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.Author summary: Egger regression (MR-Egger) has been increasingly applied in Mendelian randomization (MR) analyses for its easy use and perceived robustness, though MR-Egger requires the InSIDE assumption, which in turn depends on the orientation of SNPs. The implications of this dependence to its practical use may not be well understood yet. In particular, it is unrealistic to assume that the InSIDE assumption holds for many or all arbitrarily chosen coding schemes of the SNPs; instead, it is more reasonable to assume that InSIDE holds for only one specific, but usually unknown, coding scheme of SNPs, under which, however, we show that use of other coding schemes of SNPs in general leads to the violation of InSIDE, and thus to biased causal estimates. The technical reason is due to the seemingly non-restrictive assumption of the random direct effects with a non-zero mean (i.e. directional pleiotropy) in MR-Egger (and related methods), which depends on the orientation of SNPs. This problem persists for many other related MR and instrumental variable regression methods, regardless whether GWAS summary data or individual-level data are used. Given the popularity of MR-Egger in practice, one should be aware of this issue and hence be cautious when applying MR-Egger.