Two-phase study designs are appealing since they allow for the oversampling of rare sub-populations which improves efficiency. In this paper we describe a Bayesian hierarchical model for the analysis of two-phase data. Such a model is particularly appealing in a spatial setting in which random effects are introduced to model between-area variability. In such a situation, one may be interested in estimating regression coefficients or, in the context of small area estimation, in reconstructing the population totals by strata. The efficiency gains of the two-phase sampling scheme are compared to standard approaches using 2011 birth data from the research triangle area of North Carolina. We show that the proposed method can overcome small sample difficulties and improve on existing techniques. We conclude that the two-phase design is an attractive approach for small area estimation.

中文翻译：

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用于两阶段研究的平滑的贝叶斯分层模型，应用于小面积估计。

两阶段研究设计很吸引人，因为它们允许对稀有亚群进行过度采样，从而提高了效率。在本文中，我们描述了用于两相数据分析的贝叶斯层次模型。这种模型在空间环境中特别有吸引力，在空间环境中，引入随机效应来模拟区域之间的可变性。在这种情况下，人们可能会对估算回归系数感兴趣，或者在小面积估算的背景下，对按层重建总体总数感兴趣。使用来自北卡罗来纳州研究三角地区的2011年出生数据，将两阶段采样方案的效率增益与标准方法进行了比较。我们表明，所提出的方法可以克服小样本困难并在现有技术上进行改进。