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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.03480 |
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Table of Contents:
- Borrowing external data can improve estimation efficiency but may introduce bias when populations differ in covariate distributions or outcome variability. A proper balance needs to be maintained between the two datasets to justify the borrowing. We propose a propensity score weighting borrowing-by-parts power prior (PSW-BPP) that integrates causal covariate adjustment through propensity score weighting with a flexible Bayesian borrowing approach to address these challenges in a unified framework. The proposed approach first applies propensity score weighting to align the covariate distribution of the external data with that of the current study, thereby targeting a common estimand and reducing confounding due to population heterogeneity. The weighted external likelihood is then incorporated into a Bayesian model through a borrowing-by-parts power prior, which allows distinct power parameters for the mean and variance components of the likelihood, enabling differential and calibrated information borrowing. Additionally, we adopt the idea of the minimal plausibility index (mPI) to calculate the power parameters. This separate borrowing provides greater robustness to prior-data conflict compared with traditional power prior methods that impose a single borrowing parameter. We study the operating characteristics of PSW-BPP through extensive simulation and a real data example. Simulation studies demonstrate that PSW-BPP yields more efficient and stable estimation than no borrowing and fixed borrowing, particularly under moderate covariate imbalance and outcome heterogeneity. The proposed framework offers a principled and extensible methodological contribution for Bayesian inference with external data in observational and hybrid study designs.