# Modeling opioid overdose events recurrence with a covariate-adjusted triggering point process

## TL;DR

This paper introduces a new model to predict opioid overdose events by considering both risk factors and how past overdoses influence future ones.

## Contribution

The novel contribution is a covariate-adjusted triggering point process model that captures inter-event dependencies and risk factors.

## Key findings

- The proposed model achieved the lowest prediction errors for 30- to 180-day-ahead forecasts.
- Around 47% of opioid overdose recurrence was explained by the triggering mechanism.
- The model provides insights into inter-event dependencies and improves prediction accuracy.

## Abstract

Substance use disorder, particularly opioid-related, is a serious public health challenge in the U.S. Accurately predicting opioid overdose events and stratifying the risk of having such an event are critical for healthcare providers to deliver effective interventions in patients with opioid overdose. Despite a large body of literature investigating various risk factors for the prediction, the existing research to date has not explicitly investigated and quantitatively modeled how an individual’s past opioid overdose events affect future occurrences. In this paper, we proposed a covariate-adjusted triggering point process to simultaneously model the effect of various risk factors on opioid overdose events and the triggering mechanism among opioid overdose events. The prediction performance was assessed by the U.S. state-wise Medicaid reimbursement claims data. Compared with commonly used prediction models, the proposed model achieved the lowest Mean Absolute Errors and Mean Absolute Percentage Errors on 30-, 60-, 90, 120-, 150-, and 180-day-ahead predictions. In addition, our results showed the statistical significance of considering the triggering mechanism for recurrent opioid overdose events prediction. On average, around 47% of the event recurrence were explained by the triggering mechanism.

In complex natural systems, discrete event sequences often occur stochastically, such as earthquakes, financial transactions, and drug overdoses. The occurrence of these events is typically influenced by various factors (e.g., the occurrence of earthquakes is influenced by tectonic zones experiencing deformation). Given these known factors, however, such events do not appear independently. Instead, the occurrence of one event additionally influences the rate of subsequent events (e.g., a mainshock increasing the rate of subsequent aftershocks). A similar pattern can be observed in drug overdose events, where occurrences are related to various risk factors, and an just occurred overdose increases the risk of subsequent overdoses. Existing methods that identify associations between overdoses and the risk factors provide limited insight into inter-event dependencies. Recently, the triggering event point process has been used to capture these complex inter-event dependencies. In this study, we propose a covariate-adjusted triggering point process, extending the conventional models to simultaneously account for the impacts of various factors and inter-event dependency on event occurrence. The results of the real data analysis demonstrates that proposed model has the potential to provide unique insights into the nature of inter-event dependencies and significantly improve prediction accuracy.