The use of the triangular test with response-adaptive treatment allocation.

A clinical trial is considered in which two treatments with binary responses are to be compared. A popular sequential stopping rule, the triangular test, is studied when various response-adaptive treatment allocation rules are applied, such as the recently proposed drop-the-loser rule, an urn randomization scheme. The paper extends previous work by Coad and Rosenberger, who combined the triangular test with the randomized play-the-winner rule. The purpose of the paper is to investigate to what extent the variability of an adaptive design affects the overall performance of the triangular test. The adaptive rules under consideration are described and some of their asymptotic properties are summarized. Simulation is then used to assess the performance of the triangular test when combined with the various adaptive rules. The main finding is that the drop-the-loser rule is the most promising of the adaptive rules considered in terms of a less variable allocation proportion and a smaller number of treatment failures. The use of this rule with the triangular test is beneficial compared with the triangular test with equal allocation, since it yields fewer treatment failures on average while providing comparable power with similar expected sample size. The results of an AIDS trial are used to illustrate the performance of the triangular test when combined with the drop-the-loser rule.