Urn models in clinical trial

In sequential medical experiments on a cohort of patients, there is an ethical imperative to provide the best possible medical care for the individual. In recent years, adaptive designs have been proposed to achieve this goal using sequentially accruing outcome data to dynamically update the probability of assignment to one of two or more treatments. The Response Adaptive Randomization for clinical trials is able to modify the probability of allocation according to the previous treatment and the related response and uses adaptive designs that include the urn model. The urn scheme became the prototype for constructing probabilistic models and can be described by a probabilistic process of increasing chances of success. We started considering the Pòlya urn and, then, we focused on one modification proposed by Muliere, Paganoni and Secchi, i.e. Randomly Reinforced Urn (RRU), a randomly reinforcement process.[2] The RRU-design is different from the other response-adaptive designs presented in literature, because has the ethically optimal property that the superior treatment will be selected with probability one thanks to its asymptotic convergence throughout the sequential trial, while these selection probability of the inferior treatment converges to zero.[4]Moreover the random reinforcement permits to increase the velocity of convergence to the better treatment, assuring an economic advantage too. In this context it is crucial the choice of the transformation function, the function that captures the reinforcement level. This function can be expressed in various form according to what utility function is assumed: different utility functions U imply different properties for the RRU-design, in terms of rate of convergence and skewness of allocations. We conclude this work comparing a classical statistical inferential design and the RRU-design. Specifically, through extended computer simulations, the conditions that have been explored had to be satisfied to ensure that the nonparametric model outperformed the classical inferential design.