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Preventing periodontal diseases (PD) and maintaining the structure andfunction of teeth are important goals for personal oral care. To understand theheterogeneity in patients with diverse PD patterns, we develop BAREB, aBayesian repulsive biclustering method that can simultaneously cluster the PDpatients and their tooth sites after taking the patient- and site- levelcovariates into consideration. BAREB uses the determinantal point process (DPP)prior to induce diversity among different biclusters to facilitate parsimonyand interpretability. Since PD progression is hypothesized to bespatially-referenced, BAREB factors in the spatial dependence among toothsites. In addition, since PD is the leading cause for tooth loss, the missingdata mechanism is non-ignorable. Such nonrandom missingness is incorporatedinto BAREB. For the posterior inference, we design an efficient reversible jumpMarkov chain Monte Carlo sampler. Simulation studies show that BAREB is able toaccurately estimate the biclusters, and compares favorably to alternatives. Forreal world application, we apply BAREB to a dataset from a clinical PD study,and obtain desirable and interpretable results. A major contribution of thispaper is the Rcpp implementation of BAREB, available athttps://github.com/YanxunXu/ BAREB.

BAREB: A Bayesian repulsive biclustering model for periodontal data