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A statistical framework for the analysis of multivariate infectious disease surveillance counts

Department of Statistics, University of Munich, Munich, Germany, leonhard.held{at}stat.uni-muenchen.de

Michael Höhle

Department of Statistics, University of Munich, Munich, Germany

Mathias Hofmann

Department of Statistics, University of Munich, Munich, Germany

A framework for the statistical analysis of counts from infectious disease surveillance databases is proposed. In its simplest form, the model can be seen as a Poisson branching process model with immigration. Extensions to include seasonal effects, time trends and overdispersion are outlined. The model is shown to provide an adequate fit and reliable one-step-ahead prediction intervals for a typical infectious disease time series. In addition, a multivariate formulation is proposed, which is well suited to capture space-time dependence caused by the spatial spread of a disease over time. An analysis of two multivariate time series is described. All analyses have been done using general optimization routines, where ML estimates and corresponding standard errors are readily available.

Key Words: branching process with immigration • infectious disease surveillance • maximum likelihood • multivariate time series of counts • observation-driven • parameter-driven • space-time models

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