Improving Survey Inference in Two-phase Designs Using Bayesian Machine Learning

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.