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

拟议的研究努力开发一个新的框架，估计和推断的动态治疗方案（DTR），现代实施的实验设计，相关的纵向记录的数据所产生的观察或随机研究。本主题涉及决策规则的统计学研究，其特征在于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，如治疗的启动或增强。最佳动态治疗规则的估计和推理是复杂的潜在的高维问题，随时间变化的混杂的存在下，以及规律性条件往往不成立，使非标准的渐近性是必需的。 所提出的方法源于一个重要的见解，即一种特殊形式的加权学习可以用来估计决策规则参数。估计和推断的完整框架的发展将包括非正规渐近理论，计算元素和试验设计工具，包括样本量和功效公式和程序。 这项工作的影响将是改变研究人员进行动态政权参数估计的方式，并通过提供一个简单的，加权的回归估计框架，促进使用更广泛的结果，包括离散效用。这项工作还将提供重要的见解的范围和性质的非规律性的估计，以及随之而来的推理挑战。更一般地说，这项工作将有助于重要的和不断增长的文献渐近在边界的参数空间，这将是使用更广泛的统计观众。

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.