Abstract
When an hypothesized peer effect (also termed social influence or contagion) is believed to act between units (e.g., hospitals) above the level at which data is observed (e.g., patients), a network autocorrelation model may be embedded within a hierarchical data structure thereby formulating the peer effect as a dependency between latent variables. In such a situation, a patient's own hospital can be thought of as a mediator between the effects of peer hospitals and their outcome. However, as in mediation analyses, there may be interest in allowing the effects of peer units to directly impact patients of other units. To accommodate these possibilities, we develop two hierarchical network autocorrelation models that allow for direct and indirect peer effect pathways between hospitals when modeling individual outcomes of the patients cared for at the hospitals. A Bayesian approach is used for model estimation while a simulation study is used to assess the performance of the models and sensitivity of results to different prior distributions. We construct a United States New England region patient-sharing hospital network and apply our Bayesian hierarchical models to study the diffusion of robotic surgery and hospital peer effects in patient outcomes using a cohort of United States Medicare beneficiaries in 2016 and 2017. The comparative fit of models to the data is assessed using Deviance information criteria tailored to hierarchical models that include peer effects as latent variables.