Fig. 2: Simulations comparing methods across different scenarios.

We evaluated three scenarios: confounding pleiotropy, horizontal pleiotropy and mediated pleiotropy (columns of graphs, with DAGs illustrating the scenarios. See Methods for full details). The x-axis of each graph represents the proportion of variants used to instrument x that were similated to exhibit pleiotropic effects. Typically, 30 instruments were simulated directly for x but this varies across scenarios where necessary. The y-axis of the first row of graphs represents the proportion of simulations that lead to unbiased effect estimates of x on y. The y-axis of the second row of graphs represents the sensitivity and specificity of the analysis across the simulations, where the area under the receiving operating curve (AUROC) represents the ability of the method to distinguish between simulations in which the causal effect of x on y is either null or not null. For all graphs, higher y-axis values are better. Seven methods are evaluated at each simulation. Raw = IVW random effects estimates applied to all detected instruments; Removed = either all outliers are removed, or only outliers detected to associate with a candidate trait; MVMR = multivariable MR using either candidate traits detected to associate with any instrument or using only candidate traits associated with outlier instruments; Adjusted = adjusting SNP–outcome associations for candidate traits applied either only to variants detected to be outliers, or all variants regardless of outlier status.