A sequential design for a clinical trial with a linear prognostic factor

We study a randomized adaptive design to assign one of the L treatments to patients who arrive sequentially by means of an urn model. At each stage n, a reward is distributed between treatments. The treatment applied is rewarded according to its response, 0⩽Yn⩽1, and 1-Yn is distributed among the other treatments according to their performance until stage n-1. Patients can be classified in K+1 levels and we assume that the effect of this level in the response to the treatments is linear. We study the asymptotic behavior of the design when the ordinary least square estimators are used as a measure of performance until stage n-1.