New Statistical Methods for the Analysis of Periodontal Data

Diagnostic (measurement) error is prevalent in medical research 15;21;28;30;35;41;52;67;77;79;87. Clinical studies in periodontology often produce large amounts of data subject to measurement error with potentially complex correlation structures2;3;13;21;35;87. The periodontal probing depth (PPD) and clinical attachment level (CAL) are measures often used to assess periodontal disease status. PPD and CAL are commonly used as covariates or in the calculation of covariates when investigating outcomes of interest in periodontal studies. Current methods of measuring PPD and CAL are prone to measurement error21;35;67;87. It has long been recognized that when regressing on independent variables measured with error, the estimate describing the relationship between outcome and covariate is most often attenuated toward zero, effectively weakening the true quantification of association6;15. The majority of statistical measurement error correction methods either use an available definitive standard for calibration data, or in the absence of a definitive standard, utilize latent class models for assessing relative errors in discrete measurements15;28;30;68;74;77;79 . Although these models are effective, an attractive alternative would account for varying types of correlation while producing equivalent or superior results without the need for the costly and time consuming collection of calibration data or the assumptions needed for latent class models36.;Data from clinical studies in periodontology have also been found to possess serially correlated, spatially correlated, and clustered structure. There are very few accounts in the literature of studies focused on accommodating complex correlation structures in dental data.;This study addresses two issues: (a) correction for classical, nondifferential, additive measurement error in PPD measurements, and (b) adjusting for spatially referenced and clustered dental data. For (a), we considered several models to obtain estimates of periodontal disease incidence in the presense of diagnostic error: 1) the Carlos-Senning and Lu models, developed to investigate bias in caries determination through method of moments ideas, and 2) the misclassification---simulation extrapolation (MC-SIMEX) method, which proposes an algorithm to investigate and correct the effect of measurement error on a naive estimator via simulation13;15;28;71;79. For (b), in order to capture the structure of the data previously not accommodated, we propose two new models extending previous beta regression models: 1) a random effect spatial beta regression model in a Bayesian paradigm which accounts for complex correlation structures for multivariate and spatially-referenced data, and 2) a zero- and one-augmented random effect spatial beta regression model that not only accounts for complex correlation structures, but also accounts for the excess zero and one values present in these data which are not sufficiently modeled by the Beta distribution.;For the correction of measurement error, this study will compare and evaluate the performance of the Carlos-Senning, Lu, MC-SIMEX corrected, and naive models for the estimate of periodontal disease incidence. Through an innovative simulation study, the research will provide a direct basis for model selection under exact incidence and misclassification rates for diseased and non-diseased status. We will compare the bias of the estimator of incidence and corresponding confidence interval coverage from the nonparametric methods with those from the naive estimator that does not accommodate diagnostic error. We propose new methodology in the area of spatial beta regression under a Bayesian framework to adjust for spatially referenced and clustered dental data when assessing the effect of covariates on periodontal disease experience. Bayesian models will be compared with the deviance information criterion, DIC3, as described by Celeux et al.17, the conditional predictive ordinate CPO, and the log pseudo marginal likelihood (LPML) measures.