  The use of genetic variants as instrumental variables - an approach known as
Mendelian randomization - is a popular epidemiological method for estimating
the causal effect of an exposure (phenotype, biomarker, risk factor) on a
disease or health-related outcome from observational data. Instrumental
variables must satisfy strong, often untestable assumptions, which means that
finding good genetic instruments among a large list of potential candidates is
challenging. This difficulty is compounded by the fact that many genetic
variants influence more than one phenotype through different causal pathways, a
phenomenon called horizontal pleiotropy. This leads to errors not only in
estimating the magnitude of the causal effect but also in inferring the
direction of the putative causal link. In this paper, we propose a Bayesian
approach called BayesMR that is a generalization of the Mendelian randomization
technique in which we allow for pleiotropic effects and, crucially, for the
possibility of reverse causation. The output of the method is a posterior
distribution over the target causal effect, which provides an immediate and
easily interpretable measure of the uncertainty in the estimation. More
importantly, we use Bayesian model averaging to determine how much more likely
the inferred direction is relative to the reverse direction.
