A Bayesian functional data model for surveys collected under informative sampling with application to mortality estimation using NHANES

• Published in: Biometrics Vol. 79; no. 2; pp. 1397 - 1408
• Main Authors: Parker, Paul A., Holan, Scott H.
• Format: Journal Article
• Language: English
• Published: United States Blackwell Publishing Ltd 01.06.2023
• Subjects: Bayesian analysis; Data analysis; Data models; functional data analysis; Health surveys; horseshoe prior; Mortality; Multivariate analysis; National Health and Nutrition Examination Survey (NHANES); Physical activity; pseudo‐likelihood; pólya‐Gamma; Surveys; National Health and Nutrition Examination Survey (NHANES); functional data analysis; horseshoe prior; pólya-Gamma; pseudo-likelihood
• ISSN: 0006-341X; 1541-0420
• DOI: 10.1111/biom.13696

Functional data are often extremely high‐dimensional and exhibit strong dependence structures but can often prove valuable for both prediction and inference. The literature on functional data analysis is well developed; however, there has been very little work involving functional data in complex survey settings. Motivated by physical activity monitor data from the National Health and Nutrition Examination Survey (NHANES), we develop a Bayesian model for functional covariates that can properly account for the survey design. Our approach is intended for non‐Gaussian data and can be applied in multivariate settings. In addition, we make use of a variety of Bayesian modeling techniques to ensure that the model is fit in a computationally efficient manner. We illustrate the value of our approach through two simulation studies as well as an example of mortality estimation using NHANES data.