Poisson regression charts for the monitoring of surveillance time series

Abstract

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.