By way of comparison between the robust methods, similar results were seen in this example as in the simulation study. The median‐based methods were consistently and substantially more precise than the MR‐Egger regression method, with standard errors reduced by around 30–50%. The precision of the weighted median methods, in particular the penalized weighted median method, was not much worse than that of the IVW method, and in some cases was slightly better. The simple median method was not as impressive, suggesting a causal effect of HDL‐c on CAD risk, and giving less precise estimates than those from the weighted median methods. The MR‐Egger regression method performed well despite doubts about the InSIDE assumption in the case of HDL‐c; many variants associated with HDL‐c are also associated with LDL‐c and triglycerides, and these associations are approximately proportional (see Supporting Information Figure A1), hence pleiotropic effects on CAD risk may operate via LDL‐c and triglycerides. This may be the reason why the MR‐Egger estimate changed sign in the analysis using variants having primary association with HDL‐c.
