Temporally validated district-level tuberculosis case-count modeling in Indonesia using negative binomial regression and PSO-optimized explainable ensembles

Abstract

Indonesia has a high tuberculosis (TB) burden and heterogeneous district-level notification counts. We analyzed 5,140 observations from 514 districts/municipalities in 2016-2025 using separate inferential and predictive approaches. Contemporaneous count regression used a log-population offset and district-clustered robust uncertainty. Among Poisson, generalized Poisson, NB1, and NB2 models fitted to 2016-2024, NB2 had the lowest AIC (66,458.61); Poisson Pearson dispersion was 320.07. For prediction, previous-year regional characteristics were used to estimate the following year’s recorded counts, excluding previous TB counts. Random Forest, XGBoost, and LightGBM baselines and PSO-optimized variants were compared with predictive negative binomial regression using five expanding-window folds for outcome years 2020-2024. XGBoost-PSO was selected by the lowest mean weighted absolute percentage error (WAPE; 32.74%). On the temporally separated 2025 outcome year, it achieved WAPE 19.39%, mean absolute error 327.25 cases, root mean squared error 714.36 cases, and mean Poisson deviance 121.56. RF-PSO had slightly lower WAPE (19.32%) and lower deviance (111.58), while XGBoost-PSO minimized RMSE. PSO reduced holdout WAPE relative to each baseline, but a separate persistence reference performed better than all seven candidates (WAPE 7.55%). Monte Carlo SHAP identified population (57.55%) and density (15.52%) as the largest global contributions to 2025 predictions. After refitting the model through the 2025 outcome, the projected total for 2026 was 792,909.68 recorded cases, with Bogor District having the highest district-level projection. The 2025 outcomes had been examined in earlier versions, so this is a retrospective temporal evaluation. The 2026 point predictions lack calibrated prediction intervals and require prospective validation. The framework separates ecological rate associations, restricted covariate-based forecasting, and model-specific predictive explanations.