Response-adaptive randomization (RAR) methods can be used to adapt randomization probabilities based on accumulating data, 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 can also increase the risk of assigning patients to inferior treatments and lead to inferential problems such as confidence interval undercoverage. We propose a principled method based on Bayesian hypothesis testing to address these issues: We introduce a null hypothesis postulating equal effectiveness of treatments. Bayesian model averaging then 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 method balances highly variable Thompson sampling with static equal randomization. A simulation study demonstrates that the method can mitigate issues with 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 free and open-source R package brar, enabling experimenters to easily perform null hypothesis Bayesian RAR and support more effective randomization of patients.

翻译：响应自适应随机化方法可利用累积数据调整随机化概率，旨在提高患者分配至有效治疗的概率。汤普森采样是一种常用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随机分配患者。然而，该方法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，并导致置信区间覆盖率不足等推断问题。我们提出一种基于贝叶斯假设检验的原理性方法以解决这些问题：引入零假设以假定各治疗方案具有等效性。通过贝叶斯模型平均法向等概率随机化方向收缩，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，可分别得到等概率随机化和汤普森采样两种特例。仿真与真实案例表明，该方法能在高变异性的汤普森采样与静态等概率随机化之间取得平衡。模拟研究证明，该方法能缓解汤普森采样的缺陷，其统计特性与经过常见临时修正（如幂变换和概率封顶）的汤普森采样相当。我们已在免费开源的R软件包brar中实现该方法，使实验者能够便捷地执行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。