For propensity score matching on binary outcome variables, why can the effect of treatment only be reported as the ATT instead of the ATE?

Question

I read in this paper An Introduction to Propensity Score Methods for Reducing the Effects of Confounding in Observational Studies, that

"If the outcome is dichotomous (self-report of the presence or absence of depression), the effect of treatment can be estimated as the difference between the proportion of subjects experiencing the event in each of the two groups (treated vs. untreated) in the matched sample. With binary outcomes, the effect of treatment can also be described using the relative risk..."

It seems to me that the difference of the proportions of subjects experiencing the event under treatment and non-treatment refers to the estimator for the Average Treatment Effect on the Treated (ATT), instead of the Average Treatment Effect (ATE).

Is calculating the ATE impossible under a binary outcome?

Answer 1

Calculating the ATE under a binary outcome is possible. That being said, yes, you are correct to suspect that through Propensity Score Matching (PSM) we are probably looking an ATT estimate or an even more constrained treatment effect because we might not have good overlap (common support) between the two treatment groups.

The passage you quote, correctly implies that a reasonable estimate of ATE is obtainable; it explicitly mentions that this calculation takes place "in the matched sample". To that respect, the opening paragraph of the section the passage comes from also states that: "(Thus), in a set of subjects all of whom have the same propensity score, the distribution of observed baseline covariates will be the same between the treated and untreated subjects.". i.e. ATE estimates are theoretically coherent.

I think that the best way to consider ATT/ATC/ATE estimates is by examining them within a counterfactual framework that is relevant to our research question. That way we can assess in a straight-forward manner what each difference refers at. We state the assumptions made (e.g. $E[Y^0|A = 1, X] = E[Y^0|A= 0, X] \approx$ if people in treatment group $A=1$ would do "as bad" as the control group $A=0$ if they were not treated, given information on covariates $X$) and then we calculate the difference we care for. Generally assessing "differences in the groups" can be potentially misinterpreted.

Morgan & Winship's "Counterfactuals and Causal Inference", Chapt. 5 "Matching Estimators of Causal Effects" has a very smooth exposition of the subject.