A comparison of CUSUM, EWMA, and temporal scan statistics for detection of increases in poisson rates

Various control chart methods have been used in healthcare and public health surveillance to detect increases in the rates of diseases or their symptoms. Although the observations in many health surveillance applications are often discrete, few efforts have been made to explore the behavior of detection methods in discrete distributions. Joner et al. (Statist. Med. 2008; 27:2555-2575) investigated and compared the performance of the scan statistic methods with the cumulative sum (CUSUM) charts under a Bernoulli distribution. In this paper we compare the performance of three detection methods: temporal scan statistic, CUSUM, and exponential weighted moving average (EWMA) when the observations follow the Poisson distribution. A simulation study showed that the Poisson CUSUM and EWMA charts generally outperformed the Poisson scan statistic methods. In comparisons between CUSUM and EWMA, the CUSUM charts were superior in dealing with a large shift with a later change in time. However, the EWMA charts outperformed the CUSUM charts in situations with a small shift and an early change in time. The methods were also compared with thyroid cancer using a real data set.