Robust methods in Mendelian randomization via penalization of heterogeneous causal estimates

Summary

Methods have been developed for Mendelian randomization that can obtain consistent causal estimates under weaker assumptions than the standard instrumental variable assumptions. The median-based estimator and MR-Egger are examples of such methods. However, these methods can be sensitive to genetic variants with heterogeneous causal estimates. Such heterogeneity may arise from over-dispersion in the causal estimates, or specific variants with outlying causal estimates. In this paper, we develop three extensions to robust methods for Mendelian randomization with summarized data: 1) robust regression (MM-estimation); 2) penalized weights; and 3) Lasso penalization. Methods using these approaches are considered in two applied examples: one where there is evidence of over-dispersion in the caus