The two-phase sampling design is a cost-effective strategy widely used in public health research. Analyzing the Phase II sample often involves creating subsample-specific weights. However, these weights can be highly variable, leading to unstable weighted analyses. Alternatively, the rich data collected during the first phase can be leveraged to improve survey inference for the Phase II sample. In this paper, we propose a Bayesian tree-based multiple imputation (MI) approach for estimating population means using the Phase II sample, where the parent survey was conducted using a complex survey design. The design features of the parent survey, such as strata and clusters, are incorporated into the tree-based imputation models. Through simulations, we demonstrate that the tree-based MI method outperforms traditional weighted estimators, yielding smaller bias, lower root mean squared error, and narrower 95% confidence intervals, with coverage rates closer to the nominal level. Furthermore, we show that Rubin's variance estimation method provides valid statistical inference for population mean estimation in our setting. We illustrate the application of the proposed tree-based MI method using data from a cellphone survey on COVID-19 vaccination in Uganda, which represents a subcohort sample drawn from the 2020 Uganda Population-based HIV Impact Assessment Survey.

翻译：二阶段抽样设计是一种广泛用于公共卫生研究的成本效益策略。分析第二阶段样本通常涉及创建子样本特定权重。然而，这些权重可能高度可变，导致不稳定的加权分析。另一种方法是利用第一阶段收集的丰富数据来改进第二阶段样本的调查推断。在本文中，我们提出了一种基于贝叶斯树的多重插补（MI）方法，用于使用第二阶段样本估计总体均值，其中原始调查采用复杂调查设计进行。原始调查的设计特征，如分层和聚类，被纳入基于树的插补模型中。通过模拟，我们证明了基于树的MI方法优于传统加权估计量，产生的偏差更小、均方根误差更低、95%置信区间更窄，且覆盖概率更接近名义水平。此外，我们展示了鲁宾方差估计方法在我们设定的总体均值估计中提供了有效的统计推断。我们利用乌干达一项关于COVID-19疫苗接种的手机调查数据（该数据代表了从2020年乌干达基于人群的HIV影响评估调查中抽取的子队列样本），说明了所提出的基于树的MI方法的应用。