A spatial scan statistic for zero-inflated Poisson process

TL;DR

This paper introduces a new spatial scan statistic tailored for zero-inflated Poisson data, addressing biases in traditional methods caused by excess zeros, and demonstrates its effectiveness through simulations and real data analysis.

Contribution

The paper develops a closed-form scan statistic for zero-inflated spatial count data, improving cluster detection accuracy over traditional Poisson-based methods.

Findings

Scan-Poisson deteriorates with more zeros, causing bias.

Proposed Scan-ZIP and Scan-ZIP+EM outperform or match Scan-Poisson.

Method effective on both simulated and real datasets.

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.