title: 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.
authors.affiliation: Institute of Biological Psychiatry, Mental Health Centre Sct. Hans, Mental Health Services, Copenhagen, Denmark.|The Lundbeck Foundation Initiative for Integrative Psychiatric Research, iPSYCH, Copenhagen, Denmark.|Department of Psychiatry, University of California, San Diego, La Jolla, California, United States of America.
authors.forename: Wesley K
authors.initials: WK
authors.lastname: Thompson
authors.affiliation: Division of Mental Health and Addiction, Oslo University Hospital, Oslo, Norway.
authors.forename: Yunpeng
authors.initials: Y
authors.lastname: Wang
authors.affiliation: Department of Cognitive Science, University of California, San Diego, La Jolla, California, United States of America.
authors.forename: Andrew J
authors.initials: AJ
authors.lastname: Schork
authors.affiliation: Division of Mental Health and Addiction, Oslo University Hospital, Oslo, Norway.
authors.forename: Aree
authors.initials: A
authors.lastname: Witoelar
authors.affiliation: Division of Mental Health and Addiction, Oslo University Hospital, Oslo, Norway.
authors.forename: Verena
authors.initials: V
authors.lastname: Zuber
authors.affiliation: Department of Psychiatry, University of California, San Diego, La Jolla, California, United States of America.
authors.forename: Shujing
authors.initials: S
authors.lastname: Xu
authors.affiliation: Institute of Biological Psychiatry, Mental Health Centre Sct. Hans, Mental Health Services, Copenhagen, Denmark.|The Lundbeck Foundation Initiative for Integrative Psychiatric Research, iPSYCH, Copenhagen, Denmark.|Department of Clinical Medicine, University of Copenhagen, Copenhagen, Denmark.
authors.forename: Thomas
authors.initials: T
authors.lastname: Werge
authors.affiliation: Multimodal Imaging Laboratory, University of California at San Diego, La Jolla, California, United States of America.
authors.forename: Dominic
authors.initials: D
authors.lastname: Holland
authors.affiliation: Division of Mental Health and Addiction, Oslo University Hospital, Oslo, Norway.
authors.forename: Ole A
authors.initials: OA
authors.lastname: Andreassen
authors.affiliation: Multimodal Imaging Laboratory, University of California at San Diego, La Jolla, California, United States of America.
authors.forename: Anders M
authors.initials: AM
authors.lastname: Dale
mesh_terms: D001499:Bayes Theorem; D003424:Crohn Disease / Q000235:genetics; D020022:Genetic Predisposition to Disease; D055106:Genome-Wide Association Study / Q000379:methods*; D006801:Humans; D008957:Models, Genetic; D020641:Polymorphism, Single Nucleotide; D012559:Schizophrenia / Q000235:genetics