Temporal surveillance using scan statistics

Abstract

We describe two classes of statistics for testing an arbitrary model of disease incidence over time against an alternative model involving a spike (pulse) superimposed on this background. The statistics are each based on taking the maximum of some function comparing observed and expected numbers of events in a window of width w. One approach applies p‐values for scan statistics calculated for a constant background rate to this more general problem. For a fixed window, w, the approach gives a simple formula to determine p‐values for retrospective analysis, or to sound an alarm for either continuous or grouped prospective data. The latter application involves a new approximation for the distribution of the maximum number of cases in wconsecutive intervals. The second approach based on generalized likelihood ratio tests (GLRTs), sounds an alarm for a higher than anticipated rate of events in a scanning window of fixed length, or for window sizes that lie in a region. GLRTs are constructed for continuous observations, for grouped data, or for a sequence of trials. As for GLRTs used in retrospective evaluations, simulation is required to implement the prospective procedure. For grouped surveillance data, we compare by simulation, operating characteristics of the P‐scan with fixed windows (both correctly specified and not), the fixed‐window GLRT, the variable‐window GLRT, and a variant of the CUSUM. The simulations demonstrate a very high correlation between the P‐scan and corresponding fixed‐window GLRT. Copyright © 2005 John Wiley & Sons, Ltd.