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Mendelian randomization (MR) is a statistical method exploiting geneticvariants as instrumental variables to estimate the causal effect of modifiablerisk factors on an outcome of interest. Despite wide uses of various populartwo-sample MR methods based on genome-wide association study summary leveldata, however, those methods could suffer from potential power loss or/andbiased inference when the chosen genetic variants are in linkage disequilibrium(LD), and also have relatively large direct effects on the outcome whosedistribution might be heavy-tailed which is commonly referred to as theidiosyncratic pleiotropy phenomenon. To resolve those two issues, we propose anovel Robust Bayesian Mendelian Randomization (RBMR) model that uses the morerobust multivariate generalized t-distribution to model such direct effects ina probabilistic model framework which can also incorporate the LD structureexplicitly. The generalized t-distribution can be represented as a Gaussianscaled mixture so that our model parameters can be estimated by the EM-typealgorithms. We compute the standard errors by calibrating the evidence lowerbound using the likelihood ratio test. Through extensive simulation studies, weshow that our RBMR has robust performance compared to other competing methods.We also apply our RBMR method to two benchmark data sets and find that RBMR hassmaller bias and standard errors. Using our proposed RBMR method, we find thatcoronary artery disease is associated with increased risk of critically illcoronavirus disease 2019 (COVID-19). We also develop a user-friendly R packageRBMR for public use.

A Two-Sample Robust Bayesian Mendelian Randomization Method Accounting  for Linkage Disequilibrium and Idiosyncratic Pleiotropy with Applications to  the COVID-19 Outcome