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Bayesian Network Modeling in Discovering Risk Factors of Dental Caries in Three-Year-Old Children.


Dental caries is a worldwide problem. According to Global Burden of Disease, untreated caries in deciduous teeth is the 10th most prevalent condition which affects about 621 million children [1].

Dental caries has been recently included in a group of non-communicable diseases because it is caused by behaviorally based risk factors. Several general and local aspects promoting the development of carious lesions were identified. Among general risk factors, the most frequently indicated were gender, age, ethnicity, geographic location, and socioeconomic background. Other variables were the pattern of oral hygiene, consumption of sugar, frequency of dental checkups, and use of fluorides.

Several studies were conducted to establish associations between the prevalence and experience of dental caries and a particular risk factor. Most of these studies adopted classical statistical methods.

Bayesian networks [2] are graphical models that are based on sound rules of the probability theory. They offer a framework for explicit modeling of probabilistic relationships which can be elicited from domain experts or learned directly from the data by means of existing algorithms. Learning Bayesian network algorithms allow to discover relationships between modeled variables which are represented by means of an acyclic directed graph. The graphical structure of Bayesian networks offers an additional insight into the modeled domain while reasoning with these models provides an explanation of their outcomes. The Bayesian network modeling proved to be a powerful tool for modeling complex uncertain knowledge. It was successfully applied in solving diagnostic or prognostic problems in medicine [3].

It was also proved that the Bayesian network modeling could be useful in epidemiological research [4].

However, the Bayesian network modeling was applied only in a limited number of studies on dental caries [5-10].

This paper presents the capabilities of Bayesian network model analysis in discovering risk factors of dental caries in three-year-old children. The analysis was conducted on the basis of the questionnaire data and resulted in the development of a probabilistic graphical model used to investigate dependencies among the features gathered in the surveys on dental caries.



Our analysis was based on the retrospective data collected between 2002 and 2003 from 255 children (108 girls and 147 boys) aged between 36 and 48 months (mean age of 43 months) in randomly selected kindergartens in Bialystok and in small towns and villages in the Podlasie region, Poland. That data was previously analyzed by one of the authors (JB) [11].

The collected data contained a dental examination and a self-administered questionnaire consisting of two parts. The first part (30 questions) was developed at the Department of Epidemiology, Medical University of Lodz, Poland, for the purpose of the Polish National Oral Health Survey; the second part (4 questions) was developed by the authors. The dental status was assessed with the dmft (the dmft index stands for decayed, missing, and filled teeth) index with a plane dental mirror and a periodontal probe according to the WHO guidelines [12].

Each tooth was described as caries-free, decayed (d), extracted due to caries (m) or with dental filling (f).

The questionnaire was filled out by 255 parents or guardians. The questionnaire contained questions of socioeconomic, demographic, and medical nature.

The collected data allowed us to analyze the impact of various socioeconomic factors such as habits, wealth, or the level of education on the condition of teeth in three-year-old children.

Based on the dental examination results, we divided the studied sample into three groups depending on the severity of dental caries:

* all teeth were healthy (healthy teeth)

* there were one up to three teeth with dental caries (moderate dental caries)

* there were more than four teeth with dental caries (significant dental caries). The questionnaire data showed that 18.4% of examined children had healthy teeth, 35.3% had moderate dental caries, and 46.3% were classified as children with significant dental caries.

The characteristics of our data with respect to gender and dental caries status were shown in Table 1.


To analyze the data, we have applied the Bayesian network modeling that is a multivariate approach incorporating several variables in one framework. The Bayesian network consists of two parts: (1) a graphical structure modeling variables by means of nodes and probabilistic relationships among these variables represented by directed arcs; (2) conditional probability distributions that quantify relationships among neighboring variables. To explain the approach, we have created a simplified Bayesian network that models Body Mass Index (BMI), Income, and Smoking as risk factors of Diabetes and Number of teeth as an effect of Diabetes. An example Bayesian network model was presented in Fig. 1. The arcs between the nodes in Fig. 1 represent probabilistic relationships, for example, the arc between BMI and Diabetes indicates that abnormal BMI can lead to Diabetes. This relationship was also quantified by a conditional probability distribution P (Diabetes/'BMI, Income) and was presented in Fig. 1.

Once a Bayesian network model has been built, we can perform a reasoning, i.e. given observed variables in the model we can calculate a posterior probability distribution that can be further interpreted as a quantitative risk value. For example, we could calculate the posterior probability of Diabetes given observed values of the nodes BMI, and Income:

* P (Diabetes = yes | BMI = normal, Income = high) = 0.08,

* P (Diabetes = yes | BMI = overweight_or_obese, Income = low) = 0.32.

The Bayesian network modeling approach allows making in-depth analyses e.g. on the strength of influence or the diagnostic value.

The strength of influence is calculated on the basis of differences between the a posterior marginal probability of a child node, as a parent node changes [13].

The higher value, the stronger dependency between two variables was observed. In our example model, we have identified the following pairs of nodes with the highest strength of influence:

* Diabetes and Number of teeth

* BMI and Diabetes.

The diagnostic value allows analyzing the impact of observable variables on a target variable. Target variables are defined as variables with a diagnostic or explanatory interest.

In our example Bayesian network, we set the Diabetes as a target variable.

The assessment of diagnostic value is based on the cross-entropy between each of the observed variables and the target variable.

The higher diagnostic value we observed the bigger impact the variable had on the target variable. Fig. 2 shows a list of observable variables ranked by their diagnostic value.

The left-hand side of Fig. 2 presents two possible states of Diabetes.

The right-hand side of Fig. 2 shows the model variables sorted by their diagnostic value descending. The example shows that the BMI has the biggest impact on Diabetes.

A graphical structure and numerical parameters of Bayesian networks can be learned from data, elicited from expert knowledge or both. Bayesian network models learned from data are the examples of an unsupervised machine learning method.

This approach allows dealing with large data sets with thousands of variables. In this article, we described a model that was founded on data with some expert knowledge introduced.

Our Bayesian network models were created and tested using SMILE, an inference engine, and GeNIe, a development environment for reasoning in graphical probabilistic models, both developed at the Decision Systems Laboratory, University of Pittsburgh, and available at http://www.bayesfusion. co m.


Learning the Bayesian network model

The collected data and the expert knowledge allowed us to build a Bayesian network model.

The data contained 255 observations and 33 variables. Our model was built based on 33 variables: 31 variables were of socioeconomic and demographic nature while two variables were of a medical nature and represented dental caries (dental caries and dental filling).

The discrete type of studied data allowed us to use a PC algorithm [14] to learn a Bayesian network structure. The resulting model includes 33 nodes, 39 arcs, and 2,037 numerical parameters. The PC algorithm identified relationships between the variables as presented in Fig. 3.

The Bayesian network modeling allows combining objective data with expert knowledge. While building the model, we have focused on time tiers to avoid a situation where a future event depends on the past one. For example, dental caries cannot influence breast-feeding, whereas dental caries may possibly be caused by breast-feeding.

In our model we have identified the following pairs of nodes with the highest strength of influence:

* brushing teeth by a child and time of day toothbrush (child),

* education and deepening knowledge (guardian),

* complete family and employment (father)

* the guardian cleans or holds the child's hand and the guardian observes the child while cleaning,

* falling asleep with a bottle and used dental facilities (guardian).

Fig. 4 shows a list of variables ranked by their diagnostic value.

The left-hand side of Fig. 4 presents the levels of dental caries.

The right-hand side of Fig. 4 shows the model variables sorted by their diagnostic value descending. The variables with the highest diagnostic value in our model are:

* falling asleep with a bottle,

* since the oral cavity is cleaned,

* brushing teeth by a child.

Bayesian network models allow to observe how a change in an observable variable influences the probability distribution of the variable in question. Fig. 5 and Fig. 6 show a part of the model presented in Fig. 3. In our analysis, we have focused on six variables with the highest diagnostic value. Fig. 5 shows our model with two observed variables, i.e., high consumption of sweets and secondary education level of a guardian. In this case, the posterior probability of lack of dental caries is equal to 19%. Fig. 6 shows our model with the observed low consumption of sweets and high education of the guardian. In this scenario, the posterior probability for the state lack of dental caries is equal to 26%.

We would like to note that the above observations propagate to other nodes in the model. Based on the subset of the model presented in Fig. 5 and Fig. 6, it can be observed that the posterior probability of the variable Falling asleep with a bottle for the state no has changed from 53% to 79%.


Our study showed that three-year-old children presented a very high level of dental caries. Such condition is typical for Polish children. A recent epidemiological survey revealed that only 20% of Polish children aged between 5 and 12 were caries-free [15] while for the European countries the World Health Organization (WHO) aimed at no more than 20% of six-year-olds suffering from dental caries by 2020.

The possibility of reasoning under uncertainty makes the Bayesian network modeling a powerful analytic tool for a multifactorial disease like dental caries. By learning the model from the data, we have discovered relationships between the variables. Such analysis also reduces the bias associated with small and non-randomized samples [6].

Bagihska, while analyzing the same data [11], identified a relationship between the gender and the condition of teeth, whereas our Bayesian network analysis indicated that the dependency between the two variables was weak. According to Bagihska [11], there were three main risk factors of the caries prevalence: age since the oral cavity was cleaned, falling asleep with a bottle and consumption of sweets. Our Bayesian network model indicated that falling asleep with a bottle and age since the oral cavity is cleaned had a significant impact on dental caries. Furthermore, according to our model, the frequency of sugary food consumption at the age of three years seemed to be less important for the development of dental caries in children of this age. However, improper eating habits at the age of three may determine the future progression of the disease.

The Bayesian network analysis clearly indicated which children were at a great risk of developing dental caries. Based on our results, a simple questionnaire could be developed and used during routine pediatric check-ups to identify the most exposed children and to provide them adequate prevention strategies. Our model also showed how changes in daily routine can influence the probability of the disease. A modification of only one aspect (e.g. guardian education) decreased the chances of feeding a child during the sleep by several percentages, thereby reduced a risk of caries development. Such information is of a great educational value. Less educated parents of preschool children probably have to be more motivated to avoid risky behaviours.

To our knowledge, there are only a few studies that applied Bayesian network modeling to evaluate dental caries risk factors and dental status. Kemoli and Chepkwony [10] found this type of modeling suitable to discriminate specific factors of early childhood caries in Kenyan three- to six-year-old children. Similarly to us, they concluded that dietary habits were not significant in predicting the levels of the dmft index and that parents' education and employment status influenced child's oral condition. However, contrary to our results, they found boys being more prone to caries than girls. Wen et al. [5] used a Bayesian network analysis to establish the influence of household variables on the prevalence of dental caries in siblings in a high-risk population. They confirmed that this approach was more accurate than a generalized linear mixed model. Bhatia et al. [7] proposed using Bayesian networks to build a decision-making tool for dentists that would assist them in choosing the best treatment plan for dental caries.


The aim of this study was to use probabilistic graphical models to determine the risk factors of dental caries in three-year-old children. We have applied the real-world data to learn a Bayesian network model. The process of Bayesian network model building was additionally assisted by a dental expert. The results of our analysis suggest that the dietary and hygiene habits in the first three years of life have the most significant impact on the occurrence of dental caries in three-year-old children.


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Laguna W. (*1, A-F), Baginska J. (2, B C E F), Onisko A. (1, A, C-F)

(1.) Bialystok University of Technology, Faculty of Computer Science, Poland

(2.) Medical University of Bialystok, Department of Dentistry Propaedeutics, Poland

(A)- Conception and study design; (B) - Collection of data; (C) - Data analysis; (D) - Writing the paper; (E)- Review article; (F) - Approval of the final version of the article; (G) - Other (please specify)


(*) Corresponding author

Wojcich Laguna

Bialystok University of Technology, Faculty of Computer Science, Poland


Received: 19.03.2019

Accepted: 17.04.2019
Table 1. The intensity of dental caries in the studied group

                 Healthy teeth  Moderate dental  Advanced dental caries
       Quantity                 caries

                 Qty (%)        Qty (%)          Qty (%)

Girls  108       21 (19.4%)     44 (40.7%)        43 (39.8%)
Boys   147       26 (17.7%)     46 (31.3%)        75 (51.0%)
Total  255       47 (18.4%)     90 (35.3%)       118 (46.3%)
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Author:Laguna, W.; Baginska, J.; Onisko, A.
Publication:Progress in Health Sciences
Date:Jun 1, 2019
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