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Hofmann, Mathias (2007): Statistical Models for Infectious Disease Surveillance Counts. Dissertation, LMU München: Faculty of Mathematics, Computer Science and Statistics
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Abstract

Models for infectious disease surveillance counts have to take into account the specific characteristics of this type of data. While showing a regular, often seasonal, pattern over long time periods, there are occasional irregularities or outbreaks. A model which is a compromise between mechanistic models and empirical models is proposed. A key idea is to distinguish between an endemic and an epidemic component, which allows to separate the regular pattern from the irregularities and outbreaks. This is of particular advantage for outbreak detection in public health surveillance. While the endemic component is parameter-driven, the epidemic component is based on observationdriven approaches, including an autoregression on past observations. A particular challenge of infectious disease counts is the modelling of the outbreaks and irregularities in the data. We model the autoregressive parameter of the epidemic component by a Bayesian changepoint model, which shows an adaptive amount of smoothing, and is able to model the jumps and fast increases as well as the smooth decreases in the data. While the model can be used as a generic approach for infectious disease counts, it is particularly suited for outbreak detection in public health surveillance. Furthermore, the predictive qualities of the Bayesian changepoint model allow for short term predictions of the number of disease cases, which are of particular public health interest. A sequential update using a particle filter is provided, that can be used for a prospective analysis of the changepoint model conditioning on fixed values for the other parameters, which is of particular advantage for public health surveillance. A suitable multivariate extension is provided, that is able to explain the interactions between units, e.g. age groups or spatial regions. An application to influenza and meningococcal disease data shows that the occasional outbreaks of meningococcal disease can largely be explained by the influence of influenza on meningococcal disease. The risk of a future meningococcal disease outbreak caused by influenza can be predicted. The comparison of the different models, including a model based on Gaussian Markov random fields shows that the inclusion of the epidemic component as well as a time varying epidemic parameter improves the fit and the predictive qualities of the model.