Nonparametric spatial models for clustered ordered periodontal data

Dipankar Bandyopadhyay, Antonio Canale
Journal of the Royal Statistical Society. Series C, Applied Statistics 2016, 65 (4): 619-640
Clinical attachment level (CAL) is regarded as the most popular measure to assess periodontal disease (PD). These probed tooth-site level measures are usually rounded and recorded as whole numbers (in mm) producing clustered (site measures within a mouth) error-prone ordinal responses representing some ordering of the underlying PD progression. In addition, it is hypothesized that PD progression can be spatially-referenced, i.e., proximal tooth-sites share similar PD status in comparison to sites that are distantly located. In this paper, we develop a Bayesian multivariate probit framework for these ordinal responses where the cut-point parameters linking the observed ordinal CAL levels to the latent underlying disease process can be fixed in advance. The latent spatial association characterizing conditional independence under Gaussian graphs is introduced via a nonparametric Bayesian approach motivated by the probit stick-breaking process, where the components of the stick-breaking weights follows a multivariate Gaussian density with the precision matrix distributed as G-Wishart. This yields a computationally simple, yet robust and flexible framework to capture the latent disease status leading to a natural clustering of tooth-sites and subjects with similar PD status (beyond spatial clustering), and improved parameter estimation through sharing of information. Both simulation studies and application to a motivating PD dataset reveal the advantages of considering this flexible nonparametric ordinal framework over other alternatives.

Full Text Links

Find Full Text Links for this Article


You are not logged in. Sign Up or Log In to join the discussion.

Related Papers

Remove bar
Read by QxMD icon Read

Search Tips

Use Boolean operators: AND/OR

diabetic AND foot
diabetes OR diabetic

Exclude a word using the 'minus' sign

Virchow -triad

Use Parentheses

water AND (cup OR glass)

Add an asterisk (*) at end of a word to include word stems

Neuro* will search for Neurology, Neuroscientist, Neurological, and so on

Use quotes to search for an exact phrase

"primary prevention of cancer"
(heart or cardiac or cardio*) AND arrest -"American Heart Association"