A shared spatial model for multivariate extreme-valued binary data with non-random missingness.

Area of Science:

• Biostatistics
• Dental Research
• Epidemiology

Background:

• Periodontal disease (PD) clinical data present statistical challenges including skewed binary outcomes and spatial correlations.
• Non-random missing data in PD studies often correlates with disease status, complicating standard analyses.
• Existing statistical models may not adequately address the complexities of extreme PD progression and spatial dependencies.

Purpose of the Study:

• To develop and validate a statistical model that addresses extreme periodontal disease progression.
• To account for spatial correlations in tooth-level PD status.
• To incorporate non-randomly missing data within a unified analytical framework.

Main Methods:

• A shared (spatial) latent factor model was employed, integrating generalized extreme value regression for extreme PD responses.
• Probit regression was used to model non-randomly missing tooth data.
• A Bayesian inferential framework utilizing within-Gibbs Hamiltonian Monte Carlo techniques was implemented.

Main Results:

• The proposed model demonstrated superior model fit compared to alternative methods.
• The model yielded more precise parameter estimates in simulation studies and real-world PD data analysis.
• The approach effectively handled skewed binary data, spatial dependencies, and non-random missingness.

Conclusions:

• The developed shared latent factor model offers a robust approach for analyzing complex periodontal disease data.
• This method enhances the understanding of extreme PD progression by accurately modeling spatial and missing data issues.
• The Bayesian framework provides a powerful tool for precise estimation in challenging clinical datasets.