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

Area of Science:

• Public Health Research
• Survey Methodology
• Biostatistics

Background:

• Two-phase sampling is cost-effective but Phase II subsample weights can be unstable.
• Leveraging Phase I data can improve survey inference for Phase II samples.
• Complex survey designs present analytical challenges.

Purpose of the Study:

• To propose a Bayesian tree-based multiple imputation (MI) approach for estimating population means from Phase II samples.
• To incorporate complex survey design features into imputation models.
• To evaluate the performance of the proposed method against traditional weighted estimators.

Main Methods:

• Bayesian tree-based multiple imputation (MI).
• Incorporation of parent survey design features (strata, clusters) into imputation models.
• Simulation studies comparing the proposed MI method with traditional weighted estimators.

Main Results:

• The tree-based MI method demonstrated smaller bias and lower root mean squared error.
• The proposed method yielded narrower confidence intervals with coverage rates closer to the nominal level.
• Rubin's variance estimation method was found to provide valid statistical inference.

Conclusions:

• The Bayesian tree-based MI approach offers a more stable and accurate alternative to traditional weighting methods for two-phase sampling.
• The method effectively utilizes rich Phase I data to enhance Phase II sample inference.
• The proposed method is applicable to real-world public health surveys, as illustrated by a COVID-19 vaccination survey example.