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A Zero-Inflated Poisson Based Spatial Scan Statistic


The spatial scan statistic proposed by Kulldorff has been widely used in spatial disease surveillance and other spatial cluster detection applications. In one of its versions, such scan statistic was developed for inhomogeneous Poisson process. However, the underlying Poisson process may not be suitable to properly model the data. Particularly, for diseases with very low prevalence, the number of cases may be very low and zero excess may cause bias in the inferences.

Lambert introduced the zero-inflated Poisson (ZIP) regression model to account for excess zeros in counts of manufacturing defects. The use of such model has been applied to innumerous situations. Count data, like contingency tables, often contain cells having zero counts. If a given cell has a positive probability associated to it, a zero count is called a sampling zero. However, a zero for a cell in which it is theoretically impossible to have observations is called structural zero.



The scan statistic is widely used in spatial cluster detection applications of inhomogeneous Poisson processes. However, real data may present substantial departure from the underlying Poisson process. One of the possible departures has to do with zero excess. Some studies point out that when applied to zero-inflated data the spatial scan statistic may produce biased inferences. Particularly, Gomez-Rubio and Lopez-Quılez argue that Kulldorff’s scan statistic may not be suitable for very rare diseases problems. In this work we develop a closed-form scan statistic for cluster detection of spatial count data with zero excess.

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