Application of Spatial Covariance Structure to Post-radiation Tooth Destruction

Objective: Compound symmetric covariance structure is commonly used in dental research for modeling tooth-level data within subjects. However, the special relative position of teeth within the mouth may violate the underlying assumptions of compound symmetry and inflate Type I error. This study applied spatial covariance structure to model tooth destruction as a function of tooth-level radiation and compare results to those obtained using compound symmetry covariance matrix. Methods: A three-dimensional coordinate system accounting for tooth position according to arch, proximity to adjacent teeth, and morphology was developed and used to create different spatial covariance matrices. Data from seventy-one subjects who had received head and neck radiotherapy was used. The performance of various spatial covariance structures, including isotropic spatial exponential covariance, anisotropic spatial correlation model with a power correlation function and with an exponential correlation function was evaluated and compared to models with compound symmetry. Akaike's Information Criterion (AIC) was used for model comparison. Results: AIC for compound symmetry, isotropic spatial exponential covariance, anisotropic spatial correlation model with a power correlation function and with an exponential correlation function were 821, 738, 657, and 602, respectively. Estimates of standard errors in the anisotropic model were smaller than those obtained with compound symmetry. Conclusions: Evidence suggests that the three-dimensional spatial covariance matrices were better than compound symmetry for modeling tooth destruction as a function of tooth-level dose and subject-level covariates. Of the spatial approaches, the spatial anisotropic exponential structure produced the best model fit. Moreover, the less biased standard errors improve the accuracy of the subsequent statistical decisions. Supported in part by NIH/NIDCR K23 DE01623