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A Spatio-temporal Cluster-aware Supervised Learning Framework for Predicting County-level Drug Overdose Deaths
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Proposes CASL, a time-series cluster-aware supervised learning model that jointly clusters counties and predicts county-level drug overdose deaths while handling CDC-suppressed counts via a custom hinge/MAE loss.
Problem
Predicting annual county-level US drug overdose deaths is hard because counties are heterogeneous, observations are spatially/socially correlated, and over half of public CDC WONDER counts are suppressed (values ≤9).
Approach
Extends the cross-sectional cluster-aware supervised learning of Chen and Xie (2022) to county-year panel data, with a loss that uses MAE for unsuppressed counts and a scaled hinge loss for suppressed counts, and clusters counties (not county-years) via regularized alternating minimization.
Key results
- On 2021 testing, increasing mixing weight ω from 0.1 to 100 reduced FPR from 0.14 to 0.03 while MAE rose from 11.89 to 14.60 (K=4).
- CASL (K=2, ω=10) achieved FPR 0.0125 with MAE 16.97 versus lasso (ω=100) FPR 0.0125 with MAE 16.7 in 2020, i.e., comparable performance.
- Imputing suppressed values (zero or MICE) and random cluster assignment gave higher mixed-error scores than CASL in both years, per the ablation.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use CASL rather than random forest or lasso regression | County-level overdose death prediction · 2020 and 2021 test | Balance of MAE and FPR | Mixed |
| Increase mixing parameter ω from 0.1 to 100 | CASL (K=4) · 2021 test | FPR: 0.14 to 0.03 | Helped |
| Increase mixing parameter ω from 0.1 to 100 | CASL (K=4) · 2021 test | MAE: 11.89 to 14.60 | Hurt |
| Use one cluster (remove clustering) instead of multiple clusters (ablation) | CASL · Prediction with small ω | MAE | Helped |
| Vary the number of clusters K (ablation) | CASL · Cross-validation across ω values | Mixed-error score | Mixed |
| Impute suppressed values with 0 instead of using the suppression-aware loss (ablation) | CASL · 2020 and 2021 predictions | Mixed-error score | Hurt |
| Impute suppressed values using MICE instead of using the suppression-aware loss (ablation) | CASL · 2020 and 2021 predictions | Mixed-error score | Hurt |
| Learn county clusters rather than assign counties randomly (ablation) | CASL · 2020 and 2021 predictions | Mixed-error score | Helped |
Surprising findings
- Fewer clusters (K=1) gave the lowest MAE when ω was small, so clustering did not help unsuppressed accuracy at low ω.
Limitations
- Only annual granularity; omits time-varying policy, supply, and treatment program factors.
- Same feature space used for both prediction and clustering.
- Fairness and bias across rural/urban and vulnerable communities not evaluated.
Experimental setup
Datasets: CDC WONDER overdose death counts NIBRS drug-related crime incidents NFLIS fentanyl seizure percentages County Health Rankings Google Maps distance matrix API
Benchmarks: county-level overdose deaths 2020 and 2021 (held-out testing)
Metrics: mean absolute error (MAE) on unsuppressed counties false positive rate (FPR) on suppressed counties mixed-error score
Baselines: random forest lasso regression MICE imputation zero imputation random cluster assignment
Builds on: Chen and Xie (2022) cluster-aware supervised learning regularized alternating minimization
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