Polygenic Variance Components Research Articles

Bayesian Inference for Mixed Model-Based Genome-Wide Analysis of Expression Quantitative Trait Loci by Gibbs Sampling.

The importance of expression quantitative trait locus (eQTL) has been emphasized in understanding the genetic basis of cellular activities and complex phenotypes. Mixed models can be employed to effectively identify eQTLs by explaining polygenic effects. In these mixed models, the polygenic effects are considered as random variables, and their variability is explained by the polygenic variance component. The polygenic and residual variance components are first estimated, and then eQTL effects are estimated depending on the variance component estimates within the frequentist mixed model framework. The Bayesian approach to the mixed model-based genome-wide eQTL analysis can also be applied to estimate the parameters that exhibit various benefits. Bayesian inferences on unknown parameters are based on their marginal posterior distributions, and the marginalization of the joint posterior distribution is a challenging task. This problem can be solved by employing a numerical algorithm of integrals called Gibbs sampling as a Markov chain Monte Carlo. This article reviews the mixed model-based Bayesian eQTL analysis by Gibbs sampling. Theoretical and practical issues of Bayesian inference are discussed using a concise description of Bayesian modeling and the corresponding Gibbs sampling. The strengths of Bayesian inference are also discussed. Posterior probability distribution in the Bayesian inference reflects uncertainty in unknown parameters. This factor is useful in the context of eQTL analysis where a sample size is too small to apply the frequentist approach. Bayesian inference based on the posterior that reflects prior knowledge, will be increasingly preferred with the accumulation of eQTL data. Extensive use of the mixed model-based Bayesian eQTL analysis will accelerate understanding of eQTLs exhibiting various regulatory functions.

Genetics of Factor VIII Inhibitor Development in Hemophilia Patients: Novel Statistical Approaches in the PATH Study

Here we apply state-of-the-art statistical genetic approaches toward investigating the genetic architecture of factor VIII (FVIII) inhibitor (FEI) development in Hemophilia A (HA). A total of 442 North American HA patients (237 Whites and 205 Blacks; 88% severely affected) enrolled in the PATH Study were: 1) ImmunoChip genotyped at ~167,000 single nucleotide polymorphisms (SNPs) in genes previously implicated in autoimmune disease risk; 2) Evaluated by DNA sequencing and assays for the recurrent intron (I)1 and I22 inversions to identify their causative F8 mutations; and 3) Tested with the Bethesda assay to determine their FEI status. The ImmunoChip genotypes were used to construct a genetic relationship matrix (GRM), denoted by K, following our previously published method,1 and the F8 sequence data along with results from the I1 and I22 inversion assays were used to construct a shared F8-mutation matrix, denoted by F. We analyzed a dichotomous FEI variable under the statistical genetic threshold/liability model (a probit regression in the fixed effects) in conjunction with a variance components model for the FEI liability phenotypic covariance matrix, denoted by P, to model potentially important random effects. For the latter, we specifically assumed independent additive genetic, F8-mutation, and residual environmental random effects. By the independence assumption, the covariance matrix is then decomposable as a sum of the additive genetic (Va), F8-mutation (Vf), and residual environmental (Ve) variances respectively structured by K, F, and the identity matrix I. The variance component model is given as: P = K*Va + F*Vf + I*Ve. Heritability, denoted by h2, is defined as the ratio of Va to the total phenotypic variance (Vp): h2 = Va / Vp. We can further speak of the total heritability given as: h2t = h2r + h2f + h2snp, where the subscripts t, r, f, and snp respectively denote total, residual additive genetic, F8-mutation-specific, and SNP heritabilities. Using eigenstructure methods,2 we can compute power under a simpler model in which Va and Vf are combined as a single variance component. We computed power to detect genetic association as measured by SNP-specific heritability for a set of 403 SNPs in or near 14 candidate immune response genes previously implicated in FEI risk. To account for multiple hypothesis testing, power was computed at the Bonferroni-adjusted significance level of 0.05/403 = 1.2 × 10-4. Under the simplified model, we computed the statistical power to detect causal SNPs for our sample and study design for the sample FEI prevalences, denoted by Kp, for Whites (22.5%) and Blacks (45%), across a range of total heritabilities, h2t = 15%, 35%, and 55%, where the lattermost total heritability was observed for FEI liability in the current study (Figure 1). It should be noted that because the liability heritability is known to be biased upward, we applied the Dempster-Lerner correction to both the total and SNP-specific heritabilities.3 Close inspection of Figure 1 reveals that varying h2t from 15% to 35% to 55% results in slight decreases in power due to the decreasing ratio of the SNP-specific heritability to the total heritability. However, as seen in all three panels, the more important determinant of power is clearly the FEI prevalence in that the power curve for a Kp of 45% is associated with greater power than the power curve for a Kp of 22.5% across the range of total heritabilities examined. As seen in Figure 1, we have adequate power to detect SNP heritabilities as low as 5% and 6%, respectively, for a Kp of 45% and 22.5%. As noted above, we observed a FEI liability total heritability of 55% consisting of a 47% residual additive genetic heritability (p = 0.019) and 8% F8-mutation specific heritability (p = 0.005). This is the first study to use a GRM based on genotype data and a shared causal F8 mutation matrix to model additive genetic and F8-mutation specific effects.Almeida M, Peralta J, Farook V, …, Blangero J. Pedigree-based random effect tests to screen gene pathways. BMC Proc. 2014; 8(Suppl 1 Genetic Analysis Workshop): S100.Blangero J, Diego VP, Dyer T, …, Göring H. A kernel of truth: statistical advances in polygenic variance component models for complex human pedigrees. Adv Genetics. 2013; 81: 1-31.Glahn D, Williams J, McKay D, …, Blangero J. Discovering schizophrenia endophenotypes in randomly ascertained pedigrees. Biol Psychiatry. 2015; 77(1): 75-83. [Display omitted] DisclosuresChitlur:Baxter, Bayer, Biogen Idec, and Pfizer: Honoraria; Novo Nordisk Inc: Consultancy. Dinh:Haplomics Biotechnology Corporation: Employment, Equity Ownership. Howard:Haplomics Biotechnology Corporation: Equity Ownership, Other: Chief Scientific Officer, Patents & Royalties: Patent applications and provisional patent applications ; CSL Behring: Research Funding.

Genomic-polygenic and polygenic predictions for milk yield, fat yield, and age at first calving in Thai multibreed dairy population using genic and functional sets of genotypes

The objectives of this research were to estimate genomic-polygenic and polygenic variance components and parameters, and to compare prediction accuracies and rankings of animals for 305-d milk yield (MY), 305-d fat yield (FY), and age at first calving (AFC) using three genomic-polygenic models and a polygenic model (PM). Data came from 8361 first-lactation cows from the Thai multibreed dairy population. The genomic-polygenic models utilized the complete set of SNP from GeneSeek GGP80k (ssGBLUP), a genic set composed of SNP associated with MY, FY, and AFC located inside or within 2500 bp of genes in the NCBI database (ssGBLUPS1), and a functional set was a subset of the genic set that included only those SNP that were present in enriched pathways involving these traits (ssGBLUPS2). The 3-trait ssGBLUP, ssGBLUPS1, ssGBLUPS2, and PM included contemporary group (herd-year-season) and heterosis as fixed effects, and animal additive genetic and residual as random effects. REML genomic-polygenic and polygenic variance components and parameters were estimated with program AIREMLF90. MY and FY ssGBLUP heritabilities were higher than PM (0.25 vs. 0.15 for MY, 0.18 vs. 0.14 for FY), but lower than PM for AFC (0.16 vs. 0.19). Genetic correlations were positive between MY and FY (0.65 for ssGBLUP; 0.72 for PM), and negative between MY and AFC (−0.11 for ssGBLUP; −0.08 for PM) and between FY and AFC (−0.17 for ssGBLUP; −0.22 for PM). Accuracies of the EBV for MY, FY, and AFC from ssGBLUP and ssGBLUPS1 were similar and higher than those from ssGBLUPS2 and PM. ssGBLUP and ssGBLUPS1 EBV yielded the highest rank correlations of all pairs of models among sires, cows, and all animals for all traits. The similarity between EBV accuracies and rank correlations from ssGBLUP and ssGBLUPS1 indicated that the set of SNP markers in the genic set could be a feasible alternative to the complete SNP set from GeneSeek GGP80k for genomic-polygenic evaluation and selection of animals in the Thai multibreed dairy population. However, an annual reassessment of the set of SNP markers included in the genic set would be advisable as additional phenotypic, pedigree, and genotypic information becomes available in future years.

Associations of the Inflammatory Marker YKL-40 with Measures of Obesity and Dyslipidaemia in Individuals at High Risk of Type 2 Diabetes.

IntroductionCirculating levels of the inflammatory marker YKL-40 are elevated in cardiovascular disease and obesity-related type 2 diabetes (T2D), and serum YKL-40 levels are related to elements of dyslipidaemia.ObjectiveWe aimed to investigate the associations between serum YKL-40 and obesity-related traits in a Danish sample of non-diabetic relatives to T2D patients and, furthermore, to estimate the heritability of YKL-40.Research Design and Methods324 non-diabetic individuals with family relation to a T2D patient were included in the study. The participants underwent oral- and intravenous glucose tolerance tests for estimation of glucose tolerance and surrogate measures of insulin sensitivity. Anthropometric measures were retrieved and biochemical measures of the plasma lipid profile and serum YKL-40 levels were obtained. Association-analyses between serum YKL-40 and obesity-related traits and estimates of the narrow sense heritability of YKL-40 were based on a polygenic variance component model.ResultsFasting serum levels of YKL-40 were positively associated with waist-hip-ratio (p<0.001) and fasting plasma triglyceride levels (p<0.001). None of the insulin sensitivity indexes were significantly associated with YKL-40. According to the AE model, the familiality-estimate h 2 of YKL-40 was 0.45 (SE 0.13). When the ACE-model was applied, the heritability-estimate h 2 of YKL-40 did not reach statistical significance.ConclusionsOur results suggest a role of serum YKL-40 in obesity-related low grade inflammation, but do not indicate that YKL-40 is directly involved in the development of T2D.

High heritability and genetic correlation of intravenous glucose- and tolbutamide-induced insulin secretion among non-diabetic family members of type 2 diabetic patients

The aim of this study was to estimate the heritability of quantitative measures of glucose regulation obtained from a tolbutamide-modified frequently sampled IVGTT (t-FSIGT) and to correlate the heritability of the glucose-stimulated beta cell response to the tolbutamide-induced beta cell response. In addition, single nucleotide polymorphisms (SNPs) having an exclusive effect on either glucose- or tolbutamide-stimulated insulin release were identified. Two hundred and eighty-four non-diabetic family members of patients with type 2 diabetes underwent a t-FSIGT with intravenous injection of glucose at t = 0 min and tolbutamide at t = 20 min. Measurements of plasma glucose, serum insulin and serum C-peptide were taken at 33 time points from fasting to 180 min. Insulin secretion rate, acute insulin response (AIR), disposition index (DI) after glucose and disposition index after tolbutamide (DIT), insulin sensitivity (SI), glucose effectiveness (SG) and beta cell responsiveness to glucose were calculated. A polygenic variance component model was used to estimate heritability, genetic correlations and associations. We found high heritabilities for acute insulin secretion subsequent to glucose stimulation (AIRglucose h (2) ± SE: 0.88 ± 0.14), but these were slightly lower after tolbutamide (AIRtolbutamide h (2) ± SE: 0.69 ± 0.14). We also estimated the heritabilities for SI (h (2) ± SE: 0.26 ± 0.12), SG (h (2) ± SE: 0.47 ± 0.13), DI (h (2) ± SE: 0.56 ± 0.14), DIT (h (2) ± SE: 0.49 ± 0.14) and beta cell responsiveness to glucose (h (2) ± SE: 0.66 ± 0.12). Additionally, strong genetic correlations were found between measures of beta cell response after glucose and tolbutamide stimulation, with correlation coefficients ranging from 0.77 to 0.88. Furthermore, we identified five SNPs with an exclusive effect on either glucose-stimulated (rs5215, rs1111875, rs11920090) or tolbutamide-stimulated (rs10946398, rs864745) insulin secretion. Our data demonstrate that both glucose- and tolbutamide-induced insulin secretions are highly heritable traits, which are largely under the control of the same genes.

Underestimation of heritability using a mixed model with a polygenic covariance structure in a genome-wide association study for complex traits

Recently, the use of a mixed model methodology in genome-wide association studies (GWAS) has been considered effective for controlling population stratification and explaining the polygenic effects of complex traits. However, estimating polygenic variance components and heritability was biased when the mixed model was used. This bias results from a diluted genetic relationship covariance structure, particularly with a limited number of underlying causal variants. We simulated disease and quantitative phenotypes with a variety of heritabilities (0.1, 0.2, 0.3, 0.4, and 0.5), prevalence rates (0.1, 0.2, 0.3, and 0.5), and causal variant numbers (10, 30, 50, and 100). Heritabilities from the simulated data using restricted maximum likelihood were underestimated in many populations (P<0.05). The underestimation increased with a large heritability, a small prevalence, and a small number of causal variants. The underestimation was larger in analyzing disease traits compared with quantitative traits. This study suggests an underestimated heritability in GWAS upon using the mixed model methodology with an excessively larger number of variants versus causal variants.

Chapter One - A Kernel of Truth: Statistical Advances in Polygenic Variance Component Models for Complex Human Pedigrees

Statistical genetic analysis of quantitative traits in large pedigrees is a formidable computational task due to the necessity of taking the nonindependence among relatives into account. With the growing awareness that rare sequence variants may be important in human quantitative variation, heritability and association study designs involving large pedigrees will increase in frequency due to the greater chance of observing multiple copies of rare variants among related individuals. Therefore, it is important to have statistical genetic test procedures that utilize all available information for extracting evidence regarding genetic association. Optimal testing for marker/phenotype association involves the exact calculation of the likelihood ratio statistic which requires the repeated inversion of potentially large matrices. In a whole genome sequence association context, such computation may be prohibitive. Toward this end, we have developed a rapid and efficient eigen simplification of the likelihood that makes analysis of family data commensurate with the analysis of a comparable sample of unrelated individuals. Our theoretical results which are based on a spectral representation of the likelihood yield simple exact expressions for the expected likelihood ratio test statistic (ELRT) for pedigrees of arbitrary size and complexity. For heritability, the ELRT is where h2 and λgi are, respectively, the heritability and eigenvalues of the pedigree-derived genetic relationship kernel (GRK). For association analysis of sequence variants, the ELRT is given by where ht2, hq2, and hr2 are the total, quantitative trait nucleotide, and residual heritabilities, respectively. Using these results, fast and accurate analytical power analyses are possible, eliminating the need for computer simulation. Additional benefits of eigen simplification include a simple method for calculation of the exact distribution of the ELRT under the null hypothesis which turns out to differ from that expected under the usual asymptotic theory. Further, when combined with the use of empirical GRKs-estimated over a large number of genetic markers-our theory reveals potential problems associated with nonpositive semidefinite kernels. These procedures are being added to our general statistical genetic computer package, SOLAR.

Short communication: Evidence for a major gene by polygene interaction for milk production traits in German Holstein dairy cattle

The present study investigated putative interaction effects between the DGAT1 K232A mutation and the polygenic term (i.e., all genes except DGAT1) for 5 milk production traits in the German Holstein dairy cattle population. Mixed models were used, and the test for interaction relied on the comparison of polygenic variance components depending on the sire's genotypes at DGAT1 K232A. Substitution effects were highly significant for all traits. Significant interaction effects were found for milk fat and protein percentage.

Changes in Variance Components of Flanking Marker Genotypes Under Varying Selection Intensities

Selection is practically ubiquitous during marker-QTL linkage analysis with an experimental population. Thus, it is necessary to investigate the impacts of selection upon linkage analyses in order to obtain unbiased estimates of QTL position and effect. In this article, by exploiting flanking markers through the widely applied half-sib design, we have developed the structures of three variance components, i.e., variance component between marker genotypes, polygenic variance component and recombinant variance component within marker genotypes. Changes in these variance components under varying selection intensities were investigated in this study to formulate the effects of selection on various variance components. Results showed clearly that all variance components presented were quite sensitive to changes in selection intensity. As selection intensity increased, all variance components declined by differing extents in a quadratic fashion. Comparatively speaking, the variance between marker genotypes decreased most drastically, followed by the polygenic variance within marker genotypes and then the recombinant variance within marker genotypes, which suggested a decrease of power for QTL linkage analysis. Therefore, steps should be taken to avoid as much as possible the presence of selection in real populations, so as to further eliminate the negative effects of selection on QTL linkage analysis.

Fine mapping of a quantitative trait locus for twinning rate using combined linkage and linkage disequilibrium mapping.

A novel and robust method for the fine-scale mapping of genes affecting complex traits, which combines linkage and linkage-disequilibrium information, is proposed. Linkage information refers to recombinations within the marker-genotyped generations and linkage disequilibrium to historical recombinations before genotyping started. The identity-by-descent (IBD) probabilities at the quantitative trait locus (QTL) between first generation haplotypes were obtained from the similarity of the marker alleles surrounding the QTL, whereas IBD probabilities at the QTL between later generation haplotypes were obtained by using the markers to trace the inheritance of the QTL. The variance explained by the QTL is estimated by residual maximum likelihood using the correlation structure defined by the IBD probabilities. Unlinked background genes were accounted for by fitting a polygenic variance component. The method was used to fine map a QTL for twinning rate in cattle, previously mapped on chromosome 5 by linkage analysis. The data consisted of large half-sib families, but the method could also handle more complex pedigrees. The likelihood of the putative QTL was very small along most of the chromosome, except for a sharp likelihood peak in the ninth marker bracket, which positioned the QTL within a region <1 cM in the middle part of bovine chromosome 5. The method was expected to be robust against multiple genes affecting the trait, multiple mutations at the QTL, and relatively low marker density.