In social or medical science, we sometimes have different treatments (likely to affect the same outcome) which have been applied simultaneously, i.e. some units have received treatment A, others have received treatment B, others have received treatment A and B and others have received nothing?

is there a rigorous way to measure ex post the relative effectiveness of treatments A and B, in the form of Average Treatment Effect or more sophisticated estimands capturing the heterogeneity of impacts? e.g. if there are n interventions, i can use 2^n control groups to study all the interactions.

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