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：随着数字地图集在传达空间变异方面的普及，对稳健小区域估计的需求日益增长。然而，当前的小区域估计方法在数据极其稀疏或需要对人口极少的区域进行估计时，会面临多种建模问题，尤其是在处理比例数据时更为突出。此外，近期研究已表明在个体和区域层面同时建模具有显著优势。我们提出了一种针对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；同时利用仅含个体层面的调查协变量和区域层面的人口普查协变量；降低直接估计的不稳定性；并为缺乏调查数据的小区域生成患病率估计值。通过模拟研究，我们证明，与现有的贝叶斯小区域估计方法相比，我们的模型在各种数据条件下（包括极其稀疏和不稳定的数据）能提供比例的最优预测性能（贝叶斯均方根相对误差均值、平均绝对相对偏差及覆盖率）。为评估该模型的实际应用效果，我们结合2017-2018年国家健康调查数据与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的比较。