Direct-Assisted Bayesian Unit-level Modeling for Small Area Estimation of Rare Event Prevalence

Area of Science:

• Statistics
• Public Health
• Demography

Background:

• Small area estimation faces challenges with sparse data, especially for rare events, leading to high uncertainty with direct estimators.
• Model-based approaches can over-smooth estimates and cause aggregation inconsistencies when borrowing strength from neighboring areas.

Purpose of the Study:

• To propose novel unit-level Bayesian models for small area estimation of rare event prevalence.
• To enhance aggregation consistency by incorporating design-based direct estimates at higher area levels.
• To develop a framework suitable for sparse data from two-stage stratified cluster sampling.

Main Methods:

• Developed two unit-level Bayesian models incorporating random spatial effects.
• Integrated design-based direct estimates from higher area levels into the models.
• Utilized a simulation study to evaluate model performance.
• Applied the models to estimate neonatal mortality rates in Zambia using 2014 Demographic Health Surveys data.

Main Results:

• The proposed models demonstrated improved consistency in aggregation compared to traditional model-based approaches.
• The Bayesian framework effectively handled sparse data characteristic of two-stage stratified cluster sampling.
• The application to Zambian neonatal mortality data provided reliable small area estimates.

Conclusions:

• The novel Bayesian models offer a robust solution for small area estimation of rare events with sparse data.
• The approach enhances the reliability of estimates, particularly in resource-limited settings.
• This methodology improves the consistency of estimates across different aggregation levels.