Abstract:
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Periodontal studies generate clustered data (viz. clinical attachment level, or CAL, per tooth-site, in mm) that are routinely analyzed using linear mixed models assuming normality of the random effects and errors. However, a careful look reveals that these data might exhibit skewness and tail behavior. In addition, periodontal progression might be spatially referenced, i.e., diseased tooth-sites are proximally located. Also, the presence/absence of a tooth is informative, given the number and location of missing teeth informs about the periodontal health in that region. In this talk, we develop a Bayesian (shared) random effects model for CAL responses and binary presence/absence status of a tooth. The random effects are modeled using a spatial skew-normal/independent (S-SNI) distribution, whose covariance follows a conditionally autoregressive (CAR) density. Both simulation studies and application to a real data examining periodontal health status of Gullah-speaking African-Americans reveal the advantages of our proposition over the available standard alternatives.
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