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Abstract:
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Clinical attachment level 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 producing clustered, error-prone ordinal responses representing some ordering of the underlying PD state. In addition, PD progression maybe spatially-referenced. In this talk, we present a Bayesian multivariate probit framework for these ordinal responses, where the cut-point parameters linking the observed ordinal levels to the latent 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. Both simulation studies and application to a real data reveal the advantages of this 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.
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