STATISTICAL INFERENCE FOR THE MEAN OUTCOME UNDER A POSSIBLY NON-UNIQUE OPTIMAL TREATMENT STRATEGY
By Alexander Luedtke, M. J. van der Laan. 2016
244 citations recorded by the source corpus.
We consider challenges that arise in the estimation of the mean outcome under an optimal individualized treatment strategy defined as the treatment rule that maximizes the population mean outcome, where the candidate treatment rules are restricted to depend on baseline covariates. We prove a necessary and sufficient condition for the pathwise differentiability of the optimal value, a key condition needed to develop a regular and asymptotically linear (RAL) estimator of the optimal value. The stated condition is slightly more general than the previous condition implied in the literature. We then describe an approach to obtain root-n rate confidence intervals for the optimal value even when the parameter is not pathwise differentiable. We provide conditions under which our estimator is RAL and asymptotically efficient when the mean outcome is pathwise differentiable. We also outline an extension of our approach to a multiple time point problem. All of our results are supported by simulations.
Subfields: Statistics and Probability
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In Statistics and Probability
- Stefan Wager
- Susan Athey
- Sanjog Misra
- Christian Hansen
- Damian Kozbur
- Victor Chernozhukov
- Guido W. Imbens
- Mihaela van der Schaar
Citations in the corpus
- Faster Rates for Policy Learning (2017, background): “3] and [7] for definitions and proofs of these facts.”
- Policy Learning With Observational Data (2017, methodology): “Policy learning from observational data has also been considered in parallel literatures developed in both statistics (Luedtke and van der Laan, 2016; Qian and Murphy, 2011; Zhang, Tsiatis, Davidian, Zhang, and Laber, 2012; Zhao, Zeng, Rush, and Kosorok, 2012) and machine learning (Beygelzimer and…”
- Targeted Undersmoothing. (2017, background): “18See [8] and [50] for interesting approaches to estimating and performing inference for optimal treatment strategies.”