Results from the simulation study are given in Table 1 for 10 000 simulated datasets. Each row of the table corresponds to a particular simulation scenario and study size pairing. In each case, the mean F statistic across the 25 variants is also shown, in order to indicate the average instrument strength. This is a marker of the effective sample size of each scenario. The IVW and MR-Egger methods were implemented using weighted linear regression, as described in the Web Appendix (available as Supplementary data at IJE online). Standard errors and P-values (from t-tests) were taken directly from the regression output. All tests were two-sided and performed at a nominal significance level of 5%. Table 1.Performance of inverse-variance weighted and MR-Egger regression estimates in simulation study for two-sample Mendelian randomization with a null (β = 0) and a positive (β = 0.05) causal effect. All tests are performed at 5% significance levelInverse-variance weightedMR-Egger regressionMean FMean estimatePower to detectMean estimatePower ofPower to detectNstatistic(mean SE)causal effect(mean SE)MR-Egger testcausal effectNo causal effect: β = 0Scenario (a) no pleiotropy, InSIDE satisfied25010.40.000 (0.022)0.0550.000 (0.047)0.0520.05250019.80.000 (0.015)0.0500.000
