Poisson regression charts for the monitoring of surveillance time series

This paper presents a Poisson control chart for monitoring time
series of counts typically arising in the surveillance of
infectious diseases. The in-control mean is assumed to be
time-varying and linear on the log-scale with intercept and
seasonal components. If a shift in the intercept occurs the system
goes out-of-control. Novel is that the magnitude of the shift does
not have to be specified in advance: using the generalized
likelihood ratio (GLR) statistic a monitoring scheme is formulated
to detect on-line whether a shift in the intercept occurred. For
this specific Poisson chart the necessary quantities of the GLR
detector can be efficiently computed by recursive formulas.
Extensions to more general Poisson charts e.g. containing an
autoregressive epidemic component are discussed. Using Monte Carlo
simulations run length properties of the proposed schemes are
investigated. The practicability of the charts is demonstrated by
applying them to the observed number of salmonella hadar cases in
Germany 2001-2006.