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

Small area estimation using survey data can be achieved by using either a design-based or a model-based inferential approach. Design-based direct estimators are generally preferable because of their consistency, asymptotic normality, and reliance on fewer assumptions. However, when data are sparse at the desired area level, as is often the case when measuring rare events, these direct estimators can have extremely large uncertainty, making a model-based approach preferable. A model-based approach with a random spatial effect borrows information from surrounding areas at the cost of inducing shrinkage. As a result, estimates may be over-smoothed and inconsistent with design-based estimates at higher area levels when aggregated. We propose two unit-level Bayesian models for small area estimation of rare event prevalence which use design-based direct estimates at a higher area level to increase consistency in aggregation. This model framework is designed to accommodate sparse data obtained from two-stage stratified cluster sampling, which is particularly relevant to applications in low- and middle-income countries. After introducing the model framework and its implementation, we conduct a simulation study to evaluate its properties and apply it to the estimation of the neonatal mortality rate in Zambia, using 2014 Demographic Health Surveys data.