Nonparametric spatial models for clustered ordered periodontal data.

Area of Science:

• Biostatistics
• Periodontology
• Computational Biology

Background:

• Clinical attachment level (CAL) is a primary measure for periodontal disease (PD).
• CAL data are typically ordinal, rounded, and clustered within subjects, leading to potential measurement error and challenges in modeling PD progression.
• PD progression may exhibit spatial dependencies, with adjacent tooth sites showing similar disease status.

Purpose of the Study:

• To develop a flexible Bayesian multivariate probit framework for analyzing ordinal CAL data in periodontal disease assessment.
• To incorporate latent spatial associations into the model to account for the spatial nature of PD progression.
• To improve the accuracy and robustness of PD assessment by addressing data clustering and ordinal properties.

Main Methods:

• Development of a Bayesian multivariate probit model for ordinal responses.
• Implementation of a nonparametric Bayesian approach using a stick-breaking process to model latent spatial associations.
• Utilizing a G-Wishart distribution for the precision matrix within a multivariate Gaussian density for stick-breaking weights.
• Fixing cut-point parameters to link observed ordinal CAL levels to the latent disease process.

Main Results:

• The proposed framework offers a computationally simple, robust, and flexible approach to capture latent disease status.
• The model naturally clusters tooth-sites and subjects with similar PD status, extending beyond simple spatial clustering.
• Improved parameter estimation is achieved through information sharing across sites and subjects.
• Simulations and a real-world PD dataset demonstrated the advantages of this nonparametric ordinal framework over existing methods.

Conclusions:

• The developed Bayesian nonparametric ordinal framework provides a superior method for analyzing periodontal disease progression using CAL data.
• This approach effectively handles the complexities of ordinal, clustered, and spatially correlated data in periodontology.
• The findings suggest this flexible model can lead to more accurate PD assessment and potentially better treatment strategies.