Bayesian analysis of a time series of counts with covariates: an application to the control of an infectious disease

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Abstract
This paper presents a Bayesian analysis of a time series of counts to assess its dependence on an explanatory variable. The time series represented is the incidence of the infectious disease ESBL‐producing Klebsiella pneumoniae in an Australian hospital and the explanatory variable is the number of grams of antibiotic (third generation) cephalosporin used during that time. We demonstrate that there is a statistically significant relationship between disease occurrence and use of the antibiotic, lagged by three months. The model used is a parameter‐driven model in the form of a generalized linear mixed model. Comparison of models is made in terms of mean square error.

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