title: Multi-armed Bandit Models for the Optimal Design of Clinical Trials: Benefits and Challenges.
abstract: Multi-armed banditproblems (MABPs) are a special type of optimal control problem well suited to model resource allocation under uncertainty in a wide variety of contexts. Since the first publication of the optimal solution of theclassicMABP by a dynamic index rule, the bandit literature quickly diversified and emerged as an active research topic. Across this literature, the use of bandit models to optimally design clinical trials became a typical motivating application, yet little of the resulting theory has ever been used in the actual design and analysis of clinical trials. To this end, we review two MABP decision-theoretic approaches to the optimal allocation of treatments in a clinical trial: the infinite-horizon Bayesian Bernoulli MABP and the finite-horizon variant. These models possess distinct theoretical properties and lead to separate allocation rules in a clinical trial design context. We evaluate their performance compared to other allocation rules, including fixed randomization. Our results indicate that bandit approaches offer significant advantages, in terms of assigning more patients to better treatments, and severe limitations, in terms of their resulting statistical power. We propose a novel bandit-based patient allocation rule that overcomes the issue of low power, thus removing a potential barrier for their use in practice.
authors.affiliation: Investigator Statistician at MRC BSU, Cambridge and Biometrika post-doctoral research fellow.
authors.forename: Sofía S
authors.initials: SS
authors.lastname: Villar
authors.affiliation: Senior Investigator Statistician at MRC BSU, Cambridge.
authors.forename: Jack
authors.initials: J
authors.lastname: Bowden
authors.affiliation: Senior Investigator Statistician at MRC BSU, Cambridge, MRC Biostatistics Unit, Cambridge Institute of Public Health, Forvie Site, Robinson Way, Cambridge Biomedical Campus, Cambridge CB2 0SR, United Kingdom.
authors.forename: James
authors.initials: J
authors.lastname: Wason
keywords: Gittins index; Multi-armed bandit; Whittle index; patient allocation; response adaptive procedures