Optimal and Efficient Sample Size Re-estimation: A Dynamic Cost Framework

2025-09-20

AI Summary

This study addresses the decision dilemma in sample size re-estimation for clinical trials by proposing a dynamic cost framework that balances interim evidence strength against the cost-effectiveness of additional enrollment. Methodologically, it introduces two novel explicit decision rules—based on likelihood ratios and return on investment—and proves that prevailing approaches can be unified as implicit dynamic cost functions. Through adaptive re-estimation, interim analysis, expected net benefit modeling, and extensive simulation, the framework demonstrates substantial average sample size reduction (zero power loss) under weak signal scenarios, mitigates risks of futile sample expansion, and improves resource efficiency. Its core contribution lies in shifting sample size decisions from static cost assumptions to data-driven, dynamic economic evaluation, thereby achieving synergistic optimization of statistical power and investment return.

Technology Category

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

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience

Abstract

Adaptive sample size re-estimation (SSR) is a well-established strategy for improving the efficiency and flexibility of clinical trials. Its central challenge is determining whether, and by how much, to increase the sample size at an interim analysis. This decision requires a rational framework for balancing the potential gain in statistical power against the risk and cost of further investment. Prevailing optimization approaches, such as the Jennison and Turnbull (JT) method, address this by maximizing power for a fixed cost per additional participant. While statistically efficient, this paradigm assumes the cost of enrolling another patient is constant, regardless of whether the interim evidence is promising or weak. This can lead to impractical recommendations and inefficient resource allocation, particularly in weak-signal scenarios. We reframe SSR as a decision problem under dynamic costs, where the effective cost of additional enrollment reflects the interim strength of evidence. Within this framework, we derive two novel rules: (i) a likelihood-ratio based rule, shown to be Pareto optimal in achieving smaller average sample size under the null without loss of power under the alternative; and (ii) a return-on-investment (ROI) rule that directly incorporates economic considerations by linking SSR decisions to expected net benefit. To unify existing methods, we further establish a representation theorem demonstrating that a broad class of SSR rules can be expressed through implicit dynamic cost functions, providing a common analytical foundation for their comparison. Simulation studies calibrated to Phase III trial settings confirm that dynamic-cost approaches improve resource allocation relative to fixed-cost methods.

Problem

• Optimizing sample size adjustments in clinical trials when costs vary with evidence strength
• Addressing limitations of fixed-cost methods that lead to inefficient resource allocation
• Developing novel decision rules that balance statistical power against dynamic enrollment costs

Innovation

• Dynamic cost framework for sample size re-estimation
• Likelihood-ratio rule achieving Pareto optimal efficiency
• Return-on-investment rule incorporating economic net benefit