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.
Bibliographical noteFunding Information:
Both the first and second author contributed equally. Brian J. Reich is Assistant Professor, Department of Statistics, North Carolina State University, Raleigh, NC 27695 (E-mail: brian email@example.com). Dipankar Bandyopadhyay is Associate Professor, Division of Biostatistics, School of Public Health, University of Minnesota, Minneapolis, MN 55455 (E-mail: firstname.lastname@example.org). Howard D. Bondell is Associate Professor, Department of Statistics, North Carolina State University, Raleigh, NC 27695 (E-mail: email@example.com). The authors thank the Center for Oral Health Research (COHR) at the Medical University of South Carolina, and particularly the study Principal investigator Dr. J. Fernandes for providing the motivating data, and the context behind this work, as well as the editor, associate editor, and referees for their valueable contributions. The research of the authors were supported by Grants P20RR017696-06, R03DE020114, R03DE021762, P01 CA142538-01, R01 ES014843-02, and R01 MH084022-01A1 from the US National Institutes of Health.
- Attachment level
- Dirichlet process
- Kernel convolution