Forecasting U.S. Drug Overdose Mortality By Age

The drug epidemic in the U.S. remains a major crisis, with overdose deaths increasing fivefold since 1999 and surpassing 100,000 annual fatalities every year since 2020. According to the U.S. Centers for Disease Control and Prevention (CDC), peak mortality occurred in 2022 (during the COVID-19 pandemic) with 112,000 deaths, roughly 74,000 of which were due to fentanyl. The CDC tallied roughly 110,000 fatal overdoses in 2023, with 73,000 from fentanyl.

Several distinct "waves" of drug overdoses have been identified in the U.S., starting with the initial opioid prescription crisis of the late 1990s and followed by a heroin wave that emerged in the late 2000s, after regulations limited the prescription of opioid analgesics. The most recent wave is driven by fentanyl: a cheap, synthetic, and potent opioid that first appeared in the U.S. illegal drug market in 2013 [13]. A fourth wave is on the horizon, driven by polysubstance use and the mixing of stimulants (such as methamphetamines) and opioids—some even more potent than fentanyl—which often leads to unpredictable and deadly outcomes. These waves have disproportionately impacted some geographical regions and demographic groups (by age, sex, and race). For example, the mortality rate for Black males in Washington, D.C., in 2020 (134 fatalities per 100,000 people) was nine times higher than that of White males (14 fatalities per 100,000 people) [4].

The first step towards developing proper intervention strategies is to quantify and understand the problem. Both the CDC and the National Center for Health Statistics have systematically collected overdose mortality data since 1999. The dataset is publicly accessible via the CDC’s Wide-ranging Online Data for Epidemiologic Research (WONDER) portal; this portal is updated annually at the end of each calendar year with finalized data from the previous year, resulting in a one-year reporting lag. 

To date, most analytical or data-driven efforts have utilized the CDC WONDER portal or other similar databases to track past overdose deaths and provide valuable insights about the drug epidemic’s progression thus far [7]. A major step forward would be to build upon past data to generate forecasts of future trends and overdose patterns, thereby facilitating the development of targeted, specific prevention and preparedness tools. Given the demographic, political, and legislative differences across the U.S., forecasts at the local scale would be the most impactful to capture the unique drug market dynamics, socioeconomic conditions, cultural factors, and geohistorical attributes of a given region. Figure 1 depicts the spatial heterogeneity of drug-related mortality across the U.S.

To move beyond the study of historical trends, we developed a forecasting approach that merges observational data with mechanistic modeling [1, 2]. Our work is based on data assimilation techniques that originated in the geological and atmospheric sciences to produce weather and climate forecasts [3, 11]. These techniques enable the integration of high-dimensional dynamical systems with extensive datasets, and can incorporate interpretable parameters that relate to the underlying dynamics.

Specifically, we use an ensemble Kalman filter (EnKF) [6] to assimilate observational data on overdose mortality from the CDC WONDER database. We combine the EnKF with a structured population model based on Kermack–McKendrick theory [5, 8-10, 12] that describes an age-structured, drug-using population that includes individuals with substance use disorder as well as occasional or first-time users. The age-structured model allows us to define parameters that quantify interpretable processes, such as age-dependent initiation of high-risk substance use and drug-induced mortality. Figure 2 provides a schematic overview of our approach.

In Figures 3a and 3b, we illustrate the change in the U.S. general population and overdose fatalities from 1999 to 2021. Figure 3a shows the age-structured population distribution and evolution of two prominent population peaks—one that is currently between the ages of 20 and 30 and another between 50 and 60—while Figure 3b depicts the age distribution of fatal overdoses. From 1999 to 2014, the highest number of overdose deaths occurred in individuals between the ages of 40 and 50. However, from 2015 onwards, peak overdose fatalities began to occur at younger ages — between 35 and 40. Finally, a rapid rise in overdose deaths emerged in 2020, coinciding with the start of the COVID-19 pandemic. Knowledge of these trends informs the implementation of our age-structured mathematical model. 

We use the mathematical model to predict the evolution of relevant system states in a series of iterative steps. At each step, new overdose fatality data are used to update theoretical state values and refine model estimates. The updated state values are then utilized for subsequent forecasts. Since finalized CDC WONDER data are available from 1999 onwards, forecasts for drug overdose fatalities in a given year $Y$ are based on assimilated observational data from 1999 through $Y-1$. 

Figures 3c, 3d, and 3e display age-stratified overdose forecasts alongside corresponding observational data for the years 2001, 2011, and 2021. The nationwide forecasts closely align with the observed data. Despite the sudden, unforeseeable surge in overdose fatalities in 2020, the EnKF forecast for age-stratified overdose deaths in 2021 is consistent with reported fatality counts.

Because our method is tied to an underlying mechanistic model, we can define and analyze the evolution of key epidemiological parameters like drug-induced mortality rate. This rate has increased by a factor of almost six over the past two decades and now exceeds a staggering 1.1 percent per year among individuals who use high-risk drugs. We also find that drug overdose has become the leading cause of death in the under-60, high-risk drug-using population.

We applied our method to three representative areas—Los Angeles County in California, Cook County in Illinois, and the five boroughs of New York City—and found significant geographical variations in overdose fatality trends. For example, although the mortality rate among drug users in Los Angeles County in the early 2000s was higher than Cook County and New York City, its 2021 rate (at 0.5 percent per year) was lower than both Cook County (at 1.9 percent per year) and New York City (at 1.1 percent per year). The annual number of overdose deaths in Cook County and New York City has also increased much faster than in Los Angeles County in recent years, thus indicating a delayed but severe rise in drug overdoses — particularly in Cook County. Additional visualizations of both national- and state-level forecasts are available in the literature [2].

The data and our results paint a sobering picture that will undoubtedly be further complicated in the coming years by the introduction of new illegal drugs, such as carfentanyl, xylazines, and nitazenes. The generational shift toward drug use in younger individuals, geographical heterogeneity of drug overdose deaths, and evolving consumption and regulation patterns all emphasize the need for more focused intervention and prevention strategies. By providing near-term forecasts, quantifying epidemiological parameters, and capturing local overdose trends, our data assimilation approach has the potential to facilitate efforts to reduce drug-induced deaths in the U.S.

Lucas Böttcher delivered a contributed presentation and Maria R. D’Orsogna delivered a minisymposium presentation related to this research at the 2024 SIAM Conference on the Life Sciences, which took place in Portland, Ore., last year.

Acknowledgements: This work was supported by the U.S. Army Research Office through grant W911NF-23-1-0129.

References
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