Developing and Comparing Four Families of Bayesian Network Autocorrelation Models for Binary Outcomes: Estimating Peer Effects Involving Adoption of Medical Technologies

Despite the extensive use of network autocorrelation models in social network analysis, network autocorrelation models for binary dependent variables have received surprisingly scant attention. In this paper, we develop four network autocorrelation models for a binary random variable defined by whether the peer effect (also termed social influence or contagion) acts on latent continuous outcomes leading to an indirect effect under a normal or a logistic distribution or on the probability of the observed outcome itself under a probit or a logit link function defining a direct effect to account for interdependence between outcomes. For all models, we use a Bayesian approach for model estimation under a uniform prior on a transformed peer effect parameter ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:semantics><mml:mi>ρ</mml:mi> <mml:annotation>$\rho$</mml:annotation></mml:semantics> </mml:math> ) designed to enhance model computation and compare results to those under the uniform prior for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:semantics><mml:mi>ρ</mml:mi> <mml:annotation>$\rho$</mml:annotation></mml:semantics> </mml:math> . We use simulation to assess the performance of Bayesian point and interval estimators for each of the four models when the model that generated the data is used for estimation (precision assessment) and when each of the other three models instead generated the data (robustness assessment). We construct a United States New England region patient-sharing hospital network and apply the four network autocorrelation models to study the adoption of robotic surgery, a new medical technology, among hospitals using a cohort of United States Medicare beneficiaries in 2016 and 2017. Finally, we develop a deviance information criterion for each of the four models to compare their fit to the observed data and use posterior predictive p-values to assess the models' ability to recover specified features of the data. The results find that although the indirect peer effect of the propensity of peer hospital adoption on that of the focal hospital is positive under both latent response autocorrelation models, the direct peer effect of the peer hospital's probability of adopting robotic surgery on the probability of the focal hospital adopting robotic surgery decreases under both mean autocorrelation data models. However, neither of these associations is statistically significant.