Spatial skew-normal/independent models for nonrandomly missing clustered data

Clinical studies on periodontal disease (PD) often lead to data collected which are clustered in nature (viz. clinical attachment level, or CAL, measured at tooth-sites and clustered within subjects) that are routinely analyzed under a linear mixed model framework, with underlying normality assumptions of the random effects and random errors. However, a careful look reveals that these data might exhibit skewness and tail behavior, and hence the usual normality assumptions might be questionable. Besides, PD progression is often hypothesized to be spatially associated, that is, a diseased tooth-site may influence the disease status of a set of neighboring sites. Also, the presence/absence of a tooth is informative, as the number and location of missing teeth informs about the periodontal health in that region. In this paper, we develop a (shared) random effects model for site-level CAL and binary presence/absence status of a tooth under a Bayesian paradigm. The random effects are modeled using a spatial skew-normal/independent (S-SNI) distribution, whose dependence structure is conditionally autoregressive (CAR). Our S-SNI density presents an attractive parametric tool to model spatially referenced asymmetric thick-tailed structures. Both simulation studies and application to a clinical dataset recording PD status reveal the advantages of our proposition in providing a significantly improved fit, over models that do not consider these features in a unified way.