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

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.