Hot-spots detection in count data by Poisson assisted smooth sparse tensor decomposition

Abstract

Count data occur widely in many bio-surveillance and healthcare applications, e.g. the numbers of new patients of different types of infectious diseases from different cities/counties/states repeatedly over time, say, daily/weekly/monthly. For this type of count data, one important task is the quick detection and localization of hot-spots in terms of unusual infectious rates so that we can respond appropriately. In this paper, we develop a method called Poisson assisted Smooth Sparse Tensor Decomposition (PoSSTenD), which not only detect when hot-spots occur but also localize where hot-spots occur. The main idea of our proposed PoSSTenD method is articulated as follows. First, we represent the observed count data as a three-dimensional tensor including (1) a spatial dimension for location patterns, e.g. different cities/countries/states; (2) a temporal domain for time patterns, e.g. daily/weekly/monthly; (3) a categorical dimension for different types of data sources, e.g. different types of diseases. Second, we fit this tensor into a Poisson regression model, and then we further decompose the infectious rate into two components: smooth global trend and local hot-spots. Third, we detect when hot-spots occur by building a cumulative sum (CUSUM) control chart and localize where hot-spots occur by their LASSO-type sparse estimation. The usefulness of our proposed methodology is validated through numerical simulation studies and a real-world dataset, which records the annual number of 10 different infectious diseases from 1993 to 2018 for 49 mainland states in the United States.

Keywords:

• Hot-spots detection
• spatio-temporal model
• tensor decomposition
• CUSUM
• Poisson regression

Acknowledgments

The authors are grateful to the Editor, the Associate Editor and two anonymous reviewers for their constructive comments that greatly improved the quality and presentation of this article.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

This project is partially supported by Dr Huo's funding in the Transdisciplinary Research Institute for Advancing Data Science (TRIAD), http://triad.gatech.edu, which is a part of the TRIPODS program at NSF and locates at Georgia Tech, enabled by the NSF [grant number CCF-1740776]. Dr Huo is also supported in part by NSF [grant number DMS-2015363]. Dr Mei's research was supported in part by NSF [grant number DMS-2015405], and in part by the National Center for Advancing Translational Sciences of the National Institutes of Health under Award Number UL1TR000454.