Although the only mechanism for generating invalid IVs considered in this paper was pleiotropy, median‐based methods are agnostic to the mechanism by which the invalid IVs violate the IV assumptions. Consistent estimates would be guaranteed if some genetic variants were invalid IVs due to other mechanisms, such as linkage disequilibrium, population stratification, or differential survival (Bochud et al., 2008). One potential source of bias that may not be resolved by the proposed robust methods is selection bias (Hernán et al., 2004). This could arise from differential selection of individuals in the datasets from which the genetic associations are obtained, or else the selection of genetic variants based on their strength in the dataset under analysis, or if genetic variants were discovered as associated with the exposure in the dataset under analysis. Selection bias may affect all genetic variants in a particular analysis, and so is unlikely to be addressed by the use of the median‐based methods proposed in this paper.
