Spatiotemporal bio surveillance under non-homogeneous population

Motivated by the applications in healthcare surveillance, this paper discusses the spatiotemporal surveillance problem of detecting the mean change of Poisson count data in a non-homogeneous population environment. Through Monte Carlo simulations, we investigate several likelihood ratio-based approaches and compare them under various scenarios depending on four factors (1) the population trend, (2) the change time, (3) the change magnitude, and (4) the change coverage. Most literature of spatiotemporal surveillance evaluated the performance based on the average run length if a change occurs at the beginning of surveillance, which is often noted by ARL1. On the other hand, our comparison is based on the average run length after the time when a change occurs later. Our simulation study shows that no method is uniformly better than others in all scenarios. It is found that the difference between generalized likelihood ratios (GLR) approach and weighted likelihood ratios (WLR) approach depends on population trend and change time, not the change coverage or change magnitude.