Detecting a rate increase using a Bernoulli scan statistic.

Scan statistics are used in public health applications to detect increases in rates or clusters of disease indicated by an unusually large number of events. Most of the work has been for the retrospective case, in which a single set of historical data is to be analyzed. A modification of this retrospective scan statistic has been recommended for use when incidences of an event are recorded as they occur over time (prospectively) to determine whether the underlying incidence rate has increased, preferably as soon as possible after such an increase. In this paper, we investigate the properties of the scan statistic when used in prospective surveillance of the incidence rate under the assumption of independent Bernoulli observations. We show how to evaluate the expected number of Bernoulli observations needed to generate a signal that the incidence rate has increased. We compare the performance of the prospective scan statistic method with that obtained using the Bernoulli-based cumulative sum (CUSUM) technique. We show that the latter tends to be more effective in detecting sustained increases in the rate, but the scan method may be preferred in some applications due to its simplicity and can be used with relatively little loss of efficiency.