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The present article is related to a comparison between two competing treatments, say  A  and  B  in the context of a Phase III clinical trial. This comparison is made through a  U -statistic estimator of the functional, where  X  and  Y  represent the continuous responses on treatments  A  and  B  respectively. Suppose the subjects are coming sequentially to a clinic and they are to be treated either by  A  or  B . The recruitment of the subjects is done by following a two-stage ethical allocation design with an optimal sequential allocation at the first stage. Here a sequential sampling scheme with equal randomization is adopted to optimize the stage 1 sample size for a given the total sample size of the trial. Then, a response-adaptive randomization rule is employed at the second-stage with a view to achieve ethical gain measured in terms of the proportion of allocations on the better treatment. The motivation of the proposed two stage design is to assign a larger number of subjects to the more promising treatment. Here we study various asymptotic results associated with the proposed design and compare its performance with a single stage equal allocation design. Also, the proposed procedure is illustrated through a real-life data set on carcinoma in the oropharynx.

An optimal design in a two-stage ethical allocation based on U -statistics