Efficient randomized adaptive designs for multi-arm clinical trials

In clinical trials, response-adaptive randomization (RAR) has gained increasing attention due to its ability to assign more patients to better-performing treatments. Consequently, several RAR methods have been proposed in recent years. Among them, the efficient response adaptive randomization design (ERADE), proposed by Hu et al. (2009), stands out as an optimal approach, with the asymptotic variance of the allocation proportion achieving the Cramér-Rao lower bound, demonstrating its statistical efficiency. However, the original ERADE is limited to trials with only two treatment arms. Given the growing prevalence of multi-arm trials in modern clinical development, the original ERADE design no longer meets all practical needs. In this paper, we extend ERADE for use in multi-arm clinical trials, proposing the multi-arm ERADE algorithm. We establish the asymptotic properties of this generalized design and demonstrate its effectiveness in finite sample settings through simulations and a real-world trial redesign.