Sequential Randomization Tests Using e-values: Applications for trial monitoring

Sequential monitoring of randomized trials traditionally relies on parametric assumptions or asymptotic approximations. We discuss a nonparametric sequential test and its application to continuous and time-to-event endpoints that derives validity solely from the randomization mechanism. Using a betting framework, these tests 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 and present simulation studies demonstrating calibration and power. These methods provide a conservative, assumption-free complement to model-based sequential analyses.