Bayesian Hierarchical Network Autocorrelation Models for Modeling the Diffusion of Hospital-Level Quality of Care

A network autocorrelation model may be embedded within a hierarchical data structure involving a complex network, when the peer effect (also referred to as social influence or contagion) is believed to act between units (e.g., hospitals) above the level at which data is observed. We develop two hierarchical network autocorrelation models to represent peer effects between hospitals when modeling individual outcomes of the patients who attend those hospitals. We use a Bayesian approach for model estimation and assess the performance of the models and sensitivity of results to different prior distributions using a simulation study. We construct a United States New England region patient-sharing hospital network and apply our models and Bayesian estimation procedures to study the diffusion of the adoption of robotic surgery and hospital-peer effects in the quality of patients outcomes using a cohort of United States Medicare beneficiaries in 2016 and 2017.