Dowhy causal inference estimates equal from two different models - why?

I am using a python package based on judea pearls book of why. I Tried two different models which i have depicted below, these structures would go in the digraph section of the code below. After running the code below for these two different graphical models i get exactly the same estimate. My question is how is this happening?

causal_graph = """digraph {

}"""

#print(df_dowhy)
model = dowhy.CausalModel(data=df_dowhy,
graph=causal_graph.replace("\n", " "),
treatment="drug",
outcome="outcome")
model.view_model()
from IPython.display import Image, display
display(Image(filename="causal_model.png"))

identified_estimand = model.identify_effect(proceed_when_unidentifiable=True)

estimate = model.estimate_effect(identified_estimand,
method_name='backdoor.propensity_score_stratification',
target_units="att")
print(estimate)


I don't understand how these backdoor variables (in grey) are being taken into account if remvoing them gives me same estimate (model i tested on right). Since i am using propensity score stratification could it be that the same control and treated groups are being selected?

I am using backdoor criterion and propensity score stratification for this- I thought in backdoor criterion all the variables in grey are conditioned on, but since i get exactly the same estimate for model on right (omitting grey variables) doesn't this imply the estimand is the exact same for both and it's disregarding the backdoor variables?

1 Answer

Those grey variables are not backdoor variables. Backdoor variables are positioned on a backdoor path between the treatment ("DRUG") and the outcome. Those grey variables don't satisfy this condition. They, could, however, be used as instrumental variables.

It is also, intuitively quite reasonable, directly from consulting the image, that, if there are really only those two paths from "DRUG" to "outcome", then the grey variables can't interfere in this causal relation.

Note, that "v3", however, is a backdoor variable on the backdoor path "DRUG"->"v3"->"outcome".

• so are instrument variables simply ignored? There is no need for me then to even include b1-b3 in the model Jul 22 at 15:06
• Instrument variables are used in other contexts. For your scenario, they are not relevant. Jul 22 at 15:20