In applications where the study data are collected within cluster units (e.g., patients within transplant centers), it is often of interest to estimate and perform inference on the treatment effects of the cluster units. However, it is well-established that cluster-level confounding variables can bias these assessments, and many of these confounding factors may be unobservable. In healthcare settings, data sharing restrictions often make it impossible to directly fit conventional risk-adjustment models on patient-level data, and existing privacy-preserving approaches cannot adequately adjust for both observed and unobserved cluster-level confounding factors. In this paper, we propose a privacy-preserving model for cluster-level confounding that only depends on publicly-available summary statistics, can be fit using a single optimization routine, and is robust to outlying cluster unit effects. In addition, we develop a Pseudo-Bayesian inference procedure that accounts for the estimated cluster-level confounding effects and corrects for the impact of unobservable factors. Simulations show that our estimates are robust and accurate, and the proposed inference approach has better Frequentist properties than existing methods. Motivated by efforts to improve equity in transplant care, we apply these methods to evaluate transplant centers while adjusting for observed geographic disparities in donor organ availability and unobservable confounders.

翻译：在许多研究数据按集群单元（如移植中心内的患者）收集的应用场景中，估计并推断集群单元的治疗效应往往是重要的。然而，集群级混杂变量会偏倚这些评估是公认的问题，且许多混杂因素可能无法观测。在医疗环境中，数据共享限制通常导致无法直接基于患者级数据拟合传统的风险调整模型，而现有隐私保护方法无法充分调整已观测和未观测的集群级混杂因素。本文提出一种适用于集群级混杂的隐私保护模型，该模型仅依赖于公开可用的汇总统计量，可通过单一优化程序拟合，并对异常集群单元效应具有鲁棒性。此外，我们开发了一种伪贝叶斯推断程序，该程序考虑了估计的集群级混杂效应并校正了未观测因素的影响。模拟实验表明，我们的估计具有鲁棒性和准确性，且所提出的推断方法在频率学派性质上优于现有方法。受改善移植护理公平性努力的启发，我们将这些方法应用于评估移植中心，同时调整了供体器官可用性的地理差异（已观测）及未观测混杂因素。