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?

enter image description here

  • $\begingroup$ Are the Zs observed? $\endgroup$
    – dimitriy
    Dec 6, 2022 at 4:21
  • $\begingroup$ @dimitriy Yes they are $\endgroup$
    – RobertF
    Dec 6, 2022 at 4:23

1 Answer 1


$Y_0$ 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 $Z_2$.

  • $\begingroup$ (+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 $Y_1$? $\endgroup$
    – usεr11852
    Dec 7, 2022 at 2:28
  • $\begingroup$ Thanks Noah - my initial thoughts were Y0 is a mediator lying on the paths between Z1, Z2, and Y1. And Y0 could also be a collider since two causal arrows from Z1 and Z2 converge on Y0. $\endgroup$
    – RobertF
    Dec 7, 2022 at 3:25
  • $\begingroup$ If the X <- Y0 -> Y1 path didn't exist, then Y0 would be a collider that ought to be excluded since it blocks the Y1 <- Z2 -> Y0 <- Z1 -> X path. But the Y1 <- Y0 -> X path complicates things. $\endgroup$
    – RobertF
    Dec 7, 2022 at 4:13
  • 1
    $\begingroup$ 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. $\endgroup$
    – Noah
    Dec 7, 2022 at 15:05
  • 1
    $\begingroup$ That's correct. For your second question, check out this article. $\endgroup$
    – Noah
    Dec 8, 2022 at 17:50

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.