Forecasting drug-overdose mortality by age in the United States at the national and county levels

Fig. 1.. Forecasting nationwide overdose fatalities. a and b) United States population and overdose deaths as a function of age (0–100 years) and time (1999–2021). c–e) Forecasts of overdose deaths as a function of age. Solid red curves and red-shaded areas indicate mean predictions and 3σ (i.e. 3-standard deviation) intervals, respectively. Observed fatalities are indicated by dashed black curves. Ages are binned in 5-year intervals and prediction values are displayed at the center of each bin interval. f) Evolution of the estimated drug-caused mortality rate μ^d and the corresponding 3σ intervals. g) Evolution of the estimated ages for which the onset of high-risk drug use is largest and corresponding 3σ intervals. To account for potential population shifts, we utilize two age-stratified influxes peaked at a^1max,a^2max. The thickness of the curves is proportional to their respective magnitudes r^1 and r^2. As can be visually inferred, the influx peaked at the younger age a^1max begins to carry more weight than its counterpart peaked at a^2max around 2015, indicating a shift toward a preponderance of younger persons using high-risk drugs. We set a lower limit of 19 years for a^1max to…

Fig. 2.. Forecasting nationwide overdose fatalities for 2022–2024. a) Forecasts of overdose deaths in the United States as a function of age (0–100 years) for the year 2022. The forecast (solid red curve) is higher than 2020 and 2021 observations (dash-dotted curve gray and dashed black curve) due to the EnKF following the trend set by the pandemic years 2020 and 2021, both marked by large increases in overdose deaths. Provisional data for 2022 (not shown) suggests that overdose deaths in each age group are comparable to the 2021 counts. Light red-shaded regions show values within the 3σ range. b and c) Forecasts of overdose deaths in the United States as a function of age (0–100 years) for the years 2023 and 2024, using 2022 provisional data in the EnKF. The predicted number of overdose deaths will remain near the record highs of 2021. Due to the lack of observation data in 2023, the CIs increase in 2024 due to the larger uncertainty as time progresses. Ages are binned in 5-year intervals and prediction values are displayed at the center of each bin interval.

Fig. 3.. Drug-overdose fatalities in the United States at the county level. a) Histogram of county-stratified drug-overdose fatalities for different years (blue disks: 2020, orange crosses: 2015, green diamonds: 2010, red inverted triangles: 2005, purple triangles: 2000). b) Histogram of county-stratified crude rate data for different years. d) County-stratified drug-overdose fatalities as a function of the corresponding county populations. e) County-stratified crude rates as a function of the corresponding county populations. c), f) Crude rates across different counties in 2020 and 2000. The scales of the two color bars differ by a factor of 10. In the gray regions, either no data or a statistically not significant number of cases were reported. In all panels, we did not include data for which at least one database entry (e.g. fatalities and crude rate) was marked unreliable. The minimum number of deaths in the remaining data is 20. Hence, the crude rate data in e) lies above of the minimum crude rate given by 2×106/Population. g) The three counties with the largest overdose death tolls in 2020, 2010, and 2000. h) The three counties with the largest overdose crude rates in 2020, 2010,…

Fig. 4.. Forecasting overdose fatalities in select United States jurisdictions. a–d) Forecasts of overdose deaths in Los Angeles County as a function of age (0100 years) for 2001, 2011, 2021, and 2023. Solid red curves and shaded regions indicate mean predictions and 3σ intervals, respectively. Observed fatalities are indicated by dashed black curves. Because observational data for 2023 are not available at the time of writing, we show 2020 data (dash-dotted gray curve) and 2021 data (dashed black curve) in panels d, h, and l). e–h) Forecasts for Cook County using the same graphic representations as in panels a–d and for the years 2015, 2018, 2021, 2023. i–l) Forecasts for the five boroughs that comprise New York City (The Bronx, Brooklyn, Manhattan, Queens, and Staten Island) using the same graphic representations as in panels a–d and for the years 2007, 2014, 2021, 2023. Although the numerical escalation in drug-overdose deaths in Cook County (2015–2021) and New York City (2007–2021) is similar to what is observed for Los Angeles County, the timelines are much accelerated. In 2021, the population of Los Angeles County was 9.7 million, in Cook County 5.1 million, and in New York City 8.3…

Fig. 5.. Age-structured overdose crude rates in the United States. Age-structured overdose crude rates in the United States, distinguished by gender: a) males and b) females.

Fig. 6.. Age-structured United States population data. a) Interpolated age-structured population data. The interpolation is based on bivariate splines of degree 2. b) The overall United States population increases almost linearly between 1999 and 2021.

Fig. 7.. EnKF schematic. We use an EnKF to combine a mechanistic model of drug-overdose fatalities with corresponding observational data. Blue boxes show the main steps (i.e. projection and update) in an EnKF cycle. Green boxes represent the initial sample generation process and perturbations that are added during the projection and update steps. The schematic is adapted from Ref. (95).

Fig. 8.. Population, overdose, and drug-type trends in Los Angeles County, Cook County, and New York City. a–c) The population distribution across age groups (0–100 years) and time (1999–2021) in Los Angeles County, Cook County, and the five boroughs of New York City, with ages grouped in 10-year intervals. d–f) Overdose deaths in the same regions as a function of age (0–100 years) and time (1999–2021). g–i) Crude rates associated with fentanyl (T40.4), methamphetamines (T43.6), prescription opioids (T40.2), and heroin (T40.1) in Los Angeles County, Cook County, and the five boroughs of New York City from 1999 to 2021.

Fig. 9.. Comparison of EnKF forecasts with forecasting heuristics. a) Nationwide overdose deaths in the United States as obtained from the CDC WONDER database (black disks) and corresponding forecasts (blue squares: recency heuristic I; orange inverted triangles: recency heuristic II; green triangles: EnKF) for the period 1999–2021. In recency heuristic I, the projected number of total overdose deaths in a specific age group in year Y is given by the number of overdose deaths in the same age group in year Y−1. In recency heuristic II, the projected number of overdose deaths in a specific age group in year Y is calculated as the sum of the number of overdose deaths in that age group in year Y−1 and the difference between the number of overdose deaths in the same age group in years Y−1 and Y−2. For each year, we calculate the total number of deaths by summing across all age groups. Error bars represent EnKF 3σ intervals. b) Absolute errors associated with both forecasting heuristics and the EnKF forecast.