Non-Parametric Spatial Models for Clustered Ordered Periodontal Data
针对牙周病临床附着水平这一有序、聚类且存在空间相关性的数据，提出一种贝叶斯多元probit非参数空间模型，能更好捕捉潜在疾病状态并改进参数估计。
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.