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With the rise in popularity of digital Atlases to communicate spatialvariation, there is an increasing need for robust small-area estimates.However, current small-area estimation methods suffer from various modelingproblems when data are very sparse or when estimates are required for areaswith very small populations. These issues are particularly heightened whenmodeling proportions. Additionally, recent work has shown significant benefitsin modeling at both the individual and area levels. We propose a two-stageBayesian hierarchical small area estimation approach for proportions that can:account for survey design; reduce direct estimate instability; and generateprevalence estimates for small areas with no survey data. Using a simulationstudy we show that, compared with existing Bayesian small area estimationmethods, our approach can provide optimal predictive performance (Bayesian meanrelative root mean squared error, mean absolute relative bias and coverage) ofproportions under a variety of data conditions, including very sparse andunstable data. To assess the model in practice, we compare modeled estimates ofcurrent smoking prevalence for 1,630 small areas in Australia using the2017-2018 National Health Survey data combined with 2016 census data.

A Two-Stage Bayesian Small Area Estimation Approach for Proportions