STATISTICAL INFERENCE FOR THE MEAN OUTCOME UNDER A POSSIBLY NON-UNIQUE OPTIMAL TREATMENT STRATEGY
STATISTICAL INFERENCE FOR THE MEAN OUTCOME UNDER A POSSIBLY NON-UNIQUE OPTIMAL TREATMENT STRATEGY
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DOI：
10.1214/15-aos1384
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发表时间：
2016-04-01
影响因子：
4.5
通讯作者：
van der Laan, Mark J.
中科院分区：
文献类型：
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作者：
Luedtke, Alexander R.;van der Laan, Mark J.
我们考虑的挑战，在估计的平均结果下，最佳的个性化治疗策略定义为治疗规则，最大限度地提高人口的平均结果，候选治疗规则被限制为依赖于基线协变量。我们证明了一个必要和充分条件的最优值的路径可微，一个关键的条件需要开发一个定期和渐近线性（RAL）估计的最优值。所述条件比文献中所暗示的先前条件稍微更一般。然后，我们描述了一种方法来获得根-n率置信区间的最佳值，即使当参数不是路径可微。我们提供的条件下，我们的估计是RAL和渐近有效的平均结果是路径可微的。我们还概述了我们的方法扩展到多个时间点的问题。我们所有的结果都得到了模拟的支持。
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.