Distance‐Based Methods for Spatial and Spatio‐Temporal Surveillance

The emergence of new infectious diseases and the threat of biological attacks have lead to a growing interest in methods of surveillance, including the accompanying statistical methods, for the early detection of an outbreak. Statistically, what we would like to do is detect the time point when there is an increase in the number of infected individuals, an increase that may also be accompanied by a change in the spatial distribution of these patients, either, or both, of which might indicate an outbreak of some sort; a disturbance of normalcy. The time element is critical in that a less than timely detection would make the methods essentially useless. The timeliness is an extra consideration that possibly distinguishes the newer surveillance methods from those in the older literature. The older ones are often related to such issues as the detection of cancer clusters (see for example Alexander and Boyle, 1996) which sometimes use data that was collected over a period of years prior to analysis which, parenthetically, makes the existence of a cluster questionable. This is not meant as a criticism of the classical methods as the time element is inherent in those methods, too. When considering spatial methods for cluster detection, no method seems to be uniformly better than all others, so it is beneficial to review a number of these meth-