Medication for Opioid Use Disorder and Criminal Justice Referral Outcomes In the U.S. Deep South: Evidence from a Variance Adaptive Gradient Boosted Bootstrap Model

Background: Medication for opioid use disorder (MOUD) reduces opioid-related harm and criminal legal system involvement, yet its relationship with referral outcomes remains unclear within high-dimensional treatment systems. This study examines the association between MOUD and criminal legal referral outcomes in the U.S. Deep South using a variance adaptive gradient boosted bootstrap modeling approach (VAGBBM).

Methods: A retrospective analysis was conducted using over 150,000 treatment episodes from the Treatment Episode Data Set in the U.S. Deep South. VAGBBM integrates gradient boosting, bootstrap resampling, and variance adaptive weighting to improve model stability. Logistic calibration enhanced probability estimates. Model performance was evaluated using classification metrics, discrimination (AUC, AUPRC), calibration (Brier score), and SHapley Additive exPlanations (SHAP)-based interpretability. Data management was performed in Stata v18, and modeling was conducted in RStudio.

Results: The model demonstrated strong predictive performance, with moderate discrimination (AUC = 0.757) and high sensitivity (0.841), indicating robust identification of criminal legal referral cases within an imbalanced outcome (13.6% prevalence). Specificity (0.605) and overall accuracy (0.637) were acceptable, with balanced accuracy (0.723) reflecting stable performance across classes. The Matthews correlation coefficient (0.307) indicated modest but meaningful overall predictive signal. Precision–recall performance (AUPRC = 0.250) was consistent with class imbalance, suggesting high recall at the expense of precision. Probabilistic accuracy was strong (Brier = 0.106; log loss = 0.337), with calibration analyses indicating slight underestimation at higher predicted probabilities but minimal improvement following post hoc calibration. Bootstrap predictions stabilized after 13 iterations, demonstrating rapid convergence and ensemble stability. MOUD was associated with referral outcomes, with absence of MOUD corresponding to higher predicted risk. SHAP analyses revealed context dependent effects for MOUD (−0.040 to +0.050), while structural factors such as insurance status, gender, and co-occurring conditions exerted stronger overall influence on model predictions.

Conclusions and Implications: MOUD is associated with reduced likelihood of criminal legal referral and improves risk stratification within high-dimensional models. Referral outcomes reflect multilevel structural and demographic influences. VAGBBM provides a robust and interpretable framework for modeling these relationships. Findings support expansion of MOUD alongside structural interventions. VAGBBM offers a scalable tool for identifying high-risk individuals, informing targeted interventions, and improving decision making and resource allocation.