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I am trying to make some causal inference estimates in a dataset and was hoping someone here could help me out with a question I have coming out of my background reading.

It seems that a very prevalent technique is to use a propensity score (as described by Rosenbaum, the probability of receiving the treatment as a function of a valid set of confounders) as the balancing mechanism when the set of confounders is very high dimension.

My understanding is that doing so would ensure that treatment is essentially random given any combination of the values of the confounders, and thus mimicking a randomized control trial.

However, this randomization of treatment seems to me to be only part of what makes an RCT the gold standard of causal inference. In an RCT, randomization of treatment also ensures the random distribution of potential outcomes between treatment and control groups.

And this is where I am struggling. In certain sets of observational data, it seems entirely possibly that balancing on treatment propensity would not ensure balance on potential outcomes propensity. In other words, within any given stratified propensity score bucket, the treated audience could have a different potential outcomes propensity than the control audience. And thus the difference between the two groups averages would be a biased causal effect estimate.

Is there something that I am missing here, and thus this isn’t a concern in practice? If not, are there other causal inference techniques out there that attempt to address this potential introduction of bias?

Any help here is much appreciated!

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You might be missing the key assumption required for propensity score methods (and all methods that rely on covariate adjustment, of which propensity score methods are a set, and likely not even among the best methods) to yield valid estimates of the causal effect: strong ignorability. String ignorability says that the potential outcomes are functions of the variables you are adjusting for (i.e., balancing) and possibly other variables that are independent of the treatment. That means by balancing the covariates, you are balancing the potential outcomes (at least, the components of the potential outcomes that are otherwise associated with treatment). If strong ignorability is not met, then methods of covariate adjustment do not balance the potential outcomes. Some argue strong ignorability can never be met in empirical applications, implying covariate adjustment methods are never valid for estimating causal effects.

My answer here on potential outcomes might be helpful.

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  • $\begingroup$ Perfectly stated. Anyone using propensity scores who casually assumes that the list of adjustment variables is complete is not doing causal inference. PS is more of a data reduction technique than a causal inference technique. $\endgroup$ Commented Nov 25, 2023 at 13:21

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