(129) Recurrent Overdose Survival Modeling for Smarter Harm Reduction Deployment

Background & Introduction: The fentanyl era has compressed the window for overdose rescue, elevating the importance of rapid, low-barrier access to naloxone and related harm-reduction supplies (Zhang et al., 2025; Wagner et al., 2022). Milwaukee County has experienced sustained elevations in fatal and nonfatal overdoses since 2018, with a sharp step increase in early 2020 and high levels thereafter (Forati et al., 2023; Ghose et al., 2025). In 2023, the county expanded 24/7, no-cost distribution points to reach people who may not engage with traditional services, aligning with implementation evidence on low-barrier dispensing (Zhang et al., 2025; Wagner et al., 2022).
This study evaluates whether proximity to Harm Reduction Vending Machines (HRVMs) corresponds to changes in overdose recurrence risk and timing among Milwaukee residents. Using six years of linked emergency medical and medical examiner data, we quantified recurrent overdose burden, estimated survival to next event across successive orders, and compared recurrence patterns by proximity to HRVMs. A countywide interrupted time-series (ITS) analysis contextualized these findings within broader temporal trends. Our overarching goal was to translate a novel, equity-oriented public-health intervention into rigorous, practice-ready evidence that can inform siting, outreach partnerships, and longitudinal evaluation as harm-reduction infrastructure expands across U.S. jurisdictions.

Methods: We analyzed all Milwaukee County nonfatal overdoses from January 2018 to December 2023 (n = 28,108; 20,300 individuals). Events were geocoded, de-duplicated, and classified as single or multiple overdoses. Each person’s inter-event intervals were tracked from one overdose to the next. HRVM exposure was defined by residence or event location within ≤ 30 minutes versus > 30 minutes walking distance of a machine. Kaplan–Meier survival curves characterized recurrence timing, and mean cumulative functions summarized average overdose counts over time. A county-level ITS model evaluated pre/post-HRVM trends in nonfatal overdose counts. To identify the most suitable analytic framework, we implemented a method-selection pipeline comparing Andersen–Gill (AG), Prentice–Williams–Peterson, and modern Cox-based machine-learning models (XGBoost, LightGBM, CatBoost, DeepSurv) following best practices for recurrent-event prediction (Watson et al., 2024). The AG gap-time model achieved the best discrimination (C_uno = 0.614; AUC = 0.619) and was used for inference. Covariates included age, gender, race, jurisdiction, location type, patient disposition, and proximity. Proportionality assumptions and convergence were verified, and results expressed as adjusted hazard ratios with 95% confidence intervals.

Results: From 2018 to 2023, there were 28,108 nonfatal overdoses among more than 20,000 people; 3,803 individuals experienced multiple events, accounting for 11,611 overdoses, yielding a mean of 3.05 among the multi-overdose group and 1.38 per person overall. The progression of risk by event order was steep and visually monotonic: the Kaplan Meyer (KM) curve for 1st→2nd overdose (n=20,992 intervals) remained highest, while curves for 2→3 (n=3,906), 3→4 (n=1,680), 4→5 (n=856), 5→6 (n=506), and higher orders descended rapidly, indicating progressively shorter gaps before the next event and underscoring the urgency of secondary and tertiary prevention. Proximity-specific KM for time from first to second overdose showed subtly higher survival within 30 minutes of a machine compared with beyond 30 minutes throughout follow-up. At risk sets numbered n=10,315 for the within-30-minute group and n=11,782 for the beyond-30-minute group; separation was modest but consistent, with overlapping confidence bands. Correspondingly, the empirical MCF curves rose more slowly within 30-minute zones, reaching a mean of roughly 1.36 overdoses by about six years beyond the first event compared with about 1.41 in the farther group, again suggesting small differences that favor machine-proximate areas without indicating a large effect. The Andersen–Gill gap-time model, selected through our performance pipeline, achieved the strongest discrimination (C_uno = 0.614; AUC = 0.619). Proximity to HRVMs carried a non-significant adjusted hazard ratio of 1.03 (95% CI 1.00–1.06; p = 0.037, borderline), indicating no clear reduction in short-term recurrence risk. In contrast, younger age emerged as a consistent predictor of more rapid recurrence (HR ≈ 0.998 per year), and overdoses occurring in public or commercial locations—especially streets and business establishments—were strongly associated with faster re-occurrence (HR ≈ 1.05–1.16, p < 0.001). These findings suggest that environmental exposure and mobility may outweigh structural proximity effects in early implementation stages. Collectively, the modeling and descriptive results indicate that Milwaukee’s HRVMs have begun to stabilize, but not yet materially reduce, recurrent-event risk—consistent with an early-phase harm-reduction infrastructure whose measurable impact may emerge only with expanded coverage and longer follow-up.

Conclusion & Discussion: Milwaukee’s HRVM program demonstrates a proactive public-health innovation designed to shift overdose outcomes from fatal to survivable. Analyses integrating geospatial proximity, survival modeling, and time-series trends show that early implementation modestly slowed cumulative overdose accumulation near machines. The Andersen–Gill gap-time model outperformed all alternatives, identifying younger individuals and overdoses in public or commercial venues as the strongest predictors of rapid recurrence (Watson et al., 2024). These findings underscore the persistence of high-risk exposure environments and highlight opportunities to pair vending-machine access with mobile outreach and medication linkage (Forati et al., 2023; Ghose et al., 2025). As coverage expands and machine data integrate with individual uptake and naloxone use records, future analyses can test whether sustained exposure attenuates recurrence. Collectively, these results support continued HRVM deployment as part of Milwaukee’s evolving harm-reduction ecosystem and provide a replicable analytical framework for other jurisdictions evaluating similar interventions.

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