Analysis of network interventions with an application to hospital-acquired infections

Regional interventions to prevent the spread of hospital-acquired infections, vaccination campaigns, and information dissemination strategies are examples of treatment interventions applied to members of a network with the intent of effecting a network-wide change. In designing clinical trials or determining policy changes, it may not be cost effective or otherwise possible to treat all actors of a network. There is a notable lack of study designs and statistical frameworks with which to plan a network-wide intervention in this context and analyze the resulting data. This paper builds off of the network autocorrelation model in order to provide such a framework for a pre-post study design. We derive key quantitative measures of the network-wide treatment effect, exact formulas for power analyses of these measures, and extensions for the context in which the network is unknown. As the treatment assignation is part of the network-wide treatment, we provide methods for determining the assignation which optimizes the overall treatment effect over all members of the network subject to any arbitrary set of implementation costs and cost constraint. We implement these methods on Clostridioides difficile data for the state of California, where the hospitals are linked through patient sharing.