Data-Driven Analysis of Maternal and Neonatal Mortality for Sustainable Health Interventions Using Type II Trivariate Zero-Inflated Poisson Generalized Inverse Gaussian Regression

Maternal and neonatal mortality remain critical public health issues in regions with heterogeneous socioeconomic, geographic, and healthcare conditions. This study applies the Type II Trivariate Zero-Inflated Poisson Generalized Inverse Gaussian Regression (TZIPGIGR) model to jointly analyze Maternal deaths during delivery, postpartum maternal deaths, and neonatal asphyxia deaths in 85 sub-districts across Lumajang, Probolinggo, Situbondo, and Bondowoso Regencies, East Java, Indonesia. The model accommodates excess zeros, overdispersion, and multiple joint zero-nonzero response patterns in trivariate count data. Descriptive analysis showed high zero proportions and variance-to-mean ratios greater than one for all responses, indicating excess zeros and overdispersion. All eight trivariate zero-nonzero patterns were observed, with the most frequent patterns being no deaths in all outcomes and neonatal asphyxia deaths only. Model comparison using AICc and convergence diagnostics showed that the Type II TZIPGIGR model achieved the most stable convergence, with the smallest gradient norm and the fewest function evaluations. Parameter estimation indicated that Chronic Energy Deficiency and Preeclampsia were significant predictors of Maternal deaths during delivery, while Anemia significantly affected neonatal asphyxia deaths. These findings support joint modeling of maternal and neonatal mortality outcomes and provide evidence for targeted health policy planning aligned with Sustainable Development Goal 3.