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, event-only, and continuous endpoints. All active variants derive validity from the randomization mechanism. Using a betting framework, each test constructs a test martingale by sequentially wagering on randomized assignments or observed event labels before using the current label in the wealth update. Under the null hypothesis of no treatment effect, the expected wealth cannot grow, guaranteeing anytime-valid Type I error control regardless of stopping rule. The default e-RT posture is effect-size agnostic: monitoring can begin without specifying a hypothesized treatment effect. Alternatively, fixed design-calibrated wagers, including growth-rate-optimal (GROW) wagers, may be used as optional efficiency tools when a clinically meaningful design alternative is credible. We present simulation studies demonstrating calibration and power, and discuss the principled asymmetry in betting strategies across outcome types. These methods provide a conservative, assumption-light complement to model-based sequential analyses.

翻译：传统上，随机化试验的序贯监测依赖参数假设或渐近近似。本文讨论了一类用于二分类、仅事件型及连续型终点的非参数序贯检验——统称为e-RT。所有有效变体均从随机化机制获得有效性。通过赌注框架，每个检验在利用当前标签更新财富之前，通过依次对随机分配或观察到的事件标签下赌注来构建检验鞅。在无治疗效应的零假设下，预期财富无法增长，从而保证了无论采用何种停止规则都能实现任意时刻有效的I类错误控制。默认的e-RT姿态与效应量无关：无需指定假设的治疗效应即可开始监测。或者，当临床意义的设计备择假设可信时，可将固定的设计校准赌注（包括最优增长率赌注）作为可选的效率工具。我们展示了校准与效能的模拟研究，并讨论了不同结局类型下赌注策略的合理不对称性。这些方法为基于模型的序贯分析提供了一种保守且弱假设的补充方案。