A spatial scan statistic for zero-inflated Poisson process

Abstract

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 data with excess zeros, the spatial scan statistic may produce biased inferences. In this work, we develop a closed-form scan statistic for cluster detection of spatial zero-inflated count data. We apply our methodology to simulated and real data. Our simulations revealed that the Scan-Poisson statistic steadily deteriorates as the number of zeros increases, producing biased inferences. On the other hand, our proposed Scan-ZIP and Scan-ZIP+EM statistics are, most of the time, either superior or comparable to the Scan-Poisson statistic.

An unconditional space–time scan statistic for ZIP‐distributed data

“…The scan statistic proposed above (call it UC‐ZIP) differs from that given by Cançado et al (; PB‐ZIP) in three major ways. Analyses conducted with the PB‐ZIP statistic are conditional on the total observed count: To conduct hypothesis testing by Monte Carlo replication, new counts are simulated conditional on that their total equals the total seen in the original data.…”

“…A solution can instead be obtained numerically, for example, by an EM algorithm (Dempster, Laird, & Rubin, ). A similar algorithm was given for a conditional (on the total observed count) ZIP scan statistic in the work of Cançado et al (), which was formulated for a different setting and outbreak model; these differences will be clarified after the definition of the scan statistic in Section 2.3. To derive an EM algorithm for estimating q W , we will first take a look at the complete data likelihood function, that is, when it is known which zeros are structural zeros.…”

“…Motivated by the need for such “unconditional” scan statistics and the inability of many current scan statistics to handle excess zeros, we take inspiration from the work of Cançado et al () and propose a prospective scan statistic for spatiotemporal counts governed by a zero‐inflated Poisson (ZIP) distribution. The proposed scan statistic, along with several others, is made available in the open‐source R package scanstatistics, which can be seen as a complement to the SaTScan (Kulldorff, ) software and its R interface rsatscan (Kleinman, ) as well as to more general disease surveillance packages such as surveillance (Salmon, Schumacher, & Höhle, ).…”

“…This distribution is a natural first choice for rare event data or for count data with a large or an unclear upper bound. However, scan statistics that rely on the Poisson assumption have been criticized on two points in particular: their inability to capture overdispersion in the data (de Lima, Duczmal, Neto, & Pinto, 2015;Tango, Takahashi, & Kohriyama, 2011) and their inability to handle zero-inflated counts (Cançado, da-Silva, & da Silva, 2014;de Lima et al, 2015). Additionally, a debate has recently flared up around the use of traditional scan statistics, such as those implemented in the software SaTScan (Kulldorff, 2016), and the hypothesis testing procedures used when carrying out prospective analyses (Correa, Assunção, & Costa, 2015a, 2015bKulldorff & Kleinman, 2015).…”

Prospective Detection of Outbreaks

“…For this type of data, a scan statistic based on e.g. the zeroinflated Poisson distribution (see Cançado et al, 2014;Allévius and Höhle, 2017) may perform better. 0.3.2.1.6 Developments in space-time scan statistics Kulldorff's 2001 prospective scan statistic was introduced above to present the general procedure of using a scan statistic to detect space-time disease clusters.…”