Deciphering hospital networks using graph theory methods

Abstract

In France, the hospital restructuration that has been observable for more than 20 years is the result of decisions made within the framework of the planning policies and strategies adopted by the establishments. Beyond its consequences, how to describe the network of health care facilities? To identify the factors characterizing the topology of the network, the conventional test statistics are insufficient. For this purpose, we propose in this methodological article, to study the usefulness of models from graph theory for the modeling of patient transfers between short-stay establishments (ie Medicine-Surgery-Obstetrics, MCO) and follow-up care and rehabilitation (SSR) from the French national hospital discharge information system. Erdös-Renyi (ER) models and Constrainted Degree Sequence Model (CDSM) models test the significance of assortativity measures. In our study, they demonstrate the propensity of health care facilities of the same legal status to exchange patients. Block models make it possible to build clusters of establishments based on common characteristics. In our context, they emphasize in particular the territorial dynamics of exchanges between establishments. Finally, Exponential Random Graph Models (ERGMs) and the assortativity measure quantify the simultaneous influence of geographical proximity and legal status in the relationship between hospitals. In conclusion, the graph theory methods offer perspectives for identifying and quantifying the impact of factors that can influence the topology of hospital relations.