Bayesian Small Area Estimation Methods for Sparse Complex Survey Data

Abstract

Small area estimation (SAE) of health and demographic outcomes in low- and middle-income countries (LMICs) is central to policy evaluation and resource allocation, yet it is complicated by the sparsity and complex design of the survey data on which such estimates typically rely. Household surveys like the Demographic and Health Surveys (DHS) are generally powered at the first administrative (admin1) level, so design-based estimates at lower levels are often imprecise or unavailable, particularly for rare outcomes. Model-based approaches can address this sparsity by borrowing strength across areas through spatial random effects, but this borrowing can induce extreme shrinkage when data are limited, affecting both point and variance estimates. This dissertation develops a set of Bayesian hierarchical spatial models which address instability and excessive shrinkage in SAE, motivated throughout by subnational estimation of child health outcomes in LMICs. The first methodological contribution is the direct-assisted Bayesian unit-level (DABUL) model, designed for estimating rare event prevalence at an administrative level too sparse to support standard area-level models. The DABUL model incorporates higher-level design-based estimates from the same underlying data as benchmarks via either a hard constraint or a soft constraint which accounts for uncertainty of the benchmarks. By applying this method to simulated data and neonatal mortality rate (NMR) estimation in Zambia using the 2013 DHS, we show that the soft DABUL model reduces aggregation discrepancy and both variants of the DABUL model yield more conservative intervals than those under a standard unit-level model, which may be particularly preferable for extreme areas. The second contribution addresses a different source of instability. The design-based variance estimates used as input in Fay-Herriot (FH) models are themselves estimated with error which is frequently ignored despite their affect on interval estimation, particularly when sample size is low. Two candidate sampling distributions for the design variance estimator are proposed and incorporated into a variance-smoothing FH framework. One sampling distribution incorporates complex survey design assumptions, while the other, simpler sampling distribution relies on stronger design assumptions. A simulation study and application to height-for-age z-scores in Kenya using the 2022 DHS show that both variance-smoothing approaches outperform a standard FH model without variance smoothing under proper scoring rules, with the simpler sampling distribution recommended for its more favorable shrinkage behavior and ease of implementation. The third contribution extends multivariate areal spatial modeling frameworks from the disease mapping literature to the FH setting and proposes a class of multivariate latent models using a BYM2 spatial structure that includes independent, correlated, and shared-component variants. Theoretical results characterize how the conditional posterior mean and variance of a primary outcome depend on the relationship between sampling and latent covariance structures. A simulation study and application to NMR estimation in Kenya using the 2022 DHS show that joint modeling with correlated outcomes can substantially improve estimation of a noisy primary outcome relative to a univariate FH model, particularly when latent correlation exceeds sampling correlation or auxiliary outcomes carry lower uncertainty than the primary outcome. Together, these three contributions demonstrate that explicitly modeling design-based sampling error and structured dependence across administrative levels, areas, or outcomes, offers a coherent strategy for improving SAE for LMICs in the data-sparse settings characteristic of complex surveys.