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In applications where the study data are collected within cluster units(e.g., patients within transplant centers), it is often of interest to estimateand perform inference on the treatment effects of the cluster units. However,it is well-established that cluster-level confounding variables can bias theseassessments, and many of these confounding factors may be unobservable. Inhealthcare settings, data sharing restrictions often make it impossible todirectly fit conventional risk-adjustment models on patient-level data, andexisting privacy-preserving approaches cannot adequately adjust for bothobserved and unobserved cluster-level confounding factors. In this paper, wepropose a privacy-preserving model for cluster-level confounding that onlydepends on publicly-available summary statistics, can be fit using a singleoptimization routine, and is robust to outlying cluster unit effects. Inaddition, we develop a Pseudo-Bayesian inference procedure that accounts forthe estimated cluster-level confounding effects and corrects for the impact ofunobservable factors. Simulations show that our estimates are robust andaccurate, and the proposed inference approach has better Frequentist propertiesthan existing methods. Motivated by efforts to improve equity in transplantcare, we apply these methods to evaluate transplant centers while adjusting forobserved geographic disparities in donor organ availability and unobservableconfounders.

Robust Privacy-Preserving Models for Cluster-Level Confounding: Recognizing Disparities in Access to Transplantation