Abstract
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-
Citation
Alexander R. Luedtke. Mark J. van der Laan. "Statistical inference for the mean outcome under a possibly non-unique optimal treatment strategy." Ann. Statist. 44 (2) 713 - 742, April 2016. https://doi.org/10.1214/15-AOS1384
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