title: Estimating Effect Sizes and Expected Replication Probabilities from GWAS Summary Statistics.
abstract: Genome-wide Association Studies (GWAS) result in millions of summary statistics ("z-scores") for single nucleotide polymorphism (SNP) associations with phenotypes. These rich datasets afford deep insights into the nature and extent of genetic contributions to complex phenotypes such as psychiatric disorders, which are understood to have substantial genetic components that arise from very large numbers of SNPs. The complexity of the datasets, however, poses a significant challenge to maximizing their utility. This is reflected in a need for better understanding the landscape of z-scores, as such knowledge would enhance causal SNP and gene discovery, help elucidate mechanistic pathways, and inform future study design. Here we present a parsimonious methodology for modeling effect sizes and replication probabilities, relying only on summary statistics from GWAS substudies, and a scheme allowing for direct empirical validation. We show that modeling z-scores as a mixture of Gaussians is conceptually appropriate, in particular taking into account ubiquitous non-null effects that are likely in the datasets due to weak linkage disequilibrium with causal SNPs. The four-parameter model allows for estimating the degree of polygenicity of the phenotype and predicting the proportion of chip heritability explainable by genome-wide significant SNPs in future studies with larger sample sizes. We apply the model to recent GWAS of schizophrenia (N = 82,315) and putamen volume (N = 12,596), with approximately 9.3 million SNP z-scores in both cases. We show that, over a broad range of z-scores and sample sizes, the model accurately predicts expectation estimates of true effect sizes and replication probabilities in multistage GWAS designs. We assess the degree to which effect sizes are over-estimated when based on linear-regression association coefficients. We estimate the polygenicity of schizophrenia to be 0.037 and the putamen to be 0.001, while the respective sample sizes required to approach fully explaining the chip heritability are 10(6) and 10(5). The model can be extended to incorporate prior knowledge such as pleiotropy and SNP annotation. The current findings suggest that the model is applicable to a broad array of complex phenotypes and will enhance understanding of their genetic architectures.
authors.affiliation: Multimodal Imaging Laboratory, University of CaliforniaSan Diego, La Jolla, CA, USA; Department of Neurosciences, University of CaliforniaSan Diego, La Jolla, CA, USA.
authors.forename: Dominic
authors.initials: D
authors.lastname: Holland
authors.affiliation: Multimodal Imaging Laboratory, University of CaliforniaSan Diego, La Jolla, CA, USA; Department of Neurosciences, University of CaliforniaSan Diego, La Jolla, CA, USA; NORMENT, KG Jebsen Centre for Psychosis Research, Institute of Clinical Medicine, University of OsloOslo, Norway; Division of Mental Health and Addiction, Oslo University HospitalOslo, Norway.
authors.forename: Yunpeng
authors.initials: Y
authors.lastname: Wang
authors.affiliation: Department of Psychiatry, University of California San Diego, La Jolla, CA, USA.
authors.forename: Wesley K
authors.initials: WK
authors.lastname: Thompson
authors.affiliation: Multimodal Imaging Laboratory, University of CaliforniaSan Diego, La Jolla, CA, USA; Department of Cognitive Sciences, University of CaliforniaSan Diego, La Jolla, CA, USA.
authors.forename: Andrew
authors.initials: A
authors.lastname: Schork
authors.affiliation: Multimodal Imaging Laboratory, University of CaliforniaSan Diego, La Jolla, CA, USA; Department of Radiology, University of CaliforniaSan Diego, La Jolla, CA, USA.
authors.forename: Chi-Hua
authors.initials: CH
authors.lastname: Chen
authors.affiliation: Multimodal Imaging Laboratory, University of CaliforniaSan Diego, La Jolla, CA, USA; Department of Radiology, University of CaliforniaSan Diego, La Jolla, CA, USA.
authors.forename: Min-Tzu
authors.initials: MT
authors.lastname: Lo
authors.affiliation: NORMENT, KG Jebsen Centre for Psychosis Research, Institute of Clinical Medicine, University of OsloOslo, Norway; Division of Mental Health and Addiction, Oslo University HospitalOslo, Norway.
authors.forename: Aree
authors.initials: A
authors.lastname: Witoelar
authors.affiliation: Institute of Biological Psychiatry, MHC, Sct. Hans Hospital and University of Copenhagen Copenhagen, Denmark.
authors.forename: Thomas
authors.initials: T
authors.lastname: Werge
authors.affiliation: MRC Centre for Neuropsychiatric Genetics and Genomics, School of Medicine, Cardiff University Cardiff, UK.
authors.forename: Michael
authors.initials: M
authors.lastname: O'Donovan
authors.affiliation: NORMENT, KG Jebsen Centre for Psychosis Research, Institute of Clinical Medicine, University of OsloOslo, Norway; Division of Mental Health and Addiction, Oslo University HospitalOslo, Norway.
authors.forename: Ole A
authors.initials: OA
authors.lastname: Andreassen
authors.affiliation: Multimodal Imaging Laboratory, University of CaliforniaSan Diego, La Jolla, CA, USA; Department of Neurosciences, University of CaliforniaSan Diego, La Jolla, CA, USA; Department of Psychiatry, University of CaliforniaSan Diego, La Jolla, CA, USA; Department of Radiology, University of CaliforniaSan Diego, La Jolla, CA, USA.
authors.forename: Anders M
authors.initials: AM
authors.lastname: Dale
keywords: GWAS; Gaussian mixture model; SNP discovery; effect size; heritability; putamen; schizophrenia