Background:

Bayesian response-adaptive designs, which data adaptively alter the allocation ratio in favor of the better performing treatment, are often criticized for engendering a non-trivial probability of a subject imbalance in favor of the inferior treatment, inflating type I error rate, and increasing sample size requirements. The implementation of these designs using the Thompson sampling methods has generally assumed a simple beta-binomial probability model in the literature; however, the effect of these choices on the resulting design operating characteristics relative to other reasonable alternatives has not been fully examined. Motivated by the Advanced R² Eperfusion STrategies for Refractory Cardiac Arrest trial, we posit that a logistic probability model coupled with an urn or permuted block randomization method will alleviate some of the practical limitations engendered by the conventional implementation of a two-arm Bayesian response-adaptive design with binary outcomes. In this article, we discuss up to what extent this solution works and when it does not.

Methods:

A computer simulation study was performed to evaluate the relative merits of a Bayesian response-adaptive design for the Advanced R² Eperfusion STrategies for Refractory Cardiac Arrest trial using the Thompson sampling methods based on a logistic regression probability model coupled with either an urn or permuted block randomization method that limits deviations from the evolving target allocation ratio. The different implementations of the response-adaptive design were evaluated for type I error rate control across various null response rates and power, among other performance metrics.

Results:

The logistic regression probability model engenders smaller average sample sizes with similar power, better control over type I error rate, and more favorable treatment arm sample size distributions than the conventional beta-binomial probability model, and designs using the alternative randomization methods have a negligible chance of a sample size imbalance in the wrong direction.

Conclusion:

Pairing the logistic regression probability model with either of the alternative randomization methods results in a much improved response-adaptive design in regard to important operating characteristics, including type I error rate control and the risk of a sample size imbalance in favor of the inferior treatment.

中文翻译：

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具有二元结果的贝叶斯响应自适应随机化的替代模型和随机化技术

背景：

贝叶斯反应自适应设计，即数据自适应地改变分配比率，以支持性能更好的治疗，经常受到批评，因为它会产生有利于较差治疗的受试者不平衡的非平凡概率，夸大第一类错误率，并增加样本量要求。使用汤普森抽样方法实现这些设计在文献中通常假设一个简单的贝塔二项式概率模型；然而，这些选择相对于其他合理替代方案对最终设计运行特性的影响尚未得到充分研究。受难治性心脏骤停试验的高级 R ² Eperfusion 策略的启发，我们假设逻辑概率模型与瓮或置换块随机化方法相结合将减轻双臂贝叶斯响应的传统实施所产生的一些实际限制 -具有二元结果的自适应设计。在本文中，我们将讨论该解决方案在多大程度上有效以及何时无效。

方法：

进行了计算机模拟研究，以评估难治性心脏骤停试验的高级 R ² Eperfusion 策略的贝叶斯响应自适应设计的相对优点，该设计使用基于逻辑回归概率模型的汤普森采样方法，并结合瓮或排列块限制与不断变化的目标分配比率的偏差的随机化方法。响应自适应设计的不同实现针对各种空响应率和功率以及其他性能指标的 I 类错误率控制进行了评估。

结果：

与传统的β二项式概率模型相比，逻辑回归概率模型产生更小的平均样本量，但具有相似的功效，更好地控制I型错误率，以及更有利的治疗组样本量分布，并且使用替代随机化方法的设计的机会可以忽略不计样本量不平衡的方向错误。

结论：

将逻辑回归概率模型与任何一种替代随机化方法配对，可以在重要的操作特征方面大大改进响应自适应设计，包括 I 型错误率控制和有利于较差治疗的样本量不平衡的风险。