TY - JOUR
T1 - A nonparametric spatial model for periodontal data with nonrandom missingness
AU - Reich, Brian J.
AU - Bandyopadhyay, Dipankar
AU - Bondell, Howard D.
PY - 2013/12/16
Y1 - 2013/12/16
N2 - 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.
AB - 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.
KW - Attachment level
KW - Dirichlet process
KW - Kernel convolution
KW - Nonnormality
KW - Nonstationarity
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U2 - 10.1080/01621459.2013.795487
DO - 10.1080/01621459.2013.795487
M3 - Article
AN - SCOPUS:84890056786
VL - 108
SP - 820
EP - 831
JO - Journal of the American Statistical Association
JF - Journal of the American Statistical Association
SN - 0162-1459
IS - 503
ER -