Temporal analysis of hospital network data by hierarchical Bayesian p2 models with covariates

Motivated by an application about interhospital connections, we propose a modelling approach for data referred to a temporal network. The approach may be seen as an extension of the one recently proposed in Bianchi et al. [(2020). Longitudinal networks of dyadic relationships using latent trajectories: Evidence from the European interbank market. Journal of the Royal Statistical Society: Series C, 69(4), 711-739] and, in turn, of the popular p(1) and p(2) models by Holland and Leinhardt [(1981). An exponential family of probability distributions for directed graphs. Journal of the American Statistical Association, 76(373), 33-50] and van Duijn et al. [(2004). p2: A random effects model with covariates for directed graphs. Statistica Neerlandica, 58(2), 234-254], on which the latter is built. The proposed extension consists in the introduction of covariates and in the adoption of a hierarchical Bayesian inferential approach that shows advantages in the specific application. For Bayesian inference we rely on a Markov chain Monte Carlo algorithm that produces samples from the posterior distribution of the model parameters. The application is based on original data on patient referral relations among 127 hospitals serving a large regional community of patients in Italy from 2014 to 2018. Results indicate that interhospital collaborative behaviours are primarily local and that collaborative attitudes vary at different time occasions of the considered period and in accordance with the level of competition faced by hospital organisations.