On detection of a change in the dynamics of rare health events

Abstract

In monitoring a sequence of observations generated by a dynamics of rare events, an important problem is to detect a change in the dynamics as soon as possible when it occurs. Formally this problem is usually faced by constructing suitable stopping rules. We consider here a stopping rule by which common surveillance schemes are obtainable. A particular class of schemes, playing a fundamental role in health surveillance, is then discussed, and the analytical expression of the average run length derived. An “optimal” procedure to determine the involved parameters is also presented and explicitly described when the dynamics follows a Poisson process.