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Estimating Effect Sizes and Expected Replication Probabilities from GWAS Summary Statistics

Dominic Holland, Yunpeng Wang, Wesley K. Thompson, Andrew Schork, Chi-Hua Chen, Min-Tzu Lo, Aree Witoelar, Schizophrenia Working Group of the Psychiatric Genomics Consortium, Enhancing Neuro Imaging Genetics through Meta Analysis Consortium, Thomas Werge, Michael O’Donovan, Ole A. Andreassen, Anders M. Dale
doi: https://doi.org/10.1101/032474
Dominic Holland
aMultimodal Imaging Laboratory, University of California at San Diego, La Jolla, CA 92093, USA
bDepartment of Neurosciences, University of California, San Diego, La Jolla, CA 92093, USA
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  • For correspondence: dominic.holland@gmail.com
Yunpeng Wang
aMultimodal Imaging Laboratory, University of California at San Diego, La Jolla, CA 92093, USA
bDepartment of Neurosciences, University of California, San Diego, La Jolla, CA 92093, USA
cNORMENT, KG Jebsen Centre for Psychosis Research, Institute of Clinical Medicine, University of Oslo 0424 Oslo, Norway
dDivision of Mental Health and Addiction, Oslo University Hospital, 0407 Oslo, Norway
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Wesley K. Thompson
eDepartment of Psychiatry, University of California, San Diego, La Jolla, CA 92093, USA
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Andrew Schork
aMultimodal Imaging Laboratory, University of California at San Diego, La Jolla, CA 92093, USA
fDepartment of Cognitive Sciences, University of California at San Diego, La Jolla, CA 92093, USA
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Chi-Hua Chen
aMultimodal Imaging Laboratory, University of California at San Diego, La Jolla, CA 92093, USA
gDepartment of Radiology, University of California, San Diego, La Jolla, CA 92093, USA
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Min-Tzu Lo
aMultimodal Imaging Laboratory, University of California at San Diego, La Jolla, CA 92093, USA
gDepartment of Radiology, University of California, San Diego, La Jolla, CA 92093, USA
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Aree Witoelar
cNORMENT, KG Jebsen Centre for Psychosis Research, Institute of Clinical Medicine, University of Oslo 0424 Oslo, Norway
dDivision of Mental Health and Addiction, Oslo University Hospital, 0407 Oslo, Norway
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Thomas Werge
hInstitute of Biological Psychiatry, MHC, Sct. Hans Hospital and University of Copenhagen, 4000 Copenhagen, Denmark
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Michael O’Donovan
iMRC Centre for Neuropsychiatric Genetics and Genomics, School of Medicine, Cardiff University, Heath Park, Cardiff, CF14 4XN, UK
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Ole A. Andreassen
cNORMENT, KG Jebsen Centre for Psychosis Research, Institute of Clinical Medicine, University of Oslo 0424 Oslo, Norway
dDivision of Mental Health and Addiction, Oslo University Hospital, 0407 Oslo, Norway
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Anders M. Dale
aMultimodal Imaging Laboratory, University of California at San Diego, La Jolla, CA 92093, USA
bDepartment of Neurosciences, University of California, San Diego, La Jolla, CA 92093, USA
eDepartment of Psychiatry, University of California, San Diego, La Jolla, CA 92093, USA
gDepartment of Radiology, University of California, San Diego, La Jolla, CA 92093, USA
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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 that does not require raw genotype data, 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 – the proportion of SNPs (after uniform pruning, so that large LD blocks are not over-represented) likely to be in strong LD with causal/mechanistically associated SNPs – 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 additionally, for purposes of illustration, 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 estimate 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 106 and 105. 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.

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Posted November 21, 2015.
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Estimating Effect Sizes and Expected Replication Probabilities from GWAS Summary Statistics
Dominic Holland, Yunpeng Wang, Wesley K. Thompson, Andrew Schork, Chi-Hua Chen, Min-Tzu Lo, Aree Witoelar, Schizophrenia Working Group of the Psychiatric Genomics Consortium, Enhancing Neuro Imaging Genetics through Meta Analysis Consortium, Thomas Werge, Michael O’Donovan, Ole A. Andreassen, Anders M. Dale
bioRxiv 032474; doi: https://doi.org/10.1101/032474
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Estimating Effect Sizes and Expected Replication Probabilities from GWAS Summary Statistics
Dominic Holland, Yunpeng Wang, Wesley K. Thompson, Andrew Schork, Chi-Hua Chen, Min-Tzu Lo, Aree Witoelar, Schizophrenia Working Group of the Psychiatric Genomics Consortium, Enhancing Neuro Imaging Genetics through Meta Analysis Consortium, Thomas Werge, Michael O’Donovan, Ole A. Andreassen, Anders M. Dale
bioRxiv 032474; doi: https://doi.org/10.1101/032474

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