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With the rise in popularity of digital Atlases to communicate spatial
variation, there is an increasing need for robust small-area estimates.
However, current small-area estimation methods suffer from various modeling
problems when data are very sparse or when estimates are required for areas
with very small populations. These issues are particularly heightened when
modeling proportions. Additionally, recent work has shown significant benefits
in modeling at both the individual and area levels. We propose a two-stage
Bayesian hierarchical small area estimation approach for proportions that can:
account for survey design; reduce direct estimate instability; and generate
prevalence estimates for small areas with no survey data. Using a simulation
study we show that, compared with existing Bayesian small area estimation
methods, our approach can provide optimal predictive performance (Bayesian mean
relative root mean squared error, mean absolute relative bias and coverage) of
proportions under a variety of data conditions, including very sparse and
unstable data. To assess the model in practice, we compare modeled estimates of
current smoking prevalence for 1,630 small areas in Australia using the
2017-2018 National Health Survey data combined with 2016 census data.
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