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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?

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  • $\begingroup$ 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

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$Y_0$ 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 $Z_2$.

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  • $\begingroup$ (+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
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    $\begingroup$ 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
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    $\begingroup$ That's correct. For your second question, check out this article. $\endgroup$
    – Noah
    Dec 8, 2022 at 17:50

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