Count data regression charts for the monitoring of surveillance time series

Control charts based on the Poisson and negative binomial distribution for monitoring time series of counts typically arising in the surveillance of infectious diseases are presented. 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. Using the generalized likelihood ratio (GLR) statistic a monitoring scheme is formulated to detect on-line whether a shift in the intercept occurred. In the case of Poisson the necessary quantities of the GLR detector can be efficiently computed by recursive formulas. Extensions to more general alternatives e.g. containing an auto-regressive epidemic component are discussed. Using Monte Carlo simulations run-length properties of the proposed schemes are investigated and the Poisson scheme is compared to existing methods. The practicability of the charts is demonstrated by applying them to the observed number of salmonella hadar cases in Germany 2001-2006.