Adaptive clinical trials based on design-optimal e-values with automatic curtailment: An application to single-arm trials with binary data

2026-05-27

AI Summary

This work proposes an e-value–based adaptive design for small-sample, single-arm clinical trials with binary outcomes, enabling flexible interim analyses and automatic futility stopping while rigorously controlling Type I error. It is the first to apply a finite-horizon optimal e-value framework to this setting, leveraging a betting interpretation combined with constrained dynamic programming to optimize either finite-sample statistical power or expected sample size. Compared to conventional approaches and asymptotically optimal e-value designs, the proposed method demonstrates superior performance in small samples, offering both robustness and efficiency. Moreover, it facilitates real-time futility detection through extremely small e-values, allowing early termination when treatment efficacy is implausible.

Abstract

The e-value is gaining traction as a robust alternative to p-values and Bayes factors for quantifying statistical evidence. e-values are a promising method for adaptive clinical trials due to their anytime-validity: e-values ensure type I error rate control at any stopping time, facilitating repeated interim analyses, complex stopping rules, and valid inference under protocol deviations. The e-value literature focuses mostly on asymptotic optimality; however, sample sizes in clinical trials are often limited. To this end, we investigate e-value-based designs with finite-horizon optimality for single-arm multi-stage clinical trials with binary data. This setting is relevant in early-phase cancer trials, but it also facilitates an accessible introduction to the betting interpretation of e-values, which we use to construct e-values that either (1) maximize statistical power, or (2) minimize the expected sample size, with or without constraints on the minimum power. We construct these designs through (constrained) dynamic programming based on the currently observed e-value, the maximum sample size, and the pre-specified significance level. Using exact calculations, we show that, next to robustness, e-value-based designs can provide competitive operating characteristics to standard (non-)adaptive designs with and without futility stopping and outperform growth-rate-optimal e-values in finite samples. In addition, small e-values automatically indicate trial continuation is futile, e.g., an e-value of zero indicates the impossibility of an efficacy conclusion. Hence, e-value-based designs provide a viable alternative to the current state-of-the-art in single-arm binary trials, warranting extension to other adaptive clinical trial settings such as multi-arm multi-stage and response-adaptive designs.

Problem

• adaptive clinical trials
• e-values
• binary data
• single-arm trials
• finite-horizon optimality

Innovation

• e-values
• adaptive clinical trials
• finite-horizon optimality
• dynamic programming
• automatic curtailment