A Practical Framework for Incorporating Complex Survey Design in Bayesian Kernel Machine Regression

Area of Science:

• Environmental Epidemiology
• Biostatistics
• Statistical Modeling

Background:

• Large-scale population datasets often use complex sampling designs (stratification, clustering, unequal probabilities).
• Standard Bayesian Kernel Machine Regression (BKMR) does not inherently account for these complex survey designs.
• Survey weights are crucial for obtaining population-representative estimates.

Purpose of the Study:

• To evaluate the performance of standard BKMR versus a design-aware workflow using complex survey-like data.
• To assess the impact of accounting for sampling design features on BKMR model inference.
• To provide a practical strategy for integrating survey design into BKMR analyses.

Main Methods:

• Generated finite populations with correlated exposures and nonlinear relationships.
• Drew stratified two-stage cluster samples with informative and non-informative selection.
• Compared a naïve, unweighted BKMR approach with a design-aware workflow using resampling and existing software.
• Evaluated methods based on bias, interval width, and empirical 95% coverage.

Main Results:

• Naïve BKMR showed significant bias and under-coverage (0-40%) under informative sampling.
• The design-aware workflow improved empirical coverage to approximately 40-60%.
• Neither method fully achieved nominal coverage, indicating limitations in uncertainty quantification.

Conclusions:

• Accounting for complex survey designs in BKMR is crucial for reducing bias and improving coverage.
• The proposed design-aware workflow offers a practical improvement over standard BKMR for survey data.
• Further methodological advancements are necessary for robust uncertainty quantification in complex survey settings.