  Mendelian randomization (MR) considers using genetic variants as instrumental
variables (IVs) to infer causal effects in observational studies. However, the
validity of causal inference in MR can be compromised when the IVs are
potentially invalid. In this work, we propose a new method, MR-Local, to infer
the causal effect in the existence of possibly invalid IVs. By leveraging the
distribution of ratio estimates around the true causal effect, MR-Local selects
the cluster of ratio estimates with the least uncertainty and performs causal
inference within it. We establish the asymptotic normality of our estimator in
the two-sample summary-data setting under either the plurality rule or the
balanced pleiotropy assumption. Extensive simulations and analyses of real
datasets demonstrate the reliability of our approach.
