Conditioning despite post-treatment/collider bias

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I have this DAG, which represents the following variables:

  • G: exposure variable, two factors (control and treatment)
  • S: Pre-treatment variable, Continuous
  • PT: Post-treatment variable, Continuous
  • Y: Outcome of interest, Continuous

dl_t2_dg_cv_p
dl_t2_dg_cv_p3840×2400 120 KB

Is there a way to estimate an unbiased contrast effect between the two factors of G across the values of PT using regression analysis? I ask this because my basic understanding of causal inference tells me that conditioning on PT would incur post-treatment bias on the estimate, as well as being a collider. @Solomon , I suspect you might be able to help here.

Cheers

  • Operating System: Windows 10
  • brms Version: 2.19.0
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My understanding is actually quite limited in this case. If it were me, I’d drop PT entirely and only focus on the causal effect of G for Y, using S as a baseline covariate to increase power/precision. There might be a tricky way to include PT, maybe with instrumental variable methods. Others will have to provide guidance on that, though.

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Thanks for the guidance here @Solomon, I’ll take a look at instrumental variable methods.

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