Mendelian randomization with Egger pleiotropy correction and weakly informative Bayesian priors.

Background: The MR-Egger (MRE) estimator has been proposed to correct for directional pleiotropic effects of genetic instruments in an instrumental variable (IV) analysis. The power of this method is considerably lower than that of conventional estimators, limiting its applicability. Here we propose a novel Bayesian implementation of the MR-Egger estimator (BMRE) and explore the utility of applying weakly informative priors on the intercept term (the pleiotropy estimate) to increase power of the IV (slope) estimate. Methods: This was a simulation study to compare the performance of different IV estimators. Scenarios differed in the presence of a causal effect, the presence of pleiotropy, the proportion of pleiotropic instruments and degree of 'Instrument Strength Independent of Direct Effect' (InSIDE) assumption violation. Based on empirical plasma urate data, we present an approach to elucidate a prior distribution for the amount of pleiotropy. Results: A weakly informative prior on the intercept term increased power of the slope estimate while maintaining type 1 error rates close to the nominal value of 0.05. Under the InSIDE assumption, performance was unaffected by the presence or absence of pleiotropy. Violation of the InSIDE assumption biased all estimators, affecting the BMRE more than the MRE method. Conclusions: Depending on the prior distribution, the BMRE estimator has more power at the cost of an increased susceptibility to InSIDE assumption violations. As such the BMRE method is a compromise between the MRE and conventional IV estimators, and may be an especially useful approach to account for observed pleiotropy.