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Abstract
The need for rigorous and timely health and demographic summaries has provided the impetus for an explosion in geographic studies in low- and middle-income countries. Many of these studies present fine-scale pixel-level maps in an attempt to answer the needs of the current era of precision public health. However, even though household surveys with a two-stage cluster design stratified by region and urbanicity are a major source of data, cavalier approaches are taken to acknowledging the survey design. We investigate the extent to which accounting for the sample design affects the predictive performance at the aggregate level of interest for health policy decisions. We consider various commonly used models and introduce a new Bayesian cluster-level model with a discrete spatial smoothing prior. The investigation is performed through a simulation study in which realistic sampling frames are created for Kenya, based on the population and demographic information, with a survey design that mimics a Demographic Health Survey (DHS). We find that including stratification and cluster-level random effects can improve predictive performance. Spatially smoothed direct (weighted) estimates and area-level models accounting for stratification were robust to the underlying population and survey design. Continuous spatial models showed some promise in the presence of fine-scale variation; however, these models require the most "hand holding." Subsequently, we examine how the models perform on real data, estimating the prevalence of secondary education for women aged 20–29 and neonatal mortality rates, using data from the 2014 Kenya DHS.

AbstractIntroductionHIV planning requires granular estimates for the number of people living with HIV (PLHIV), antiretroviral treatment (ART) coverage and unmet need, and new HIV infections by district, or equivalent subnational administrative level. We developed a Bayesian small‐area estimation model, called Naomi, to estimate these quantities stratified by subnational administrative units, sex, and five‐year age groups.MethodsSmall‐area regressions for HIV prevalence, ART coverage and HIV incidence were jointly calibrated using subnational household survey data on all three indicators, routine antenatal service delivery data on HIV prevalence and ART coverage among pregnant women, and service delivery data on the number of PLHIV receiving ART. Incidence was modelled by district‐level HIV prevalence and ART coverage. Model outputs of counts and rates for each indicator were aggregated to multiple geographic and demographic stratifications of interest. The model was estimated in an empirical Bayes framework, furnishing probabilistic uncertainty ranges for all output indicators. Example results were presented using data from Malawi during 2016–2018.ResultsAdult HIV prevalence in September 2018 ranged from 3.2% to 17.1% across Malawi's districts and was higher in southern districts and in metropolitan areas. ART coverage was more homogenous, ranging from 75% to 82%. The largest number of PLHIV was among ages 35 to 39 for both women and men, while the most untreated PLHIV were among ages 25 to 29 for women and 30 to 34 for men. Relative uncertainty was larger for the untreated PLHIV than the number on ART or total PLHIV. Among clients receiving ART at facilities in Lilongwe city, an estimated 71% (95% CI, 61% to 79%) resided in Lilongwe city, 20% (14% to 27%) in Lilongwe district outside the metropolis, and 9% (6% to 12%) in neighbouring Dowa district. Thirty‐eight percent (26% to 50%) of Lilongwe rural residents and 39% (27% to 50%) of Dowa residents received treatment at facilities in Lilongwe city.ConclusionsThe Naomi model synthesizes multiple subnational data sources to furnish estimates of key indicators for HIV programme planning, resource allocation, and target setting. Further model development to meet evolving HIV policy priorities and programme need should be accompanied by continued strengthening and understanding of routine health system data.