The influence of unmeasured confounding on the MR Steiger approach

The Mendelian Randomization (MR) Steiger approach is used to determine the direction of a possible causal effect between two phenotypes [1]. For two phenotypes, denoted phenotype 1 and 2, the MR Steiger approach is composed of two parts: (1) MR is performed for a set of single nucleotide polymorphisms (SNPs) that serve as instrumental variables for phenotype 1 and (2) the difference of two correlations, the correlation between the SNPs and phenotype 1 and the correlation between the SNPs and phenotype 2, is calculated. These two parts are then used to determine the direction of a possible causal effect between the two phenotypes. The original MR Steiger paper [1] shows that unmeasured confounding of the two phenotypes affects the validity of the MR Steiger approach, but does not elucidate as to how this occurs. In particular, it was argued that if the magnitude of the observational variance explained between the two phenotypes is above 0.2, the MR Steiger method may return the incorrect causal direction due to unmeasured confounding. This may initially seem surprising since unmeasured confounding does not induce spurious associations between the SNP and phenotype 2, as we demonstrate using directed acyclic graphs. In this note, we show that this is because unmeasured confounding may rescale the magnitude of a non-zero association, and thereby distort the comparison of the correlation between the SNP and phenotype 2 and the correlation between the SNP and phenotype 1. We will end with a number of cautionary remarks on the MR Steiger method, which are partly motivated by this and mentioned in the original MR Steiger paper [1].