Sequential Randomization Tests Using E-values: A Betting Approach for Clinical Trials

Abstract: Sequential monitoring of randomized trials traditionally relies on parametric assumptions or asymptotic approximations. We present a nonparametric sequential test, the randomization e-process (e-RT), that derives validity solely from the randomization mechanism. Using a betting framework, e-RT 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. The e-RT provides a conservative, assumption-free complement to model-based sequential analyses.