Robust Distribution-free Multivariate CUSUM Charts for Spatiotemporal Biosurveillance in the Presence of Spatial Correlation

Abstract

Multivariate CUSUM (MCUSUM) charts with fixed and variable scan radii have been used to detect increases of disease incidence counts in spatiotemporal biosurveillance. Biosurveillance through MCUSUM charts often requires intensive modeling of the monitored process, which can be challenging in cases involving a large number of monitored regions, an arbitrary marginal data distribution, and spatial correlation. Unlike other MCUSUM charts in the literature which assume a multivariate normal distribution for the disease count data, the MCUSUM chart we suggest in this paper is robust to non-normal distributions such as the Poisson. Our chart does not require extensive modeling of the underlying process and searches for its control limits via simple simulation and interpolation. While maintaining satisfactory accuracy of its control limits, the chart provides reliable performance under various data distributions, scan radii, and spatial correlation structures.