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Bayesian large-scale multiple regression with summary statistics from genome-wide association studies

Xiang Zhu, Matthew Stephens
doi: https://doi.org/10.1101/042457
Xiang Zhu
1Department of Statistics, University of Chicago E-mail:
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  • For correspondence: xiangzhu@uchicago.edu
Matthew Stephens
2Department of Statistics and Department of Human Genetics, University of Chicago E-mail:
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  • For correspondence: mstephens@uchicago.edu
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Abstract

Bayesian methods for large-scale multiple regression provide attractive approaches to the analysis of genome-wide association studies (GWAS). For example, they can estimate heritability of complex traits, allowing for both polygenic and sparse models; and by incorporating external genomic data into the priors they can increase power and yield new biological insights. However, these methods require access to individual genotypes and phenotypes, which are often not easily available. Here we provide a framework for performing these analyses without individual-level data. Specifically, we introduce a “Regression with Summary Statistics” (RSS) likelihood, which relates the multiple regression coefficients to univariate regression results that are often easily available. The RSS likelihood requires estimates of correlations among covariates (SNPs), which also can be obtained from public databases. We perform Bayesian multiple regression analysis by combining the RSS likelihood with previously-proposed prior distributions, sampling posteriors by Markov chain Monte Carlo. In a wide range of simulations RSS performs similarly to analyses using the individual data, both for estimating heritability and detecting associations. We apply RSS to a GWAS of human height that contains 253,288 individuals typed at 1.06 million SNPs, for which analyses of individual-level data are practically impossible. Estimates of heritability (52%) are consistent with, but more precise, than previous results using subsets of these data. We also identify many previously-unreported loci that show evidence for association with height in our analyses. Software implementing RSS is available at https://github.com/stephenslab/rss.

Footnotes

  • * This work is supported by a grant from the Gordon and Betty Moore Foundation (Grant GBMF # 4559) and NIH grant HG02585 to M.S.

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The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC-ND 4.0 International license.
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Posted March 04, 2016.
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Bayesian large-scale multiple regression with summary statistics from genome-wide association studies
Xiang Zhu, Matthew Stephens
bioRxiv 042457; doi: https://doi.org/10.1101/042457
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Bayesian large-scale multiple regression with summary statistics from genome-wide association studies
Xiang Zhu, Matthew Stephens
bioRxiv 042457; doi: https://doi.org/10.1101/042457

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