A nonparametric spatial model for periodontal data with non-random missingness

• Published in: Journal of the American Statistical Association Vol. 108; no. 503
• Main Authors: Reich, Brian J, Bandyopadhyay, Dipankar, Bondell, Howard D
• Format: Journal Article
• Language: English
• Published: United States 01.09.2013
• Subjects: Dirichlet process; Attachment level; Non-normality; Kernel convolution; Non-stationarity
• ISSN: 0162-1459; 1537-274X
• DOI: 10.1080/01621459.2013.795487

Periodontal disease 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 6 locations per tooth throughout the mouth (excluding the molars), it gives rise to a dependent data set-up. 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, non-stationarity, and non-normality. Also, many subjects have a considerable proportion of missing teeth which cannot be considered missing at random because periodontal disease 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 data set 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 presence of complexities posed by these data.