Under the independent mechanisms assumption, survivor average causal effects and conditional separable effects are identified without adjustment for common causes of the post-treatment event and the outcome.
A generalized theory of separa- ble effects in competing event settings.Lifetime Data Analysis, 27(4):588–631
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Effects conditional on post-treatment events generated by independent mechanisms
Under the independent mechanisms assumption, survivor average causal effects and conditional separable effects are identified without adjustment for common causes of the post-treatment event and the outcome.