On Multiply Robust Mendelian Randomization (MR2) With Many Invalid Genetic Instruments

Mendelian randomization (MR) is a popular instrumental variable (IV) approach, in which genetic markers are used as IVs. In order to improve efficiency, multiple markers are routinely used in MR analyses, leading to concerns about bias due to possible violation of IV exclusion restriction of no direct effect of any IV on the out-come other than through the exposure in view. To address this concern, we introduce a new class of Multiply Robust MR (MR 2 ) estimators that are guaranteed to remain consistent for the causal effect of interest provided that at least one genetic marker is a valid IV without necessarily knowing which IVs are invalid. We show that the proposed MR 2 estimators are a special case of a more general class of estimators that remain consistent provided that a set of at least k † out of K candidate instrumental variables are valid, for k † ≤ K set by the analyst ex ante, without necessarily knowing which IVs are invalid. We provide formal semiparametric theory supporting our results, and characterize the semiparametric efficiency bound for the exposure causal effect which cannot be improved upon by any regular estimator with our favorable robustness property. We conduct extensive simulation studies and apply our methods to a large-scale analysis of UK Biobank data, demonstrating the superior empirical performance of MR 2 compared to competing MR methods.