RESPONSE - ADAPTIVE CLINICAL TRIALS

The question we posed at the beginning of this thesis was whether, in the presence of a clinical superiority of one of two possible treatments, it was possible to find an appropriate statistical methodology that would allow us to reach this goal. We were thus led to explore many possibilities to carry out this analysis and randomly assign patients to the two treatments, as required by the particular nature of these experiments. Specifically, we made a close examination of the methods of randomization, especially appreciating the flexibility of the adaptive responses, and could see the strengths of urn models. We started with the study of the urn for excellence, Polya's urn. Next, we analyzed some extensions and generalizations, focusing especially on two kinds of urns with random reinforcement. We exposed the results obtained throughout simulations concerning the convergence of the proportion of the best treatment, which came from the comparison of the models studied. In the end, we showed how the urn model works in a real case, comparing two treatments with continuous response in one ICU trial on Melatonin. We'll see how the properties demonstrated in theory are confirmed in practice. The project ends by giving a hint of a new adaptive model that we have started to idealize in collaboration with the team of Prof. Parmigiani and Prof. Trippa of the "Biostatistics and Computational Biology" Department, Harvard T.H. Chan School of Public Health.