Obtaining reliable estimates about health outcomes for areas or domains where only few to no samples are available is the goal of small area estimation (SAE). Often, we rely on health surveys to obtain information about health outcomes. Such surveys are often characterised by a complex design, stratification, and unequal sampling weights as common features. Hierarchical Bayesian models are well recognised in SAE as a spatial smoothing method, but often ignore the sampling weights that reflect the complex sampling design. In this paper, we focus on data obtained from a health survey where the sampling weights of the sampled individuals are the only information available about the design. We develop a predictive model-based approach to estimate the prevalence of a binary outcome for both the sampled and non-sampled individuals, using hierarchical Bayesian models that take into account the sampling weights. A simulation study is carried out to compare the performance of our proposed method with other established methods. The results indicate that our proposed method achieves great reductions in mean squared error when compared with standard approaches. It performs equally well or better when compared with more elaborate methods when there is a relationship between the responses and the sampling weights. The proposed method is applied to estimate asthma prevalence across districts.

小区域估计 (SAE) 的目标是获得关于只有很少或没有可用样本的区域或领域的健康结果的可靠估计。通常，我们依靠健康调查来获取有关健康结果的信息。此类调查的共同特点往往是设计复杂、分层、抽样权重不均等。分层贝叶斯模型在 SAE 中被广泛认为是一种空间平滑方法，但常常忽略反映复杂采样设计的采样权重。在本文中，我们重点关注从健康调查中获得的数据，其中抽样个体的抽样权重是有关设计的唯一可用信息。我们开发了一种基于预测模型的方法，使用考虑抽样权重的分层贝叶斯模型来估计抽样和非抽样个体的二元结果的普遍性。进行了模拟研究，以将我们提出的方法与其他已建立的方法的性能进行比较。结果表明，与标准方法相比，我们提出的方法大大降低了均方误差。当响应和采样权重之间存在关系时，与更复杂的方法相比，它的性能同样好甚至更好。所提出的方法适用于估计各地区的哮喘患病率。