A comparison of surveillance methods for small incidence rates.

A number of methods have been proposed for detecting an increase in the incidence rate of a rare health event, such as a congenital malformation. Among these are the sets method, two modifications of the sets method, and the CUSUM method based on the Poisson distribution. We consider the situation where data are observed as a sequence of Bernoulli trials and propose the Bernoulli CUSUM chart as a desirable method for the surveillance of rare health events. We compared the performance of the sets method and its modifications with that of the Bernoulli CUSUM chart under a wide variety of circumstances. Chart design parameters were chosen to satisfy a minimax criteria. We used the steady-state average run length to measure chart performance instead of the average run length (ARL), which was used in nearly all previous comparisons involving the sets method or its modifications. Except in a very few instances, we found that the Bernoulli CUSUM chart has better steady-state ARL performance than the sets method and its modifications for the extensive number of cases considered. Thus, we recommend the use of the Bernoulli CUSUM chart to monitor small incidence rates and provide practical advice for its implementation.