Fig. 6. Effect of participation bias on MR estimates of exposure–outcome associations.

a,b, Summary of results obtained from weighted (${\widehat{\alpha }}_{\mathrm{w}}$) and standard ($\widehat{\alpha }$) MR. MR estimates subject to overestimation ($\mid \widehat{\alpha }\mid -\mid {\widehat{\alpha }}_{\mathrm{w}}\mid >0.1$) as a result of participation bias are highlighted in violet. MR estimates subject to underestimation ($\mid \widehat{\alpha }\mid -\mid {\widehat{\alpha }}_{\mathrm{w}}\mid <-0.1$) are highlighted in cyan. The asterisks highlight results where $\widehat{\alpha }$ and ${\widehat{\alpha }}_{\mathrm{w}}$ showed significant (P_FDR < 0.05) differences. The error bars (b) indicate the 95% confidence intervals corresponding to $\widehat{\alpha }$ and ${\widehat{\alpha }}_{\mathrm{w}}$. All P values are from two-sided tests and are corrected for multiple testing using FDR correction (controlled at 5%).