A comparison of weighted CUSUM procedures that account for monotone changes in population size

The CUSUM procedure has been popularly used for detecting a shift in the incidence rate of a rare health event. Many CUSUM methods are developed based on a Poisson model with a constant mean number of events. In practice, the expected number of events is likely to vary over time as the population size at risk is not constant but often grows over time. An increase in the baseline incidence rate tends to be masked by the population growth. To efficiently detect an increase in the baseline incidence rate, it is appealing to assign more weight to recent observations and less weight to older observations. This paper compares weighted CUSUM (WCUSUM) and conventional CUSUM procedures in the presence of monotone changes in population size. The simulation results show that the WCUSUM method may be more efficient than the conventional CUSUM methods in detecting increases in the incidence rate, especially for small shifts. An example based on mortality data from New Mexico is used to illustrate the implementation of the WCUSUM method.