Random Forest vs Elastic-Net Penalized Logistic Regression for Patient Discharge Classification in BPJS Primary Care

This study analyzes and compares Random Forest and Penalized Logistic Regression (Elastic Net, SAGA solver) for classifying patient discharge status at BPJS Kesehatan primary care facilities (FKTP). The large-scale dataset consists entirely of nominal predictors with class imbalance (~64.9% majority). The experimental design applies an 80/20 train–test split, one-hot encoding, and class_weight = balanced for both models. Hyperparameters are tuned via a staged coarse→fine randomized search with a local-optimum convergence rule (improvement threshold ε = 1e−6, patience = 10), followed by 10-fold cross-validation for internal validation and final testing on the hold-out set. We evaluate three primary metrics: F1-Score, Precision–Recall AUC (PR-AUC), and Brier Score. On the test set, Random Forest attains F1 = 0.996679, PR-AUC = 0.999933, and Brier = 0.002646; Penalized Logistic Regression attains F1 = 0.996676, PR-AUC = 0.999928, and Brier = 0.002017. The near-identical F1 and PR-AUC indicate comparable discrimination between methods, while the lower Brier Score for Penalized Logistic Regression demonstrates superior probability calibration. Overall, both approaches lie on the same performance plateau for discrimination, with a consistent calibration advantage for Penalized Logistic Regression; method choice can thus be guided by whether operational needs prioritize calibrated probabilities or flexible non-linear decision boundaries.