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Bayesian non-response models for categorical data from small areas: an application to BMD and age
Balgobin Nandram1, Ning Liu, Jai Won Choi
1National Center for Health Statistics, CDC 3311 Toledo Road, Hyattsville, MD 20782, USA. balnan@wpi.edu
Statistics in Medicine
|November 27, 2004
Summary
This study uses Bayesian analysis to model bone mineral density (BMD) and age in white females, accounting for missing BMD data. Hierarchical models improve precision by borrowing strength across counties.
Area of Science:
- Biostatistics
- Epidemiology
- Gerontology
Background:
- Bone mineral density (BMD) is crucial for assessing osteoporosis risk, particularly in aging populations.
- Missing BMD data in large surveys like NHANES presents analytical challenges.
- Understanding the relationship between age and BMD is vital for public health interventions.
Purpose of the Study:
- To perform a Bayesian analysis of BMD and age categories in white females using NHANES data.
- To develop and compare ignorable and non-ignorable non-response models for handling missing BMD measurements.
- To utilize hierarchical models for improved inference across 35 counties.
Main Methods:
- Bayesian analysis applied to categorized data on age and bone mineral density.
- Comparison of ignorable and non-ignorable non-response models, with non-ignorable models as generalizations.
- Hierarchical modeling to incorporate data from 35 counties, enabling 'borrowing of strength'.
- Markov chain Monte Carlo (MCMC) methods used for fitting complex models and obtaining posterior densities.
- Bayes factor used to assess the relationship between BMD and age within each county.
Main Results:
- Non-ignorable non-response models provide broader inference compared to ignorable models.
- Hierarchical models significantly reduce variation in estimates by pooling information across counties.
- Sensitivity analysis revealed minor differences in inference based on assumed levels of association between BMD and age.
- Simulation studies indicated minimal differences between baseline ignorable and non-ignorable non-response models.
Conclusions:
- Bayesian hierarchical models effectively address missing data and enhance precision in BMD and age analysis.
- The developed non-ignorable non-response models offer a more robust framework for analyzing complex survey data.
- Findings contribute to a better understanding of age-related bone mineral density changes in white females.
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