A practical problem with Egger regression in Mendelian randomization

Mendelian randomization (MR) is an instrumental variable (IV) method using genetic variants such as single nucleotide polymorphisms (SNPs) as IVs to disentangle the causal relationship between an exposure and an outcome. Since any causal conclusion critically depends on the three valid IV assumptions, which will likely be violated in practice, MR methods robust to the IV assumptions are greatly needed. As such a method, Egger regression stands out as one of the most widely used due to its easy use and perceived robustness. Although Egger regression is claimed to be robust to directional pleiotropy under the instrument strength independent of direct effect (InSIDE) assumption, it is known to be dependent on the orientations/coding schemes of SNPs (i.e. which allele of an SNP is selected as the reference group). The current practice, as recommended as the default setting in some popular MR software packages, is to orientate the SNPs to be all positively associated with the exposure, which however, to our knowledge, has not been fully studied to assess its robustness and potential impact. We use both numerical examples (with both real data and simulated data) and analytical results to demonstrate the practical problem of Egger regression with respect to its heavy dependence on the SNP orientations. Under the assumption that InSIDE holds for some specific (and unknown) coding scheme of the SNPs, we analytically show that other coding schemes would in general lead to the violation of InSIDE. Other related MR and IV regression methods may suffer from the same problem. Cautions should be taken when applying Egger regression (and related MR and IV regression methods) in practice.