Abstract
We propose to develop novel Bayesian models, including joint models, for longitudinal data that are
clustered and non-continuous (more specifically, count and ordinal). Using these newly developed
models, we will undertake a comprehensive and refined statistical examination of the total accumulation
of dental caries and fluorosis data obtained from Iowa Fluoride Study participants. Thus, the current
project will fit longitudinal statistical models to caries and fluorosis scores data obtained at ages five,
nine, thirteen, seventeen, and twenty-three, for the participants in this cohort study of Iowa children. The
overall goal will be to study the time-varying (in particular, long-term) and joint effects of various risk
and protective factors for dental caries and fluorosis outcomes.
Iowa Fluoride Study (IFS) is a unique data source of valuable information resulting from a cohort of Iowa
children that began in 1991, led by Dr. Steven Levy, who is a co-I on this proposal. These rich and
complex data allow development of models to study two important oral health conditions, caries and
fluorosis, in childhood, adolescence, and early adulthood. Besides the caries and fluorosis scores, this
dataset has information on a number of important supporting variables, including fluoride, calcium, and
sugared-beverage intakes which can be used as explanatory variables in statistical models. The outcome
measures are non-Gaussian (count and ordinal), and the data on different teeth, surfaces, and zones of a
given individual are correlated due to various shared factors such as toothbrushing behaviors;
additionally, the correlations are spatio-temporal in nature. Overall, off-the-shelf statistical methods are
not able to provide a full understanding of these data. Aided by our collaborative experiences analyzing
previous aspects of IFS data in earlier R03s, we plan to undertake our investigation at a more
comprehensive level. In particular, incorporation of data at age 23 when participants reached early
adulthood will be significant both from scientific and statistical modeling standpoints. In addition, novel
examination of the best choices of the covariate information, the random effects structure leading to
spatio-temporal correlations, development of a joint model for caries and fluorosis outcomes, and their
predictive distributions, and handling of missing data components will be important novel features of this
current proposal.
Thus, the following two sequential aims will be undertaken. We will develop a new longitudinal count
data regression model and use it to analyze the caries data at ages 5, 9, 13, 17, and 23 (Aim 1a). Alongside,
we will develop a new longitudinal ordinal data regression model and use it to analyze the fluorosis data
at ages 9, 13, 17, and 23 (Aim 1b). Finally, we will develop a joint longitudinal model when one response
component is count and the other ordinal, and use it for the caries and fluorosis data together to obtain
more statistically efficient estimators and to establish predictive models for future outcomes given the
covariate profiles of a child (Aim 2).
Algorithms for efficient Bayesian computation will be developed for each of these aims. We will compare
our results to those obtained from existing approaches (whenever they exist) and also results available in
the existing caries and fluorosis literature. Statistical software (OpenBUGS, STAN and/or R
packages/codes) implementing the temporal clustered count data and ordinal analysis methods will be
freely distributed through the PI's web-site and through the Comprehensive R Archive Network.