Data Fusion with Distributional Equivalence Test-then-pool

2026-03-12

AI Summary

This study addresses the challenge of leveraging historical control data in randomized controlled trials to mitigate insufficient current control samples, a practice often compromised by population distributional differences that introduce bias and by existing methods’ difficulty in simultaneously controlling Type I error and maintaining statistical power. To resolve this, the authors propose a novel post-test fusion framework: first, a kernel-based two-sample equivalence test using Maximum Mean Discrepancy (MMD) assesses whether historical and current controls can be safely pooled; if equivalence is established, inference proceeds via a hybrid approach combining elements of the bootstrap and permutation tests. This method rigorously controls Type I error while substantially enhancing statistical power, thereby enabling robust and efficient utilization of historical control data.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Mixed Discrete/Continuous Search
• Intelligent Robots: State Estimation

Application Category

• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Randomized controlled trials (RCTs) are the gold standard for causal inference, yet practical constraints often limit the size of the concurrent control arm. Borrowing control data from previous trials offers a potential efficiency gain, but naive borrowing can induce bias when historical and current populations differ. Existing test-then-pool (TTP) procedures address this concern by testing for equality of control outcomes between historical and concurrent trials before borrowing; however, standard implementations may suffer from reduced power or inadequate control of the Type-I error rate. We develop a new TTP framework that fuses control arms while rigorously controlling the Type-I error rate of the final treatment effect test. Our method employs kernel two-sample testing via maximum mean discrepancy (MMD) to capture distributional differences, and equivalence testing to avoid introducing uncontrolled bias, providing a more flexible and informative criterion for pooling. To ensure valid inference, we introduce partial bootstrap and partial permutation procedures for approximating null distributions in the presence of heterogeneous controls. We further establish the overall validity and consistency. We provide empirical studies demonstrating that the proposed approach achieves higher power than standard TTP methods while maintaining nominal error control, highlighting its value as a principled tool for leveraging historical controls in modern clinical trials.

Problem

• data fusion
• historical controls
• distributional equivalence
• Type-I error control
• randomized controlled trials

Innovation

• test-then-pool
• maximum mean discrepancy
• equivalence testing
• partial bootstrap
• data fusion