Urn Model-Based Adaptive Multi-arm Clinical Trials: A Stochastic Approximation Approach.

Summary This paper presents the link between stochastic approximation and multi-arm clinical trials based on randomized urn models investigated in Bai et al. (J. Multivar. Anal. 81(1):1–18, 2002) where the urn updating depends on the past performances of the treatments. We reformulate the dynamics of the urn composition, the assigned treatments and the successes of assigned treatments as standard stochastic approximation (SA) algorithms with remainder. Then, we derive the a.s. convergence of the normalized procedure under less stringent assumptions by calling upon the ODE and a new asymptotic normality result (Central Limit Theorem CLT) by calling upon the SDE methods.