The application of multilevel modelling to dental caries data

Randomized Clinical Trial on Sodium Fluoride with Tricalcium Phosphate

This 24-mo randomized controlled trial was based on a double-blind parallel design, and it compared the effectiveness of 2 fluoride application protocols in arresting dentine caries in primary teeth. Three-year-old children with active dentine caries were recruited and randomly allocated to 2 treatment groups. Children in group A received a semiannual application of a 25% silver nitrate (AgNO₃) solution followed by a commercially available varnish with 5% sodium fluoride (NaF) on the carious tooth surfaces. Children in group B received a semiannual application of a 25% AgNO₃ solution followed by another commercially available varnish with 5% NaF containing functionalized tricalcium phosphate (fTCP). Carious tooth surfaces that were hard when probing were classified as arrested. Intention-to-treat analysis and a hierarchical generalized linear model were undertaken. A total of 408 children with 1,831 tooth surfaces with active dentine caries were recruited at baseline, and 356 children (87%) with 1,607 tooth surfaces (88%) were assessed after 24 mo. At the 24-mo evaluation, the mean (SD) number of arrested carious tooth surfaces per child were 1.8 (2.2) and 2.6 (3.3) for group A (without fTCP) and group B (with fTCP), respectively (P = 0.003). The arrest rates at the tooth surface level were 42% for group A and 57% for group B (P < 0.001). Results of the hierarchical generalized linear model indicated that protocol B (with fTCP) had a higher predicted probability (PP = 0.656) in arresting dentine caries than protocol A (without fTCP; PP = 0.500) when the carious lesions were on buccal/lingual surfaces, were on anterior teeth, had dental plaque coverage, and were in children from low-income families (P = 0.046). In conclusion, protocol B, which applied a 25% AgNO₃ solution followed by a commercially available 5% NaF varnish with fTCP semiannually, is more effective in arresting dentine caries in primary teeth as compared with protocol A, which applied a 25% AgNO₃ solution followed by another commercially available 5% NaF varnish without fTCP semiannually (ClinicalTrials.gov NCT03423797).

Association between grandparent co-residence, socioeconomic status and dental caries among early school-aged children in Japan: A population-based prospective study

Globally many children are living with grandparents, and it has been suggested that grandparent co-residence may be associated with dental caries in infants and toddlers possibly through passive parenting style, accompanied by children's cariogenic behaviors such as feeding sugary sweets. However, little is known about this association in schoolchildren, adjusted for socioeconomic status. Therefore, this study investigates the association between grandparent co-residence, socioeconomic status, and dental caries among schoolchildren. All caregivers of first-grade children (age 6-7 years) in Adachi City, Tokyo, were administered a questionnaire about children's grandparent co-residence status and oral health-related behaviors, and responses were linked with dental examination records conducted by school dentists (N = 3,578). Multilevel Poisson regression analysis was applied to examine the association between grandparent co-residence, socioeconomic status, and dental caries status for each individual tooth, adjusting for potential covariates. The percentage of dental caries experience was higher among children living with grandparents (48.9%) than among children living without grandparents (44.0%). The risk for caries, however, did not differ according to grandparent co-residence status when tooth type, child's age and sex, and parental socio-economic status and structure were adjusted (PR, 1.13; 95%CI, 0.90, 1.42). The association between grandparent co-residence and dental caries among early school-aged children in urban Japan was confounded by socioeconomic status.

Risk of Dental Caries in Primary Teeth with Developmental Defects of Enamel: A Longitudinal Study with a Multilevel Approach

The risk of dental caries seems to be greater in the presence of developmental defects of enamel (DDE). The aim was to determine whether the presence of DDE in the primary teeth of preschool children increases the risk of dental caries in the primary dentition after a period of approximately 2 years. This study was conducted in two stages: baseline (T0) and follow-up (T1). At T0, examinations were conducted for the diagnosis of enamel defects using the DDE index (FDI, 1992), dental caries, and oral hygiene. The participants were allocated to two groups according to the presence (affected) or absence (unaffected) of DDE. At the second evaluation (T1), examinations were performed for the diagnosis of dental caries. Poisson regression analysis with a multilevel approach was used to determine the association between DDE and dental caries. The two levels of the analysis were tooth and child. Among the 339 children (113 affected and 226 unaffected) examined at baseline (T0), 325 were re-examined at follow-up (T1). According to the multilevel analysis, teeth with enamel hypoplasia had a greater risk of having dental caries (RR: 1.99; 95% CI: 1.19-3.33). The risk of caries was greater on posterior teeth (RR: 2.59; 95% CI: 2.18-3.07) and maxillary teeth (RR: 1.48; 95% CI: 1.26-1.75) that had DDE at T0. On the child level, dental caries at T1 was associated with having dental caries at T0 (RR: 1.38; 95% CI: 1.32-1.46). In conclusion, enamel hypoplasia and previous dental caries are risk factors for carious lesions in the primary dentition.

A BAYESIAN HIERARCHICAL SPATIAL MODEL FOR DENTAL CARIES ASSESSMENT USING NON-GAUSSIAN MARKOV RANDOM FIELDS

Research in dental caries generates data with two levels of hierarchy: that of a tooth overall and that of the different surfaces of the tooth. The outcomes often exhibit spatial referencing among neighboring teeth and surfaces, i.e., the disease status of a tooth or surface might be influenced by the status of a set of proximal teeth/surfaces. Assessments of dental caries (tooth decay) at the tooth level yield binary outcomes indicating the presence/absence of teeth, and trinary outcomes at the surface level indicating healthy, decayed, or filled surfaces. The presence of these mixed discrete responses complicates the data analysis under a unified framework. To mitigate complications, we develop a Bayesian two-level hierarchical model under suitable (spatial) Markov random field assumptions that accommodates the natural hierarchy within the mixed responses. At the first level, we utilize an autologistic model to accommodate the spatial dependence for the tooth-level binary outcomes. For the second level and conditioned on a tooth being non-missing, we utilize a Potts model to accommodate the spatial referencing for the surface-level trinary outcomes. The regression models at both levels were controlled for plausible covariates (risk factors) of caries, and remain connected through shared parameters. To tackle the computational challenges in our Bayesian estimation scheme caused due to the doubly-intractable normalizing constant, we employ a double Metropolis-Hastings sampler. We compare and contrast our model performances to the standard non-spatial (naive) model using a small simulation study, and illustrate via an application to a clinical dataset on dental caries.

The clustering effects of surfaces within the tooth and teeth within individuals

The objectives of this study were 1) to provide an estimate of the value of the intraclass correlation coefficient (ICC) for dental caries data at tooth and surface level, 2) to provide an estimate of the design effect (DE) to be used in the determination of sample size estimates for future dental surveys, and 3) to explore the usefulness of multilevel modeling of cross-sectional survey data by comparing the model estimates derived from multilevel and single-level models. Using data from the United Kingdom Adult Dental Health Survey 2009, the ICC and DE were calculated for surfaces within a tooth, teeth within the individual, and surfaces within the individual. Simple and multilevel logistic regression analysis was performed with the outcome variables carious tooth or surface. ICC estimated that 10% of the variance in surface caries is attributable to the individual level and 30% of the variance in surfaces caries is attributable to variation between teeth within individuals. When comparing multilevel with simple logistic models, β values were 4 to 5 times lower and the standard error 2 to 3 times lower in multilevel models. All the fit indices showed multilevel models were a better fit than simple models. The DE was 1.4 for the clustering of carious surfaces within teeth, 6.0 for carious teeth within an individual, and 38.0 for carious surfaces within the individual. The ICC for dental caries data was 0.21 (95% confidence interval [CI], 0.204-0.220) at the tooth level and 0.30 (95% CI, 0.284-0.305) at the surface level. The DE used for sample size calculation for future dental surveys will vary on the level of clustering, which is important in the analysis-the DE is greatest when exploring the clustering of surfaces within individuals. Failure to consider the effect of clustering on the design and analysis of epidemiological trials leads to an overestimation of the impact of interventions and the importance of risk factors in predicting caries outcome.

Can Bayesian models play a role in dental caries epidemiology? Evidence from an application to the BELCAP data set

OBJECTIVES

The aim of this study was to show the potential of Bayesian analysis in statistical modelling of dental caries data. Because of the bounded nature of the dmft (DMFT) index, zero-inflated binomial (ZIB) and beta-binomial (ZIBB) models were considered. The effects of incorporating prior information available about the parameters of models were also shown.

METHODS

The data set used in this study was the Belo Horizonte Caries Prevention (BELCAP) study (Böhning et al. (1999)), consisting of five variables collected among 797 Brazilian school children designed to evaluate four programmes for reducing caries. Only the eight primary molar teeth were considered in the data set. A data augmentation algorithm was used for estimation. Firstly, noninformative priors were used to express our lack of knowledge about the regression parameters. Secondly, prior information about the probability of being a structural zero dmft and the probability of being caries affected in the subpopulation of susceptible children was incorporated.

RESULTS

With noninformative priors, the best fitting model was the ZIBB. Education (OR = 0.76, 95% CrI: 0.59, 0.99), all interventions (OR = 0.46, 95% CrI: 0.35, 0.62), rinsing (OR = 0.61, 95% CrI: 0.47, 0.80) and hygiene (OR = 0.65, 95% CrI: 0.49, 0.86) were demonstrated to be factors protecting children from being caries affected. Being male increased the probability of being caries diseased (OR = 1.19, 95% CrI: 1.01, 1.42). However, after incorporating informative priors, ZIB models' estimates were not influenced, while ZIBB models reduced deviance and confirmed the association with all interventions and rinsing only.

DISCUSSION

In our application, Bayesian estimates showed a similar accuracy and precision than likelihood-based estimates, although they offered many computational advantages and the possibility of expressing all forms of uncertainty in terms of probability. The overdispersion parameter could expound why the introduction of prior information had significant effects on the parameters of the ZIBB model, while ZIB estimates remained unchanged. Finally, the best performance of ZIBB compared to the ZIB model was shown to catch overdispersion in data.

Italian deprivation index and dental caries in 12-year-old children: a multilevel Bayesian analysis

Evidence from the literature has shown that people with a lower socioeconomic status enjoy less good health than people with a higher socioeconomic status. The Italian deprivation index (DI) was used with the aim to evaluate the association between the DMFT index and risk factors for dental caries, including city population and DI. The study included 4,305 12-year-old children living in 38 cities classified by demographic size as small, midsize and large. Zero-inflated negative binomial multilevel regression models were used to assess risk factors for DMFT and to address excess of zero DMFT and overdispersion through a Bayesian approach. The difference in the average level of DMFT among children living in cities with different DI quintile was not statistically significant (p = 0.578). The DI and ln(population), included as city-level fixed effects in the two-level variance components model, were not statistically significant. Consuming sweet drinks on average increased the mean DMFT of a susceptible child, while having a highly educated mother reduced it. Unobserved heterogeneity among cities was detected for the probability to be non-susceptible to caries (city-level variance = 0.26 with 95% credibility interval 0.09-0.57), while no territorial effect was found for the mean DMFT of the susceptible children. Our results suggest that the DI and city population did not play a role in explaining between-city variability. Interventions against social deprivation can be influential on the perception of oral health in Italian 12-year-old children to the extent that they can also affect individual level factors.

Statistical power of multilevel modelling in dental caries clinical trials: a simulation study

Outcome data from dental caries clinical trials have a naturally hierarchical structure, with surfaces clustered within teeth, clustered within individuals. Data are often aggregated into the DMF index for each individual, losing tooth- and surface-specific information. If these data are to be analysed by tooth or surface, allowing exploration of effects of interventions on different teeth and surfaces, appropriate methods must be used to adjust for the clustered nature of the data. Multilevel modelling allows analysis of clustered data using individual observations without aggregating data, and has been little used in the field of dental caries. A simulation study was conducted to investigate the performance of multilevel modelling methods and standard caries increment analysis. Data sets were simulated from a three-level binomial distribution based on analysis of a caries clinical trial in Scottish adolescents, with varying sample sizes, treatment effects and random tooth level effects based on trials reported in Cochrane reviews of topical fluoride, and analysed to compare the power of multilevel models and traditional analysis. 40,500 data sets were simulated. Analysis showed that estimated power for the traditional caries increment method was similar to that for multilevel modelling, with more variation in smaller data sets. Multilevel modelling may not allow significant reductions in the number of participants required in a caries clinical trial, compared to the use of traditional analyses, but investigators interested in exploring the effect of their intervention in more detail may wish to consider the application of multilevel modelling to their clinical trial data.

A model for the analysis of caries occurrence in primary molar tooth surfaces

Recently methods of caries quantification in the primary dentition have moved away from summary 'whole mouth' measures at the individual level to methods based on generalised linear modelling (GLM) approaches or survival analysis approaches. However, GLM approaches based on logistic transformation fail to take into account the time-dependent process of tooth/surface survival to caries. There may also be practical difficulties associated with casting parametric survival-based approaches in a complex multilevel hierarchy and the selection of an optimal survival distribution, while non-parametric survival methods are not generally suitable for the assessment of supplementary information recorded on study participants. In the current investigation, a hybrid semi-parametric approach comprising elements of survival-based and GLM methodologies suitable for modelling of caries occurrence within fixed time periods is assessed, using an illustrative multilevel data set of caries occurrence in primary molars from a cohort study, with clustering of data assumed to occur at surface and tooth levels. Inferences of parameter significance were found to be consistent with previous parametric survival-based analyses of the same data set, with gender, socio-economic status, fluoridation status, tooth location, surface type and fluoridation status-surface type interaction significantly associated with caries occurrence. The appropriateness of the hierarchical structure facilitated by the hybrid approach was also confirmed. Hence the hybrid approach is proposed as a more appropriate alternative to primary caries modelling than non-parametric survival methods or other GLM-based models, and as a practical alternative to more rigorous survival-based methods unlikely to be fully accessible to most researchers.

Order restricted inference for multivariate binary data with application to toxicology

In many applications researchers collect multivariate binary response data under two or more, naturally ordered, experimental conditions. In such situations one is often interested in using all binary outcomes simultaneously to detect an ordering among the experimental conditions. To make such comparisons we develop a general methodology for testing for the multivariate stochastic order between K ≥ 2 multivariate binary distributions. The proposed test uses order restricted estimators which, according to our simulation study, are more efficient than the unrestricted estimators in terms of mean squared error. The power of the proposed test was compared with several alternative tests. These included procedures which combine individual univariate tests for order, such as union intersection tests and a Bonferroni based test. We also compared the proposed test with unrestricted Hotelling's T(2) type test. Our simulations suggest that the proposed method competes well with these alternatives. The gain in power is often substantial. The proposed methodology is illustrated by applying it to a two-year rodent cancer bioassay data obtained from the US National Toxicology Program (NTP). Supplemental materials are available online.

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

One of the most important indicators of dental caries prevalence is the total count of decayed, missing or filled surfaces in a tooth. These count data are often clustered in nature (several count responses clustered within a subject), over-dispersed as well as spatially referenced (a diseased tooth might be positively influencing the decay process of a set of neighbouring teeth). In this article, we develop a multivariate spatial betabinomial (BB) model for these data that accommodates both over-dispersion as well as latent spatial associations. Using a Bayesian paradigm, the re-parameterised marginal mean (as well as variance) under the BB framework are modelled using a regression on subject/tooth-specific co-variables and a conditionally autoregressive prior that models the latent spatial process. The necessity of exploiting spatial associations to model count data arising in dental caries research is demonstrated using a small simulation study. Real data confirms that our spatial BB model provides a superior estimation and model fit as compared to other sub-models that do not consider modelling spatial associations.

The Monitor Practice Programme: is non-invasive management of dental caries in private practice cost-effective?

BACKGROUND

The objective of this research was to assess the efficacy and cost-effectiveness of a non-invasive approach to dental caries management in private dental practice.

METHODS

Private dental practices from a variety of locations in New South Wales were randomly allocated to either non-invasive management of caries, or continue with usual care. Patients were followed for three years and caries incidence assessed. A patient-level decision analytic model was constructed to assess the cost-effectiveness of the intervention at two years, three years, and hypothetical lifetime.

RESULTS

Twenty-two dental practices and 920 patients were recruited. Within the clinical trial there was a significant difference in caries increment favouring non-invasive therapy at both two and three years. Efficacy was independent of age, gender, medical concerns, fluoride history, or previous history of dental caries, in a population of patients attending for treatment in private dental practices, in a variety of locations both urban and rural. Cost per DMFT avoided estimate was A$1287.07 (two years), A$1148.91 (three years) decreasing to A$702.52 in (medium) and A$545.93 (high) risk patients (three years).

CONCLUSIONS

A joint preventive and non-invasive therapeutic approach appears to be cost-effective in patients at medium and high risk of developing dental caries when compared to the standard care provided by private dental practice.

Measurement, analysis and interpretation of examiner reliability in caries experience surveys: some methodological thoughts

Data obtained from calibration exercises are used to assess the level of agreement between examiners (and the benchmark examiner) and/or between repeated examinations by the same examiner in epidemiological surveys or large-scale clinical studies. Agreement can be measured using different techniques: kappa statistic, percentage agreement, dice coefficient, sensitivity and specificity. Each of these methods shows specific characteristics and has its own shortcomings. The aim of this contribution is to critically review techniques for the measurement and analysis of examiner agreement and to illustrate this using data from a recent survey in young children, the Smile for Life project. The above-mentioned agreement measures are influenced (in differing ways and extents) by the unit of analysis (subject, tooth, surface level) and the disease level in the validation sample. These effects are more pronounced for percentage agreement and kappa than for sensitivity and specificity. It is, therefore, important to include information on unit of analysis and disease level (in validation sample) when reporting agreement measures. Also, confidence intervals need to be included since they indicate the reliability of the estimate. When dependency among observations is present [as is the case in caries experience data sets with typical hierarchical structure (surface-tooth-subject)], this will influence the width of the confidence interval and should therefore not be ignored. In this situation, the use of multilevel modelling is necessary. This review clearly shows that there is a need for the development of guidelines for the measurement, interpretation and reporting of examiner reliability in caries experience surveys.

Modeling the long-term cost-effectiveness of the caries management system in an Australian population

OBJECTIVES

The Monitor Practice Program demonstrated that regular monitoring and noninvasive management of dental caries is effective in reducing the incremental DMFT (decayed, missing, and filled teeth) in patients, within the construct of a 3-year randomized clinical trial. This analysis evaluates the long-term cost-effectiveness of the preventive approach underpinning the Caries Management System, used in the general practice setting and modeled to the Australian population.

METHODS

An individual patient-simulation Markov model was developed to compare the long-term costs and outcomes of the Caries Management System versus standard dental care in a hypothetical sample representative of the Australian population. Eight Markov submodels were developed, representing eight molar teeth (excluding wisdom teeth), each consisting of 11 health states simulating the incidence and progression of dental caries, and future interventions such as fillings and crowns. Transition probabilities and costs assigned to health states were based on claims data from the second largest private health insurer in Australia. The economic evaluation was performed from the Australian private dental practitioner perspective. The incremental cost per DMFT avoided was calculated at three time points: 2 years, 3 years, and lifetime. Univariate sensitivity analysis was conducted to test the robustness of the results.

RESULTS

The incremental cost per DMFT avoided at 2 years, 3 years, and lifetime was estimated to be $1287.07, $1148.91, and $1795.06, respectively.

CONCLUSION

The analysis suggests that the Caries Management System is most cost-effective in patients with a high risk of dental caries.

Bayesian modeling of multivariate spatial binary data with applications to dental caries

Dental research gives rise to data with potentially complex correlation structure. Assessments of dental caries yield a binary outcome indicating the presence or absence of caries experience for each surface of each tooth in a subject's mouth. In addition to this nesting, caries outcome exhibit spatial structure among neighboring teeth. We develop a Bayesian multivariate model for spatial binary data using random effects autologistic regression that controls for the correlation within tooth surfaces and spatial correlation among neighboring teeth. Using a sample from a clinical study conducted at the Medical University of South Carolina, we compare this autologistic model with covariates to alternative models to demonstrate the improvement in predictions and also to assess the effects of covariates on caries experience.

The Monitor Practice Programme: is non-invasive management of dental caries in private practice effective?

BACKGROUND

This paper reviews the efficacy of an intensive, preventive-based, non-invasive approach to the management of dental caries within a randomized controlled trial.

METHODS

The primary efficacy measure was the two-year DMFS increment. Changes in risk status, fluoride history, number of emergency visits and toothaches, along with demographic variables such as age, gender, health problems, and the location of the dental practice attended were measured. Regression analysis was undertaken to adjust for potential confounding variables.

RESULTS

Nine hundred and two patients were recruited within 22 dental practices between May 2005 and March 2006. Baseline DMFS did not differ significantly between the control and study groups (p = 0.83). Age (p < 0.001), health status (p = 0.005), baseline risk (p < 0.001) and fluoride history (p < 0.001) were all independent significant predictors of two-year DMFS increment. Gender approached significance (p = 0.08). There were no statistically significant differences between the groups in the incidence of toothaches (p = 0.1) or number of treatment visits required (p = 0.35). There was a significant difference in the two-year incremental DMFS score in the study group compared to the control group (mean difference 2.2; p < 0.001). After adjusting for confounding variables the difference in the DMFS increment between the control and study groups remained significant (mean difference 1.7; p < 0.001).

CONCLUSIONS

The results indicate efficacy of the preventive programme. Efficacy was independent of age, gender, medical concerns, fluoride history, or previous history of dental caries, in a population of patients attending for treatment in private dental practices, in a variety of locations, on a relatively short-term basis (two years). While encouraging, it will be essential that these results are followed over a longer period of time in order to determine whether the benefits are maintained.

The effect of smoking on periodontal health of 15- to 16-year-old adolescents

BACKGROUND

Smoking is a severe risk factor for periodontal health in adults, but data on the effect of smoking on periodontal health in teenage populations are sparse. The aim of this study was to investigate the effect of duration and quantity of smoking on periodontal health in teenagers and possible differences between genders.

METHODS

The oral health of 501 adolescents (15- to 16-year-old boys [n = 258] and girls [n = 243]) was examined. A structured questionnaire about self-reported smoking and health habits was filled out, and bitewing x-rays were taken. Clinical examinations included measuring periodontal indexes, such as visible plaque index, bleeding on probing, root calculus (RC), probing depth, and attachment loss. Results were analyzed by generalized linear logistic regression.

RESULTS

Twenty-five percent of boys and 27% of girls were smokers. The boys and girls who smoked had higher RC values than non-smokers (P <0.001). The adjusted scores for smoking boys and girls were 17.3 (95% confidence interval [CI]: 8.6 to 31.7) and 13.6 (95% CI: 5.5 to 29.7), respectively. The adjusted scores for non-smokers were 10.4 (95% CI: 5.7 to 18.3) and 7.7 (95% CI: 3.3 to 17.3), respectively. Smoking boys and girls also had more periodontal pockets > or =4 mm than non-smokers: the score for boys was 4.6 (95% CI: 2.2 to 9.1), and the score for girls was 5.4 (95% CI: 1.1 to 23.2; P <0.001).

CONCLUSION

Smoking significantly impaired periodontal health in teenagers.