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March 2021 Point process modeling of drug overdoses with heterogeneous and missing data
Xueying Liu, Jeremy Carter, Brad Ray, George Mohler
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Ann. Appl. Stat. 15(1): 88-101 (March 2021). DOI: 10.1214/20-AOAS1384


Opioid overdose rates have increased in the United States over the past decade and reflect a major public health crisis. Modeling and prediction of drug and opioid hotspots, where a high percentage of events fall in a small percentage of space–time, could help better focus limited social and health services. In this work we present a spatial-temporal point process model for drug overdose clustering. The data input into the model comes from two heterogeneous sources: (1) high volume emergency medical calls for service (EMS) records containing location and time but no information on the type of nonfatal overdose, and (2) fatal overdose toxicology reports from the coroner containing location and high-dimensional information from the toxicology screen on the drugs present at the time of death. We first use nonnegative matrix factorization to cluster toxicology reports into drug overdose categories, and we then develop an EM algorithm for integrating the two heterogeneous data sets, where the mark corresponding to overdose category is inferred for the EMS data and the high volume EMS data is used to more accurately predict drug overdose death hotspots. We apply the algorithm to drug overdose data from Indianapolis, showing that the point process defined on the integrated data out-performs point processes that use only coroner data (AUC improvement 0.81 to 0.85). We also investigate the extent to which overdoses are contagious, as a function of the type of overdose, while controlling for exogenous fluctuations in the background rate that might also contribute to clustering. We find that drug and opioid overdose deaths exhibit significant excitation with branching ratio ranging from 0.72 to 0.98.


This work was supported in part by NSF Grants ATD-1737996 and SCC-1737585.


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Xueying Liu. Jeremy Carter. Brad Ray. George Mohler. "Point process modeling of drug overdoses with heterogeneous and missing data." Ann. Appl. Stat. 15 (1) 88 - 101, March 2021.


Received: 1 November 2019; Revised: 1 July 2020; Published: March 2021
First available in Project Euclid: 18 March 2021

Digital Object Identifier: 10.1214/20-AOAS1384

Rights: Copyright © 2021 Institute of Mathematical Statistics


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Vol.15 • No. 1 • March 2021
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