LAUSR

The Mendelian Randomization (MR) Steiger approach is used to determine the direction of a possible causal effect between two phenotypes (Hemani et al., 2017). 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 (Hemani et al., 2017) shows that unmeasured confounding of the two phenotypes affects the validity of the MR Steiger approach, but does not elucidate how this occurs. In particular, it was argued that in most cases for the parameter values explored, the MR Steiger method may return the incorrect causal direction due to unmeasured confounding when the linear regression with phenotype 2 denoted y as the outcome and phenotype 1denoted x as the exposure returns an R < 0.2. This threshold was based on simulations studies for a specific generating mechanism that involved an unmeasured confounder. By virtue of the confounder being unmeasured, this mechanism for the unmeasured confounding would not be known in real applications and it is therefore unclear whether the threshold is generally applicable. That unmeasured confounding affects the MR Steiger approach 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 (Hemani et al., 2017). Let g denote the SNP, x denote phenotype 1, y denote phenotype 2, and u denote an unmeasured confounder of the association between both phenotypes. Then, x and y can be modeled as follows in the original MR Steiger paper (Hemani et al., 2017):