Bayesian Weighted Mendelian Randomization for Causal Inference based on Summary Statistics
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The results from Genome-Wide Association Studies (GWAS) on thousands of phenotypes provide an unprecedented opportunity to infer the causal effect of one phenotype (exposure) on another (outcome). Mendelian randomization (MR), an instrumental variable (IV) method, has been introduced for causal inference using GWAS data. Due to the polygenic architecture of complex traits/diseases and the ubiquity of pleiotropy, however, MR has many unique challenges compared to conventional IV methods. In this paper, we propose a Bayesian weighted Mendelian randomization (BWMR) for causal inference to address these challenges. In our BWMR model, the uncertainty of weak effects owing to polygenicity has been taken into account and the violation of IV assumption due to pleiotropy has been addressed through outlier detection by Bayesian weighting. To make the causal inference based on BWMR computationally stable and efficient, we developed a variational expectation-maximization (VEM) algorithm. Moreover, we have also derived an exact closed-form formula to correct the posterior covariance which is well known to be underestimated in variational inference. Through comprehensive simulation studies, we evaluated the performance of BWMR, demonstrating the advantage of BWMR over its competitors. Then we applied BWMR to 10,762 pairs of exposure and outcome traits from 54 GWAS, uncovering novel casual relationship between exposure and outcome traits. The BWMR package is available at https://github.com/jiazhao97/BWMR.
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