Sequential urn designs with elimination for comparing K > or =3 treatments

A fully sequential procedure is proposed for comparing K > or =3 treatments with immediate binary responses. The procedure uses an adaptive urn design to randomize patients to the treatments and stopping rules are incorporated for eliminating less promising treatments. Simulation is used to assess the performance of the procedure for several adaptive urn designs, in terms of expected numbers of treatment failures and allocation proportions, and the effect on estimation at the end of the trial is also addressed. It is concluded that the drop-the-loser rule is more effective than equal allocation and all of the other designs considered. The practical benefits of the procedure are illustrated using the results of a three-treatment lung cancer study. It is then shown how the sequential elimination procedure may be used in dose-finding studies and its performance is compared with a recently proposed method. Several possible extensions to the work are briefly indicated.