Abstract

National household surveys are the backbone of health statistics in sub-Saharan Africa, but they are designed to estimate indicators for countries and regions, not for the lower administrative level at which services are planned. Small area estimation (SAE) combines imprecise direct survey estimates with auxiliary data and, in its spatial forms, with information from neighbouring areas. Spatial SAE models in routine use assume a stationary covariance: two areas inform each other according to their geographic separation in the same way everywhere. For indicators driven by access to services this is unrealistic, because the processes that make areas alike shared facility catchments, remoteness, wealth, population density are not functions of distance alone; and the assumption matters most precisely where SAE is needed most, in areas with little or no sample.
We propose a nonstationary geostatistical small area estimation (NGSAE) model that embeds, within the area-level Fay–Herriot framework, a covariance family in which the area effects follow a Gaussian process indexed by location and by area-level covariates, so that two areas are correlated when they are close in space or similar in the covariates that govern the outcome. The stationary spatial model is nested and testable. Direct estimates from several surveys are pooled under one linking model through an incidence matrix with survey-specific offsets, and auxiliary data available for every area, including routine administrative data, enter the linking model. Covariance parameters are estimated by restricted maximum likelihood, area parameters by empirical best linear unbiased prediction, and mean squared errors by parametric bootstrap, with estimates benchmarked to reliable higher-level survey totals. A simulation study compares the model with the Fay–Herriot model, stationary spatial alternatives and a covariate-dependent-range model, with attention to poorly sampled and unsampled areas and to interval calibration.
As a case study we estimate district-level coverage of the first measles dose, the third pentavalent dose and full basic vaccination among children aged 12–23 months in Ethiopia, where routine reports imply administrative coverage above 100% in many districts while the surveys contain a single cluster or none in most. The model pools the 2024–25 Ethiopia DHS and the 2026 Ethiopia PMA survey, uses district-level DHIS2 reports as auxiliary information, and let’s travel time to the nearest health facility and household wealth drive the covariance. We discuss what the resulting district estimates, and their uncertainty offer for immunization planning and present the open-source R package nsgeo that implements the methods.
Keywords: small area estimation; Fay–Herriot model; nonstationary spatial covariance; routine health information systems; immunization coverage; Ethiopia; government data.