Our procedure has some similarity to Egger regression applied to Mendelian randomisation (MR-Egger)33. Both procedures assume the structure in Fig. 1, regress SNP effects on one trait on SNP effects on another, and require an independence assumption. However, while the focus of MR-Egger is on the slope of the regression (the causal effect of exposure on outcome), and on the intercept (the magnitude of directional pleiotropy), our focus here is on the residuals, which provide the adjusted effect estimates when added to the intercept.
