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I am reading the vignette for the R mediation package.

At page 4 it makes the sequential ignorability assumption, and says that

Equation 6 requires that the mediator is also ignorable given the observed treatment and pre-treatment confounders. This additional assumption is quite strong because ut excludes the existence of (measured or unmeasured) post-treatment confounders as well as that of unmeasured pre-treatment confounders.

What are "post-treament confounders" and what are "pre-treatment counfounders"?

I know what a confounder is, but I don't know what the qualifiers "pre-treatment" and "post-treatment" mean in this context.

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  • $\begingroup$ Well, what would you say a confounder is? $\endgroup$ Jun 22, 2021 at 13:38
  • $\begingroup$ @AdrianKeister A variable that determines both treatment and outcome $\endgroup$ Jun 22, 2021 at 14:08
  • $\begingroup$ As causes must precede effects, so a confounder as you've defined it must precede the treatment. A so-called "post-treatment confounder" isn't actually a confounder. It might be a mediator, but it can't set up a backdoor path from the treatment to the effect because the causal arrow is going out of the treatment. $\endgroup$ Jun 22, 2021 at 14:24

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In the context of mediation analysis, there are two causal variables of interest: the treatment and the mediator. Pre-treatment confounders are common causes of the treatment, mediator, and/or outcome that are measured before treatment. Adjusting for these is necessary for consistent estimates of the mediation effects, but there are many ways to do so in a straightforward manner (including using the mediation package). Post-treatment confounders are common causes of the mediator and outcome that are measured after treatment. These are more challenging to address, and the methods that underlie the mediation package are not equipped to address them. They are particularly problematic because if they are caused by treatment, conditioning on them in the mediation analysis will induce post-treatment selection bias (Elwert & Winship, 2014).

See the graph below, which comes from Acharya, Blackwell, and Sen (2016):

enter image description here

The variable $Z$ is a post-treatment (i.e., intermediate) confounder. Although many mediation methods require the assumption that these do not exist, in reality, they very likely do, especially if there is a lot of time between the treatment and the measurement of the mediator.


Acharya, A., Blackwell, M., & Sen, M. (2016). Explaining Causal Findings Without Bias: Detecting and Assessing Direct Effects. American Political Science Review, 110(3), 512–529. https://doi.org/10.1017/S0003055416000216

Elwert, F., & Winship, C. (2014). Endogenous Selection Bias: The Problem of Conditioning on a Collider Variable. Annual Review of Sociology, 40(1), 31–53. https://doi.org/10.1146/annurev-soc-071913-043455

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