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A Latent Spatial Factor Approach for Synthesizing Opioid-Associated Deaths and Treatment Admissions in Ohio Counties

Hepler, Stacia; McKnight, Erinb,c; Bonny, Andreab,c; Kline, Davidd

doi: 10.1097/EDE.0000000000000978
Social Epidemiology

Background: Opioid misuse is a major public health issue in the United States and in particular the state of Ohio. However, the burden of the epidemic is challenging to quantify as public health surveillance measures capture different aspects of the problem. Here, we synthesize county-level death and treatment counts to compare the relative burden across counties and assess associations with social environmental covariates.

Methods: We construct a generalized spatial factor model to jointly model death and treatment rates for each county. For each outcome, we specify a spatial rates parameterization for a Poisson regression model with spatially varying factor loadings. We use a conditional autoregressive model to account for spatial dependence within a Bayesian framework.

Results: The estimated spatial factor was highest in the southern and southwestern counties of the state, representing a higher burden of the opioid epidemic. We found that relatively high rates of treatment contributed to the factor in the southern part of the state, whereas relatively higher rates of death contributed in the southwest. The estimated factor was also positively associated with the proportion of residents 18–64 years of age on disability and negatively associated with the proportion of residents reporting white race.

Conclusions: We synthesized the information in the opioid-associated death and treatment counts through a spatial factor model to estimate a latent factor representing the consensus between the two surveillance measures. We believe this framework provides a coherent approach to describe the epidemic while leveraging information from multiple surveillance measures.

From the aDepartment of Mathematics and Statistics, College of Arts and Sciences, Wake Forest University, Winston-Salem, NC

bDivision of Adolescent Medicine, Nationwide Children’s Hospital, Columbus, OH

cDepartment of Pediatrics, College of Medicine, The Ohio State University, Columbus, OH

dCenter for Biostatistics, Department of Biomedical Informatics, College of Medicine, The Ohio State University, Columbus, OH.

Submitted June 8, 2018; accepted January 23, 2019.

The authors report no conflicts of interest.

Supplemental digital content is available through direct URL citations in the HTML and PDF versions of this article (

Data Accessibility: Death counts are publicly available from the Ohio Department of Health website ( and were obtained from the Ohio Public Health Data Warehouse Ohio Resident Mortality Data. Treatment counts are not publicly available but can be obtained through a data use agreement with the Ohio Department of Mental Health and Drug Addiction Services. Computer code for the analysis is available online.

D.K. and S.H. contributed equally to this work.

Correspondence: Staci Hepler, Department of Mathematics and Statistics, Wake Forest University, 127 Manchester Hall, Winston-Salem, NC 27109. E-mail:

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