Urn Models in Clinical Trials

The principal question that this paper will investigate is the following: "when there is a significant difference between two possible treatments in a clinical trial, is it possible to construct a methodology that permits to allocate the higher number of patients to the best treatment?" The urn scheme became the prototype to build probabilistic models and can be described by a probabilistic process of increasing chances of success. We started considering the Pòlya urn and, then, one of its principal generalizations used in clinical contest: the Randomly Reinforced Urn. We concluded this project with a comparative study of a classical statistical inferential design and a randomized response adaptive design. We demonstrated, through computer simulations, that the nonparametric model outperformed the classical inferential design.