A Nonparametric Spatial Model for Periodontal Data With Nonrandom Missingness

Periodontal disease (PD) progression is often quantified by clinical attachment level (CAL) defined as the distance down a tooth's root that is detached from the surrounding bone. Measured at six locations per tooth throughout the mouth (excluding the molars), it gives rise to a dependent data setup. These data are often reduced to a one-number summary, such as the whole-mouth average or the number of observations greater than a threshold, to be used as the response in a regression to identify important covariates related to the current state of a subject's periodontal health. Rather than a simple one-number summary, we set forward to analyze all available CAL data for each subject, exploiting the presence of spatial dependence, nonstationarity, and nonnormality. Also, many subjects have a considerable proportion of missing teeth, which cannot be considered missing at random because PD is the leading cause of adult tooth loss. Under a Bayesian paradigm, we propose a nonparametric flexible spatial (joint) model of observed CAL and the location of missing tooth via kernel convolution methods, incorporating the aforementioned features of CAL data under a unified framework. Application of this methodology to a dataset recording the periodontal health of an African-American population, as well as simulation studies reveal the gain in model fit and inference, and provides a new perspective into unraveling covariate--response relationships in the presence of complexities posed by these data.