A summary of the median‐based and other methods considered in this paper is given in Table 5. Of particular interest is the comparison between the weighted median approach and MR‐Egger regression. MR‐Egger regression can give consistent estimates when 100% of genetic variants are invalid IVs, whereas the weighted median method requires 50% of the weight to come from valid IVs. However, the weighted median approach allows the IV assumptions to be violated in a more general way for the invalid IVs, whereas MR‐Egger regression replaces one set of untestable assumptions (IV2 and IV3) with a weaker, but still untestable assumption (the InSIDE assumption). Additionally, weighted median estimates were substantially more precise than those from MR‐Egger regression in the simulation study and applied example. MR‐Egger regression estimates are likely to be particularly imprecise if all genetic variants have similar magnitudes of association with the exposure.
