Improving teeth aesthetics using a spatially shared-parameters model for independent regular lattices

An important feature in dentistry is teeth gloss. During an intervention, the doctor applies a resin and a polishing to achieve the lowest roughness and the highest gloss possible. This work aims to evaluate the effect of four polishing protocols in teeth surface roughness and gloss when combined with two different resins and eventually indicate the best combination (treatment). An atomic force microscope is used for measuring the in vitro roughness of a dental surface surrogate. We consider a shared parameters approach for linking the information carried by those two correlated variables. The model fitted to the gloss considers some features of the roughness, namely the information conveyed by a set of spatial structured random effects, specific to each treatment, and the within treatment variance, which allows interpreting how the heterogeneity and the variability of the surface roughness impacts a tooth gloss. The statistical model here developed is an alternative to the "traditional" two-way ANOVA used in dentistry journals. The results, using the recent R-NIMBLE package in R, show that variability characteristics of the surface's roughness are central for explaining differences among the gloss achieved after each treatment and not just the mean roughness of that surface.