paper, we demonstrate that there is also substantial power in pairs that are only moderately discordant, and that designs using moderately discordant pairs can yield a more practical balance between phenotyping and genotyping efforts. The power we demonstrate for moderately discordant pairs stems from a new statistical result. Statistical analysis in discordant-pair studies is generally done by testing for reduced identity by descent (IBD) sharing in the pairs. By contrast, the most commonly-used statistical methods for more standard QTL mapping are Haseman-Elston regression and variance-components analysis. Both of these use statistics that are functions of the trait values given IBD information for the pedigree. We show that IBD sharing statistics and "trait value given IBD" statistics contribute complementary rather than redundant information, and thus that statistics of the two types can be combined to form more powerful tests of linkage. We propose a simple composite statistic, and test it with simulation studies. The simulation results show that our composite statistic increases power only minimally for extremely discordant pairs. However, it boosts the power of moderately discordant pairs substantially and makes them a very practical alternative. Our composite statistic is straightforward to calculate with existing software; we give a practical example of its use by applying it to a Genetic Analysis Workshop (GAW) data set.     

Fine-mapping using the weighted average method for a case-control study

We present a new method for fine-mapping a disease susceptibility locus using a case-control design. The new method, termed the weighted average (WA) statistic, averages the Cochran-Armitage (CA) trend test statistic and the difference between the Hardy-Weinberg disequilibrium test statistic for cases and controls (the HWD trend). The main characteristics of the WA statistic are that it improves on the weaknesses, and maintains the strengths, of both the CA trend test and the HWD trend test. Data from three different populations in the Genetic Analysis Workshop 14 (GAW14) simulated dataset (Aipotu, Karangar, and Danacaa) were first subjected to model-free linkage analysis to find regions exhibiting linkage. Then, for fine-scale mapping, 140 SNPs within the significant linkage regions were analyzed with the WA test statistic on replicates of the three populations, both separately and combined. The regions that were significant in the multipoint linkage analysis were also significant in this fine-scale mapping. The most significant regions that were obtained using the WA statistic were regions in chromosome 3 (B03T3056-B03T3058, p-value < 1 x 10(-10)) and chromosome 9 (B09T8332-B09T8334, p-value 1 x 10(-6)). Based on the results of the simulated GAW14 data, the WA test statistic showed good performance and could narrow down the region containing the susceptibility locus. However, the strength of the signal depends on both the strength of the linkage disequilibrium and the heterozygosity of the linked marker.     

Nonparametric disequilibrium mapping of functional sites using haplotypes of multiple tightly linked single-nucleotide polymorphism markers

As the speed and efficiency of genotyping single-nucleotide polymorphisms (SNPs) increase, using the SNP map, it becomes possible to evaluate the extent to which a common haplotype contributes to the risk of disease. In this study we propose a new procedure for mapping functional sites or regions of a candidate gene of interest using multiple linked SNPs. Based on a case-parent trio family design, we use expectation-maximization (EM) algorithm-derived haplotype frequency estimates of multiple tightly linked SNPs from both unambiguous and ambiguous families to construct a contingency statistic S for linkage disequilibrium (LD) analysis. In the procedure, a moving-window scan for functional SNP sites or regions can cover an unlimited number of loci except for the limitation of computer storage. Within a window, all possible widths of haplotypes are utilized to find the maximum statistic S* for each site (or locus). Furthermore, this method can be applied to regional or genome-wide scanning for determining linkage disequilibrium using SNPs. The sensitivity of the proposed procedure was examined on the simulated data set from the Genetic Analysis Workshop (GAW) 12. Compared with the conventional and generalized TDT methods, our procedure is more flexible and powerful.     

Comparison of linkage and association strategies for quantitative traits using the COGA dataset

Genome scans using dense single-nucleotide polymorphism (SNP) data have recently become a reality. It is thought that the increase in information content for linkage analysis as a result of the denser scans will help refine previously identified linkage regions and possibly identify new regions not identifiable using the sparser, microsatellite scans. In the context of the dense SNP scans, it is also possible to consider association strategies to provide even more information about potential regions of interest. To circumvent the multiple-testing issues inherent in association analysis, we use a recently developed strategy, implemented in PBAT, which screens the data to identify the optimal SNPs for testing, without biasing the nominal significance level. We compare the results from the PBAT analysis to that of quantitative linkage analysis on chromosome 4 using the Collaborative Study on the Genetics of Alcoholism data, as released through Genetic Analysis Workshop 14.     

Robust testing of haplotype/disease association

Haplotypes, the combination of closely linked alleles that fall on the same chromosome, show great promise for studying the genetic components of complex diseases. However, when only multilocus genotype data are available, statistical approaches need to be employed to resolve haplotype phase ambiguity. Recently, we have proposed an approach to testing and estimating haplotype/disease association that is invariant to any existing genetic structure in the population. Here we evaluate this approach by applying it to the Genetic Analysis Workshop 14 simulated data.     

Multivariate linkage analysis using the electrophysiological phenotypes in the COGA alcoholism data

Multivariate linkage analysis using several correlated traits may provide greater statistical power to detect susceptibility genes in loci whose effects are too small to be detected in univariate analysis. In this analysis, we apply a new approach and perform a linkage analysis of several electrophysiological phenotypes of the Collaborative Study on the Genetics of Alcoholism data of the Genetic Analysis Workshop 14. Our approach is based on a variance-component model to map candidate genes using repeated or longitudinal measurements. It can take into account covariate effects and time-dependent genetic effects in general pedigree data. We compare our results with the ones obtained by SOLAR using single measurement data. Our multivariate linkage analysis found linkage evidence on two regions on chromosome 4: around marker GABRB1 at 51.4 cM and marker FABP2 at 116.8 cM (unadjusted p-value = 0.00006).     

Genome-wide linkage analysis of systolic blood pressure: a comparison of two approaches to phenotype definition

Problem 1 of the Genetic Analysis Workshop 13(GAW13) contains longitudinal data of cardiovascular measurements from 330 pedigrees. The longitudinal data complicates the phenotype definition because multiple measurements are taken on each individual. To address this complication, we propose an approach that uses generalized estimating equations to obtain residuals for each time point for each person. The mean residual is then taken as the new phenotype with which to use in a variance components linkage analysis. We compare our phenotype definition approach to an approach that first reduces the multiple measurements to a single measurement and then models these summary statistics as regression terms in a variance components analysis. For each approach, multipoint linkage analysis was performed using the residuals and the SOLAR computer program. Our results show little difference between the methods based on the LOD scores.     

Combining dependent tests for linkage or association across multiple phenotypic traits

A robust statistical method to detect linkage or association between a genetic marker and a set of distinct phenotypic traits is to combine univariate trait-specific test statistics for a more powerful overall test. This procedure does not need complex modeling assumptions, can easily handle the problem with partially missing trait values, and is applicable to the case with a mixture of qualitative and quantitative traits. In this note, we propose a simple test procedure along this line, and show its advantages over the standard combination tests for linkage or association in the literature through a data set from Genetic Analysis Workshop 12 (GAW12) and an extensive simulation study.     

Comparison of family-based association tests in chromosome regions selected by linkage-based confidence intervals

We use the Genetic Analysis Workshop 14 simulated data to explore the effectiveness of a two-stage strategy for mapping complex disease loci consisting of an initial genome scan with confidence interval construction for gene location, followed by fine mapping with family-based tests of association on a dense set of single-nucleotide polymorphisms. We considered four types of intervals: the 1-LOD interval, a basic percentile bootstrap confidence interval based on the position of the maximum Zlr score, and asymptotic and bootstrap confidence intervals based on a generalized estimating equations method. For fine mapping we considered two family-based tests of association: a test based on a likelihood ratio statistic and a transmission-disequilibrium-type test implemented in the software FBAT. In two of the simulation replicates, we found that the bootstrap confidence intervals based on the peak Zlr and the 1-LOD support interval always contained the true disease loci and that the likelihood ratio test provided further strong confirmatory evidence of the presence of disease loci in these regions.     

Nonparametric longitudinal allele-sharing model

Basically no methods are available for the analysis of quantitative traits in longitudinal genetic epidemiological studies. We introduce a nonparametric factorial design for longitudinal data on independent sib pairs, modelling the phenotypic quadratic differences as the dependent variable. Factors are the number of alleles shared identically by descent (IBD) and the age categories at which the dependent variable is measured, allowing for dependence due to age. To identify a linked marker a rank statistic tests the influence of IBD group on phenotypic quadratic differences. No assumptions are made on normality or variances of the dependent variable. We apply our method to 71 sib pairs from the Framingham Heart Study data provided at the Genetic Analysis Workshop 13. For all 15 available markers on chromosome 17 we analyzed the influence on systolic blood pressure. In addition, different selection strategies to sample from the whole data are discussed.     

Whole-genome linkage analysis in mapping alcoholism genes using single-nucleotide polymorphisms and microsatellites

There is currently a great interest in using single-nucleotide polymorphisms (SNPs) in genetic linkage and association studies because of the abundance of SNPs as well as the availability of high-throughput genotyping technologies. In this study, we compared the performance of whole-genome scans using SNPs with microsatellites on 143 pedigrees from the Collaborative Studies on Genetics of Alcoholism provided by Genetic Analysis Workshop 14. A total of 315 microsatellites and 10,081 SNPs from Affymetrix on 22 autosomal chromosomes were used in our analyses. We found that the results from the two scans had good overall concordance. One region on chromosome 2 and two regions on chromosome 7 showed significant linkage signals (i.e., NPL >or= 2) for alcoholism from both the SNP and microsatellite scans. The different results observed between the two scans may be explained by the difference observed in information content between the SNPs and the microsatellites.     

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.     

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.     

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.     

Detecting Signatures of Selection Through Haplotype Differentiation Among Hierarchically Structured Populations

The detection of molecular signatures of selection is one of the major concerns of modern population genetics. A widely used strategy in this context is to compare samples from several populations and to look for genomic regions with outstanding genetic differentiation between these populations. Genetic differentiation is generally based on allele frequency differences between populations, which are measured by F_ST or related statistics. Here we introduce a new statistic, denoted hapFLK, which focuses instead on the differences of haplotype frequencies between populations. In contrast to most existing statistics, hapFLK accounts for the hierarchical structure of the sampled populations. Using computer simulations, we show that each of these two features—the use of haplotype information and of the hierarchical structure of populations—significantly improves the detection power of selected loci and that combining them in the hapFLK statistic provides even greater power. We also show that hapFLK is robust with respect to bottlenecks and migration and improves over existing approaches in many situations. Finally, we apply hapFLK to a set of six sheep breeds from Northern Europe and identify seven regions under selection, which include already reported regions but also several new ones. We propose a method to help identifying the population(s) under selection in a detected region, which reveals that in many of these regions selection most likely occurred in more than one population. Furthermore, several of the detected regions correspond to incomplete sweeps, where the favorable haplotype is only at intermediate frequency in the population(s) under selection.     

Effect of genotype x alcoholism interaction on linkage analysis of an alcoholism-related quantitative phenotype

Studies have shown that genetic and environmental factors and their interactions affect several alcoholism phenotypes. Genotype x alcoholism (GxA) interaction refers to the environmental (alcoholic and non-alcoholic) influences on the autosomal genes contributing to variation in an alcoholism-related quantitative phenotype. The purpose of this study was to examine the effects of GxA interaction on the detection of linkage for alcoholism-related phenotypes. We used phenotypic and genotypic data from the Collaborative Study on the Genetics of Alcoholism relating to 1,388 subjects as part of Genetic Analysis Workshop 14 problem 1. We analyzed the MXDRNK phenotype to detect GxA interaction using SOLAR. Upon detecting significant interaction, we conducted variance-component linkage analyses using microsatellite marker data. For maximum number of drinks per a 24 hour period, the highest LODs were observed on chromosomes 1, 4, and 13 without GxA interaction. Interaction analysis yielded four regions on chromosomes 1, 4, 13, and 15. On chromosome 4, a maximum LOD of 1.5 at the same location as the initial analysis was obtained after incorporating GxA interaction effects. However, after correcting for extra parameters, the LOD score was reduced to a corrected LOD of 1.1, which is similar to the LOD observed in the non-interaction analysis. Thus, we see little differences in LOD scores, while some linkage regions showed large differences in the magnitudes of estimated quantitative trait loci heritabilities between the alcoholic and non-alcoholic groups. These potential hints of differences in genetic effect may influence future analyses of variants under these linkage peaks.     

A method for incorporating ages at onset in affected sibpair linkage studies

Data with varying age at disease onset arise frequently in studies of mapping disease associated genes. Naively combining affected subjects with different ages at onset may result in a much reduced power in detecting the disease genes. In this paper we present a weighted score test statistic to detect the linkage between marker and latent disease loci using affected sibpairs, where the weight is used for assigning differential contribution due to the varying age at onset of each affected sibpair to the test statistic. We show that the weighted test has a correct type I error rate asymptotically. For an illustrative purpose, we analyze a data set from the 12th Genetic Analysis Workshop. The result shows that the weighted tests appear to be able to pinpoint the location of latent disease genes better than the mean IBD test with equal weight with respect to the age at onset. To avoid the potential power loss due to the improper weight, we propose to use a combined test statistic, taking the maximum of two tests, one that is weighted by the age-dependent penetrance function and the other that may be invariant to the age. We conduct an analytical study, comparing the combined test with weighted and equal weight with respect to age test. It shows that the combined test retains the most power of the better one of the two tests being combined.     

Haplotype sharing correlation of alcohol dependence on chromosomes 1-6 in 93 nuclear families

Haplotype data contain signatures of ancestral alleles and increased information for mapping genes associated with complex traits. The motivation of this paper is to test the feasibility of a recently developed haplotype reconstruction algorithm and to perform haplotype-sharing correlation (HSC) analysis in nuclear families using data provided by the Genetic Analysis Workshop 14 and the Collaborative Study of the Genetics of Alcoholism. As an exemplary analysis, haplotype data on chromosomes 1-6 were reconstructed from genotype data in 93 nuclear families by minimizing both the recombinants in within-family haplotypes and the tree distance in between-family haplotypes. HSC analysis was performed using the best set of reconstructed haplotypes, and chromosome-wide significance was evaluated using a permutation procedure. Three markers were found to have significant haplotype associations with DSM-IV alcohol dependence that exceeded the 0.05 level of chromosome-wide significance: marker rs895941 at 36.7 cM on chromosome 3 (p = 0.03), marker rs1631833 at 109.1 cM on chromosome 4 (p = 0.008), and marker rs953887 at 74.2 cM on chromosome 6 (p = 0.02). These results indicated the usefulness of HSC analysis and provided further evidence on chromosome regions associated with alcohol dependence.     

Resistance or emigration: response of the high-alpine plant Eritrichium nanum (L.) Gaudin to the ice age within the Central Alps

Two main possibilities regarding glacial survival of the mountain flora of the Alps during the Quaternary have been discussed: the tabula rasa and the nunatak hypotheses. Eritrichium nanum (L.) Gaudin (Boraginaceae) is a perennial cushion plant, occurring at high elevations of the Central Alps and having a preference for extreme habitats. It belongs to a group of high-alpine plants, for which in situ glacial survival on nunataks is ecologically possible. By investigating 20 populations of E. nanum of potential nunatak and peripheral refugial regions using amplified fragment length polymorphism, considerable genetic differences between populations from the Central Alps and populations from peripheral refugia were detected; hence, the latter probably did not serve as potential sources for the re-colonization of the Central Alps after glaciation. Genetic variation was hierarchically structured (AMOVA), and three genetically distinct regions could be identified in the Central Alps. Two of these, the Penninic and Rhaetic Alps, correspond to nunatak regions proposed in the biogeographic literature. Populations from the Lepontic Alps formed a third genetic group. Genetic correlation (Mantel statistics) was highest within populations, with a modest decline among populations within specific nunatak regions and a negative correlation outside the genetic influence of specific nunatak regions. In situ glacial survival in E. nanum could be a model for the Quaternary history of other alpine plants, especially those that also occur at high elevations and in similar habitats.