Small area estimation (SAE) entails estimating characteristics of interest for domains, often geographical areas, in which there may be few or no samples available. SAE has a long history and a wide variety of methods have been suggested, from a bewildering range of philosophical standpoints. We describe design-based and model-based approaches and models that are specified at the area-level and at the unit-level, focusing on health applications and fully Bayesian spatial models. The use of auxiliary information is a key ingredient for successful inference when response data are sparse and we discuss a number of approaches that allow the inclusion of covariate data. SAE for HIV prevalence, using data collected from a Demographic Health Survey in Malawi in 2015-2016, is used to illustrate a number of techniques. The potential use of SAE techniques for outcomes related to COVID-19 is discussed.
Keywords: Area-level models; Bayesian methods; complex surveys; design-based inference; direct estimation; indirect estimation; model-based inference; spatial smoothing; unit-level models; weighting.