Modelling tooth emergence data based on multivariate interval-censored data

Bayesian Analysis of Clustered Interval-censored Data

The recording of multiple interval-censored failure times is common in dental research. Modeling multilevel data has been a difficult task. This paper aims to use the Bayesian approach to analyze a set of multilevel clustered interval-censored data from a clinical study to investigate the effectiveness of silver diamine fluoride and sodium fluoride varnish in arresting active dentin caries in Chinese pre-school children. The time to arrest dentin caries on a surface was measured. A three-level random-effects Weibull regression model was used. Analysis was performed with WinBUGS. Results revealed a strong positive correlation (0.596) among the caries lesions’ arrest times on different surfaces from the same child. The software WinBUGS made the above complicated estimation simple. In conclusion, the annual application of silver diamine fluoride on caries lesions, and caries removal before the application, were found to shorten the arrest time.

Analyzing the emergence times of permanent teeth: an example of modeling the covariance matrix with interval-censored data

Based on a data set obtained in a large dental longitudinal study, conducted in Flanders (Belgium), the joint emergence distribution of seven teeth was modeled as a function of gender and caries experience on primary teeth. Besides establishing the marginal dependence of emergence on the covariates, there was also interest in examining the impact of the covariates on the association among emergence times. This allows the establishment of the preferred rankings of emergence and their dependence on covariates. To this end, the covariance matrix was modeled as a function of covariates. Modeling the covariance matrix in this way needs to ensure the positive definiteness of the covariance matrix and it is preferable that the regression parameters of the model are interpretable. The modified Cholesky decomposition of the covariance matrix, as suggested by Pourahmadi, splits up the covariance matrix into two parts where the parameters can be interpreted, given a natural ranking of the responses. This approach was used here taking into account that the emergence times are interval-censored. Hence, we opted for a Bayesian implementation of the data augmentation algorithm.

A Bayesian analysis of amalgam restorations in the Royal Air Force using the counting process approach with nested frailty effects

Survival analysis methods are increasingly used in dental research to measure risk of tooth eruption and caries as well as life spans of amalgam restorations. Analyses have been extended to account for lack of independence in the data, which arises from the clustering of observations within units such as tooth-surfaces, teeth and subjects. There are various analytical strategies and modelling approaches now available to us in dealing with clustered dental data. In this article, the modelling strategy of Cox’s proportional hazards regression is formulated using the counting process approach, which can easily be extended to include time-variant covariates as well as nested random frailty effects. A semi-parametric Bayesian method is presented for the analysis of the proposed model. The methodology is applied to an analysis of nested clustered data on life-span of amalgam restorations in the UK Royal Air Force. These data have previously been analysed using a non-Bayesian approach. The Gibbs sampler, a Markov chain Monte Carlo method, is used to generate samples from the marginal posterior distribution of the parameters of this Bayesian model.

Oral health research: A source for innovative new statistical developments

This article reviews the challenges and opportunities that oral health research may offer to a statistician. To illustrate this, we focus on the Signal Tandmobiel® study, a longitudinal oral health survey that triggered many statistical explorations and developments over the last two decades. For example, non-standard distributions are more the rule than the exception in oral health research. In addition, often measurement error problems need to be addressed. The hierarchical structure of the oral health data also poses non-standard challenges. For instance, caries experience in the mouth is spatially correlated with, however, a specific metric defining the distance between two occurrences. In addition, since caries experience in the context of an epidemiological study is only measured at intervals, analysis of survival involves interval-censoring. Finally, when analyzing a realistic data set in oral health, all the above issues may have to be dealt with simultaneously.

Estimating the distribution of probable age-at-death from dental remains of immature human fossils

In two historic longitudinal growth studies, Moorrees et al. (Am J Phys Anthropol 21 (1963) 99-108; J Dent Res 42 (1963) 1490-1502) presented the "mean attainment age" for stages of tooth development for 10 permanent tooth types and three deciduous tooth types. These findings were presented graphically to assess the rate of tooth formation in living children and to age immature skeletal remains. Despite being widely cited, these graphical data are difficult to implement because there are no accompanying numerical values for the parameters underlying the growth data. This analysis generates numerical parameters from the data reported by Moorrees et al. by digitizing 358 points from these tooth formation graphs using DataThief III, version 1.5. Following the original methods, the digitized points for each age transition were conception-corrected and converted to the logarithmic scale to determine a median attainment age for each dental formation stage. These values are subsequently used to estimate age-at-death distributions for immature individuals using a single tooth or multiple teeth, including estimates for 41 immature early modern humans and 25 immature Neandertals. Within-tooth variance is calculated for each age estimate based on a single tooth, and a between-tooth component of variance is calculated for age estimates based on two or more teeth to account for the increase in precision that comes from using additional teeth. Finally, we calculate the relative probability of observing a particular dental formation sequence given known-age reference information and demonstrate its value in estimating age for immature fossil specimens.

Bayesian latent variable models for spatially correlated tooth-level binary data in caries research

Analysis of dental caries is traditionally based on aggregated scores, which are summaries of caries experience for each individual. A well-known example of such scores is the decayed, missing and filled teeth or tooth surfaces index introduced in the 1930s. Although these scores have improved our understanding of the pattern of dental caries, there are still some fundamental questions that remain unanswered. As an example, it is well believed among dentists that there are spatial symmetries in the mouth with respect to caries, but this has never been evaluated in a statistical sense. An answer to this question requires the analysis to be performed at subunits within the mouth, which necessitates the use of methods for correlated data. We propose a Bayesian generalized latent variable model coupled with an undirected graphical model to investigate the unique spatial distribution of tooth-level caries outcomes in the mouth. Data from the Signal Tandmobiel(®) study in Flanders, a dental longitudinal survey, are used to illustrate the methodology.

Analysis of multilevel grouped survival data with time-varying regression coefficients

Correlated or multilevel grouped survival data are common in medical and dental research. Two common approaches to analyze such data are the marginal and the random-effects approaches. Models and methods in the literature generally assume that the treatment effect is constant over time. A researcher may be interested in studying whether the treatment effects in a clinical trial vary over time, say fade out gradually. This is of particular clinical value when studying the long-term effect of a treatment. This paper proposed to extend the random effects grouped proportional hazards models by incorporating the possibly time-varying covariate effects into the model in terms of a state-space formulation. The proposed model is very flexible and the estimation can be performed using the MCMC approach with non-informative priors in the Bayesian framework. The method is applied to a data set from a prospective clinical trial investigating the effectiveness of silver diamine fluoride (SDF) and sodium fluoride (NaF) varnish in arresting active dentin caries in the Chinese preschool children. It is shown that the treatment groups with caries removal prior to the topical fluoride applications are most effective in shortening the arrest times in the first 6-month interval, but their effects fade out rapidly since then. The effects of treatment groups without caries removal prior to topical fluoride application drop at a very slow rate and can be considered as more or less constant over time. The applications of SDF solution is found to be more effective than the applications of NaF vanish.

Multilevel modelling of clustered grouped survival data using Cox regression model: an application to ART dental restorations

In some controlled clinical trials in dental research, multiple failure time data from the same patient are frequently observed that result in clustered multiple failure time. Moreover, the treatments are often delivered by more than one operator and thus the multiple failure times are clustered according to a multilevel structure when the operator effects are assumed to be random. In practice, it is often too expensive or even impossible to monitor the study subjects continuously, but they are examined periodically at some regular pre-scheduled visits. Hence, discrete or grouped clustered failure time data are collected. The aim of this paper is to illustrate the use of the Monte Carlo Markov chain (MCMC) approach and non-informative prior in a Bayesian framework to mimic the maximum likelihood (ML) estimation in a frequentist approach in multilevel modelling of clustered grouped survival data. A three-level model with additive variance components model for the random effects is considered in this paper. Both the grouped proportional hazards model and the dynamic logistic regression model are used. The approximate intra-cluster correlation of the log failure times can be estimated when the grouped proportional hazards model is used. The statistical package WinBUGS is adopted to estimate the parameter of interest based on the MCMC method. The models and method are applied to a data set obtained from a prospective clinical study on a cohort of Chinese school children that atraumatic restorative treatment (ART) restorations were placed on permanent teeth with carious lesions. Altogether 284 ART restorations were placed by five dentists and clinical status of the ART restorations was evaluated annually for 6 years after placement, thus clustered grouped failure times of the restorations were recorded. Results based on the grouped proportional hazards model revealed that clustering effect among the log failure times of the different restorations from the same child was fairly strong (corr(child)=0.55) but the effects attributed to the dentists could be regarded as negligible (corr(dentist)=0.03). Gender and the location of the restoration were found to have no effects on the failure times and no difference in failure times was found between small restorations placed on molars and non-molars. Large restorations placed on molars were found to have shorter failure times compared to small restorations. The estimates of the baseline parameters were increasing indicating increasing hazard rates from interval 1 to 6. Results based on the logistic regression models were similar. In conclusion, the use of the MCMC approach and non-informative prior in a Bayesian framework to mimic the ML estimation in a frequentist approach in multilevel modelling of clustered grouped survival data can be easily applied with the use of the software WinBUGS.

Effect of caries experience in primary molars on cavity formation in the adjacent permanent first molar

This study sought to address the influence of a sound versus affected first and/or second deciduous molar on the incidence of visible caries experience in the adjacent permanent first molar. Clinical and questionnaire data were obtained from a 6-year prospective oral health screening project in Flanders, Belgium (Signal-Tandmobiel project), where 4,468 children (born in 1989) were examined annually during their primary school time. A multiple survival model allowing for dependent data with possible censoring was applied. The impact of timing of tooth emergence (determining the period at risk), gender, presence of sealants and reported oral hygiene habits was also considered. Cavity formation in permanent first molars was clearly influenced by the status of the adjacent primary molars;the effect of the second deciduous molar was most pronounced. Moreover, if both deciduous molars experienced caries and the child presented with poor oral hygiene, a peak in cavity formation of the permanent first molar 1-2 years after emergence was noticed. On the other hand, if a child presented with good oral hygiene, no peak was observed; caries risk increased slightly over time. No significant benefit from restoring primary molars could be demonstrated, possibly because of methodological limitations.

Multivariate survival analysis for the identification of factors associated with cavity formation in permanent first molars

This investigation used a multivariate survival model, which allowed for dependent caries data with possible censoring, to analyse the impact of timing of tooth emergence, gender and several reported oral hygiene and dietary habits on the incidence of cavity formation in permanent first molars (PFM) in young children. A 6-yr prospective oral health screening project in Flanders, Belgium, provided clinical and questionnaire data on 4,468 children. The results revealed that PFM in children who reported frequent brushing, who had no visible caries experience in the primary dentition, and who presented without occlusal plaque on the PFM had the best survival estimates. Girls had a higher incidence than boys of cavity formation in mandibular molars. The multiple survival analysis confirmed the major impact of the caries status of the deciduous dentition and self-reported oral hygiene habits on the incidence of cavities in permanent first molars.

Long-term patency of saphenous vein and left internal mammary artery grafts after coronary artery bypass surgery: results from a Department of Veterans Affairs Cooperative Study

OBJECTIVES

This study defined long-term patency of saphenous vein grafts (SVG) and internal mammary artery (IMA) grafts.

BACKGROUND

This VA Cooperative Studies Trial defined 10-year SVG patency in 1,074 patients and left IMA patency in 457 patients undergoing coronary artery bypass grafting (CABG).

METHODS

Patients underwent cardiac catheterizations at 1 week and 1, 3, 6, and 10 years after CABG.

RESULTS

Patency at 10 years was 61% for SVGs compared with 85% for IMA grafts (p < 0.001). If a SVG or IMA graft was patent at 1 week, that graft had a 68% and 88% chance, respectively, of being patent at 10 years. The SVG patency to the left anterior descending artery (LAD) (69%) was better (p < 0.001) than to the right coronary artery (56%), or circumflex (58%). Recipient vessel size was a significant predictor of graft patency, in vessels >2.0 mm in diameter SVG patency was 88% versus 55% in vessels </=2.0 mm (p < 0.001). Other positive significant predictors of graft patency were use of aspirin after bypass, older age, lower serum cholesterol, and lowest Canadian Functional Class (p < 0.001 to 0.058).

CONCLUSIONS

The 10-year patency of IMA grafts is better than SVGs. The 10-year patency for SVGs is better and the 10-year patency for IMA grafts is worse than expected. The 10-year patency of SVGs to the LAD is better than that to the right or circumflex. The best long-term predictors of SVG graft patency are grafting into the LAD and grafting into a vessel that is >2.0 mm in diameter.

Impact of caries experience in the deciduous molars on the emergence of the successors

The purpose of this study was to evaluate the effect of caries experience in a primary molar (decayed and/or restored vs. extracted) on the timing of emergence of its successor. Data were obtained from a longitudinal epidemiological study in a sample of 4468 Flemish children. Survival analyses with log-logistic distribution were performed to calculate median emergence ages and 95% confidence intervals (CI); caries experience was added as a covariate. The results indicate that the emergence of the maxillary and mandibular premolars was accelerated by 2-8 months when its predecessor had been decayed and or restored but had not been extracted. Premature loss of maxillary primary molars resulted in a significant acceleration of the emergence of the premolars; this was not observed in the mandible. In conclusion, when considering permanent tooth emergence ages, caries experience in the primary dentition should be taken into account.