For time-varying treatments, the expected outcome of an oracle that picks the best dynamic strategy per patient is sharply bounded between the optimal observed-history DTR value and a union-bound recursion, with analogous CDF bounds for continuous outcomes.
Proceedings of the Second Seattle Symposium in Biostatistics: analysis of correlated data , pages=
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As Good as it Gets: Bounds for Oracle Time-Varying Treatment Strategies
For time-varying treatments, the expected outcome of an oracle that picks the best dynamic strategy per patient is sharply bounded between the optimal observed-history DTR value and a union-bound recursion, with analogous CDF bounds for continuous outcomes.