In Supporting Information Tables A1 and A2, results are presented in a one‐sample setting. Each of the methods suffers from weak instrument bias in this setting, and Type 1 error rates are inflated. Estimates from MR‐Egger regression are substantially more biased than those from other methods. However, the median‐based methods remain a reasonable sensitivity analysis, as Type 1 error rates are similar to those of the IVW method in Scenario 1, and substantially lower in Scenarios 2 and 3. In Supporting Information Table A3, results are presented in a two‐sample setting for the simple median estimator, and a weighted median estimator using inverse‐standard error weights rather than the inverse‐variance weights used above. Simple median estimates are slightly less precise than those from the weighted median methods, and have similar bias and Type 1 error properties in Scenarios 1 and 2, but much improved Type 1 error rates in Scenario 3. This is because the invalid variants in this scenario are stronger than the valid variants, and so receive more weight in the weighted analyses. It is unclear that this would
