by Conditional exchangeability and causal inference In observational data, it is unrealistic to assume that the treatment groups are exchangeable. In other words, there is no reason to expect that the groups are the same in all relevant variables other than the treatment. However, if we control for relevant variables by conditioning, then maybe the subgroups will be exchangeable. We will clarify what the “relevant variables” are, but for now, let’s just say they are all of the covariates ?. Then, we can state conditional exchangeability formally … The idea is that although the treatment and potential outcomes may be unconditionally associated (due to confounding), within levels of ?, they are not associated. In other words, there is no confounding within
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Conditional exchangeability and causal inference
In observational data, it is unrealistic to assume that the treatment groups are exchangeable. In other words, there is no reason to expect that the groups are the same in all relevant variables other than the treatment. However, if we control for relevant variables by conditioning, then maybe the subgroups will be exchangeable. We will clarify what the “relevant variables” are, but for now, let’s just say they are all of the covariates ?. Then, we can state conditional exchangeability formally …
The idea is that although the treatment and potential outcomes may be unconditionally associated (due to confounding), within levels of ?, they are not associated. In other words, there is no confounding within levels of ? because controlling for ? has made the treatment groups comparable …
Conditional exchangeability is the main assumption necessary for causal inference. Armed with this assumption, we can identify the causal effect within levels of ?, just like we did with (unconditional) exchangeability …
This marks an important result for causal inference … The main reason for moving from exchangeability to conditional exchangeability was that it seemed like a more realistic assumption. However, we often cannot know for certain if conditional exchangeability holds. There may be some unobserved confounders that are not part of ?, meaning conditional exchangeability is violated. Fortunately, that is not a problem in randomized experiments. Unfortunately, it is something that we must always be conscious of in observational data. Intuitively, the best thing we can do is to observe and fit as many covariates into ? as possible to try to ensure unconfoundedness.