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In the analysis of data sets consisting of (X, Y)-pairs, a tacit assumption is that each pair corresponds to the same observational unit. If, however, such pairs are obtained via record linkage of two files, this assumption can be violated as a result of mismatch error rooting, for example, in the lack of reliable identifiers in the two files. Recently, there has been a surge of interest in this setting under the term “Shuffled Data” in which the underlying correct pairing of (X, Y)-pairs is represented via an unknown permutation. Explicit modeling of the permutation tends to be associated with overfitting, prompting the need for suitable methods of regularization. In this paper, we propose an exponential family prior on the permutation group for this purpose that can be used to integrate various structures such as sparse and local shuffling. This prior turns out to be conjugate for canonical shuffled data problems in which the likelihood conditional on a fixed permutation can be expressed as product over the corresponding (X,Y)-pairs. Inference can be based on the EM algorithm in which the E-step is approximated by sampling, e.g., via the Fisher-Yates algorithm. The M-step is shown to admit a reduction from n^2 to n terms if the likelihood of (X,Y)-pairs has exponential family form. Comparisons on synthetic and real data show that the proposed approach compares favorably to competing methods. 

Opioid overdoses within the United States continue to rise and have been negatively impacting the social and economic status of the country. In order to effectively allocate resources and identify policy solutions to reduce the number of overdoses, it is important to understand the geographical differences in opioid overdose rates and their causes. In this study, we utilized data on emergency department opioid overdose (EDOOD) visits to explore the county-level spatio-temporal distribution of opioid overdose rates within the state of Virginia and their association with aggregate socio-ecological factors. The analyses were performed using a combination of techniques including Moran’s I and multilevel modeling. Using data from 2016–2021, we found that Virginia counties had notable differences in their EDOOD visit rates with significant neighborhood-level associations: many counties in the southwestern region were consistently identified as the hotspots (areas with a higher concentration of EDOOD visits) whereas many counties in the northern region were consistently identified as the coldspots (areas with a lower concentration of EDOOD visits). In most Virginia counties, EDOOD visit rates declined from 2017 to 2018. In more recent years (since 2019), the visit rates showed an increasing trend. The multilevel modeling revealed that the change in clinical care factors (i.e., access to care and quality of care) and socio-economic factors (i.e., levels of education, employment, income, family and social support, and community safety) were significantly associated with the change in the EDOOD visit rates. The findings from this study have the potential to assist policymakers in proper resource planning thereby improving health outcomes.