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An Empirical Bayes Mixture Model for Effect Size Distributions in Genome-Wide Association Studies.

ABSTRACT: Characterizing the distribution of effects from genome-wide genotyping data is crucial for understanding important aspects of the genetic architecture of complex traits, such as number or proportion of non-null loci, average proportion of phenotypic variance explained per non-null effect, power for discovery, and polygenic risk prediction. To this end, previous work has used effect-size models based on various distributions, including the normal and normal mixture distributions, among others. In this paper we propose a scale mixture of two normals model for effect size distributions of genome-wide association study (GWAS) test statistics. Test statistics corresponding to null associations are modeled as random draws from a normal distribution with zero mean; test statistics corresponding to non-null associations are also modeled as normal with zero mean, but with larger variance. The model is fit via minimizing discrepancies between the parametric mixture model and resampling-based nonparametric estimates of replication effect sizes and variances. We describe in detail the implications of this model for estimation of the non-null proportion, the probability of replication in de novo samples, the local false discovery rate, and power for discovery of a specified proportion of phenotypic variance explained from additive effects of loci surpassing a given significance threshold. We also examine the crucial issue of the impact of linkage disequilibrium (LD) on effect sizes and parameter estimates, both analytically and in simulations. We apply this approach to meta-analysis test statistics from two large GWAS, one for Crohn's disease (CD) and the other for schizophrenia (SZ). A scale mixture of two normals distribution provides an excellent fit to the SZ nonparametric replication effect size estimates. While capturing the general behavior of the data, this mixture model underestimates the tails of the CD effect size distribution. We discuss the implications of pervasive small but replicating effects in CD and SZ on genomic control and power. Finally, we conclude that, despite having very similar estimates of variance explained by genotyped SNPs, CD and SZ have a broadly dissimilar genetic architecture, due to differing mean effect size and proportion of non-null loci.

SUBMITTER: Thompson WK

PROVIDER: S-EPMC5456456 | biostudies-literature | 2015 Dec

REPOSITORIES: biostudies-literature

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An Empirical Bayes Mixture Model for Effect Size Distributions in Genome-Wide Association Studies.

Thompson Wesley K WK Wang Yunpeng Y Schork Andrew J AJ Witoelar Aree A Zuber Verena V Xu Shujing S Werge Thomas T Holland Dominic D Andreassen Ole A OA Dale Anders M AM

PLoS genetics 20151229 12

Characterizing the distribution of effects from genome-wide genotyping data is crucial for understanding important aspects of the genetic architecture of complex traits, such as number or proportion of non-null loci, average proportion of phenotypic variance explained per non-null effect, power for discovery, and polygenic risk prediction. To this end, previous work has used effect-size models based on various distributions, including the normal and normal mixture distributions, among others. In ...[more]

PMID: 26714184

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Project description:BackgroundRecently mixed linear models are used to address the issue of "missing" heritability in traditional Genome-wide association studies (GWAS). The models assume that all single-nucleotide polymorphisms (SNPs) are associated with the phenotypes of interest. However, it is more common that only a small proportion of SNPs have significant effects on the phenotypes, while most SNPs have no or very small effects. To incorporate this feature, we propose an efficient Hierarchical Bayesian Model (HBM) that extends the existing mixed models to enforce automatic selection of significant SNPs. The HBM models the SNP effects using a mixture distribution of a point mass at zero and a normal distribution, where the point mass corresponds to those non-associative SNPs.ResultsWe estimate the HBM using Gibbs sampling. The estimation performance of our method is first demonstrated through two simulation studies. We make the simulation setups realistic by using parameters fitted on the Framingham Heart Study (FHS) data. The simulation studies show that our method can accurately estimate the proportion of SNPs associated with the simulated phenotype and identify these SNPs, as well as adapt to certain model mis-specification than the standard mixed models. In addition, we analyze data from the FHS and the Health and Retirement Study (HRS) to study the association between Body Mass Index (BMI) and SNPs on Chromosome 16, and replicate the identified genetic associations. The analysis of the FHS data identifies 0.3% SNPs on Chromosome 16 that affect BMI, including rs9939609 and rs9939973 on the FTO gene. These two SNPs are in strong linkage disequilibrium with rs1558902 (Rsq =0.901 for rs9939609 and Rsq =0.905 for rs9939973), which has been reported to be linked with obesity in previous GWAS. We then replicate the findings using the HRS data: the analysis finds 0.4% of SNPs associated with BMI on Chromosome 16. Furthermore, around 25% of the genes that are identified to be associated with BMI are common between the two studies.ConclusionsThe results demonstrate that the HBM and the associated estimation algorithm offer a powerful tool for identifying significant genetic associations with phenotypes of interest, among a large number of SNPs that are common in modern genetics studies.

Dataset Information

An Empirical Bayes Mixture Model for Effect Size Distributions in Genome-Wide Association Studies.

Publications

An Empirical Bayes Mixture Model for Effect Size Distributions in Genome-Wide Association Studies.

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