Model-Assisted Uniformly Honest Inference for Optimal Treatment Regimes in High Dimension
Model-Assisted Uniformly Honest Inference for Optimal Treatment Regimes in High Dimension
复制标题
DOI：
10.1080/01621459.2021.1929246
复制
发表时间：
2021-05
影响因子：
3.7
通讯作者：
Y. Wu;Lan Wang;H. Fu
中科院分区：
文献类型：
--
作者：
Y. Wu;Lan Wang;H. Fu
摘要本文开发了新的工具来量化最优决策中的不确定性，并在考虑到测量大量变量的潜在成本的情况下，了解人们应该收集关于哪些变量的信息。我们研究同时推理，以确定在高维半参数框架中，一组变量是否与估计最优决策规则相关。未知的连接函数允许对处理和协变量之间的相互作用进行灵活的建模，但会导致高维的非凸估计，并给推理带来巨大的挑战。我们首先证明了局部约束强凸性条件是高概率成立的，并且估计问题的任何可行局部稀疏解都可以达到接近预言的估计误差界。我们进一步严格地证明了基于局部解的去偏版本的野生Bootstrap过程可以为一组变量对最优决策的影响提供渐近诚实的一致推断。诚实推理的优点是，它不需要初始估计器来实现完美的模型选择，也不需要很好地分离零和非零效应。我们还提出了一种有效的估计算法。我们的模拟结果显示了令人满意的性能。一个糖尿病研究的例子说明了它的实际应用。这篇文章的补充材料可以在网上找到。
Abstract This article develops new tools to quantify uncertainty in optimal decision making and to gain insight into which variables one should collect information about given the potential cost of measuring a large number of variables. We investigate simultaneous inference to determine if a group of variables is relevant for estimating an optimal decision rule in a high-dimensional semiparametric framework. The unknown link function permits flexible modeling of the interactions between the treatment and the covariates, but leads to nonconvex estimation in high dimension and imposes significant challenges for inference. We first establish that a local restricted strong convexity condition holds with high probability and that any feasible local sparse solution of the estimation problem can achieve the near-oracle estimation error bound. We further rigorously verify that a wild bootstrap procedure based on a debiased version of the local solution can provide asymptotically honest uniform inference for the effect of a group of variables on optimal decision making. The advantage of honest inference is that it does not require the initial estimator to achieve perfect model selection and does not require the zero and nonzero effects to be well-separated. We also propose an efficient algorithm for estimation. Our simulations suggest satisfactory performance. An example from a diabetes study illustrates the real application. Supplementary materials for this article are available online.