  Mendelian randomization (MR) is a statistical method exploiting genetic
variants as instrumental variables to estimate the causal effect of modifiable
risk factors on an outcome of interest. Despite wide uses of various popular
two-sample MR methods based on genome-wide association study summary level
data, however, those methods could suffer from potential power loss or/and
biased inference when the chosen genetic variants are in linkage disequilibrium
(LD), and also have relatively large direct effects on the outcome whose
distribution might be heavy-tailed which is commonly referred to as the
idiosyncratic pleiotropy phenomenon. To resolve those two issues, we propose a
novel Robust Bayesian Mendelian Randomization (RBMR) model that uses the more
robust multivariate generalized t-distribution to model such direct effects in
a probabilistic model framework which can also incorporate the LD structure
explicitly. The generalized t-distribution can be represented as a Gaussian
scaled mixture so that our model parameters can be estimated by the EM-type
algorithms. We compute the standard errors by calibrating the evidence lower
bound using the likelihood ratio test. Through extensive simulation studies, we
show 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 has
smaller bias and standard errors. Using our proposed RBMR method, we find that
coronary artery disease is associated with increased risk of critically ill
coronavirus disease 2019 (COVID-19). We also develop a user-friendly R package
RBMR for public use.
