Measuring the spatial accuracy of the spatial scan statistic

Abstract

The spatial scan statistic is well established in spatial epidemiology. However, studies of its spatial accuracy are infrequent and vary in approach, often using multiple measures which complicate the objective ranking of different implementations of the statistic. We address this with three novel contributions. Firstly, a modular framework into which different definitions of spatial accuracy can be compared and hybridised. Secondly, we derive a new single measure, Ω, which takes account of all true and detected clusters, without the need for arbitrary weightings and irrespective of any chosen significance threshold. Thirdly, we demonstrate the new measure, alongside existing ones, in a study of the six output filter options provided by SaTScan TM . The study suggests filtering overlapping detected clusters tends to reduce spatial accuracy, and visualising overlapping clusters may be better than filtering them out. Although we only address spatial accuracy, the framework and Ω may be extendible to spatio-temporal accuracy.

New developments in the spatial scan statistic

“…The guiding element of a stochastic process is provided by two types of values which appear in the mathematical formula: input variables, which contain observable real-world values (e.g. population density) that influence the Figure 1.Here the incidence count of some hypothetical disease in some hypothetical town is modelled as a Poisson random variable 2 , where the mean of the variable is specified as the at-risk population in the town multiplied by the disease risk in the town. If we have many years of disease incidence records for the town (the output variable), and the at-risk population in the town for each year can be estimated with reasonable accuracy (the input variable), then using this model we can work backwards to guess the level of disease risk (the parameter).…”

“…These are best explained using visual examples. 2 A Poisson random variable generates integer numbers in a manner which realistically reflects the distribution of event counts in many real world processes, such as disease incidence, traffic flow, IT failures, call volumes to telephone lines, etc. To control the probability of this variable generating any particular number, one only need specify the mean average of the variable's output.…”

“…This section presents an overview of our recent work on the SSS [2][3][4]. Section 4.1 concerns how the performance of the SSS is measured, and explains a novel measure we have developed that has several advantages over existing ones.…”

“…However, many studies share similarities in the way they measure spatial accuracy, and breaking down the measurement process into different elements makes it easier to compare different measures. For this purpose, in a recent paper [2], we introduced a five-level framework for measurements of spatial accuracy, to facilitate the comparison and hybridisation of different measures. The framework presented in [2] is necessarily technical, and the details are somewhat beyond the scope of this paper.…”

“…Our studies are presented in Section 4, and the paper concludes with a discussion of potential future research directions. Further details of the research are provided by Read et al [2][3][4].…”