Identification

In general, we are only ever able to observe one of the possible potential outcomes and it is possible that we don't observe as many as that.

If a patient participates in the Emilia trial, then she is either assigned the drug Kadcyla or she is assigned the standard chemotherapy. If she is assigned to the arm that receives Kadcyla then we may observe whether or not she survives to the two year mark. But in this case we do not observe wether or not she survives to the two year mark having taken the standard chemotherapy. We cannot observe the counterfactual. It is counter to fact.

We have a fundamental problem.

If we want to know the effect of a treatment then we must observe the difference in potential outcomes. We cannot observe the difference in potential outcomes because, at most, we can only observe one potential outcome.

There is no way around this problem without making assumptions. If we have two genetically identical mice and we give one mouse the drug treatment and one receives the standard treatment, then for each mouse there are two potential outcomes. For each mouse, we only observe one potential outcome.