In this paper we propose a new method for Mendelian randomization using summary data that offers protection against invalid instruments: the weighted median estimator. This approach can provide a consistent estimate of the causal effect even when up to 50% of the information contributing to the analysis comes from genetic variants that are invalid IVs. We explore the statistical properties of the weighted median estimator in a realistic simulation study, and compare with an alternative summary data analysis method also robust to some violations of the IV assumptions, MR‐Egger regression (Bowden et al., 2015). We explain how the two approaches differ in their assumptions, and when they each work well or fail. We provide an illustrative estimate of two‐sample Mendelian randomization using summary data on the associations of 185 genetic variants with high‐density lipoprotein cholesterol (HDL‐c), low‐density lipoprotein cholesterol (LDL‐c), and triglycerides from the GLGC, and with CAD risk from the CARDIoGRAM consortium. We conclude with a discussion of the issues raised and the potential for future research.
