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.

翻译：借用外部数据可提高估计效率，但当人群在协变量分布或结局变异性上存在差异时，可能引入偏倚。需要在两个数据集之间保持适当平衡以证明借用的合理性。我们提出了一种倾向得分加权分步借用幂先验（PSW-BPP）方法，该方法通过倾向得分加权整合因果协变量调整与灵活的贝叶斯借用方法，在统一框架内应对这些挑战。所提方法首先应用倾向得分加权使外部数据的协变量分布与当前研究对齐，从而针对共同的估计目标并减少因人群异质性导致的混杂。随后，通过分步借用幂先验将加权外部似然纳入贝叶斯模型，该先验允许对似然的均值分量和方差分量设置不同的幂参数，从而实现差异化且校准的信息借用。此外，我们采用最小合理性指数（mPI）的思想来计算幂参数。与施加单一借用参数的传统幂先验方法相比，这种分离借用方式对先验-数据冲突具有更强的稳健性。我们通过大量模拟和真实数据案例研究了PSW-BPP的操作特性。模拟研究表明，在中等程度的协变量不平衡和结局异质性下，PSW-BPP相比无借用和固定借用方法能产生更高效且更稳定的估计。所提出的框架为观察性和混合研究设计中利用外部数据进行贝叶斯推断提供了原则性且可扩展的方法学贡献。