An urn model to construct an efficient test procedure for response adaptive designs

We study the statistical performance of different tests for comparing the mean effect of two treatments. Given a reference classical test \({\mathcal {T}}_0\), we determine which sample size and proportion allocation guarantee to a test \({\mathcal {T}}\), based on response-adaptive design, to be better than \({\mathcal {T}}_0\), in terms of (a) higher power and (b) fewer subjects assigned to the inferior treatment. The adoption of a response-adaptive design to implement the random allocation procedure is necessary to ensure that both (a) and (b) are satisfied. In particular, we propose to use a Modified Randomly Reinforced Urn design and we show how to perform the model parameters selection for the purpose of this paper. Then, the opportunity of relaxing some assumptions on treatment response distributions is presented. Results of simulation studies on the test performance are reported and a real case study is analyzed.