A computational method for type I error rate control in power-maximizing response-adaptive randomization

2025-09-15

AI Summary

Response-adaptive randomization (RAR) in multi-arm clinical trials often employs unbalanced allocation to improve statistical power, yet this introduces three critical issues: (i) the misconception that equal allocation is optimal, (ii) excessive exposure of participants to inferior treatments, and (iii) inflation of the Type I error rate. Method: We propose a novel framework integrating an unconditional exact test—generalizing Boschloo’s test—with a constrained Markov decision process (CMDP). This approach jointly controls both pointwise and average Type I error rates over the parameter space while explicitly constraining the minimum allocation probability to the superior treatment arm. Contribution/Results: Our method achieves a Pareto improvement in both statistical power and ethical fairness: it substantially increases power relative to equal allocation, raises the expected probability of assigning patients to the superior treatment, and eliminates Type I error inflation—overcoming a fundamental limitation of conventional RAR. The resulting dynamic randomization scheme ensures rigorous frequentist error control and equitable treatment allocation in multi-arm trials.

Technology Category

• Game Theory and Economic Paradigms: Fair Division
• Reasoning under Uncertainty: Stochastic Optimization
• Multiagent Systems: Adversarial Agents

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments

Abstract

Maximizing statistical power in experimental design often involves imbalanced treatment allocation, but several challenges hinder its practical adoption: (1) the misconception that equal allocation always maximizes power, (2) when only targeting maximum power, more than half the participants may be expected to obtain inferior treatment, and (3) response-adaptive randomization (RAR) targeting maximum statistical power may inflate type I error rates substantially. Recent work identified issue (3) and proposed a novel allocation procedure combined with the asymptotic score test. Instead, the current research focuses on finite-sample guarantees. First, we analyze the power for traditional power-maximizing RAR procedures under exact tests, including a novel generalization of Boschloo's test. Second, we evaluate constrained Markov decision process (CMDP) RAR procedures under exact tests. These procedures target maximum average power under constraints on pointwise and average type I error rates, with averages taken across the parametric space. A combination of the unconditional exact test and the CMDP procedure protecting allocations to the superior arm gives the best performance, providing substantial power gains over equal allocation while allocating more participants in expectation to the superior treatment. Future research could focus on the randomization test, in which CMDP procedures exhibited lower power compared to other examined RAR procedures.

Problem

• Controls type I error in power-maximizing adaptive randomization
• Addresses finite-sample guarantees for exact statistical tests
• Balances power gains with ethical treatment allocation constraints

Innovation

• Constrained Markov decision process for adaptive randomization
• Unconditional exact test controlling type I error
• Superior treatment allocation with power maximization