Sequential Designs for Comparing Treatments: A review and some new results

Sequential experiments are widely used in pharmaceutical and clinical practice. These procedures are very flexible since the experimenter can modify the trial as it goes along. A large number of them have been suggested in the literature: they correspond to different purposes of the experimenters': accurate inference, cost saving, ethical preoccupations, etc. Sequential procedures, however, pose problems as regards the correct inferential paradigm. In this presentation I give some results on the asymptotic optimality of a large class of sequential designs when the responses belong to the exponential family. In particular, for designs based on the step-by-step updating of the parameter estimates by maximum likelihood, the MLE's retain the strong consistency and asymptotic normality properties. Other results concern stopping rules and inverse sampling. A mention will be made of a special type of sequential experiments, i.e. Markovian ones: they include Biased coin Designs, Urn models, and Up-and-Down Designs.