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

In health services applications where the patients are clustered within common institutions or geographic regions, it is often of interest to estimate the treatment effects of the medical providers after adjusting for confounding risk factors that are related to patients' choices of provider but beyond the providers' control. While most existing risk-adjustment methods are only capable of controlling for patient-level confounding risk factors (e.g., age or comorbidities), there are often important cluster-level confounding variables (e.g., regional or community-level risk factors) that should be accounted for in provider evaluations. These adjustments for cluster-level confounding factors are further complicated by the limited availability of protected patient health data, the inevitable influence of unobservable confounding factors, and the presence of outlying cluster units. To address these issues, we propose a privacy-preserving model and a novel Pseudo-Bayesian inference method to robustly assess the providers' treatment effects with adjustments for observed cluster-level confounders and corrections for overdispersion from unobserved cluster-level confounding factors. We derive theoretical connections between our proposed estimation method and the Correlated Random Effects model, uncovering several advantages in terms of estimation stability, computational efficiency, and privacy preservation. 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 correcting for overdispersion from unobservable confounding factors, such as the complex impact of the COVID-19 pandemic.