Robust inference of bi-directional causal relationships in presence of correlated pleiotropy with GWAS summary data
Fig 6
Empirical distributions of the estimates of the correlation ratio K for CD methods and the causal effect θ for MR method with both X and Y continuous, true θXY = 0 and θYX = 0.
The top and bottom panels show the results for ξ = 0 (i.e. no correlated pleiotropy) and ξ from a uniform distribution (i.e. with correlated pleiotropy, implying InSIDE violated), respectively. The left panels show the estimates for the causal direction of X → Y, while the right ones show that for Y → X. The horizontal dashed lines are for the true values of K or θ. The two rows of the numbers under each panel give the sample mean and standard deviation of the estimates from each method.