An Optimization Framework for Dynamic A-B Testing

A-B测试是一种统计方法，用于比较两种设计方案的有效性。它广泛应用于临床试验和电子商务中，用来比较医疗计划或营销和零售策略的表现。这个项目的重点是通过利用动态优化理论的最新进展来创建一个有效的A-B测试方案的框架。虽然该项目将考虑通用模型，但特别关注的是适应性临床试验，旨在确定一种新药或治疗是否在现有治疗的基础上有所改善。在这些动态医学试验中，实时决定将哪种治疗分配给每个患者，并考虑来自较早参与者的信息。该奖项将支持研究生的研究，这个项目的结果将被整合到一个新的分析硕士课程的课程中。PI将开发一种新的方法来设计最优的A-B考试，植根于动态优化。该项目旨在建立这样一个测试设计中隐含的动态优化问题，该问题受益于“状态空间崩溃”。这将有助于解决目前在计算上难以解决的大规模问题。从理论的角度来看，这将需要解决一个本身就是根本的随机向量着色问题。从实用的角度来看，该项目将在面对高维受试者协变量的情况下促进最佳试验的设计；当治疗效果在可观察协变量中高度非线性时，产生优化效率的能力；最后，使试验设计者能够在选择偏差(或公平性)与统计效率之间进行最佳权衡。与业界合作伙伴的合作将被用来增强本研究项目的实际影响，并丰富学生的课堂体验。

A-B testing is a statistical method used to compare the effectiveness of two design options. It is widely used in clinical trials and e-commerce to compare the performance of medical treatment plans or marketing and retail strategies. This project focuses on creating a framework for efficient A-B testing schemes by leveraging recent advances in the theory of dynamic optimization. While the project will consider generalized models, a particular focus will be on adaptive clinical trials that aim to determine whether a new drug or treatment improves on an existing treatment. In these dynamic medical trials, the decision of which treatment to assign to each patient is made in real time, taking into consideration information from the earlier participants. The award will support graduate student research, and findings resulting from this project will be integrated into coursework for a new Masters in Analytics program.The PI will develop a new approach to the design of optimal A-B tests, rooted in dynamic optimization. The project aims to establish that the dynamic optimization problem implicit in the design of such a test benefits from a "state space collapse". This would facilitate the solution of large-scale problems that are currently computationally intractable. From a theoretical perspective, this will entail the solution of a random vector-coloring problem that is fundamental in its own right. From a practical perspective, the project will facilitate the design of optimal trials in the face of high-dimensional subject covariates; yield the ability to optimize for efficiency when treatment effects are highly non-linear in observable covariates; and finally, give trial designers the ability to optimally trade off selection bias (or fairness) against statistical efficiency. Collaboration with industry partners will be used to enhance the practical impact of this research project, and to enrich the classroom experience for students.