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.
