Sequential probability ratio tests when using randomized play-the-winner allocation

Abstract

In many clinical experiments there is a conflict between ethical demands to provide the best possible medical care for the patients and the statisticians desire to obtain an efficient experiment. Play-the-winner allocations is a group of designs that, during the experiment, tends to place more patients on the treatment that seems to be better. Using a randomized play-the-winner allocation and making a suitable inference for the design, is a suggestion to perform a reasonable experiment for the above mentioned considerations. In this paper we will concentrate on sequential inference, for the case of simple hypotheses and for the case with simple hypotheses with a nuisance parameter. The response to treatment is assumed to be dichotomous. We proceed from Wald's sequential probability ratio test, SPRT, and Cox's maximum likelihood SPRT, for the two hypothesis cases above.