Extended models for nosocomial infection: parameter estimation and model selection

Thomas, Alun; Khader, Karim; Redd, Andrew; Leecaster, Molly; Zhang, Yue; Jones, Makoto; Greene, Tom; Samore, Matthew

We consider extensions to previous models for patient level nosocomial infection in several ways, provide a specification of the likelihoods for these new models, specify new update steps required for stochastic integration, and provide programs that implement these methods to obtain parameter estimates and model choice statistics. Previous susceptible-infected models are extended to allow for a latent period between initial exposure to the pathogen and the patient becoming themselves infectious, and the possibility of decolonization. We allow for multiple facilities, such as acute care hospitals or long-term care facilities and nursing homes, and for multiple units or wards within a facility. Patient transfers between units and facilities are tracked and accounted for in the models so that direct importation of a colonized individual from one facility or unit to another might be inferred. We allow for constant transmission rates, rates that depend on the number of colonized individuals in a unit or facility, or rates that depend on the proportion of colonized individuals. Statistical analysis is done in a Bayesian framework using Markov chain Monte Carlo methods to obtain a sample of parameter values from their joint posterior distribution. Cross validation, deviance information criterion and widely applicable information criterion approaches to model choice fit very naturally into this framework and we have implemented all three. We illustrate our methods by considering model selection issues and parameter estimation for data on methicilin-resistant Staphylococcus aureus surveillance tests over 1 year at a Veterans Administration hospital comprising seven wards.