The simulation results in the two‐sample setting are given in Table 2 (null causal effect) and Table 3 (positive causal effect). In Scenario 1 (balanced pleiotropy), the methods all give close to unbiased causal estimates, and have reasonable Type 1 error rates (power under the null is equal to Type 1 error). However, the power of the estimates with a positive causal effect differs substantially. The weighted median methods have lower mean standard errors than the IVW method, and generally have greater power with a positive causal effect (although not uniformly so), particularly as the proportion of invalid IVs increases. This is because invalid IVs do not influence the median estimates directly. Although Type 1 error rates from MR‐Egger regression are at nominal levels, estimates from the MR‐Egger method are considerably less precise (mean standard errors are around three times larger than IVW standard errors), and power to detect a causal effect is considerably reduced. Precision in the MR‐Egger method depends on the genetic variants having different associations with the exposure; if all genetic variants had the same magnitude of association with the exposure, then the MR‐Egger regression estimate would not be identified.
