A spatial beta-binomial model for clustered count data on dental caries

Abstract

One of the most important indicators of dental caries prevalence is the total count of decayed, missing or filled (DMF) surfaces in a tooth. These count data are often clustered in nature (several count responses clustered within a subject), over-dispersed, as well as spatially referenced (a diseased tooth might be positively influencing the decay process of a set of neighboring teeth). In this paper, we develop a multivariate spatial Beta-Binomial (BB) model for these data that accommodates both over-dispersion as well as latent spatial associations. Using a Bayesian paradigm, the re-parameterized marginal mean (as well as variance) under the BB framework are modeled using a regression on subject/tooth-specific co-variables and a conditionally autoregressive (CAR) prior that models the latent spatial process. The necessity of exploiting spatial associations to model count data arising in dental caries research is demonstrated using a small simulation study. Real data confirms that our spatial BB model provides a superior estimation and model fit as compared to other sub-models that do not consider modeling spatial associations.

Discrete Distribution Based on Compound Sum to Model Dental Caries Count Data

“…Examples of different scenarios, from different theoretical individuals, of random spells are given in Figure 2 . Dental caries can affect -or contribute to the disease affecting -a set of neighbouring teeth [Bandyopadhyay et al, 2011b], and a long-term effect of dental caries can be the initiation of new carious lesions. This means that, for each spell of caries initiation, new tooth decay can result from this spell until the age of observation.…”

“…Thus, a modification of risk factors at an individual level can lead to the development of new carious lesions, or inversely to the control of the carious disease (no new carious lesions for several years). It is also assumed that a particular tooth experiencing carious lesions tends to affect a set of neighbouring teeth in the same subject [Bandyopadhyay et al, 2011b]. Furthermore, it has been shown that caries development on one tooth could be related to caries development on other teeth, not necessarily in the direct neighbourhood of the initial lesion.…”

Functional CAR Models for Large Spatially Correlated Functional Datasets

“…For the spatial smoothing parameters ${\rho }_k^{\ast }$, a skewed prior is often used in spatial CAR modeling to encourage high spatial correlations, as seen in Diva et al (2007) and Bandyopadhyay et al (2011). Here, we assigned a Beta(1,1) prior based on our exploratory analysis, which is uniform between 0 and 1.…”

A spatial augmented beta regression model for periodontal proportion data

“…This is in stark contrast to traditional spatial referencing in disease mapping, where many responses are observed at each spatial location (Boehm et al , 2013). In addition, unlike other applications where the spatial neighbours are clearly defined by a grid, the spatial neighbourhood structure within the oral cavity is not clearly established (Bandyopadhyay et al , 2010).…”