Statistical inference for the mean outcome under a possibly non-unique optimal treatment strategy
研究了在最优治疗策略可能不唯一时，如何估计该策略下的平均结局，并给出了构造置信区间的方法，对从事因果推断和个性化治疗的学者有参考价值。
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.