Poisson approximation to a negative binomial process in the surveillance of rare health events

The Poisson approximation to a negative binomial process is evaluated regarding the surveillance of rare health events in the framework of the "Sets" scheme. This scheme defines an alarm in terms of "distance" between consecutive events of interest. The system's parameters are determined by minimizing the expected delay for an alarm when a given increase in the event rate has occurred, subject to a restriction on the rate of false alarms. It is shown that the main consequence of the Poisson approximation lies in an increase of the false alarm probability with respect to the assigned one, whilst influence on the expected delay for a true alarm is lower. It is, however, found that over a large range of practical instances, the Poisson assumption provides a reasonable description of the negative binomial process.