This paper studies statistical decisions for dynamic treatment assignment problems. Many policies involve dynamics in their treatment assignments where treatments are sequentially assigned to individuals across multiple stages and the effect of treatment at each stage is usually heterogeneous with respect to the prior treatments, past outcomes, and observed covariates. We consider estimating an optimal dynamic treatment rule that guides the optimal treatment assignment for each individual at each stage based on the individual's history. This paper proposes an empirical welfare maximization approach in a dynamic framework. The approach estimates the optimal dynamic treatment rule from panel data taken from an experimental or quasi-experimental study. The paper proposes two estimation methods: one solves the treatment assignment problem at each stage through backward induction, and the other solves the whole dynamic treatment assignment problem simultaneously across all stages. We derive finite-sample upper bounds on the worst-case average welfare-regrets for the proposed methods and show $n^{-1/2}$-minimax convergence rates. We also modify the simultaneous estimation method to incorporate intertemporal budget/capacity constraints.
翻译:本文研究动态治疗分配问题的统计决定。许多政策涉及治疗任务动态,即治疗按顺序分配给不同阶段的个人,每个阶段的治疗效果通常与先前的治疗、过去的结果和观察到的共差情况不同。我们考虑估计一个最佳的动态治疗规则,根据个人的历史指导每个阶段对每个人的最佳治疗分配。本文件提议在动态框架内采用实证福利最大化办法。本方法从实验或准实验研究的小组数据中估计最佳动态治疗规则。本文提出两种估算方法:一种是通过后向感应解决每个阶段的治疗分配问题,另一种是通过所有阶段同时解决整个动态治疗分配问题。我们从最坏情况中得出拟议方法的福利平均平均比例的有限抽样,并显示 $ ⁇ -1/2 $-minimmax 的趋同率。我们还从实验或准实验研究中得出的小组数据中估算了最佳动态治疗规则。我们还修改了同时估算方法,以纳入时际预算/能力限制。