Several statistical methods have been proposed for consistent estimation of causal effects when the IV assumptions are not all satisfied. For example, Kang et al.40 propose a scenario in which only half of the genetic variants are required to be valid IVs. If infinite data were available, the identity of the valid IVs would be clear, as they would identify the same causal effect. Kang et al. provide an estimation method based on lasso penalization41 which not only gives consistent causal estimates in infinite samples, but also has reasonable finite sample properties. However, in contrast with the method proposed in this paper, which allows all the genetic variants to be invalid IVs, Kang et al. require at least half of the genetic variants to be valid IVs. Otherwise, if causal estimates from the two sets of valid and invalid genetic variants tended towards different values, it would not be possible to distinguish which of those values is the causal effect. A similar approach is simply to calculate the causal estimates using each genetic variant individually, rank the estimates in order
