A composite likelihood approach to latent multivariate Gaussian modeling of SNP data with application to genetic association testing

Many statistical tests have been proposed for case-control data to detect disease association with multiple single nucleotide polymorphisms (SNPs) in linkage disequilibrium. The main reason for the existence of so many tests is that each test aims to detect one or two aspects of many possible distributional differences between cases and controls, largely due to the lack of a general and yet simple model for discrete genotype data. Here we propose a latent variable model to represent SNP data: the observed SNP data are assumed to be obtained by discretizing a latent multivariate Gaussian variate. Because the latent variate is multivariate Gaussian, its distribution is completely characterized by its mean vector and covariance matrix, in contrast to much more complex forms of a general distribution for discrete multivariate SNP data. We propose a composite likelihood approach for parameter estimation. A direct application of this latent variable model is to association testing with multiple SNPs in a candidate gene or region. In contrast to many existing tests that aim to detect only one or two aspects of many possible distributional differences of discrete SNP data, we can exclusively focus on testing the mean and covariance parameters of the latent Gaussian distributions for cases and controls. Our simulation results demonstrate potential power gains of the proposed approach over some existing methods.     

The impact of missing and erroneous genotypes on tagging SNP selection and power of subsequent association tests

OBJECTIVE: Single nucleotide polymorphisms (SNPs) serve as effective markers for localizing disease susceptibility genes, but current genotyping technologies are inadequate for genotyping all available SNP markers in a typical linkage/association study. Much attention has recently been paid to methods for selecting the minimal informative subset of SNPs in identifying haplotypes, but there has been little investigation of the effect of missing or erroneous genotypes on the performance of these SNP selection algorithms and subsequent association tests using the selected tagging SNPs. The purpose of this study is to explore the effect of missing genotype or genotyping error on tagging SNP selection and subsequent single marker and haplotype association tests using the selected tagging SNPs. METHODS: Through two sets of simulations, we evaluated the performance of three tagging SNP selection programs in the presence of missing or erroneous genotypes: Clayton's diversity based program htstep, Carlson's linkage disequilibrium (LD) based program ldSelect, and Stram's coefficient of determination based program tagsnp.exe. RESULTS: When randomly selected known loci were relabeled as 'missing', we found that the average number of tagging SNPs selected by all three algorithms changed very little and the power of subsequent single marker and haplotype association tests using the selected tagging SNPs remained close to the power of these tests in the absence of missing genotype. When random genotyping errors were introduced, we found that the average number of tagging SNPs selected by all three algorithms increased. In data sets simulated according to the haplotype frequecies in the CYP19 region, Stram's program had larger increase than Carlson's and Clayton's programs. In data sets simulated under the coalescent model, Carlson's program had the largest increase and Clayton's program had the smallest increase. In both sets of simulations, with the presence of genotyping errors, the power of the haplotype tests from all three programs decreased quickly, but there was not much reduction in power of the single marker tests. CONCLUSIONS: Missing genotypes do not seem to have much impact on tagging SNP selection and subsequent single marker and haplotype association tests. In contrast, genotyping errors could have severe impact on tagging SNP selection and haplotype tests, but not on single marker tests.     

Confirmation and fine‐mapping of clinical mastitis and somatic cell score QTL in Nordic Holstein cattle

A genome‐wide association study of 2098 progeny‐tested Nordic Holstein bulls genotyped for 36 387 SNPs on 29 autosomes was conducted to confirm and fine‐map quantitative trait loci (QTL) for mastitis traits identified earlier using linkage analysis with sparse microsatellite markers in the same population. We used linear mixed model analysis where a polygenic genetic effect was fitted as a random effect and single SNPs were successively included as fixed effects in the model. We detected 143 SNP‐by‐trait significant associations (P < 0.0001) on 20 chromosomes affecting mastitis‐related traits. Among them, 21 SNP‐by‐trait combinations exceeded the genome‐wide significant threshold. For 12 chromosomes, both the present association study and the previous linkage study detected QTL, and of these, six were in the same chromosomal locations. Strong associations of SNPs with mastitis traits were observed on bovine autosomes 6, 13, 14 and 20. Possible candidate genes for these QTL were identified. Identification of SNPs in linkage disequilibrium with QTL will enable marker‐based selection for mastitis resistance. The candidate genes identified should be further studied to detect candidate polymorphisms underlying these QTL.     

Characterization of polyploid wheat genomic diversity using a high‐density 90 000 single nucleotide polymorphism array

High‐density single nucleotide polymorphism (SNP) genotyping arrays are a powerful tool for studying genomic patterns of diversity, inferring ancestral relationships between individuals in populations and studying marker–trait associations in mapping experiments. We developed a genotyping array including about 90 000 gene‐associated SNPs and used it to characterize genetic variation in allohexaploid and allotetraploid wheat populations. The array includes a significant fraction of common genome‐wide distributed SNPs that are represented in populations of diverse geographical origin. We used density‐based spatial clustering algorithms to enable high‐throughput genotype calling in complex data sets obtained for polyploid wheat. We show that these model‐free clustering algorithms provide accurate genotype calling in the presence of multiple clusters including clusters with low signal intensity resulting from significant sequence divergence at the target SNP site or gene deletions. Assays that detect low‐intensity clusters can provide insight into the distribution of presence–absence variation (PAV) in wheat populations. A total of 46 977 SNPs from the wheat 90K array were genetically mapped using a combination of eight mapping populations. The developed array and cluster identification algorithms provide an opportunity to infer detailed haplotype structure in polyploid wheat and will serve as an invaluable resource for diversity studies and investigating the genetic basis of trait variation in wheat.     

Incorporating single-locus tests into haplotype cladistic analysis in case-control studies

In case-control studies, genetic associations for complex diseases may be probed either with single-locus tests or with haplotype-based tests. Although there are different views on the relative merits and preferences of the two test strategies, haplotype-based analyses are generally believed to be more powerful to detect genes with modest effects. However, a main drawback of haplotype-based association tests is the large number of distinct haplotypes, which increases the degrees of freedom for corresponding test statistics and thus reduces the statistical power. To decrease the degrees of freedom and enhance the efficiency and power of haplotype analysis, we propose an improved haplotype clustering method that is based on the haplotype cladistic analysis developed by Durrant et al. In our method, we attempt to combine the strengths of single-locus analysis and haplotype-based analysis into one single test framework. Novel in our method is that we develop a more informative haplotype similarity measurement by using p-values obtained from single-locus association tests to construct a measure of weight, which to some extent incorporates the information of disease outcomes. The weights are then used in computation of similarity measures to construct distance metrics between haplotype pairs in haplotype cladistic analysis. To assess our proposed new method, we performed simulation analyses to compare the relative performances of (1) conventional haplotype-based analysis using original haplotype, (2) single-locus allele-based analysis, (3) original haplotype cladistic analysis (CLADHC) by Durrant et al., and (4) our weighted haplotype cladistic analysis method, under different scenarios. Our weighted cladistic analysis method shows an increased statistical power and robustness, compared with the methods of haplotype cladistic analysis, single-locus test, and the traditional haplotype-based analyses. The real data analyses also show that our proposed method has practical significance in the human genetics field.     

Gene-based Genomewide Association Analysis: A Comparison Study

The study of gene-based genetic associations has gained conceptual popularity recently. Biologic insight into the etiology of a complex disease can be gained by focusing on genes as testing units. Several gene-based methods (e.g., minimum p-value (or maximum test statistic) or entropy-based method) have been developed and have more power than a single nucleotide polymorphism (SNP)-based analysis. The objective of this study is to compare the performance of the entropy-based method with the minimum p-value and single SNP–based analysis and to explore their strengths and weaknesses. Simulation studies show that: 1) all three methods can reasonably control the false-positive rate; 2) the minimum p-value method outperforms the entropy-based and the single SNP–based method when only one disease-related SNP occurs within the gene; 3) the entropy-based method outperforms the other methods when there are more than two disease-related SNPs in the gene; and 4) the entropy-based method is computationally more efficient than the minimum p-value method. Application to a real data set shows that more significant genes were identified by the entropy-based method than by the other two methods.     

SNPing away at complex diseases: analysis of single-nucleotide polymorphisms around APOE in Alzheimer disease

There has been great interest in the prospects of using single-nucleotide polymorphisms (SNPs) in the search for complex disease genes, and several initiatives devoted to the identification and mapping of SNPs throughout the human genome are currently underway. However, actual data investigating the use of SNPs for identification of complex disease genes are scarce. To begin to look at issues surrounding the use of SNPs in complex disease studies, we have initiated a collaborative SNP mapping study around APOE, the well-established susceptibility gene for late-onset Alzheimer disease (AD). Sixty SNPs in a 1.5-Mb region surrounding APOE were genotyped in samples of unrelated cases of AD, in controls, and in families with AD. Standard tests were conducted to look for association of SNP alleles with AD, in cases and controls. We also used family-based association analyses, including recently developed methods to look for haplotype association. Evidence of association (P相似文献   

Estimating haplotype frequencies and standard errors for multiple single nucleotide polymorphisms

Estimating haplotype frequencies becomes increasingly important in the mapping of complex disease genes, as millions of single nucleotide polymorphisms (SNPs) are being identified and genotyped. When genotypes at multiple SNP loci are gathered from unrelated individuals, haplotype frequencies can be accurately estimated using expectation-maximization (EM) algorithms (Excoffier and Slatkin, 1995; Hawley and Kidd, 1995; Long et al., 1995), with standard errors estimated using bootstraps. However, because the number of possible haplotypes increases exponentially with the number of SNPs, handling data with a large number of SNPs poses a computational challenge for the EM methods and for other haplotype inference methods. To solve this problem, Niu and colleagues, in their Bayesian haplotype inference paper (Niu et al., 2002), introduced a computational algorithm called progressive ligation (PL). But their Bayesian method has a limitation on the number of subjects (no more than 100 subjects in the current implementation of the method). In this paper, we propose a new method in which we use the same likelihood formulation as in Excoffier and Slatkin's EM algorithm and apply the estimating equation idea and the PL computational algorithm with some modifications. Our proposed method can handle data sets with large number of SNPs as well as large numbers of subjects. Simultaneously, our method estimates standard errors efficiently, using the sandwich-estimate from the estimating equation, rather than the bootstrap method. Additionally, our method admits missing data and produces valid estimates of parameters and their standard errors under the assumption that the missing genotypes are missing at random in the sense defined by Rubin (1976).     

Comparative LD mapping using single SNPs and haplotypes identifies QTL for plant height and biomass as secondary traits of drought tolerance in maize

Drought often delays developmental events so that plant height and above-ground biomass are reduced, resulting in yield loss due to inadequate photosynthate. In this study, plant height and biomass measured by the Normalized Difference Vegetation Index (NDVI) were used as criteria for drought tolerance. A total of 305 lines representing temperate, tropical and subtropical maize germplasm were genotyped using two single nucleotide polymorphism (SNP) chips each containing 1536 markers, from which 2052 informative SNPs and 386 haplotypes each constructed with two or more SNPs were used for linkage disequilibrium (LD) or association mapping. Single SNP- and haplotype-based LD mapping identified two significant SNPs and three haplotype loci [a total of four quantitative trait loci (QTL)] for plant height under well-watered and water-stressed conditions. For biomass, 32 SNPs and 12 haplotype loci (30 QTL) were identified using NDVIs measured at seven stages under the two water regimes. Some significant SNP and haplotype loci for NDVI were shared by different stages. Comparing significant loci identified by single SNP- and haplotype-based LD mapping, we found that six out of the 14 chromosomal regions defined by haplotype loci each included at least one significant SNP for the same trait. Significant SNP haplotype loci explained much higher phenotypic variation than individual SNPs. Moreover, we found that two significant SNPs (two QTL) and one haplotype locus were shared by plant height and NDVI. The results indicate the power of comparative LD mapping using single SNPs and SNP haplotypes with QTL shared by plant height and biomass as secondary traits for drought tolerance in maize.     

Association in multifactorial traits: how to deal with rare observations?

To detect the role of a candidate gene for a trait in a sample of individuals, we may test SNP haplotype or diplotype effects. For a limited sample size, many haplotype or diplotype categories may contain few individuals. This involves a power decrease when testing the association between the trait and the haplotypes or diplotypes as these categories provide little additional information while increasing the degrees of freedom. The present paper proposes a new strategy to group rare categories based on a measure of similarity between haplotypes or diplotypes and compares it to two other possible strategies to deal with rare categories: a SNP selection strategy based on haplotype diversity, and a grouping strategy that pools all rare categories into a single baseline group. This comparison is performed by means of simulation under four scenarios. We show that this new strategy shows the largest increase in power irrespective of the model underlying the candidate gene in the studied trait. This strategy therefore provides a powerful alternative to currently used methods to reduce the number of rare categories.     

Bayesian epistasis association mapping via SNP imputation

Genetic mutations may interact to increase the risk of human complex diseases. Mapping of multiple interacting disease loci in the human genome has recently shown promise in detecting genes with little main effects. The power of interaction association mapping, however, can be greatly influenced by the set of single nucleotide polymorphism (SNP) genotyped in a case-control study. Previous imputation methods only focus on imputation of individual SNPs without considering their joint distribution of possible interactions. We present a new method that simultaneously detects multilocus interaction associations and imputes missing SNPs from a full Bayesian model. Our method treats both the case-control sample and the reference data as random observations. The output of our method is the posterior probabilities of SNPs for their marginal and interacting associations with the disease. Using simulations, we show that the method produces accurate and robust imputation with little overfitting problems. We further show that, with the type I error rate maintained at a common level, SNP imputation can consistently and sometimes substantially improve the power of detecting disease interaction associations. We use a data set of inflammatory bowel disease to demonstrate the application of our method.     

A comparison of five methods for selecting tagging single-nucleotide polymorphisms

Our goal was to compare methods for tagging single-nucleotide polymorphisms (tagSNPs) with respect to the power to detect disease association under differing haplotype-disease association models. We were also interested in the effect that SNP selection samples, consisting of either cases, controls, or a mixture, would have on power. We investigated five previously described algorithms for choosing tagSNPS: two that picked SNPs based on haplotype structure (Chapman-haplotypic and Stram), two that picked SNPs based on pair-wise allelic association (Chapman-allelic and Cousin), and one control method that chose equally spaced SNPs (Zhai). In two disease-associated regions from the Genetic Analysis Workshop 14 simulated data, we tested the association between tagSNP genotype and disease over the tagSNP sets chosen by each method for each sampling scheme. This was repeated for 100 replicates to estimate power. The two allelic methods chose essentially all SNPs in the region and had nearly optimal power. The two haplotypic methods chose about half as many SNPs. The haplotypic methods had poor performance compared to the allelic methods in both regions. We expected an improvement in power when the selection sample contained cases; however, there was only moderate variation in power between the sampling approaches for each method. Finally, when compared to the haplotypic methods, the reference method performed as well or worse in the region with ancestral disease haplotype structure.     

Improved power by use of a weighted score test for linkage disequilibrium mapping

Association studies offer an exciting approach to finding underlying genetic variants of complex human diseases. However, identification of genetic variants still includes difficult challenges, and it is important to develop powerful new statistical methods. Currently, association methods may depend on single-locus analysis--that is, analysis of the association of one locus, which is typically a single-nucleotide polymorphism (SNP), at a time--or on multilocus analysis, in which multiple SNPs are used to allow extraction of maximum information about linkage disequilibrium (LD). It has been shown that single-locus analysis may have low power because a single SNP often has limited LD information. Multilocus analysis, which is more informative, can be performed on the basis of either haplotypes or genotypes. It may lose power because of the often large number of degrees of freedom involved. The ideal method must make full use of important information from multiple loci but avoid increasing the degrees of freedom. Therefore, we propose a method to capture information from multiple SNPs but with the use of fewer degrees of freedom. When a set of SNPs in a block are correlated because of LD, we might expect that the genotype variation among the different phenotypic groups would extend across all the SNPs, and this information could be compressed into the low-frequency components of a Fourier transform. Therefore, we develop a test based on weighted Fourier transformation coefficients, with more weight given to the low-frequency components. Our simulation results demonstrate the validity and substantially higher power of the proposed method compared with other common methods. This method provides an additional tool to existing methods for identification of causative genetic variants underlying complex diseases.     

Positional cloning by linkage disequilibrium

Recently, metric linkage disequilibrium (LD) maps that assign an LD unit (LDU) location for each marker have been developed (Maniatis et al. 2002). Here we present a multiple pairwise method for positional cloning by LD within a composite likelihood framework and investigate the operating characteristics of maps in physical units (kb) and LDU for two bodies of data (Daly et al. 2001; Jeffreys et al. 2001) on which current ideas of blocks are based. False-negative indications of a disease locus (type II error) were examined by selecting one single-nucleotide polymorphism (SNP) at a time as causal and taking its allelic count (0, 1, or 2, for the three genotypes) as a pseudophenotype, Y. By use of regression and correlation, association between every pseudophenotype and the allelic count of each SNP locus (X) was based on an adaptation of the Malecot model, which includes a parameter for location of the putative gene. By expressing locations in kb or LDU, greater power for localization was observed when the LDU map was fitted. The efficiency of the kb map, relative to the LDU map, to describe LD varied from a maximum of 0.87 to a minimum of 0.36, with a mean of 0.62. False-positive indications of a disease locus (type I error) were examined by simulating an unlinked causal SNP and the allele count was used as a pseudophenotype. The type I error was in good agreement with Wald's likelihood theorem for both metrics and all models that were tested. Unlike tests that select only the most significant marker, haplotype, or haploset, these methods are robust to large numbers of markers in a candidate region. Contrary to predictions from tagging SNPs that retain haplotype diversity, the sample with smaller size but greater SNP density gave less error. The locations of causal SNPs were estimated with the same precision in blocks and steps, suggesting that block definition may be less useful than anticipated for mapping a causal SNP. These results provide a guide to efficient positional cloning by SNPs and a benchmark against which the power of positional cloning by haplotype-based alternatives may be measured.     

Leveraging GWAS data to identify metabolic pathways and networks involved in maize lipid biosynthesis

Maize (Zea mays mays) oil is a rich source of polyunsaturated fatty acids (FAs) and energy, making it a valuable resource for human food, animal feed, and bio‐energy. Although this trait has been studied via conventional genome‐wide association study (GWAS), the single nucleotide polymorphism (SNP)‐trait associations generated by GWAS may miss the underlying associations when traits are based on many genes, each with small effects that can be overshadowed by genetic background and environmental variation. Detecting these SNPs statistically is also limited by the levels set for false discovery rate. A complementary pathways analysis that emphasizes the cumulative aspects of SNP‐trait associations, rather than just the significance of single SNPs, was performed to understand the balance of lipid metabolism, conversion, and catabolism in this study. This pathway analysis indicated that acyl‐lipid pathways, including biosynthesis of wax esters, sphingolipids, phospholipids and flavonoids, along with FA and triacylglycerol (TAG) biosynthesis, were important for increasing oil and FA content. The allelic variation found among the genes involved in many degradation pathways, and many biosynthesis pathways leading from FAs and carbon partitioning pathways, was critical for determining final FA content, changing FA ratios and, ultimately, to final oil content. The pathways and pathway networks identified in this study, and especially the acyl‐lipid associated pathways identified beyond what had been found with GWAS alone, provide a real opportunity to precisely and efficiently manipulate high‐oil maize genetic improvement.     

Association study of FOXO3A SNPs and aging phenotypes in Danish oldest‐old individuals

FOXO3A variation has repeatedly been reported to associate with human longevity, yet only few studies have investigated whether FOXO3A variation also associates with aging‐related traits. Here, we investigate the association of 15 FOXO3A tagging single nucleotide polymorphisms (SNPs) in 1088 oldest‐old Danes (age 92–93) with 4 phenotypes known to predict their survival: cognitive function, hand grip strength, activity of daily living (ADL), and self‐rated health. Based on previous studies in humans and foxo animal models, we also explore self‐reported diabetes, cancer, cardiovascular disease, osteoporosis, and bone (femur/spine/hip/wrist) fracture. Gene‐based testing revealed significant associations of FOXO3A variation with ADL (P = 0.044) and bone fracture (P = 0.006). The single‐SNP statistics behind the gene‐based analysis indicated increased ADL (decreased disability) and reduced bone fracture risk for carriers of the minor alleles of 8 and 10 SNPs, respectively. These positive directions of effects are in agreement with the positive effects on longevity previously reported for these SNPs. However, when correcting for the test of 9 phenotypes by Bonferroni correction, bone fracture showed borderline significance (P = 0.054), while ADL did not (P = 0.396). Although the single‐SNP associations did not formally replicate in another study population of oldest‐old Danes (n = 1279, age 94–100), the estimates were of similar direction of effect as observed in the Discovery sample. A pooled analysis of both study populations displayed similar or decreased sized P‐values for most associations, hereby supporting the initial findings. Nevertheless, confirmation in additional study populations is needed.     

Association mapping of morphological traits in wild and captive zebra finches: reliable within,but not between populations

Identifying causal genetic variants underlying heritable phenotypic variation is a long‐standing goal in evolutionary genetics. We previously identified several quantitative trait loci (QTL) for five morphological traits in a captive population of zebra finches (Taeniopygia guttata) by whole‐genome linkage mapping. We here follow up on these studies with the aim to narrow down on the quantitative trait variants (QTN) in one wild and three captive populations. First, we performed an association study using 672 single nucleotide polymorphisms (SNPs) within candidate genes located in the previously identified QTL regions in a sample of 939 wild‐caught zebra finches. Then, we validated the most promising SNP–phenotype associations (n = 25 SNPs) in 5228 birds from four populations. Genotype–phenotype associations were generally weak in the wild population, where linkage disequilibrium (LD) spans only short genomic distances. In contrast, in captive populations, where LD blocks are large, apparent SNP effects on morphological traits (i.e. associations) were highly repeatable with independent data from the same population. Most of those SNPs also showed significant associations with the same trait in other captive populations, but the direction and magnitude of these effects varied among populations. This suggests that the tested SNPs are not the causal QTN but rather physically linked to them, and that LD between SNPs and causal variants differs between populations due to founder effects. While the identification of QTN remains challenging in nonmodel organisms, we illustrate that it is indeed possible to confirm the location and magnitude of QTL in a population with stable linkage between markers and causal variants.     

Genome‐wide association studies for hematological traits in swine

Improving immune capacity may increase the profitability of animal production if it enables animals to better cope with infections. Hematological traits play pivotal roles in animal immune capacity and disease resistance. Thus far, few studies have been conducted using a high‐density swine SNP chip panel to unravel the genetic mechanism of the immune capability in domestic animals. In this study, using mixed model‐based single‐locus regression analyses, we carried out genome‐wide association studies, using the Porcine SNP60 BeadChip, for immune responses in piglets for 18 hematological traits (seven leukocyte traits, seven erythrocyte traits, and four platelet traits) after being immunized with classical swine fever vaccine. After adjusting for multiple testing based on permutations, 10, 24, and 77 chromosome‐wise significant SNPs were identified for the leukocyte traits, erythrocyte traits, and platelet traits respectively, of which 10 reached genome‐wise significance level. Among the 53 SNPs for mean platelet volume, 29 are located in a linkage disequilibrium block between 32.77 and 40.59 Mb on SSC6. Four genes of interest are located within the block, providing genetic evidence that this genomic segment may be considered a candidate region relevant to the platelet traits. Other candidate genes of interest for red blood cell, hemoglobin, and red blood cell volume distribution width also have been found near the significant SNPs. Our genome‐wide association study provides a list of significant SNPs and candidate genes that offer valuable information for future dissection of molecular mechanisms regulating hematological traits.     

Genetic mapping of recurrent exertional rhabdomyolysis in a population of North American Thoroughbreds

Recurrent exertional rhabdomyolysis is a heritable disorder that results in painful skeletal muscle cramping with exercise in up to 10% of all Thoroughbred racehorses. Here, we report a genome‐wide association study with 48 282 SNPs analyzed among 48 case and 37 control Thoroughbreds. The most significant SNPs spanned approximately 13 Mb on ECA16, and the P‐value of the most significant SNP after correcting for population structure was 8.0 × 10^?6. This region on ECA16 was further evaluated by genotyping 247 SNPs in both the initial population and a second population of 34 case and 98 control Thoroughbreds. Several SNPs across the 13‐Mb region on ECA16 showed significance when each population was analyzed separately; however, the exact positions of the most significant SNPs within this region on ECA16 varied between populations. This variability in location may be attributed to lack of power owing to insufficient sample sizes within each population individually, or to the relative distribution of long, conserved haplotypes, characteristic of the Thoroughbred breed. Future genome‐wide association studies with additional horses would likely improve the power to resolve casual loci located on ECA16 and increase the likelihood of detecting any additional loci on other chromosomes contributing to disease susceptibility.