Figure 4.

Mean bias across 5000 simulations of the causal effect estimate using homogeneous genetic instruments. $\beta :$ true causal effect of the exposure ($X$) on the outcome ($Y$). Scenarios A-F assume different causal relationships among $X$, $Y$, the instrument ($Z$), the covariate ($W$) and a common cause of $X$ and $W$ affected by $Z$ ($R$). In Scenarios A1-F1, there are no unmeasured confounders. In Scenarios A2-F2, there is an unmeasured common cause of $X$ and $W$. In Scenarios A3-F3, there is an unmeasured common cause of $W$ and $Y$. In Scenarios A4-F4, there is an unmeasured common cause of $X$ and $Y$. In Scenarios A5-F5, all these three unmeasured confounders are present. The scenarios are illustrated in Figure 2 and described in detail in the ‘Simulation study’ section. Scenarios where no genetic variants are selected as instruments (because adjustment for $W$ results in no open path between $Z$ and $X$) are marked in grey