🤖 AI Summary
This study addresses a central challenge in statistical inference for clinical trials: achieving high operational flexibility—such as sample size re-estimation and treatment selection—while rigorously controlling the Type I error rate. The authors systematically integrate confirmatory adaptive designs with e-value-based anytime-valid testing methods, establishing for the first time their formal equivalence through conditional error functions and combination tests, while clarifying their distinct emphases on flexibility. The work constructs a theoretical bridge between these two frameworks: the e-value paradigm enhances optional continuation and loss control, whereas adaptive design principles can refine e-value testing strategies. This synthesis lays both a theoretical foundation and a practical pathway for developing next-generation inferential methods that simultaneously ensure strict error control and substantial procedural adaptability.
📝 Abstract
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.