2000 Mathematics Subject Classification: 62P10, 62J12.Caries is the most widespread dental disease around the world. Thus, caries prevalence and intensity are repeatedly studied. Epidemiological research has been conducted covering 1636 persons from Bulgaria. A statistical model for the number of teeth damaged from caries, depending on the age and sex of the patients has been considered in this work.The research was partially supported by appropriated state funds for research allocated to Sofia University (contract 112/2010), Bulgaria

Bonev, Boyko

Daskalova, Nina

Bulgarian Digital Mathematics Library at IMI-BAS

Pliska Stud. Math. Bulgar. 20 (2011), 39–44STUDIA MATHEMATICABULGARICAABOUT THE ORAL HEALTH OF BULGARIANPOPULATION OVER 20 YEARS OLDNina Daskalova1, Boyko BonevCaries is the most widespread dental disease around the world. Thus, cariesprevalence and intensity are repeatedly studied. Epidemiological researchhas been conducted covering 1636 persons from Bulgaria. A statistical modelfor the number of teeth damaged from caries, depending on the age and sexof the patients has been considered in this work.1. IntroductionAny medical condition disturbs to some extent the individual’s capacity, comfortand ability to perform daily activities. This applies fully to the diseases oftissues and organs in the oral cavity and maxillofacial area. Caries is the mostwidespread dental disease around the world. Thus, caries prevalence and intensityare repeatedly studied. Progress of caries is characterized by irreversibility. Afterthe onset of cavitation in the hard tooth tissue process becomes irreversible.Treatment includes stationing, suspending the progress, and recovering the formand function of teeth through a variety of materials.Intensity (DMF-T) of caries is a key indicator for assessing the condition ofdental hard tissues. It shows the average number of teeth affected by caries ofone person from the study group. It is the sum of damaged by caries teeth, not1The research was partially supported by appropriated state funds for research allocated toSofia University (contract 112/2010), Bulgaria.2000 Mathematics Subject Classification: 62P10, 62J12.Key words: epidemiological research, caries, statistical data analysis, generalized linearmodels, logistic regression.40 Nina Daskalova, Boyko Bonevtreated (DECAY), missing due to caries teeth (MISSING) and treated, obturated,teeth (FILLING).An epidemiological survey conducted by Yaneva [5] in 1989 showed that DMF-T for the population over 20 years in Bulgaria is 15.9. A survey of dental health ofadults by Yolov [6] in 1996, showed that the DMF-T in those over 60 years of ageis 24.25. Boteva, Vassileva and Karova [1] in a comparative study of dental statusamong the urban population registered a significant increase in the incidence ofcaries and the number of extracted teeth for a twelve year period in male andfemale individuals from 18 to 55 years.Epidemiological research has been conducted covering 1636 persons (894 menand 741 women) over age 20 from Bulgaria. The examined individuals havebeen selected randomly from six regional cities, including Sofia and six smallermunicipalities, for representativeness. The survey consist of detailed clinicalexamination of the teeth and standardized interview in accordance with WHOrecommendations for conducting epidemiological studies since 1997. Projectparticipants have been asked to complete a standard questionnaire to determinetheir socio-demographic and health status. A statistical model for the numberof teeth damaged from caries, depending on the age and sex of the patients hasbeen considered in our work.2. Descriptive Statistics and Preliminary Data AnalysisPreliminary data analysis has been performed including several steps: detectionand management of missing data; data transformations; examination of summarystatistics. Later, an appropriate statistical model has been looked for consideringlinear and generalized linear models and particularly logistic regression. Theanalysis has been conducted in R (see [2, 4, 3]).A boxplot of DMF-T by age shows some differences between the levels of age.It is seen that the number of caries teeth increases with age. ANOVA test showsthese differences are statistically significant with very small p-value (< 2e−16) ofthe F-test. The chi-square test rejects the null hypothesis of independence withp-value = 1.56e− 11. The boxplot by gender also shows some difference betweenmen and women and the number for women exceeds the number for men. Herethe p-values of ANOVA (< 2e−16) and chi-square (0.00678) tests are also small.About the Oral Health of Bulgarian Population 4120+ 30+ 40+ 50+ 60+ 70+051015202530ageDMF−TFigure 1: DMF-T by age3. The Logistic ModelGeneralized linear models (GLM) is one of the generalisations of traditional linearmodels. If we consider a single response variable y and some candidate predictorvariables x1, x2, . . . ,xp, the distribution of y can only depend on the predictorsthrough a single linear function: η = b0+b1x1+b2x2+ . . .+bpxp The distributionbelongs to the GLM family of distributions, where there may (or may not) be anunknown scale parameter. There are a number of distributions in the GLM family.It is assumed that the linear predictor determines the mean of the response. Themean is assumed to be a (monotone) function of the linear predictor and theinverse of this function is called the link function. One of the link functionscorresponding to the binomial distribution is the logistic link. For the binomialdistribution the response is taken as the proportion of cases responding. Thusthe mean lies between 0 and 1 and the logistic link usesµ =exp(η)1 + exp(η), η = logµ1− µA logistic regression model has been estimated using generalized linear models(the glm function) in R. The complete model isglm(formula = num.nh.bin ∼ age * gend, family = "binomial", data = data.teeth),where the response num.nh.bin is binomial (the number of unhealthy vs. healthyteeth) and predictors are age (continuous) and gender (factor) variables.The coefficient of the interaction effect age:gend appears insignificant withp-value 0.152, so a second model with parallel slopes has been considered. Thesummary is given below.42 Nina Daskalova, Boyko Bonevmale female051015202530genderDMF−TFigure 2: DMF-T by genderCall:glm(formula = num.nh.bin ∼ age + gend, family = "binomial", data = data.teeth)Coefficients:Estimate Std.Error z-value Pr(>|z|)(Intercept) -2.0403568 0.0337784 -60.40 <2e-16 ***age 0.0478705 0.0007756 61.72 <2e-16 ***gendfemale 0.3756451 0.0184230 20.39 <2e-16 ***---Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1(Dispersion parameter for binomial family taken to be 1)Null deviance: 15154 on 1634 degrees of freedomResidual deviance: 10404 on 1632 degrees of freedom(1 observation deleted due to missingness)AIC: 16049Number of Fisher Scoring iterations: 4This gives coefficients bm0= −2.04, bm1= 0.05 for men, and bf0= −2.04 +0.37 = −1.67, bf1= 0.05 for women.The residual deviance is too large (P (χ21632> 10404) ≈ 0), so the logisticregression may not provide the best fit. Other models may fit better, thoughfrom the scatterplot of the data it is clear that there is great variance in it andmost models will suffer from lack of fit.Nevertheless, it could be seen from the summary that age is statisticallysignificant in the logistic regression for the DMF-T and some conclusions can beAbout the Oral Health of Bulgarian Population 43made for the slope of the increase of DMF-T. The difference between the levelsof the factor variable gender could also be inferred. Diagnostics of residuals doesnot reveal anything to disturb.agePr(DMF−T)20 30 40 50 60 70 80 900.00.20.40.60.81.0Figure 3: Logistic curves for males (black) and females (grey).Prop. of DMF-T Age SEp = 0.25: 19.67 0.42p = 0.50: 42.62 0.26p = 0.75: 65.57 0.48Table 1: The proportion of teeth affected by caries for men.Table 1 shows how the proportion of teeth affected by caries increases withthe age according to our logistic model for men. It is seen that at the age of 20,25% of the teeth has been affected on average, at the age of 43 – the half, andby age of 66 the proportion is 75%. In Table 2 the respective prediction valuesare given for women.Prop. of DMF-T Age SEp = 0.25: 12.65 0.52p = 0.50: 34.95 0.32p = 0.75: 57.26 0.49Table 2: The proportion of teeth affected by caries for women.44 Nina Daskalova, Boyko Bonev4. ConclusionsOur analysis shows that the number of teeth affected by caries strongly dependson age and gender. This number increases with age and at any age women havemore caries teeth than men (the odds ratio is 1.44). DMF-T of the Bulgarianpopulation over 20 years old has significantly increased since previous researchtook place.REFERENCES[1] E. Boteva, R. Vasileva, E. Karova. Comparative study of dental statusamong the urban population in Bulgaria. Problems of Stomatology, Sofia,2003, 7–9, (in Bulgarian).[2] J. J. Faraway. Extending the Linear Model with R: Generalized Linear,Mixed Effects and Nonparametric Regression Models, CRC Press, 2005.[3] R Development Core Team. R: A language and environment for statisticalcomputing. R Foundation for Statistical Computing, Vienna, Austria, 2010,URL http://www.R-project.org.[4] W. N. Venables, B. D. Ripley.Modern Applied Statistics with S. FourthEdition. Springer, New York, 2002.[5] Kr. Yaneva. Stomatological Morbidity and Need of Stomatological Help ofBulgarian Population. Phd. Thesis, Sofia, 1997, p. 60, (in Bulgarian).[6] Tsv. Yolov. Stomatological Health of Older People in Bulgaria. Phd.Thesis, Sofia, 2000, p. 60, (in Bulgarian).Nina DaskalovaSofia University “St.Kliment Ohridski”Faculty of Mathematics and InformaticsSofia, Bulgariae-mail: ninad@fmi.uni-sofia.bgDr. Boyko BonevMedical University of SofiaFaculty of Dental MedicineSofia, Bulgaria

About the Oral Health of Bulgarian Population over 20 Years Old

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About the Oral Health of Bulgarian Population over 20 Years Old

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