Sequential monitoring of randomized trials traditionally relies on parametric assumptions or asymptotic approximations. We discuss a family of nonparametric sequential tests - collectively called e-RT - for binary, deaths-only, continuous, time-to-event, and multi-state endpoints. All variants derive validity solely from the randomization mechanism. Using a betting framework, each test constructs a test martingale by sequentially wagering on treatment assignments given observed outcomes. Under the null hypothesis of no treatment effect, the expected wealth cannot grow, guaranteeing anytime-valid Type I error control regardless of stopping rule. We prove validity for each variant, present simulation studies demonstrating calibration and power, and discuss the principled asymmetry in betting strategies across outcome types. These methods provide a conservative, assumption-free complement to model-based sequential analyses.

翻译：随机化试验的序贯监测传统上依赖于参数假设或渐近近似。本文讨论了一族非参数序贯检验方法——统称为e-RT——适用于二值结局、仅死亡结局、连续结局、时间-事件结局以及多状态结局。所有变体的有效性均仅源自随机化机制。通过采用博弈框架，每种检验方法根据观测结果序贯地对治疗分配进行押注，从而构建检验鞅过程。在无治疗效应的原假设下，期望财富不会增长，这保证了无论采用何种停止规则，都能实现任意时间有效的第一类错误控制。我们证明了每种变体的有效性，提供了模拟研究以展示其校准效果和检验功效，并讨论了针对不同结局类型时博弈策略的原则性不对称性。这些方法为基于模型的序贯分析提供了保守且无需假设的补充方案。