Beyond Exchangeability: Distribution-Shift-Aware Integration of External Control Data in Randomized Trials
Abstract
Randomized controlled trials (RCTs) are the gold standard for evaluating causal effects but are often costly and difficult to scale; consequently, they are frequently augmented with auxiliary external controls in many applications. Prior approaches to borrowing such data typically rely on exchangeability, under which the external controls are readily usable for inference in the trial population. In practice, however, differences in eligibility criteria, standard of care, and data collection procedures may induce distribution shifts between the RCT and the external controls, making exchangeability implausible. In this paper, we propose a general framework for incorporating external controls that explicitly accounts for distribution shifts through an augmented estimating function, allowing information about the shifts to be leveraged for efficiency gains even when exchangeability does not hold. To guard against potential bias and efficiency loss due to misspecification of the distribution shift, we further develop an adaptive shrinkage estimator that preserves consistency while guaranteeing efficiency dominance over the trial-only benchmark. Synthetic experiments and a real data application demonstrate the practical advantages of the proposed approaches.
Related
- Adaptively Combining Randomized and External Control Data Using a Mixture Prior in the Presence of Heterogeneity
- Integration of external predictions for efficient estimation of the risk ratio
- Discussion on "Principled type I error rate inflation in two-arm clinical trial designs with external control information borrowing" by Silvia Calderazzo, Manuel Wiesenfarth, Vivienn Weru, and Annette Kopp-Schneider
- The relation between non-exchangeability and radial asymmetry of copulas
- Remarks on DAG exchangeability and generalized wreath products
BibTeX
@misc{shan2026beyond,
title = {{Beyond Exchangeability: Distribution-Shift-Aware Integration of External Control Data in Randomized Trials}},
author = {Jiawei Shan and Yiteng Tu and Guanbo Wang and Chao Ying and Jiwei Zhao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.28785},
eprint = {2605.28785},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.28785},
}
RIS
TY - UNPB
TI - Beyond Exchangeability: Distribution-Shift-Aware Integration of External Control Data in Randomized Trials
AU - Jiawei Shan
AU - Yiteng Tu
AU - Guanbo Wang
AU - Chao Ying
AU - Jiwei Zhao
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2605.28785
UR - https://arxiv.org/abs/2605.28785
AB - Randomized controlled trials (RCTs) are the gold standard for evaluating causal effects but are often costly and difficult to scale; consequently, they are frequently augmented with auxiliary external controls in many applications. Prior approaches to borrowing such data typically rely on exchangeability, under which the external controls are readily usable for inference in the trial population. In practice, however, differences in eligibility criteria, standard of care, and data collection procedures may induce distribution shifts between the RCT and the external controls, making exchangeability implausible. In this paper, we propose a general framework for incorporating external controls that explicitly accounts for distribution shifts through an augmented estimating function, allowing information about the shifts to be leveraged for efficiency gains even when exchangeability does not hold. To guard against potential bias and efficiency loss due to misspecification of the distribution shift, we further develop an adaptive shrinkage estimator that preserves consistency while guaranteeing efficiency dominance over the trial-only benchmark. Synthetic experiments and a real data application demonstrate the practical advantages of the proposed approaches.
ER -