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National illicit amphetamine consumption in Germany from wastewater: Bayesian source apportionment, hold-out-evaluated extrapolation and monitoring design

This study employs a Bayesian mass-balance model with hierarchical extrapolation and rigorous hold-out validation on German wastewater data to estimate that national illicit amphetamine consumption in 2025 was approximately 16.8 tonnes, while highlighting significant discrepancies with traditional survey-based figures and demonstrating the critical need for monitoring smaller catchments to reduce estimation uncertainty.

Original authors: Phil Käding

Published 2026-09-29

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Phil Käding

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Every day, millions of people flush their lives down the toilet. In the vast, hidden network of pipes that carries wastewater away from homes and cities, a chemical record of human behavior is left behind. When people use drugs, the body breaks them down and excretes the remains into the sewer system. Scientists have learned to read this chemical signature, a field known as wastewater-based epidemiology. By measuring the specific residues of drugs like amphetamine in the water at treatment plants, researchers can calculate how much of the substance a community has consumed. This method offers a direct look at drug use that bypasses the need for people to admit to their habits in surveys, which are often unreliable because users may hide their consumption or forget to report it. However, turning a measurement from a single city into a reliable picture of an entire nation is a complex puzzle. It requires separating the drug used illegally from similar chemicals that might come from medicine or from the breakdown of other drugs, and then figuring out how to apply the data from the few cities that are monitored to the thousands of towns that are not.

A new study by independent researcher Phil Käding tackles this puzzle for Germany, using thirteen years of data to estimate the country's total illicit amphetamine consumption. The research combines wastewater measurements with advanced statistical modeling to solve three specific problems. First, it had to distinguish between amphetamine used as a drug on its own, amphetamine that appears in the system because someone took methamphetamine (which the body converts into amphetamine), and amphetamine that comes from prescription medications for attention disorders. Second, it needed to estimate the drug use in the vast majority of the population that lives in areas not currently monitored by the standard testing network. Third, it had to determine how confident we can be in these numbers and where to place future monitoring stations to get the best possible picture.

The study analyzed wastewater data from sixteen German cities collected between 2013 and 2025. The researchers found that the chemical signature of amphetamine in German sewers is distinct from what has been seen in other countries. In Australia, for example, a specific ratio of amphetamine to methamphetamine has been observed, but the German data told a different story. The analysis showed that in Germany, the amount of amphetamine appearing from methamphetamine use is much lower than previously assumed, roughly half of the Australian figure. This finding was driven largely by data from Chemnitz, a city near the Czech border where methamphetamine use is concentrated. In Chemnitz, the ratio of the two chemicals was so low that if researchers had used the higher Australian numbers, the math would have suggested that no one in that city was using illicit amphetamine at all—a result that made no sense. Instead, the data indicated that the vast majority of the amphetamine found in the sewers, about 95 percent, comes from direct illicit use, with only tiny fractions coming from prescription drugs or methamphetamine metabolism.

Once the sources were separated, the team faced the challenge of scaling up. The monitoring network covers only a fraction of Germany's population, mostly in large cities. To estimate the national total, the researchers built a model that looked at how drug use varied by city size and region. They discovered a surprising pattern: smaller cities and towns in western Germany often had higher levels of amphetamine per person than the massive metropolitan centers like Berlin or Munich. If the researchers had simply taken the average from the big cities and applied it to the whole country, they would have significantly underestimated the total amount of drugs being used. Their model corrected for this by accounting for the higher usage in these smaller, unmonitored communities. The result is a national estimate for 2025 of approximately 17 tonnes of pure illicit amphetamine consumed per year, with a likely range between 7 and 58 tonnes. This figure is more than double what a simpler calculation based only on the largest cities would have produced.

The study also tested how reliable these predictions are by hiding some of the known data and seeing if the model could guess it correctly. The model performed reasonably well, predicting the drug loads in unseen cities with a median error factor of about 2.3, meaning the guess was usually within a factor of two and a half of the actual value. However, the biggest source of uncertainty remains the leap from the monitored cities to the unmonitored ones. The researchers used this uncertainty to design a better monitoring network. They found that adding just five new monitoring stations in small towns in western Germany would cut the uncertainty of the national estimate by nearly half. This is a much more effective improvement than adding more stations to already well-covered large cities.

Despite the precision of the wastewater data, a gap remains when comparing these results to other ways of measuring drug use. Official surveys of drug users and police seizure records suggest numbers that are several times lower than the wastewater estimates. The study does not resolve this discrepancy but suggests it is likely due to the limitations of surveys, which often miss heavy users or stigmatized behaviors, rather than an error in the wastewater science. The researchers conclude that while the exact number of tonnes consumed is still a range rather than a single fixed point, the method provides a robust, data-driven picture of the market that is far more detailed than previous attempts. By understanding where the uncertainty lies and where the drug use is actually happening, authorities can move beyond guessing and target their monitoring and resources more effectively.

Technical Summary: National Illicit Amphetamine Consumption in Germany from Wastewater

Problem Statement
Wastewater-based epidemiology (WBE) provides robust city-level drug load data, but deriving national consumption estimates for Germany faces two primary challenges: source apportionment and population extrapolation.

Source Apportionment: Measured amphetamine loads in wastewater represent a composite of three sources: illicit consumption, pharmaceutical excretion (primarily d-amphetamine from lisdexamfetamine prescribed for ADHD), and amphetamine excreted as a metabolite of methamphetamine. In Germany, methamphetamine use is geographically concentrated near the Czech border, where methamphetamine loads can exceed amphetamine loads by an order of magnitude. Existing methods often rely on fixed metabolic ratios (e.g., the Australian-derived 0.09 ratio) or simple subtractions that can result in physically impossible negative illicit loads in high-methamphetamine regions.
Extrapolation: Current monitoring networks (SCORE/EUDA) are purposively sampled, favoring large cities. National estimates require extrapolating per-capita loads to unmonitored populations, including smaller towns and rural areas. Deterministic approaches (e.g., imputing a median city rate to the whole population) fail to quantify uncertainty and may introduce bias if per-capita loads vary systematically with catchment size or region. Furthermore, there is a lack of quantified guidance on where additional monitoring sites would most effectively reduce national uncertainty.

Methodology
The study employs a unified Bayesian hierarchical framework to address these issues using 13 years of data (2013–2025) from 16 German catchments (95 site-weeks).

Mass-Balance Observation Model: The measured amphetamine load ( $A_{it}$ $A_{i t}$ ) is modeled as the sum of illicit load ( $I_{it}$ $I_{i t}$ ), pharmaceutical load ( $P_t$ $P_{t}$ ), and methamphetamine-derived load ( $\alpha_i M_{it}$ $α_{i} M_{i t}$ ).
- Source Separation: The cross-contribution ratio ( $\alpha$ ) is estimated directly from the data rather than fixed a priori. A hierarchical extension allows $\alpha$ to vary between sites. Pharmaceutical loads are quantified using prescription volume data (GKV) and excretion parameters.
- Illicit Load Modeling: The illicit load is modeled as a function of catchment size (log population), region (East/West), site-specific random effects, and year effects.
Population Frame and Extrapolation: A population frame is constructed using Destatis wastewater statistics, stratified by federal state and treatment plant size class (four classes ranging from <10,000 to >100,000 population equivalents). Monitored catchments are removed from their respective strata to ensure monitored and unmonitored populations are disjoint. The model transfers the observed relationship between per-capita load, size, and region to unmonitored plants within the same strata.
Back-Calculation: The illicit load entering sewers is converted to annual pure amphetamine consumption using distributions for urinary excretion fractions, in-sewer stability, and the spring-to-annual load ratio.
Validation and Design:
- Predictive Evaluation: The model's extrapolation capability is tested via "hold-out" validation (removing entire site histories) and a "downward-extrapolation" test (predicting smaller catchments using only data from the seven largest cities).
- Uncertainty Decomposition: Variance in the national estimate is decomposed to identify dominant uncertainty sources.
- Monitoring Design: A pre-posterior analysis ranks potential new monitoring sites by their projected reduction in national uncertainty.
Triangulation: Results are compared against survey data (ESA), seizure statistics, and Dutch WBE data.

Key Contributions

Data-Driven Source Apportionment: The study demonstrates that the methamphetamine-to-amphetamine cross-contribution ratio ( $\alpha$ ) can be learned from German wastewater data. The posterior estimate ( $\alpha \approx 0.05$ ) is significantly lower than the Australian reference (0.09), driven largely by the Chemnitz record where a higher ratio would imply negative illicit loads.
Quantified Extrapolation Bias: The analysis reveals that extrapolating from large cities alone underpredicts national consumption by a factor of approximately 2.2. Smaller catchments, particularly in the west (e.g., Saarbrücken, Dülmen), exhibit per-capita loads significantly higher than the largest German cities.
Uncertainty Quantification and Design: The study decomposes uncertainty, showing that extrapolation accounts for 66% of the variance in the log national estimate. It provides a quantitative ranking for network expansion, identifying that adding five small western catchments would reduce extrapolation uncertainty by 46%, a gain far exceeding the addition of large cities.

Results

National Consumption: The estimated illicit amphetamine consumption in Germany for 2025 is 16.8 tonnes per year (95% Credible Interval: 6.8–57.6 tonnes), equivalent to 0.55 mg per resident per day.
Source Apportionment: Illicit use accounts for 95% of the total amphetamine mass load. Pharmaceutical amphetamine contributes 3.6%, and methamphetamine-derived amphetamine contributes 1.1%.
Ratio Estimation: The estimated amphetamine-to-methamphetamine ratio is 0.050 (95% CrI 0.034–0.066). Fixing this ratio at the Australian value of 0.09 results in a worse model fit and implies near-zero illicit loads in Chemnitz.
Predictive Performance: The model predicts held-out site-weeks with a median absolute fold error of 2.3 and 89% coverage for 90% prediction intervals. However, models fitted only to large cities underpredict smaller catchments by a factor of 2.2.
Discrepancy with Other Metrics: The WBE estimate is several-fold higher than consumption figures derived from survey data (ESA) or seizure statistics. For instance, survey-anchored consumption estimates (based on 1–8 g per user) fall below the 2.5th percentile of the WBE posterior. Seizures represent only ~1.4% of the model-implied street-product mass.

Significance and Claims
The paper claims to provide the first national estimate of illicit amphetamine consumption in Germany that jointly separates pharmaceutical, methamphetamine-derived, and illicit sources while rigorously quantifying extrapolation uncertainty.

Methodological Rigor: By using a Bayesian framework, the study moves beyond deterministic point estimates to provide credible intervals that reflect the limitations of the data, particularly the uncertainty in extrapolating to unmonitored small catchments.
Network Optimization: The study challenges the assumption that monitoring large cities is sufficient for national estimates. It provides evidence that the current network's bias toward large cities leads to a significant underestimation of national consumption and offers a specific, quantified strategy (adding small western catchments) to reduce this uncertainty.
Multimethod Discrepancy: The author highlights a persistent, unresolved gap between WBE estimates and traditional surveillance (surveys and seizures). They suggest this is likely due to underreporting in surveys (stigma, heavy user exclusion) and potential biases in WBE (e.g., direct disposal, pH-dependent excretion), rather than a failure of either method alone.
Policy Implications: The findings suggest that national monitoring campaigns should prioritize retaining and adding smaller catchments to correct for urbanity bias and that future analyses should report source apportionment parameters (like $\alpha$ ) learned from local data rather than relying on external constants.

The study concludes that while the current estimate is robust within its model assumptions, the large uncertainty interval (7–58 tonnes) underscores the need for targeted monitoring in underrepresented catchment classes to refine national drug market sizing.

Technical Summary: National Illicit Amphetamine Consumption in Germany from Wastewater

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