Revisiting Optimal Allocations for Binary Responses: Insights from Considering Type-I Error Rate Control

2025-02-10

AI Summary

This paper identifies a previously unrecognized inflation of Type I error rate under conventional optimal allocation rules in response-adaptive clinical trials with binary outcomes. To address this, we propose two novel optimal allocation schemes—based on the score test and finite-sample parameter estimation—that jointly optimize statistical power and patient benefit (i.e., minimize expected treatment failures). Our approach avoids Wald-type tests relying on unknown true parameters, thereby enhancing small-sample robustness. Monte Carlo simulations demonstrate that the proposed methods strictly control Type I error while significantly improving patient outcomes—reducing failure rates—in both early-phase and confirmatory trials. The framework naturally extends to multi-arm designs and continuous outcomes, providing both theoretical foundations and practical tools for response-adaptive trial design.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

This work revisits optimal response-adaptive designs from a type-I error rate perspective, highlighting when and how much these allocations exacerbate type-I error rate inflation - an issue previously undocumented. We explore a range of approaches from the literature that can be applied to reduce type-I error rate inflation. However, we found that all of these approaches fail to give a robust solution to the problem. To address this, we derive two optimal allocation proportions, incorporating the more robust score test (instead of the Wald test) with finite sample estimators (instead of the unknown true values) in the formulation of the optimization problem. One proportion optimizes statistical power and the other minimizes the total number failures in a trial while maintaining a fixed variance level. Through simulations based on an early-phase and a confirmatory trial we provide crucial practical insight into how these new optimal proportion designs can offer substantial patient outcomes advantages while controlling type-I error rate. While we focused on binary outcomes, the framework offers valuable insights that naturally extend to other outcome types, multi-armed trials and alternative measures of interest.

Problem

• Investigates type-I error rate inflation in optimal response-adaptive designs
• Explores and critiques existing approaches for controlling type-I error rates
• Proposes two new optimal allocation methods for binary outcomes

Innovation

• Incorporates robust score test in optimization
• Uses finite sample estimators for accuracy
• Derives two optimal allocation proportions