# Should pre-intervention outcome variable Y0 be excluded from counterfactual model based on causal diagram?

Based on the causal diagram below, where:

• Y1 is the outcome in the post-intervention period,
• Y0 is the pre-intervention outcome,
• X is a Yes/No healthcare intervention, and
• Z1 & Z2 represent various confounder variables (diagnoses, geography, etc.).

Shouldn't Y0 be excluded from the counterfactual model estimating the effect of X on Y1 given it is both a collider and mediator variable?

Is there any reason not to exclude Y0 from the study?

• Are the Zs observed? Dec 6, 2022 at 4:21
• @dimitriy Yes they are Dec 6, 2022 at 4:23

$$Y_0$$ is not a mediator; it is a confounder. You must adjust for it. If $$Z_1$$ and $$Z_2$$ were not observed, this would induce what's sometimes called "butterfly bias"; but if you can adjust for them, then all confounding is removed. The sole minimally sufficient adjustment set is $$Y_0$$, $$Z_1$$, and $$Z_2$$.
• (+1) Wouldn't also be sensible to point out that $Y_0$ is not a mediator as there is no mediated effect between the independent variable $X$ causing $Y_0$ causing the dependent variable $Y_1$? Dec 7, 2022 at 2:28
• If you adjust for $Z_1$ and $Z_2$, then even if $Y_0$ is a collider and not a confounder, adjusting for it would not bias the treatment effect. Because it would not open any backdoor paths. Instead of thinking about classifying each variable into a causal "type", think about its role in the DAG and the consequences of adjusting for it while adjusting for others. Yes $Y_0$ is a mediator and a collider, but adjusting for it is necessary. The rule "don't adjust for colliders" is too coarse to apply to this more complicated scenario.