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Biostatistics Advance Access published online on January 11, 2006
Biostatistics, doi:10.1093/biostatistics/kxj016
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© The Author 2006. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org
Received March 29, 2005
Revised December 12, 2005
Accepted January 10, 2006

Article

A two-component model for counts of infectious diseases

Leonhard Held 1 *, Mathias Hofmann 1, Michael Höhle 1, and Volker Schmid 2

1 Department of Statistics, Ludwig-Maximilians-Universität München, Ludwigstr. 33, 80539 München, Germany
2 Institute of Biomedical Engineering, Imperial College London, UK

* To whom correspondence should be addressed.
Leonhard Held, E-mail: leonhard.held{at}stat.uni-muenchen.de


  Abstract

We propose a stochastic model for the analysis of time series of disease counts as collected in typical surveillance systems on notifiable infectious diseases. The model is based on a Poisson or negative binomial observation model with two components: A parameter-driven component relates the disease incidence to latent parameters describing endemic seasonal patterns, which are typical for infectious disease surveillance data. An observation-driven or epidemic component is modelled with an autoregression on the number of cases at the previous time points. The autoregressive parameter is allowed to change over time according to a Bayesian changepoint model with unknown number of changepoints. Parameter estimates are obtained through Bayesian model averaging using Markov chain Monte Carlo (MCMC) techniques. We illustrate our approach through analysis of simulated data and real notification data obtained from the German infectious disease surveillance system, administered by the Robert Koch Institute in Berlin (Robert Koch Institute, 2005). Software to fit the proposed model can be obtained from www.statistik.lmu.de/~mhofmann/twins.

Keywords: Bayesian changepoint model; epidemic modelling; surveillance data; reversible jump Markov chain Monte Carlo.
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