Sequential Elimination in Multi-Arm Selection Trials

Introduction
The main objective of a phase II selection trial is to identify the most promising treatment amongst multiple competing experimental regimens, when it truly exists. Utilising response-adaptive randomization (AR) in such designs, particularly useful with moderate sample sizes, has ethical advantages as it steers patients away from the inferior treatment arms.

Method
A common approach uses Bayesian AR, whereby the randomization probability to an arm is based on the posterior probability that arm has the highest response rate. We consider a frequentist alternative called sequential elimination (Levin 1981, Cheung 2008), which is a special form of AR. The design closes arms that are noticeably worse at interim evaluations, and hence channel more patients to the more promising open treatment arms. Using a simulation study based on an Acute Myeloid Leukaemia trial with four experimental arms, we compared the two approaches as well as a single stage pick-the-winner selection design (Simon et al, 1989). We also incorporated a Bayesian futility monitoring rule based on comparison to the historical response rate of standard treatment in such patients.

Results
Under the scenarios where all arms are futile, both AR designs perform better in terms of treatment selection and in-trial allocation than a single stage design (with no interim futility check). However, under scenarios where there is a winner, all approaches are comparable in terms of selection properties, but both AR approaches are more superior in allocating more patients to the best arm. The improved performance is even more evident if there is a clear winner.

Conclusion
Both the Frequentist and Bayesian adaptive randomization approaches are comparable, and are more ethical in allocating more patients to the better performing arms, compared to a single-stage selection design. It is particularly important to incorporate futility monitoring in such designs to improve the overall performance.