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Simplized causal network

Just like the Bayesian network shown above. I want to identify the average treatment effect(ATE) from Smoking to Lung Cancer. If Genetics is observable, I can easily identify the ATE with Pearl's backdoor adjustment.

But now, the Genetics is unobservable. As shown in the network, there's no front-door path between Smoking to Lung Cancer. So how to identify the causal effect?

  1. All nodes can be observed except the Genetics.
  2. There're more nodes, but those nodes aren't in any paths between Smoking and Lung_Cancer. The whole network is shown below.

Origin network

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  • $\begingroup$ Do you not have tar deposits? That is the classic Pearl example for frontdoor adjustment, in fact. Pearl inserted tar deposits between smoking and lung cancer. $\endgroup$ Dec 23, 2021 at 13:51
  • $\begingroup$ @AdrianKeister In Pearl's classic example, "Tar deposits" is a front-door path, as shown in Chapter 3 of Causality 2e. But in the exercise I am facing, "tar deposits" is gone and there is an arrow directly connecting "smoking" and "lung cancer", as shown above. $\endgroup$ Dec 24, 2021 at 1:21

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I'm sorry to say this but this seems to be a case of non-identifiability. You can't identify the ATE between Smoking and Lung Cancer there. There is an unmeasured confounder for Smoking and Lung Cancer, which is Genetics, and that's it. You can't adjust for it. There is indeed no node in the network between Smoking and Lung Cancer, which could help you with the front-door criterion, or between Genetics and Smoking or Genetics and Lung Cancer, which could help you with the back-door criterion.

You could adjust by a descendent of the unmeasured confounder (Attention Disorder) to "partially" adjust for it, but you wouldn't remove all the bias. For a crash course on good and bad controls, I recommend you A Crash Course in Good and Bad Controls by Carlos Cinelli.

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  • $\begingroup$ May the instrumental variable method help? For example, in the whole network(figure 2) there is a node called "peer pressure". This node may be exogenous and independent with "genetics". $\endgroup$ Dec 24, 2021 at 2:18
  • $\begingroup$ Oh, sure. Definitely. If it satisfies all the conditions for being an IV, you can get the LATE (not ATE, though, if I remember correctly). This reading may help. $\endgroup$ Dec 24, 2021 at 2:20
  • $\begingroup$ One thing that I would like to add, more on the biology part, is that there is also genetics related to smoking but not to lung cancer. At least one study has taken advantage of this (CHRNA5) to perform Mendelian randomization and show the causal link between smoking and lung cancer. Yes, CHRNA5 as an IV. $\endgroup$ Dec 24, 2021 at 2:25

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