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.     

A sib-pair regression model of linkage disequilibrium for quantitative traits

A multiple-regression model is described for the detection of linkage disequilibrium in quantitative trait loci. The model is developed for application to large numbers of single nucleotide polymorphism (SNP) markers genotyped on small nuclear families. Parental data are not required by the method, although it provides a direct means to test quantitative trait locus-marker allele association and to determine whether any such association is attributable to linkage disequilibrium or population admixture. Analytical expectations for the regression coefficients are derived, allowing direct interpretation of the parameter estimates. Simulation studies indicate a substantial improvement in power over classical linkage studies of sibling pairs and show the effects of population admixture on the model outcomes.     

A test for linkage and association in general pedigrees: the pedigree disequilibrium test

Family-based tests of linkage disequilibrium typically are based on nuclear-family data including affected individuals and their parents or their unaffected siblings. A limitation of such tests is that they generally are not valid tests of association when data from related nuclear families from larger pedigrees are used. Standard methods require selection of a single nuclear family from any extended pedigrees when testing for linkage disequilibrium. Often data are available for larger pedigrees, and it would be desirable to have a valid test of linkage disequilibrium that can use all potentially informative data. In this study, we present the pedigree disequilibrium test (PDT) for analysis of linkage disequilibrium in general pedigrees. The PDT can use data from related nuclear families from extended pedigrees and is valid even when there is population substructure. Using computer simulations, we demonstrated validity of the test when the asymptotic distribution is used to assess the significance, and examined statistical power. Power simulations demonstrate that, when extended pedigree data are available, substantial gains in power can be attained by use of the PDT rather than existing methods that use only a subset of the data. Furthermore, the PDT remains more powerful even when there is misclassification of unaffected individuals. Our simulations suggest that there may be advantages to using the PDT even if the data consist of independent families without extended family information. Thus, the PDT provides a general test of linkage disequilibrium that can be widely applied to different data structures.     

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.     

Evaluation of the genetic trend of milk yield in the multiple ovulation and embryo transfer populations of dairy cows, using stochastic simulation

Stochastic modeling of dairy cattle populations using multiple ovulation and embryo transfer (MOET) was used to compare 15-year genetic responses with an artificial insemination (AI) program. MOET and AI techniques were simulated in four populations, two with 100 breeding females each and two with 400 breeding females. The selection goal was to maximize genetic progress in milk yield. The reduction in genetic variation due to inbreeding and linkage disequilibrium was accounted for in the simulation process. All four MOET breeding schemes studied achieved larger genetic responses than the realized and theoretical genetic gains from the current AI progeny testing populations. Strict restriction against inbred matings slowed genetic progress significantly in the small population but would not be consequential in the larger population. However, allowing inbred matings in the smaller population caused a rapid accumulation of inbreeding. Linkage disequilibrium was as important as inbreeding in reducing genetic variation. Genetic drift variance was much smaller in the larger population.     

Robust analysis with related samples under the presence of population substructure and its application to body mass index

Recent investigations such as a more powerful quasi-likelihoods score test (MQLS) statistic have enabled the efficient association analysis with related samples. Although those approaches are robust against the mis-specified phenotypic distribution and covariance structure, it has been shown that MQLS statistic becomes violated under the presence of the population substructure if the level of population substructure depends on the genomic location. In this report, we propose a new statistical method which combines EIGENSTRAT approach and MQLS-statistic. The proposed method was evaluated with simulation data under various scenarios and we found that proposed method performs better than the traditional methods such as transmission disequilibrium test. The proposed method was applied to genetic association analysis for body mass index with Framingham heart study, and we found that rs1121980 and rs9940128 in the linkage block in FTO gene are associated with the body mass index.     

Using Principal Components of Genetic Variation for Robust and Powerful Detection of Gene-Gene Interactions in Case-Control and Case-Only Studies

Many popular methods for exploring gene-gene interactions, including the case-only approach, rely on the key assumption that physically distant loci are in linkage equilibrium in the underlying population. These methods utilize the presence of correlation between unlinked loci in a disease-enriched sample as evidence of interactions among the loci in the etiology of the disease. We use data from the CGEMS case-control genome-wide association study of breast cancer to demonstrate empirically that the case-only and related methods have the potential to create large-scale false positives because of the presence of population stratification (PS) that creates long-range linkage disequilibrium in the genome. We show that the bias can be removed by considering parametric and nonparametric methods that assume gene-gene independence between unlinked loci, not in the entire population, but only conditional on population substructure that can be uncovered based on the principal components of a suitably large panel of PS markers. Applications in the CGEMS study as well as simulated data show that the proposed methods are robust to the presence of population stratification and are yet much more powerful, relative to standard logistic regression methods that are also commonly used as robust alternatives to the case-only type methods.     

一个基于熵的对疾病基因精细定位的指数

针对人类疾病基因的精细定位,本文利用稠密的标记位点,通过比较标记的熵和条件熵,给出了一个基于熵的指数。该指数可以度量标记基因和性状位点间连锁不平衡(LD)程度。该指数的特性是它不依赖于标记基因的频率。同时它对应疾病易感位点(DSL)精细定位的哈迪-温伯格不平衡(HWD)指数。通过计算机模拟,文章调查了不同遗传参数下该指数的性质。模拟结果表明该指数用作疾病易感位点精细定位是有效的。     

Test for interaction between two unlinked loci

Despite the growing consensus on the importance of testing gene-gene interactions in genetic studies of complex diseases, the effect of gene-gene interactions has often been defined as a deviance from genetic additive effects, which is essentially treated as a residual term in genetic analysis and leads to low power in detecting the presence of interacting effects. To what extent the definition of gene-gene interaction at population level reflects the genes' biochemical or physiological interaction remains a mystery. In this article, we introduce a novel definition and a new measure of gene-gene interaction between two unlinked loci (or genes). We developed a general theory for studying linkage disequilibrium (LD) patterns in disease population under two-locus disease models. The properties of using the LD measure in a disease population as a function of the measure of gene-gene interaction between two unlinked loci were also investigated. We examined how interaction between two loci creates LD in a disease population and showed that the mathematical formulation of the new definition for gene-gene interaction between two loci was similar to that of the LD between two loci. This finding motived us to develop an LD-based statistic to detect gene-gene interaction between two unlinked loci. The null distribution and type I error rates of the LD-based statistic for testing gene-gene interaction were validated using extensive simulation studies. We found that the new test statistic was more powerful than the traditional logistic regression under three two-locus disease models and demonstrated that the power of the test statistic depends on the measure of gene-gene interaction. We also investigated the impact of using tagging SNPs for testing interaction on the power to detect interaction between two unlinked loci. Finally, to evaluate the performance of our new method, we applied the LD-based statistic to two published data sets. Our results showed that the P values of the LD-based statistic were smaller than those obtained by other approaches, including logistic regression models.     

Robust indices of Hardy-Weinberg disequilibrium for QTL fine mapping

Hardy-Weinberg disequilibrium (HWD) measures have been proposed using dense markers to fine map a quantitative trait locus (QTL) to regions < approximately 1 cM. Earlier HWD measures may introduce bias in the fine mapping because they are dependent on marker allele frequencies across loci. Hence, HWD indices that do not depend on marker allele frequencies are desired for fine mapping. Based on our earlier work, here we present four new HWD indices that do not depend on marker allele frequencies. Two are for use when marker allele frequencies in a study population are known, and two are for use when marker allele frequencies in a study population are not known and are only known in the extreme samples. The new measures are a function of the genetic distance between the marker locus and a QTL. Through simulations, we investigated and compared the fine mapping performance of the new HWD measures with that of the earlier ones. Our results show that when marker allele frequencies vary across loci, the new measures presented here are more robust and powerful.     

Detection of genes for ordinal traits in nuclear families and a unified approach for association studies

There is growing interest in genomewide association analysis using single-nucleotide polymorphisms (SNPs), because traditional linkage studies are not as powerful in identifying genes for common, complex diseases. Tests for linkage disequilibrium have been developed for binary and quantitative traits. However, since many human conditions and diseases are measured in an ordinal scale, methods need to be developed to investigate the association of genes and ordinal traits. Thus, in the current report we propose and derive a score test statistic that identifies genes that are associated with ordinal traits when gametic disequilibrium between a marker and trait loci exists. Through simulation, the performance of this new test is examined for both ordinal traits and quantitative traits. The proposed statistic not only accommodates and is more powerful for ordinal traits, but also has similar power to that of existing tests when the trait is quantitative. Therefore, our proposed statistic has the potential to serve as a unified approach to identifying genes that are associated with any trait, regardless of how the trait is measured. We further demonstrated the advantage of our test by revealing a significant association (P = 0.00067) between alcohol dependence and a SNP in the growth-associated protein 43.     

一个基于熵的精细定位数量性状位点的指数

针对数量性状位点的精细定位,本文采用群体的极端样本,利用稠密的标记位点,通过比较标记的熵和条件熵,给出了一个基于熵的指数。该指数是标记基因和性状位点间连锁不平衡系数的函数,它不依赖于标记基因的频率。该指数对应我们之前提出的数量性状位点精细定位的哈迪-温伯格不平衡(HWD)指数,但在精细定位数量性状位点时,本文提出的指数的效能要高于哈迪-温伯格不平衡(HWD)指数。通过计算机模拟,文章调查了不同遗传参数下该指数的性质。模拟结果表明该指数用作精细定位是有效的。     

Association analysis of population-based quantitative trait data: an assessment of ANOVA

The classical analysis of variance (ANOVA) compares the means of different groups under the assumption that the variances within each of the groups are equal. However, for genetic studies of complex disorders, it is not reasonable to assume that variance of a quantitative trait within each genotype at the trait locus will be equal. Thus, the use of ANOVA may lead to misleading association inferences. In this article, we perform a simulation-based study to assess the rate of false positives and the power of ANOVA under various probability distributions of the quantitative trait and different genetic parameters such as allele frequencies and coefficient of linkage disequilibrium.     

Correlations between heterozygosity and reproductive success in the blue tit (Cyanistes caeruleus): an analysis of inbreeding and single locus effects

To understand the mechanisms behind heterozygosity-fitness correlations (HFC), it is necessary to employ large numbers of markers with known function and independently estimate the variation in inbreeding in the population. Here we genotyped 794 blue tits with 79 microsatellites that were distributed across 25 chromosomes and that were classified either as "functional" (N= 58) or "neutral" (N= 21). We found a positive effect of individual heterozygosity at multiple loci on clutch size, on the number of eggs sired by males, and on the number of recruits produced by males and females. We documented the occurrence of some consanguineous matings and found evidence for a particular type of population structure that can contribute to the occurrence of inbreeding. As the set of "neutral" loci provided more power to detect HFC and identity disequilibrium, we argue that "neutral" markers are better predictors of the effects of inbreeding. The number of significant effects at single loci did not exceed the expected number of false positives and no strong effects were associated with heterozygosity at "functional" markers. Thus, the HFC found here cannot be attributed to strong effects of the loci under study.     

Mexican mestizo population sub-structure: effects on genetic and forensic statistical parameters

Since Mexican mestizos are an admixed population, it is necessary to determine the effects that the substructure of the population has on genetic and forensic parameters. With this aim, a study was performed with 15 STR loci (CODIS plus D2S1338 and D19S433) on 1,640 unrelated Mexican mestizos. We determine allele and genotypic frequencies observing departure from Hardy–Weinberg expectation (12 out of 15 loci, with an excess of homozygotes, Fis?>?0), as well as pairs of loci in an apparent linkage disequilibrium (13 of 92 loci). We conducted a test for genetic population stratification, the results show that the Mexican mestizo population is substructured into three subgroups, which are in HW and linkage equilibrium. The combination of the 15 loci in the whole population has high forensic efficiency with the capacity to genetically discriminate one individual in one quintillion (1/10¹⁸). Our data potentially validates the use of these 15 STR loci to establish forensic identity and parentage testing for legal purposes, and offers a powerful tool for genetic variation analysis. However, given that the population is stratified, we highly recommend applying a correction with the inbreeding coefficient in calculations of paternity and forensic studies to avoid erroneous assumptions.     

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.     

Robust genomic control and robust delta centralization tests for case-control association studies

The population-based case-control design is a powerful approach for detecting susceptibility markers of a complex disease. However, this approach may lead to spurious association when there is population substructure: population stratification (PS) or cryptic relatedness (CR). Two simple approaches to correct for the population substructure are genomic control (GC) and delta centralization (DC). GC uses the variance inflation factor to correct for the variance distortion of a test statistic, and the DC centralizes the non-central chi-square distribution of the test statistic. Both GC and DC have been studied for case-control association studies mainly under a specific genetic model (e.g. recessive, additive or dominant), under which an optimal trend test is available. The genetic model is usually unknown for many complex diseases. In this situation, we study the performance of three robust tests based on the GC and DC corrections in the presence of the population substructure. Our results show that, when the genetic model is unknown, the DC- (or GC-) corrected maximum and Pearson's association test are robust and have good control of Type I error and high power relative to the optimal trend tests in the presence of PS (or CR).     

Resampling methods to reduce the selection bias in genetic effect estimation in genome-wide scans

Using the simulated data of Problem 2 for Genetic Analysis Workshop 14 (GAW14), we investigated the ability of three bootstrap-based resampling estimators (a shrinkage, an out-of-sample, and a weighted estimator) to reduce the selection bias for genetic effect estimation in genome-wide linkage scans. For the given marker density in the preliminary genome scans (7 cM for microsatellite and 3 cM for SNP), we found that the two sets of markers produce comparable results in terms of power to detect linkage, localization accuracy, and magnitude of test statistic at the peak location. At the locations detected in the scan, application of the three bootstrap-based estimators substantially reduced the upward selection bias in genetic effect estimation for both true and false positives. The relative effectiveness of the estimators depended on the true genetic effect size and the inherent power to detect it. The shrinkage estimator is recommended when the power to detect the disease locus is low. Otherwise, the weighted estimator is recommended.     

Statistical equivalent of the classical TDT for quantitative traits and multivariate phenotypes

Clinical end-point traits are usually governed by quantitative precursors. Hence, there is active research interest in developing statistical methods for association mapping of quantitative traits. Unlike population-based tests for association, family-based tests for transmission disequilibrium are protected against population stratification. In this study, we propose a logistic regression model to test the association for quantitative traits based on a trio design. We show that the method can be viewed as a direct extension of the classical transmission diequilibrium test for binary traits to quantitative traits. We evaluate the performance of our method using extensive simulations and compare it with an existing method, family-based association test. We found that the two methods yield comparable powers if all families are considered. However, unlike FBAT, which yields an inflated rate of false positives when noninformative trios with all three individuals’ heterozygous are removed, our method maintains the correct size without compromising too much on power. We show that our method can be easily modified to incorporate multivariate phenotypes. Here, we applied this method to analyse a quantitative endophenotype associated with alcoholism.     

Recombination disequilibrium in ideal and natural populations

Following Hardy-Weinberg disequilibrium (HWD) occurring at a single locus and linkage disequilibrium (LD) between two loci in generations, we here proposed the third genetic disequilibrium in a population: recombination disequilibrium (RD). RD is a measurement of crossover interference among multiple loci in a random mating population. In natural populations besides recombination interference, RD may also be due to selection, mutation, gene conversion, drift and/or migration. Therefore, similarly to LD, RD will also reflect the history of natural selection and mutation. In breeding populations, RD purely results from recombination interference and hence can be used to build or evaluate and correct a linkage map. Practical examples from F₂, testcross and human populations indeed demonstrate that RD is useful for measuring recombination interference between two short intervals and evaluating linkage maps. As with LD, RD will be important for studying genetic mapping, association of haplotypes with disease, plant breading and population history.