Figure 4.

Variations of the directed acyclic graph (DAG) in Figure 2a: three exposures. Bivariate correlations between exposures are $r_{12}$ for $X_1–X_2$, $r_{13}$ for $X_1–X_3$, and $r_{23}$ for $X_2–X_3$. a) Assume all three exposures are (positively) correlated due to causation by the same source. b) There are two different sources and no correlation between $X_2$ and $X_3$: $r_{23}=0$. This simplifies the bias equations. In both cases, the bias amplification for the $X_1–Y$ association caused by adjusting for one other exposure ($X_2$ or $X_3$) will be further amplified when adjusting for all three. This is also true for the $X_2–Y$ and $X_3–Y$ associations for 4b.