Confirmatory adaptive designs were introduced more than 30 years ago and enable for example sample size re-assessments and the selection of treatments, endpoints as well as subpopulations during the course of a clinical trial. Recently, sequential tests based on e-values for an anytime-valid inference have been developed, promising seemingly similar or even more flexibility and utility. In this note, we compare these two independently developed concepts, shedding light on their formal and methodological connections and differences. Specifically, we show that adaptive design tools like conditional error functions and combination tests are formally equivalent to e-value based, anytime-valid sequential tests. However, in spite of their common fundamental intention to bring flexibility into statistical inference, they have quite different emphases: While hypothesis testing with combination tests and conditional error function usually intent to exhaust type I error rates under the offered flexibility, e-value based testing aims on the additional flexibility with regard to optional continuation, the chosen level and, in recent extensions, in the loss functions to be controlled. We also indicate how recent e-value achievements could enrich clinical trial methodology and adaptive design methodology could inspire and improve e-value based testing.

翻译：确证性自适应设计提出至今已有30余年，可在临床试验过程中实现如样本量重新评估、治疗方案选择、终点指标及亚群筛选等功能。近年来，针对任意有效推断的基于e值的序贯检验方法被开发出来，看似提供了类似甚至更强的灵活性与实用性。本文对这两种独立发展的概念进行比较，阐明其在形式与方法层面的联系与差异。具体而言，我们证明诸如条件误差函数和组合检验等自适应设计工具在形式上等价于基于e值的任意有效序贯检验。然而，尽管两者均旨在为统计推断引入灵活性，其侧重点却截然不同：使用组合检验和条件误差函数的假设检验通常旨在利用所提供的灵活性耗尽I类错误率，而基于e值的检验则更关注可选延续性、显著性水平选择以及（在最新扩展中）损失函数控制等方面的额外灵活性。我们还探讨了e值领域最新进展如何丰富临床试验方法学，以及自适应设计方法论如何启发并改进基于e值的检验。