Fig. 4: Exposure–outcome association adjusting the SNP effects on the candidate traits.

Radial plots of MR associations. The x-axis represents the weight (w) that each SNP contributes to the overall estimate, and the y-axis represents the product of the causal effect and weight of each SNP. The slopes represent causal effect estimates from different models (linetype). The arrows in this radial scatter plot indicates changes in the SNPʼs contribution to the overall causal effect estimate after conditioning on the effect of candidate traits on the outcome. The candidate traits that influence the association of the original exposure and the original outcome were listed in the box. a Empirical analysis 1: systolic blood pressure (mmHg) and coronary heart disease (log odds). b Empirical analysis 2: urate (mg/dl) and coronary heart disease (log odds). c Empirical analysis 3: sleep duration (hour/night) and schizophrenia (log odds). d Empirical analysis 4: years of schooling (years) and body mass index (kg/m²). Note that we use radial plots here as they explicitly show that one consequence of SNP-outcome effect adjustment is that the standard errors get larger (lower values on the x-axis). This leads to the adjusted variant contributing less weight to the causal effect and heterogeneity estimates, a process that acts in concert with the intention of attenuating the pleiotropic effect.