A comparison of the randomized play-the-winner rule and the triangular test for clinical trials with binary responses

We consider a clinical trial model comparing an experimental treatment with a control treatment when the responses are binary. For fixed significance level and power, we compare the expected number of treatment failures for two designs--the randomized play-the-winner rule and the triangular test. The former is an example of an adaptive design while the latter is an example of a fully sequential design. We show how to determine the sample size for the randomized play-the-winner rule and how to choose the stopping boundaries for the triangular test so that the two designs have similar power functions. With this choice of design parameters, simulation indicates that the triangular test is generally more effective at reducing the expected number of treatment failures, particularly when there is a large difference between the two probabilities of success. The expected number of treatment failures can be further reduced if the triangular test is applied using the randomized play-the-winner rule to assign each patient to one of the two treatments.