A Bayesian semi-parametric model for small area estimation

TL;DR

This paper introduces a Bayesian semi-parametric model using Dirichlet process mixtures to improve small area health outcome estimates, capturing geographic diversity more flexibly than traditional parametric models.

Contribution

The paper proposes a novel semi-parametric hierarchical model with Dirichlet process mixtures for small area estimation, addressing geographic heterogeneity more effectively.

Findings

Semi-parametric model outperforms parametric in capturing geographic variability.

Model provides more accurate estimates for small subnational areas.

Results demonstrate improved flexibility in modeling health outcomes.

Abstract

In public health management there is a need to produce subnational estimates of health outcomes. Often, however, funds are not available to collect samples large enough to produce traditional survey sample estimates for each subnational area. Although parametric hierarchical methods have been successfully used to derive estimates from small samples, there is a concern that the geographic diversity of the U.S. population may be oversimplified in these models. In this paper, a semi-parametric model is used to describe the geographic variability component of the model. Specifically, we assume Dirichlet process mixtures of normals for county-specific random effects. Results are compared to a parametric model based on the base measure of the Dirichlet process, using binary health outcomes related to mammogram usage.