A spatial beta-binomial model for clustered count data on dental caries

Bayesian modeling of spatially differentiated multivariate enamel defects of the children's primary maxillary central incisor teeth

BACKGROUND

The analysis of dental caries has been a major focus of recent work on modeling dental defect data. While a dental caries focus is of major importance in dental research, the examination of developmental defects which could also contribute at an early stage of dental caries formation, is also of potential interest. This paper proposes a set of methods which address the appearance of different combinations of defects across different tooth regions. In our modeling we assess the linkages between tooth region development and both the type of defect and associations with etiological predictors of the defects which could be influential at different times during the tooth crown development.

METHODS

We develop different hierarchical model formulations under the Bayesian paradigm to assess exposures during primary central incisor (PMCI) tooth development and PMCI defects. We evaluate the Bayesian hierarchical models under various simulation scenarios to compare their performance with both simulated dental defect data and real data from a motivating application.

RESULTS

The proposed model provides inference on identifying a subset of etiological predictors of an individual defect accounting for the correlation between tooth regions and on identifying a subset of etiological predictors for the joint effect of defects. Furthermore, the model provides inference on the correlation between the regions of the teeth as well as between the joint effect of the developmental enamel defects and dental caries. Simulation results show that the proposed model consistently yields steady inferences in identifying etiological biomarkers associated with the outcome of localized developmental enamel defects and dental caries under varying simulation scenarios as deemed by small mean square error (MSE) when comparing the simulation results to real application results.

CONCLUSION

We evaluate the proposed model under varying simulation scenarios to develop a model for multivariate dental defects and dental caries assuming a flexible covariance structure that can handle regional and joint effects. The proposed model shed new light on methods for capturing inclusive predictors in different multivariate joint models under the same covariance structure and provides a natural extension to a nested hierarchical model.

A new regression model for overdispersed binomial data accounting for outliers and an excess of zeros

Binary outcomes are extremely common in biomedical research. Despite its popularity, binomial regression often fails to model this kind of data accurately due to the overdispersion problem. Many alternatives can be found in the literature, the beta-binomial (BB) regression model being one of the most popular. The additional parameter of this model enables a better fit to overdispersed data. It also exhibits an attractive interpretation in terms of the intraclass correlation coefficient. Nonetheless, in many real data applications, a single additional parameter cannot handle the entire excess of variability. In this study, we propose a new finite mixture distribution with BB components, namely, the flexible beta-binomial (FBB), which is characterized by a richer parameterization. This allows us to enhance the variance structure to account for multiple causes of overdispersion while also preserving the intraclass correlation interpretation. The novel regression model, based on the FBB distribution, exploits the flexibility and large variety of the distribution's possible shapes (which includes bimodality and various tail behaviors). Thus, it succeeds in accounting for several (possibly concomitant) sources of overdispersion stemming from the presence of latent groups in the population, outliers, and excessive zero observations. Adopting a Bayesian approach to inference, we perform an intensive simulation study that shows the superiority of the new regression model over that of the existing ones. Its better performance is also confirmed by three applications to real datasets extensively studied in the biomedical literature, namely, bacteria data, atomic bomb radiation data, and control mice data.

Discrete Distribution Based on Compound Sum to Model Dental Caries Count Data

Methods for analysing dental caries and associated risk indicators have evolved considerably in recent decades. The use of zero-inflated or hurdle models is increasing so as to take account of the decayed, missing, and filled teeth (DMFT) distribution, which is positively skewed and has a high proportion of zero scores. However, there is a need to develop new statistical models that involve pragmatic biological considerations on dental caries in epidemiological surveys. In this paper, we show that the zero-inflated and the hurdle models can both be expressed as a compound sum. Using the same compound sum, we then present the generalized negative binomial (GNB) distribution for dental caries count data, and provide a numerical application using the data of the EPIPAP study. The GNB model generates the best score functions while handling the lifetime dental caries disease process better. In conclusion, the GNB model suits the nature of some count data, in particular when structural zeros are unlikely to occur and when several latent spells can lead to new countable events. For these reasons, the use of the GNB distribution appears to be relevant for the modelling of dental caries count data.

Functional CAR models for large spatially correlated functional datasets

We develop a functional conditional autoregressive (CAR) model for spatially correlated data for which functions are collected on areal units of a lattice. Our model performs functional response regression while accounting for spatial correlations with potentially nonseparable and nonstationary covariance structure, in both the space and functional domains. We show theoretically that our construction leads to a CAR model at each functional location, with spatial covariance parameters varying and borrowing strength across the functional domain. Using basis transformation strategies, the nonseparable spatial-functional model is computationally scalable to enormous functional datasets, generalizable to different basis functions, and can be used on functions defined on higher dimensional domains such as images. Through simulation studies, we demonstrate that accounting for the spatial correlation in our modeling leads to improved functional regression performance. Applied to a high-throughput spatially correlated copy number dataset, the model identifies genetic markers not identified by comparable methods that ignore spatial correlations.

Adaptive pair-matching in randomized trials with unbiased and efficient effect estimation

In randomized trials, pair-matching is an intuitive design strategy to protect study validity and to potentially increase study power. In a common design, candidate units are identified, and their baseline characteristics used to create the best n/2 matched pairs. Within the resulting pairs, the intervention is randomized, and the outcomes measured at the end of follow-up. We consider this design to be adaptive, because the construction of the matched pairs depends on the baseline covariates of all candidate units. As a consequence, the observed data cannot be considered as n/2 independent, identically distributed pairs of units, as common practice assumes. Instead, the observed data consist of n dependent units. This paper explores the consequences of adaptive pair-matching in randomized trials for estimation of the average treatment effect, conditional the baseline covariates of the n study units. By avoiding estimation of the covariate distribution, estimators of this conditional effect will often be more precise than estimators of the marginal effect. We contrast the unadjusted estimator with targeted minimum loss based estimation and show substantial efficiency gains from matching and further gains with adjustment. This work is motivated by the Sustainable East Africa Research in Community Health study, an ongoing community randomized trial to evaluate the impact of immediate and streamlined antiretroviral therapy on HIV incidence in rural East Africa.

SOPROLIFE system: an accurate diagnostic enhancer

Objectives. The aim of this study was to evaluate a light-emitting diode fluorescence tool, the SOPROLIFE light-induced fluorescence evaluator, and compare it to the international caries detection and assessment system-II (ICDAS-II) in the detection of occlusal caries. Methods. A total of 219 permanent posterior teeth in 21 subjects, with age ranging from 15 to 65 years, were examined. An intraclass correlation coefficient (ICC) was computed to assess the reliability between the two diagnostic methods. Results. The results showed a high reliability between the two methods (ICC = 0.92; IC = 0.901–0.940; P < 0.001). The SOPROLIFE blue fluorescence mode had a high sensitivity (87%) and a high specificity (99%) when compared to ICDAS-II. Conclusion. Compared to the most used visual method in the diagnosis of occlusal caries lesions, the finding from this study suggests that SOPROLIFE can be used as a reproducible and reliable assessment tool. At a cut-off point, categorizing noncarious lesions and visual change in enamel, SOPROLIFE shows a high sensitivity and specificity. We can conclude that financially ICDAS is better than SOPROLIFE. However SOPROLIFE is easier for clinicians since it is a simple evaluation of images. Finally in terms of efficiency SOPROLIFE is not superior to ICDAS but tends to be equivalent with the same advantages.

A spatial augmented beta regression model for periodontal proportion data

Clinical dental research generates large amounts of data with a potentially complex correlation structure from measurements recorded at several sites throughout the mouth. Clinical attachment level (CAL) is one such measure popularly used to assess the periodontal disease (PD) status. We model the proportion of sites for each tooth-type (i.e., incisor, canine, pre-molar and molar) per subject that exhibit moderate to severe PD. Disease free and highly diseased tooth-sites cause these proportion responses to lie in the closed interval [0, 1]. In addition, PD may be spatially referenced, i.e., the disease status of a site is influenced by its neighbours. While beta regression can assess the covariate-response relationship for proportion data, its support in the interval (0, 1) impairs its ability to account for the observed proportions at zero and one. In contrast to ad hoc transformations that confine responses to (0, 1), we develop a framework that augments the beta density with non-zero masses at zero and one while also controlling for spatial referencing. Our approach is Bayesian and is computationally amenable to available software. A simulation study evaluates estimation of regression effects in scenarios of varying sample size, degree of spatial dependence and response transformations. Application to real PD data provide insights into assessing covariate effects on proportion responses.

From Mouth-level to Tooth-level DMFS: Conceptualizing a Theoretical Framework

OBJECTIVE

There is no dearth of correlated count data in any biological or clinical settings, and the ability to accurately analyze and interpret such data remains an exciting area of research. In oral health epidemiology, the Decayed, Missing, Filled (DMF) index has been continuously used for over 70 years as the key measure to quantify caries experience. The DMF index projects a subject's caries status using either the DMF(T), the total number of DMF teeth, or the DMF(S), counting the total DMF teeth surfaces, for that subject. However, surfaces within a particular tooth or a subject constitute clustered data, and the DMFS mostly overlook this clustering effect to attain an over-simplified summary index, ignoring the true tooth-level caries status. Besides, the DMFT/DMFS might exhibit excess of some specific counts (say, zeroes representing the set of relatively disease-free carious state), or can exhibit overdispersion, and accounting for the excess responses or overdispersion remains a key component is selecting the appropriate modeling strategy.

METHODS & RESULTS

This concept paper presents the rationale and the theoretical framework which a dental researcher might consider at the onset in order to choose a plausible statistical model for tooth-level DMFS. Various nuances related to model fitting, selection and parameter interpretation are also explained.

CONCLUSION

The author recommends conceptualizing the correct stochastic framework should serve as the guiding force to the dental researcher's never-ending goal of assessing complex covariate-response relationships efficiently.