# Some Context:

I've read this presentation about using a BART model to find out the causal effect of a certain variable with respect to a target variable (say, how much does a specific medicine actually helps treating a certain disease).

I'm still grasping the main and essential causal inference concepts, but I'm already familiar with the idea that in observational data, if we want to find out the average causal effect of a treatment, we need to make sure we're conditioning or stratifying our target variable according to some possible confounders. In the medicine example, that could be age, weight, etc. That is, we need to guarantee some form of conditional ignorability.

I also learned that there are structural causal models, which can help choose on which input variables we'll apply this conditioning. For example, there may be an input variable that is a collider and won't really help to find out the causal effect of, say, T -> Y.

# The Question:

In this cenario, I'm assuming that a non-parametric model such as a BART model could help estimate the ACE (Average Causal Effect) by calculating the intervention data (say, the counterfactuals) and then using that to estimate the ACE.

However, I'm not sure how one would use BART if you're not sure on what input variables you should condition. Does the model handle that?

In fact, in a more general approach, if I only have a handful of variables (e.g.: A, B, C, D, E, Y) and I want to find out if any of the A-E variables have a causal effect on Y, what should I do? Then, assuming there IS a causal effect between any of those variables, which one is the largest? How can I determine that?

## Bonus:

If there's any solution to the questions I'm posing, is that solution possible to implement in R? Are there any examples of that?

BART is a method of estimating $$E[E[Y|A=1,X]] - E[E[Y|A=0,X]]$$ in a highly flexible way, where $$Y$$ is the outcome, $$A$$ is the treatment, and $$X$$ are covariates. BART is one of many such methods that estimate the same quantity, including inverse probability weighting, propensity score methods, TMLE, causal random forests, etc. This is a totally separate matter from causal inference. There is nothing special about BART for causal inference. It is just a regression method. I discuss some of its staistical advantages here.

Why do we care about estimating $$E[E[Y|A=1,X]] - E[E[Y|A=0,X]]$$? When certain assumptions are met, including strong ignorability, $$E[E[Y|A=1,X]] - E[E[Y|A=0,X]] = E[Y^1] - E[Y^0]$$, which is the average causal effect of $$A$$ on $$Y$$. The assumptions required are about the causal status of the variables in $$X$$ with respect to $$A$$ and $$Y$$. In particular, they must be a sufficient set of variables required for nonparametric identification of the causal effect. (Note that "nonparametric identification" has almost nothing to do with "nonparametric" used as a descriptor for an estimation method like BART). Some of those rules include, e.g., that no colliders are included, that all backdoor paths between the treatment and outcome are closed, etc. There are a set of rules required for nonparametric identification of the causal effect. These are discussed in most texts on causal inference.

BART can't tell you which variables are required for nonparametric identification of a causal effect. It can only estimate the causal effect once you provide it with the correct set of $$X$$. No method (to my knowledge) can tell you the causal structure of the variables without any assumptions because each joint distribution of covariates is compatible with many causal structures. Strictly speaking, there is no reason for BART to be in a talk like the one you presented except that the author of the presentation also developed the use of BART in causal effect estimation. Again, there is nothing special about BART in terms of causality. It is a highly effective method for estimating a conditional association, which is what a causal effect is under certain assumptions, but it cannot verify those assumptions.

I should note I am a huge fan of BART and this post is not meant to insult it or Dr. Hill, but just to point out that BART has the same causal status as all other regression methods, which to say, none at all except that it can be used to estimate a conditional association, which can, under certain unverifiable assumptions, be interpreted as a causal effect.

• Great answer! Thank you a lot for clarifying the topic. I'm still curious though, I know that there are a few "Causal Discovery" methods, such as PC, FCI, etc etc. To your knowledge, is it possible to automate the use of those methods for causal discovery? Apr 30, 2021 at 13:15
• Glad it was helpful. I don't know anything about causal discovery unfortunately (but I am very skeptical of it because to claim any single pathway as causal requires knowing and observing all of its confounders and I don't see that being possible for a large set of variables in a system).
– Noah
Apr 30, 2021 at 19:21
• "I should note I am a huge fan of (...), be interpreted as a causal effect." Thank you. (+1 just for that paragraph alone) Apr 30, 2021 at 21:03