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 modelling problems when data are very sparse or when estimates are required for areas with very small populations. These issues are particularly heightened when modelling proportions. Additionally, recent work has shown significant benefits in modelling at both the individual and area levels. We propose a two-stage Bayesian hierarchical small area estimation model for proportions that can: account for survey design; use both individual-level survey-only covariates and area-level census covariates; 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 model 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.

翻译：随着数字图谱在传达空间变异方面的流行，对小区域稳健估计的需求日益增加。然而，当前的小区域估计方法在数据非常稀疏或需要对人口极小的区域进行估计时，会遇到各种建模问题。这些问题在建模比例时尤为突出。此外，近期研究表明，在个体层面和区域层面同时建模具有显著优势。我们提出了一种用于比例的两阶段贝叶斯分层小区域估计模型，该模型能够：考虑调查设计；使用仅包含个体层面的调查协变量和区域层面的人口普查协变量；减少直接估计的不稳定性；以及为无调查数据的小区域生成患病率估计。通过模拟研究，我们表明，与现有的贝叶斯小区域估计方法相比，我们的模型能够在多种数据条件下（包括非常稀疏和不稳定的数据）提供最优的比例预测性能（贝叶斯平均相对均方根误差、平均绝对相对偏差和覆盖率）。为在实际中评估该模型，我们结合2017-2018年国家健康调查数据和2016年人口普查数据，对澳大利亚1630个小区域的当前吸烟患病率进行了模型估计比较。