MR‐Egger regression additionally provides an estimate for the true causal effect β^E that is consistent even if all genetic variants are invalid due to violation of IV3, but under a weaker assumption known as the InSIDE (instrument strength independent of direct effect) assumption. If the association of the jth genetic variant with the outcome Γj=βγj+αj, where αj is the pleiotropic (direct) effect of the variant, then the InSIDE assumption states that the pleiotropic effects αj must be distributed independently of the instrument strength parameters γj (Kolesár et al., 2014). (Formally, the consistency property holds both as the sample size and the number of instruments increases. For a fixed number of instruments, consistency only holds asymptotically if the correlation between the αj and γj parameters is zero.) The InSIDE assumption is likely to be satisfied if pleiotropic effects on the outcome are direct (i.e., not via a confounder). There is some empirical evidence supporting the proposition that genetic effects on separate exposures are independent (Pickrell, 2015). However, if the pleiotropic effects of genetic variants are all via a single confounder, then they will be correlated with instrument strength, and the InSIDE assumption will be violated.
