  Preventing periodontal diseases (PD) and maintaining the structure and
function of teeth are important goals for personal oral care. To understand the
heterogeneity in patients with diverse PD patterns, we develop BAREB, a
Bayesian repulsive biclustering method that can simultaneously cluster the PD
patients and their tooth sites after taking the patient- and site- level
covariates into consideration. BAREB uses the determinantal point process (DPP)
prior to induce diversity among different biclusters to facilitate parsimony
and interpretability. Since PD progression is hypothesized to be
spatially-referenced, BAREB factors in the spatial dependence among tooth
sites. In addition, since PD is the leading cause for tooth loss, the missing
data mechanism is non-ignorable. Such nonrandom missingness is incorporated
into BAREB. For the posterior inference, we design an efficient reversible jump
Markov chain Monte Carlo sampler. Simulation studies show that BAREB is able to
accurately estimate the biclusters, and compares favorably to alternatives. For
real world application, we apply BAREB to a dataset from a clinical PD study,
and obtain desirable and interpretable results. A major contribution of this
paper is the Rcpp implementation of BAREB, available at
https://github.com/YanxunXu/ BAREB.
