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

拟议的研究致力于开发一个新的框架，用于估计和推断动态治疗方案(DTRs)，这是实验设计的现代实现，与来自观察性或随机化研究的纵向记录数据相关。本课题涉及对决策规则的统计研究，其特征是将依赖时间的特征作为输入，例如症状评分，并返回要采取的治疗，例如开始或加强治疗。最优动态处理规则的估计和推理由于问题的潜在高维、时变混杂的存在以及正则性条件经常不成立而需要非标准渐近的事实而变得复杂。 所提出的方法源于一个重要的见解，即一种特定形式的加权学习可以用于估计决策规则参数。评估和推断的完整框架的开发将包括非规则渐近理论、计算元素和试验设计工具，包括样本量和幂公式和程序。 这项工作的影响将是改变研究人员对动态制度参数进行估计的方式，并通过为估计提供一个简单、加权的回归框架，促进使用更广泛的结果，包括离散的效用。这项工作还将对估计器的非正则性的范围和性质以及由此产生的推理挑战提供重要的见解。更广泛地说，这项工作将有助于有关参数空间边界的渐近性的重要和不断增长的文献，这将对更广泛的统计受众有用。

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.