Data Fusion with Distributional Equivalence Test-then-pool

TL;DR

This paper introduces a new test-then-pool framework for data fusion in clinical trials that uses kernel two-sample testing and equivalence testing to control Type-I error and improve power when combining historical and current control data.

Contribution

It develops a novel TTP method employing MMD and equivalence testing with bootstrap and permutation procedures, ensuring valid inference and higher power in data fusion.

Findings

Achieves higher power than standard TTP methods.

Maintains nominal Type-I error rate.

Provides a flexible criterion for pooling controls.

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.