Results from the simulation study when 100 genetic variants were simulated for 1 000 datasets.

Mean estimate (mean standard error), standard deviation, coverage of the 95% confidence interval (%), and power at the 5% significance level (%) of the estimates from the IVW model with: 1) the J genetic variants (IVW); 2) robust regression; 3) penalized weights; and 4) robust regression and penalized weights (R and P) for Scenarios 2-4 with a null causal effect (θ = 0) and positive causal effect (θ = 0.3) by the number of invalid instrumental variables. Results from the Lasso penalization method with the heterogeneity stopping rule are also presented.