inference - is conditioning only on propensity score sufficient to CATE estimation?

Question

I have read the paper " Adapting Neural Networks for the Estimation of Treatment Effects", which suggests a neural network architecture called Dragonnet for the estimation of treatment effects. https://papers.nips.cc/paper/2019/file/8fb5f8be2aa9d6c64a04e3ab9f63feee-Paper.pdf

Dragonnet is based on the theorem of sufficiency of propensity scores. I understand what the theorem is about, it says conditioning on propensity score is sufficient to block all the back door paths. When I think about dragonnet structure, it totally makes sense. However, I was thinking that conditional average treatment effect(CATE) is not only about the heterogeneous subgroups in a confounding variable set but also there might be other variables which are not confounding but somehow different values of that variable may create different treatment effects.

Let's assume that we have a variable 'sex', which is not a confounding variable. Let us also assume that female and male people have different treatment effects. Therefore, if I want to calculate CATE, then wouldn't it make sense to condition also on the variable 'sex' beside the confounding variables? I don't think that this is the case with dragonnet. Therefore I get a bit confused because dragonnet claims that variables which don't affect the treatment assignment are not relevant for treatment effect estimation.

What I would like to ask is that, if I only condition on propensity score to predict CATE, wouldn't I ignore the effect modification which is created by variables which are not confounding?

Answer 1

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