Modelling urban/rural fractions in low- and middle-income countries

In low- and middle-income countries, household surveys are the most reliable data source to examine health and demographic indicators at the subnational level, an exercise in small area estimation. Model-based unit-level models are favoured for producing the subnational estimates at fine scale, such as the admin-2 level. Typically, the surveys employ stratified 2-stage cluster sampling with strata consisting of an urban/rural designation crossed with administrative regions. To avoid bias and increase predictive precision, the stratification should be acknowledged in the analysis. To move from the cluster to the area requires an aggregation step in which the prevalence surface is averaged with respect to population density. This requires estimating a partition of the study area into its urban and rural components, and to do this we experiment with a variety of classification algorithms, including logistic regression, Bayesian additive regression trees, and gradient boosted trees. Pixel-level covariate surfaces are used to improve prediction. We estimate spatial HIV prevalence in women of age 15-49 in Malawi using the stratification/aggregation method we propose.