Response-adaptive randomization (RAR) methods use accumulated data to adapt randomization probabilities, aiming to increase the probability of allocating patients to effective treatments. A popular RAR method is Thompson sampling, which randomizes patients proportionally to the Bayesian posterior probability that each treatment is the most effective. However, its high variability early in a trial can also increase the risk of assigning patients to inferior treatments. We propose a principled method based on Bayesian hypothesis testing to mitigate this issue. Specifically, we introduce a point null hypothesis that postulates equal effectiveness of treatments. This induces shrinkage toward equal randomization probabilities, with the degree of shrinkage controlled by the prior probability of the null hypothesis. Equal randomization and Thompson sampling arise as special cases when the prior probability is set to one or zero, respectively. Simulated and real-world examples illustrate that the proposed method balances highly variable Thompson sampling with static equal randomization. A simulation study demonstrates that the method can mitigate issues with ordinary Thompson sampling and has comparable statistical properties to Thompson sampling with common ad hoc modifications such as power transformation and probability capping. We implement the method in the open-source R package brar, enabling experimenters to easily perform point null Bayesian RAR and support more effective randomization of patients.

翻译：响应自适应随机化方法利用累积数据动态调整随机化概率，旨在提高患者被分配至有效治疗组的概率。汤普森抽样作为一种流行的响应自适应随机化方法，其根据各治疗方案为最优效的贝叶斯后验概率按比例分配患者。然而，该方法在试验初期的高变异性也可能增加患者被分配至次优治疗方案的风险。本文提出一种基于贝叶斯假设检验的原理性方法以缓解该问题。具体而言，我们引入一个点零假设，该假设设定各治疗方案具有同等疗效。该假设会促使随机化概率向均等分配方向收缩，收缩程度由零假设的先验概率控制。当先验概率设为1或0时，可分别退化为完全均等随机化与标准汤普森抽样这两种特例。仿真与真实案例表明，所提方法能在高变异的汤普森抽样与静态均等随机化之间实现平衡。模拟研究证明，该方法能缓解传统汤普森抽样的缺陷，且其统计特性与经过常用启发式修正（如幂变换与概率截断）的汤普森抽样相当。我们已在开源R包brar中实现该方法，使实验者能便捷地执行点零假设贝叶斯响应自适应随机化，从而支持更有效的患者随机化分配。