Fig. 4: Autoregressive Integrated Moving Average (ARIMA) simulations for synthetic opioids.

a Methods summary. As an example, to obtain the mortality rate estimate for January 2023, we combined 6-month-lagged CDC data (blue trendline) with 1-month-lagged Reddit data (orange trendline). Grey bars show the observed monthly overdose death rates per 10,000 people as reported by the CDC once available; solid lines represent data incorporated into the prediction, but dashed line data is not included. In this example, the predicted overdose death rate for January 2023 is generated by CDC data from July 2022 alone (left) or in combination with Reddit data from December 2022 (right). b Predicted monthly overdose death rates per 10,000 people of rolling-origin forecast models are shown based on 1-month prediction horizons. Observed mortality is shown in grey, and monthly overdose death rates per 10,000 people as predicted by ARIMA models fitted on 6-month-lagged CDC overdose death (blue) are shown along with predictions from a model that additionally included 1-month-lagged Reddit data (orange). c The absolute errors over time of the monthly overdose deaths per 10,000 people predicted by the lagged CDC model alone (in blue) and the combined CDC/Reddit model (in orange); d shows the corresponding distributions.