Adaptive designs and Robbins-Monro algorithm

An adaptive design for a clinical trial with prognostic factors and more than two treatments is described using a generalised urn model in a random environment. The evolution of the urn composition is expressed by a recurrence equation that fits the Robbins-Monro scheme of stochastic approximation. Then, the Ordinary Differential Equation method is used to obtain strong laws. Besides, central limit theorems are also obtained. These results are useful to make inference about the parameters of the clinical trial.