BACKGROUND There is a growing interest in the use of Bayesian adaptive designs in late-phase clinical trials. This includes the use of stopping rules based on Bayesian analyses in which the frequentist type I error rate is controlled as in frequentist group-sequential designs. METHODS This paper presents a practical comparison of Bayesian and frequentist group-sequential tests. Focussing on the setting in which data can be summarised by normally distributed test statistics, we evaluate and compare boundary values and operating characteristics. RESULTS Although Bayesian and frequentist group-sequential approaches are based on fundamentally different paradigms, in a single arm trial or two-arm comparative trial with a prior distribution specified for the treatment difference, Bayesian and frequentist group-sequential tests can have identical stopping rules if particular critical values with which the posterior probability is compared or particular spending function values are chosen. If the Bayesian critical values at different looks are restricted to be equal, O'Brien and Fleming's design corresponds to a Bayesian design with an exceptionally informative negative prior, Pocock's design to a Bayesian design with a non-informative prior and frequentist designs with a linear alpha spending function are very similar to Bayesian designs with slightly informative priors.This contrasts with the setting of a comparative trial with independent prior distributions specified for treatment effects in different groups. In this case Bayesian and frequentist group-sequential tests cannot have the same stopping rule as the Bayesian stopping rule depends on the observed means in the two groups and not just on their difference. In this setting the Bayesian test can only be guaranteed to control the type I error for a specified range of values of the control group treatment effect. CONCLUSIONS Comparison of frequentist and Bayesian designs can encourage careful thought about design parameters and help to ensure appropriate design choices are made.

中文翻译：

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贝叶斯和频率论组序贯临床试验设计的比较。


背景人们对在后期临床试验中使用贝叶斯自适应设计越来越感兴趣。这包括使用基于贝叶斯分析的停止规则，其中频率论 I 类错误率像频率论组序贯设计中那样受到控制。方法本文对贝叶斯和频率论组序贯检验进行了实际比较。我们着眼于可以通过正态分布检验统计量汇总数据的设置，评估和比较边界值和操作特征。结果 尽管贝叶斯和频率论组序贯方法基于根本不同的范式，但在单臂试验或双臂比较试验中，对于治疗差异指定先验分布，贝叶斯和频率论组序贯检验可以具有相同的停止规则，如果选择与后验概率进行比较的特定临界值或特定的支出函数值。如果不同外观下的贝叶斯临界值被限制为相等，则奥布莱恩和弗莱明的设计对应于具有异常信息性先验的贝叶斯设计，波科克的设计对应于具有非信息性先验的贝叶斯设计和具有线性的频率论设计。阿尔法支出函数与具有少量先验信息的贝叶斯设计非常相似。这与针对不同组的治疗效果指定独立先验分布的比较试验的设置形成鲜明对比。在这种情况下，贝叶斯和频率论组序贯检验不能具有相同的停止规则，因为贝叶斯停止规则取决于两组中观察到的平均值，而不仅仅是它们的差异。 在此设置中，贝叶斯检验只能保证控制对照组治疗效果的指定值范围内的 I 类错误。结论 频率论和贝叶斯设计的比较可以鼓励对设计参数的仔细思考，并有助于确保做出适当的设计选择。