Response-adaptive randomization (RAR) in clinical trials aims to improve ethical and statistical efficiency by dynamically allocating patients to treatments based on observed outcomes. While RAR based on a target optimal allocation have been extensively studied for two-arms settings, their extension to multi-treatment experiments ($K \geq 2$) remains theoretically fragmented, with most existing methods focusing on specific algorithms or restricted target allocations. In this paper, we introduce a unified framework for response-adaptive targeting, the $α$-Rebalancing Targeting Strategies ($α$RTS), which generalize the ERADE two-armed strategy of Hu et al. [2009]. We prove that all designs in this family share fundamental asymptotic properties: strong consistency, asymptotic normality of allocation proportions and treatment effect estimators, and asymptotic efficiency. To address sparse target regimes (where some treatments are asymptotically eliminated), we further propose $α$RTS with Forced Exploration, a variant that guarantees infinite sampling for all treatments while preserving the asymptotic guarantees. Extensive simulations illustrate the finite-sample behavior of $α$RTS variants in a 3-armed context, highlighting in particular the critical role of forced exploration in sparse settings.

翻译：临床试验中的响应自适应随机化（RAR）旨在通过根据观察到的结果动态分配患者到不同治疗方案，以提高伦理和统计效率。尽管基于目标最优分配的RAR已在双臂设置中得到广泛研究，但其在多处理实验（K≥2）中的扩展在理论上仍较零散，现有方法大多聚焦于特定算法或受限的目标分配。本文提出了一种统一的响应自适应目标框架——α-再平衡目标分配策略（αRTS），该策略推广了Hu等人[2009]的双臂ERADE策略。我们证明该框架内的所有设计均具有基本渐近性质：强相合性、分配比例与处理效应估计量的渐近正态性，以及渐近效率。针对稀疏目标情形（部分处理被渐近消除），我们进一步提出带强制探索的αRTS——一种能在保持渐近保证的同时，确保对所有处理进行无限取样的变体。大量仿真实验展示了αRTS变体在三臂背景下的有限样本行为，特别揭示了强制探索在稀疏设置中的关键作用。