Fig. 1
From: Causal associations between risk factors and common diseases inferred from GWAS summary data
Leveraging multiple independent genetic instruments (z) to test for causality. Shown in panel a is a schematic example that if an exposure (x) has an effect on an outcome (y), any instruments (SNPs) causally associated with x will have an effect on y, and the effect of x on y (b xy ) at any of the SNPs is expected to be identical. This is further illustrated in a toy example in panel b that under a causal model, for the SNPs associated with x, the estimated effect of z on y (\(\hat b_{zy}\)) should be linearly proportional to the estimated effect of z on x (\(\hat b_{zx}\)) and the ratio between the two is an estimate of the mediation effect of x on y, i.e., \(\hat b_{xy} = \hat b_{zy}/\hat b_{zx}\)
