A new framework for estimation and inference of optimal dynamic treatment regimes

拟议的研究努力为动态治疗方案（DTRs）的估计和推断建立一个新的框架，这是一种实验设计的现代实施，与观察性或随机研究中产生的纵向记录数据相关。本主题涉及决策规则的统计研究，其特征是将时间依赖性特征作为输入，如症状评分，并返回要采取的治疗，如开始或增强治疗。最优动态处理规则的估计和推理由于问题的潜在高维性、时变混杂的存在以及规则条件通常不成立的事实而变得复杂，因此需要非标准渐近。提出的方法源于一个重要的见解，即可以使用特定形式的加权学习来估计决策规则参数。一个完整的估计和推理框架的发展将包括非正则渐近理论、计算元素和试验设计工具，包括样本量和功率公式和程序。这项工作的影响将是改变研究人员进行动态状态参数估计的方式，并通过提供一个简单的加权回归估计框架，促进使用更广泛的结果，包括离散效用。这项工作还将提供对估计器的非规律性的范围和性质的重要见解，以及随之而来的推理挑战。更一般地说，这项工作将有助于在参数空间的边界渐近的重要和不断增长的文献，这将使用更广泛的统计受众。

The proposed research endeavours to develop a new framework for estimation and inference of dynamic treatment regimes (DTRs), a modern implementation of experimental design, relevant to longitudinally recorded data arising from observational or randomized studies. This topic involves the statistical study of decision rules characterized by taking time-dependent characteristics as inputs such as a symptom score, and returning a treatment to be taken, such as initiation or augmentation of a therapy. Estimation and inference for optimal dynamic treatment rules are complicated by the potentially high-dimensionality of the problem, the presence of time-varying confounding, and the fact that regularity conditions often do not hold so that non-standard asymptotics are required. The proposed approach stems from an important insight that a particular form of weighted learning can be used to estimate decision rule parameters. The development of a complete framework for estimation and inference will include non-regular asymptotic theory, computational elements, and tools for trial design, including sample size and power formulae and programs. The impact of this work will be to change the manner in which researchers carry out estimation of dynamic regime parameters, and facilitate the use of a wider variety of outcomes, including discrete utilities, by providing a simple, weighed regression framework for estimation. The work will also provide important insights into the scope and nature of the non-regularity of the estimators, and consequent inferential challenges. More generally, the work will contribute to the important and growing literature on asymptotics at the boundary of the parameter space, which will be of use to a wider statistical audience.