So far, we’ve only focused on the ATE, but there are many other useful estimands we can use to summarize the average causal effect of some intervention or exposure. In many situations, it is not realistic to meet the assumptions of conditional exchangeability, SUTVA, AND overlap. Other causal estimands allow us to relax some of these assumptions.
The ATE summarizes the causal effect of treatment across ALL treatment conditions. But, we may only be interested in the causal effect of treatment in a particular group. In these cases, we can use a different estimand:
- Average Treatment Effect of the Treated (ATT) is the average of Y1 - Y0 for all individuals assigned to the treatment condition (Z = 1).
- Average Treatment Effect of the Control (ATC) is the average of Y1 - Y0 for all individuals assigned to the control condition (Z = 0).
There are other estimands we may encounter in causal methods, but the ATE, ATT, and ATC are three that we see in a variety of situations.
View the table in the learning environment. It shows theoretical data as well as which subsets of that data we use to calculate the ATT and ATC. Here, because the data is theoretical, we have both the factual and counterfactual outcomes for each individual, so we can compute both the ATT and the ATC.