Statistical Modelling 5 (2005), 187–199
A statistical framework for the analysis of multivariate
infectious disease surveillance counts
Leonhard Held
Department of Statistics
University of Munich
Ludwigstr. 33
D–80539 Munich
Germany
eMail:
leonhard.held@stat.uni-muenchen.de
Michael Höhle and Mathias Hofmann
Department of Statistics
University of Munich
Abstract:
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.
Keywords:
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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