A single necessary and sufficient condition on the classes of treatment-assignment probabilities and outcome distributions characterizes when the average treatment effect and the effect on the treated are identifiable from censored data.
Proof of Theorem 4.5
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What Makes Treatment Effects Identifiable? Characterizations and Estimators Beyond Unconfoundedness
A single necessary and sufficient condition on the classes of treatment-assignment probabilities and outcome distributions characterizes when the average treatment effect and the effect on the treated are identifiable from censored data.