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

TL;DR

This paper introduces a family of nonparametric, sequential e-value based tests for randomized trial monitoring that guarantee Type I error control regardless of stopping rules and do not rely on parametric assumptions.

Contribution

It develops a flexible, effect-size agnostic framework for sequential testing using e-values, applicable to various endpoint types, with simulation evidence of calibration and power.

Findings

Tests maintain Type I error control under any stopping rule.

Simulation studies show good calibration and power.

Method is a conservative, assumption-light alternative to model-based analyses.

Abstract

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.