Dental Predictors of High Caries Increment in Children M. STEINER, U. HELFENSTEIN', and T.M. MARTHALER Division of Applied Prevention, Department of Preventive Dentistry, Periodontology and Cariology, Dental Institute, University of Zurich, Plattenstrasse 11, 8028 Zurich, Switzerland; and 'Biostatistical Center, Institute of Social and Preventive Medicine, University of Zurich, Sumatrastrasse 30, 8006 Zurich, Switzerland A comprehensive set ofdental variables was investigated to find the "best" combination of predictors for high caries increment in 7/8year-old and 10/11-year-old children. Fourpopulationswithwidely different caries prevalence were studied. Logistic regression analysis supplied multiple-input models by stepwise selection of predictors. A"low number of soundprimary molars"was thebest and most consistent predictor of high caries increment. The second best predictors were "high numbers of pre-cavity lesions on permanent first molars" (discolored pits and fissures in the younger age group and white spots on the smooth parts of buccolingual surfaces in the older age group). Inclusion ofradiological variables did not substantially increase the quality of prediction. For practical application, models with various multiple inputs selected by stepwise procedures were compared with "fixed" three-input models. These threeinput models resulted in predictive quality nearly equal to those of the multiple models. Traditional one-input models, containing DMFT or dmft, were inferior to the three-input models, particularly in the older age class. The lower the caries prevalence of the source data, the better was the prediction. As a summary measure characterizing the predictive performance of a model, we used the index "area under the receiver operating characteristic curve" A. For the 1984 data and the three-input models, the area was approximately 80%, and for the 1972 data, the area was 65-70%. J Dent Res 71(12):1926-1933, December, 1992
Introduction. In recent years, many studies have been concerned with caries prediction on the basis of variables characterizing dental status. However, few authors have tried to predict caries increment by using several caries variables simultaneously (Bader et al., 1986; Abernathy et al., 1987; Sepp and Hausen, 1988). In two of these studies, additional bacteriological, socioeconomic, etc., variables were included. Recently, we made an attempt to predict caries increment by using a set of several caries variables simultaneously without resorting to additional variables (Helfenstein et al., 1991; Helfenstein and Steiner, 1992). In the present paper, the general methodology described in those papers was systematically applied to four sets of longitudinal dental caries data with progressively declining caries prevalence. These data had been collected in fouryear periods since 1972. The main characteristics of the present study are listed below: A comprehensive set of 46 dental predictors was studied. It included pre-cavity lesions as well as radiologically detected lesions and sound primary teeth. Older data sets drawn from data bases from children with "high" caries prevalence were investigated. This allowed for the study of the consistency of predictors and predictability of caries increments at four different levels of prevalence. Three different definitions of "high caries increment" were tested. Received for publication August 6, 1991 Accepted for publication June 8, 1992 This study was supported by the Swiss National Fund for Scientific Research, Grant No. 32-9536.88.
1926
Two age classes, 7/8- and 10/11-year-olds, were analyzed. In order to simplify comparisons of the models, we used the index "Area under the ROC-curve".
Materials and methods. Data sets.-The data were obtained from 16 communities of the Canton of Zurich, where large samples of schoolchildren were regularly examined every four years. The standardized method of partial examination supplies data related to most surfaces of the teeth of the right side and data from one bitewing radiograph of the right side (Marthaler, 1966; Marthaler and Steiner, 1981). Caries prevalence of these children and its continued decline have been described in detail (Marthaler et al., 1988, and unpublished observations). For this investigation, four data sets were studied: (1) children examined in 1972 as well as in 1976 (The children were drawn from a data pool in which the average DMFT of 12-yearold children was 5.30 in 1972.); (2) children examined in 1976 and 1980 (DMFT at age 12: 3.90); (3) children examined in 1980 and 1984 (DMFT at age 12: 3.22); and (4) children examined in 1984 and 1988 (DMFT at age 12: 2.39). In all four data sets, two different age groups were studied, namely, 7/8-year-olds (exact limits: 6.50 to 8.49) and 10/11-year-olds (exact limits: 9.50 to 11.49). Target variable.-The target variable measures the number of new DF sites in the permanent teeth of the right side (the teeth of the left side not having been examined) within four years. Radiological findings were included. "D" includes only lesions with cavitation (lesion grades 3 and 4). Children were classified by this variable in groups "high caries increment" or "low caries increment". "High caries increment" was defined in three different ways: (1) C2: 2 or more new DF sites; (2) C3: 3 or more new DF sites; and (3) C4: 4 or more new DF sites. The resulting proportions of high-risk children varied from 65.1% to 2.0%. The latter proportion is very low, but the sample has been included for the sake of completeness. Explanatory variables,predictors.-In order to predict whether a child would suffer from high caries increment, 46 explanatory variables were tested. All variables and the corresponding abbreviations are listed in the "Appendix". Statistical analyses.-All variables were tested as individual predictors in simple logistic regression analyses. The most promising 22 variables-significant (p < 0.001) in three or more caseswere further studied in stepwise multiple logistic regression analyses. In a first stage, radiological predictors were excluded; in a second stage, they were included. Logistic regression and the area under theROCcurve.-Logistic regression is a regression with a dichotomous dependent variable Y (Matthews and Farewell, 1988). Y takes the value 1 withprobability p ("high caries increment") and the value 0 with probability q = 1 p ("low caries increment"). The logistic regression model is then given by p
=
1/ [1 +
-(P+x++WI e
(1)
where the xk (k= 1 ....... p) represent explanatory variables or "predic
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DENTAL PREDICTORS OF HIGH CARIES INCREMENT
Vol. 71 No. 12
1927
tors". After calculation of estimates bk of the parameters (SAS, 1986; Dixon, 1990), the estimated probability p1 for high caries
the model are tested for possible elimination. When multivariableregression models are developed, great care
increment is calculated for each child (i
hastobetakenwithregardto"multicollinearity". Multicollinearity
1,
,n):
is present when sets ofpredictors are highly dependent. In this case, computed estimates of coefficients may be highly unstable, i.e., standard errors of coefficients may be highly inflated. As a protecIf the estimated probability pi is greater than a critical score or tion against multicollinearity, anewvariable was not entered when "cutpoint" pP, the child is classified as "high-risk", otherwise as it did not pass a tolerance test. The tolerance associated with a new "low-risk". The cutpoint pq, is a quantity (between zero and one) variable is 1 minus the squared multiple correlation ofthat variable with the variables already in the model. When tolerance was which may be chosen freely. Several methods are available for selection of variables for smaller than a critical level, then the variable was not included into inclusion in a model-in particular, "forward selection" (FS), "for- the model (Afifi and Clark, 1990). ward stepwise selection" (SW), and "backward elimination" (BE). The "quality" of prediction may be summarized by the two These and other methods have been described in detail by Draper measures of sensitivity SN = TP/(TP + FN) and specificity SP = TN/ and Smith (1981). Wefollowedtheirrecommendationtouse SW. In (FP + TN), where the abbreviations are defined as: TP, number of this method, after a variable has entered a model, the variables in "true positives"; FN, number of "false negatives"; FP, number of
pi= 1/ [1 + e+bl',1+ abed
(2)
TABLE 1
% high risk
RESULTS OF THE SIMPLE LOGISTIC REGRESSION ANALYSES [Age 7/8. Significance of "individual" predictors, p < 0.05 (+) and p < 0.001 (0).] 1972, n = 586 1976, n = 583 1980, n = 334 1984, n = 205 C2 C3 C4 C2 C4 C3 C2 C2 C4 C3 C4 C3 46.1 25.8 15.4 32.1 15.6 8.6 19.8 10.5 5.4 12.7 5.4 2.0 Primary teeth
SOUpr SOUprm' DFprm SOUprmr' D12prmr D34Fprmr
0 0 0 0 0
0
0
D2fi
0 0
0 0
+
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 +
0 0 0 0
0 0 0 0
0
0
0
0
0
0
+
+
+
+
+
°
+
+
+
+
0 0 0 0
+
0
0 0
+
0 + +
+
+
0
0
+
Permanent first molars
D12fi D34Ffi D2pi D12pi D2pif D12pif Dlsm D12sm
+
0 0 0
+
0 0 0 0
0 0 0 0
+
+
0
0
D2r
D12r
0 0
+
+
+
+
+
+
+
+
+
+
+
+
0 0 0 0
0 0
+ +
+
+
0
+
0 0 0 0
0 0 0
0 0 0
+
+
0
0
+
0
+
+
0
0
0 0 0
+
+
0 0 0
+ + + + +
Premolars
D2pfi D12pfi Dlpr D12pr
+ +
Anterior teeth + D12a 0 0 'The sign of the coefficient is negative. Downloaded from jdr.sagepub.com at UNIVERSITE DE MONTREAL on June 7, 2015 For personal use only. No other uses without permission.
0
+
+ +
1928
J Dent Res December 1992
STEINER et al.
"false positives"; and TN, number of "true negatives". For each prediction, one obtains A = 1 or 100%. The Fig. shows an intermechosen cutpoint pp, one obtains a set offour frequencies TP, FN, FP, diate prediction (A = 0.83 or 83%). The area under the ROC curve and TN, and the corresponding SN and SP. Therefore, SN and SP has a probabilistic interpretation: It is the (conditional) probability that the members of a "high increment/low increment" pair are are functions of p p. The information contained in a prediction model may be con- correctly classified (Hanley and McNeil, 1982). In order to study the performance of a prediction model, we used cisely summarized by means of a so-called "receiver operating characteristic" (ROC) curve: To each cutpoint p, a point (x,y) is the "split-sample approach" (Kleinbaum et al., 1988): The data set plotted into a square where x = 1 SP and y = SN. An illustrative is split into two parts with random assignment of the individuals. example is given in the Fig. The ROC curve displays the effects of The first part is used for model-building (estimation set), and the a particular model. In the context of caries prediction, it has been second is used for the study of model performance (validation set). used by ter Pelkwijk et al. (1990). The ROC curve is equivalent to the plotting of two curves, one for SN and one for SP as functions of p In order to compare different prediction models more easily, one Results. may reduce the information contained in a ROC curve to a single All 46 variables were tested as individual predictors in simple index: the area A under the ROC curve (Hanley and McNeil, 1982). logistic regression analyses. The results for the 22 most promising This concept is depicted in the Fig. The diagonal line corresponds predictors are displayed in Tables 1 and 2. Variables which were to a pure chance prediction (A = 0.5 or 50% resp.). For a perfect found to be significant in all data sets and under the three defini-
TABLE 2 RESULTS OF THE SIMPLE LOGISTIC REGRESSION ANALYSES [Age 10/11. Significance of "individual" predictors, p < 0.05 (+) and p < 0.001 (0).]
% high risk
SOUpr* SOUprm* DFprm SOUprmr* D12prmr D34Fprmr D2fi D12fi D34Ffi D2pi D12pi D2pif D12pif
Dism D12sm D2r D12r
D2pfi D12pfi
Dlpr D12pr
C2 65.1 0 0
1972, n = 372 C4 C3 31.5 46.0 0 0
0 0
1976, n = 650 1980, n = 433 C2 C4 C2 C3 C4 C3 48.0 31.2 20.3 37.6 22.2 15.7 Primary teeth 0 0 0 0 0 0 0 0 0 0 0 0
1984, n = 258 C2 C3 C4 8.1 22.5 15.5 0 0
0 0
+ +
0
0
0
+
+
+
+
+
+
+ 0 0 0 0 0 0 + 0
+ + + + + 0 + +
0 0
+ +
+
0 0
0 0
0 0
0 0
0 0
0 0
0 +
0 0 +
0 + +
Permanent first molars + +
+ 0
+
+ 0 0
+
0 0 0 0
+ 0 0
+
0 0 + +
0 0
+ 0 0 +
+
+ + + 0 0 + 0
+ + 0
0 0 + +
0 0 0 0
0
+
D12a + *The sign of the coefficient is negative.
0 0
0 + + + 0 0
0 Premolars 0 0 0 0 Anterior teeth
0 0 0 0 0 0 0 + 0
0 + + + 0 0 + 0
+ 0 + 0
0 + 0 0 0 0 0 0 0 0
0 0 0
+ 0 0
+ 0 0
0 0
0
0
+
0 0 + 0
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DENTAL PREDICTORS OF HIGH CARIES INCREMENT
Vol. 71 No. 12
tions of high caries increment C2/C3/C4 were regarded as "good" predictors. "Good" predictors were in both age classes: low numbers of sound primary molars (SOUprm), sound primary teeth (SOUpr), sound approximal surfaces of primary molars (SOUprmr), and high numbers of lesions in enamel of first molar approximal surfaces (D12r). Other variables were fairly age-specific. In the children at age 7/8, decayed/filled primary molars (DFprm), decayed/filled approximal surfaces of primary molars (D34Fprmr), and discolored pits and fissures of permanent first molars (D12pif) were "good" predictors. In the children at age 10/11, on the other hand, white spots on buccolingual surfaces of first molars (D12sm) and lesions in enamel of approximal surfaces of premolars (Dlpr/D12pr) predicted well. Variables of second molars and anterior teeth were poor predictors in both age classes and all data sets. (The results are not presented for the sake of brevity.) In Tables 3 and 4, the results of the stepwise logistic regression analyses are presented. The method chosen was forward stepwise selection. The criteria for variable entry and exit were p = 0.025 and p = 0.03, respectively. The Tables show which of the 15 variables (radiological variables excluded) were selected and in which order theyenteredthe models. Mostly, one ofthe predictors ofthe primary dentition entered the model first. The sound primary units were found to be superior to the decayed ones. Coefficients of sound primaryunits showed a negative sign. In the second step, pre-cavity lesions of permanent first molars entered the model: While precavity lesions of pit and fissure sites were superior as predictors in the younger children, white spots on lingual and buccal surfaces
1929
were favorites in the older children.
In the older age class, a further step selected pre-cavity lesions and customary DF-lesions of pits and fissures for the model. Some limited contribution to caries prediction came from premolars and anterior teeth. When radiological variables were included, there was a choice of 22 predictors. (The results are not presented for the sake ofbrevity.) In both age classes, radiological predictors were frequently selected as first or second. The best predictors were sound approximal surfaces of primary (negative correlation) molars and lesions in the
enamel of approximal surfaces of first molars. The ability of different models to predict future caries is presented in Table 5. The multiple-inputmodels with stepwise selected predictors showed the "best" results. Inclusion of radiological variables did not produce a substantial improvement. In order to evaluate model performance, we applied the "splitsample approach" to the most relevant data set (1984), to the two age classes, and the two target variables C2 and C3. Kleinbaum et al. (1988) proposed to split a sample of about 200 units in two parts of unequal size, about 3/4 for the estimation set and 1/4 for the validation set. The results concerning SN, SP, and A obtained bythe application of models constructed in the estimation sets in the validations sets are shown in Table 6. One may see how similar corresponding results are in the two sets. Using the three most frequently selected predictors (SOUprm, D12sm, D12pif), we formed "fixed" three-input models. Prediction quality was not diminished markedly (Table 5). These three-input models were compared with standard one-input models (with DMFT or dmft used as a single predictor). In general, the three-input models were found to be superior to the one-input models. However,
TABLE 3 RESULTS OF THE STEPWISE LOGISTIC REGRESSION ANALYSES [Age 7/8.Order of selected predictors (significant at p < 0.05). Sign of coefficients indicated. Radiological variables excluded.] 1984, n = 205 1980, n = 334 1976, n = 583 1972, n = 586 C4 C3 C2 C3 C4 C2 C4 C2 C3 C4 C3 C2 Primary teeth 11SOUpr 1111111SOUprm 1+ 2+ 1+ DFprm Permanent first molars 2+ 2+ D2fM 3+ 2+ D12fi 3D34Ffi 2+ D2pi 2+ D12pi 2+ D2pif 1+ 2+ 2+ D12pif
Dism 2+ Premolars: no predictors
D12sm
2+
2+
D2pfi D12pfi Anterior teeth
D12a
3+
3+
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STEINER et al.
the models with dm*ft (m*: only missing primary molars included) had nearly the same predictive power as the multiple models in the younger children. Predictability of caries increment was clearly better in the populations with low caries prevalence (1980 and 1984) than in the populations with high caries prevalence (1972 and 1976). In addition, when the threshold for "high caries increment" was raised from 2 (C2) to 4 (C4) lesions in four years, predictability increased somewhat, especially in the younger age class.
Discussion. The present investigations were based on unilateral recording. In view of the diagnostic unreliabilities, it would be preferable for research to be carried out on full-mouth data. It is reasonable to assume that SN, SP, and the area under the ROC curve might improve slightly in bilateral recording, because the variability due to diagnostic errors will be diminished. Variables based on the primary dentition supplied the best information with regard to caries prediction in all four data sets. This was true not only for the younger age group (7/8) but, surprisingly, also for the older age group (10/11). Both sound primary teeth (SOUpr) and sound primary molars (SOUprm) were significant predictors, but with a negative correlation. In the class of younger children, sound primary molars (SOUprm) could be replaced by decayed/filled units (DFprm). One is the complement of the other, as long as no primary molars are lost. For older children, DFprm was no longer a good predictor, probably because the DF count does not take into account missing primary molars and early erupted
J Dent Res December 1992
premolars (owing to extraction of decayed primary molars; Steiner et al., 1991). Bader et al. (1986), Abernathy et al. (1987), and ter Pelkwijk et al. (1990) have already shown the usefulness of dmft,
dmfs, and primary molar dmfs as predictors for younger children. While the present study confirms this finding, low numbers of sound primary molars were revealed to be more consistent predictors. The next important information concerning caries prediction was supplied by permanent first molars. Discolored fissures were already revealed as good predictors (Marthaler et al., 1990). The remarkable predictive potential ofwhite spots on lingual and buccal surfaces was documented by Kiock and Krasse (1979) and Seppa and Hausen (1988). Two other groups of authors (van Palenstein Helderman et al., 1989; Glass et al., 1990) found that the inclusion of pre-cavity lesions improved predictive power. However, Seppa and Hausen (1988) concluded that the inclusion ofpre-cavity lesions added little to the predictive power of conventional DFS scores. The inclusion of radiological predictors increased the predictability only marginally. It is therefore unreasonable to urge that radiographs be used at these ages so that caries prediction can be improved. Model performance was studied by means of the "split-sample approach". The results concerning SN, SP, and A obtained in the validation sets were similar to corresponding results in the estimation sets. However, the sample size of 51 for the validation set (the set 7/8 year old in the 1984 sample and C2) contained only 5 children with "high caries increment". The measures characterizing model performance have therefore to be interpreted with caution. As a simplification and for easy applicability, "fixed" three-input models containing SOUprm, D12pif, and D12sm were computed.
TABLE 4 RESULTS OF THE STEPWISE LOGISTIC REGRESSION ANALYSES [Age 10/11. Order of selected predictors (significant at p < 0.05). Sign of coefficients indicated. Radiological variables excluded.] 1972, n = 372 1976, n = 650 1980, n = 433 1984, n = 258 C2 C3 C4 C2 C4 C3 C2 C3 C4 C2 C4 C3 Primary teeth 1111SOUpr 111111SOUprm 1DFprm 2245Permanent first molars D2fi 4+ D12fi D34Ffi 5+ 2+ 3+ 2+ D2pi D12pi D2pif 4+ 4+ D12pif 3+ 3+ 2+ 3+ 2+ Dlsm 43+ D12sm 3+ 2+ 3+ 2+ 2+ 2+ 2+ 1+ 3+ Premolars D2pfi 2+ 3+ 3+ D12pfi Anterior teeth: no predictors D12a Downloaded from jdr.sagepub.com at UNIVERSITE DE MONTREAL on June 7, 2015 For personal use only. No other uses without permission.
DENTAL PREDICTORS OF HIGH CARIES INCREMENT
Vol. 71 No. 12
Age 7/8 SN SP A SN SP A
SN SP A SN SP A SN SP A
Age 10/11 SN SP A SN SP A
SN SP A SN SP A SN SP A
TABLE 5 SENSITIVITY (SN), SPECIFICITY (SP), AND AREA UNDER ROC CURVE (A) FOR DIFFERENT MODELS 1972, n = 586 1976, n = 583 1980, n = 334 1984, n = 205 C2 C4 C3 C2 C3 C4 C2 C3 C4 C2 C3 C4 Multiple models with stepwise selected predictors excluding radiological predictors 70 58 59 68 70 69 72 65 82 75 59 66 71 75 69 74 85 88 84 98 72 69 70 76 75 78 84 81 92 94 Multiple models with stepwise selected predictors including radiological predictors 64 72 64 70 65 74 74 71 78 65 82 100 66 54 59 65 68 77 72 75 81 88 84 84 69 69 72 73 74 82 78 83 88 81 92 94 "Fixed" 3-input models: SOUprm, D12sm, D12pif 62 74 56 67 66 68 71 69 72 62 82 75 60 53 70 64 66 71 65 71 83 87 88 91 67 68 71 69 70 74 75 76 79 79 92 94 1-input models: DMFT 61 40 42 44 50 54 0 40 39 96 100 100 37 63 63 65 64 63 100 75 74 3 9 9 50 51 52 54 57 61 51 57 55 51 55 54 1-input models: dm*ft 67 60 67 69 64 60 61 66 67 62 82 75 54 66 64 56 67 65 71 81 69 82 80 86 62 65 68 65 66 68 68 71 75 77 90 89 = = = 1972, n 372 1976, n 650 1980, n = 433 1984, n 258 C2 C4 C3 C2 C3 C4 C2 C4 C3 C2 C4 C3 Multiple models with stepwise selected predictors excluding radiological predictors 62 70 65 64 63 78 70 70 72 71 75 81 68 67 58 66 68 71 72 73 69 68 73 60 69 68 70 71 71 77 82 75 79 78 80 80 Multiple models with stepwise selected predictors including radiological predictors 62 66 64 72 71 75 66 67 71 81 75 71 72 72 65 68 59 67 68 71 70 71 76 72 74 71 70 73 78 78 78 80 82 85 70 79 "Fixed" 3-input models: SOUprm, D12sm, D12pif 62 71 65 71 75 76 55 56 59 66 69 73 62 64 71 73 72 66 63 66 63 63 56 65 82 74 75 80 80 67 66 67 69 73 75 65 DMFT models: 1-input 68 67 52 74 53 53 66 62 49 55 63 68 66 63 61 71 69 67 63 53 56 51 50 65 64 65 65 64 66 67 59 61 61 61 61 59 1-input models: dm*ft 64 34 0 59 68 52 28 57 75 71 51 49 64 100 72 48 62 62 54 30 60 60 61 59 56 51 50 60 52 64 54 51 54 58 63 53 67 58 67
72 54 69
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STEINER et al.
J Dent Res December 1992
These models showed nearly the same quality of prediction as models containing predictors selected by stepwise procedures (excluding radiographs). This signifies that (1) predictors within primary teeth and first molars are interchangeable up to a certain point, and that (2) the predictors within premolars and anterior teeth are not essential. A "fixed" model is desirable for practical reasons: It is simpler and probably more reliable in routine application, if the investigator or dentist always examines the same few sites. A comparison was made between the "fixed" three-input models and traditional models with dmft resp. DMFT as predictors. The dmf and DMF indices have been commonly used for measurement of the risk for future dental caries (dmft by Hill et al., 1967, and ter Pelkwijk et al., 1990; DMFT by Berman and Slack, 1973, and Honkalaetal., 1984). The respective predictions were inferior to the "fixed" three-input models, especially in the older age class. It is of course favorable that predictions are better in the lowcaries situation. While selective prevention is primarily indicated in populations with low caries prevalence, there is little need for selective prevention in populations with high caries prevalence, for which collective prevention is indicated.
SN 1.0
0.90.80.70.6 0.5 0.4 0.3 0.2i, . If le
.1
Acknowledgments.
i,
0.0oz
We thank Sandra Semadeni for the review of the manuscript and Adrian Bandi for the linkage of examinations and other computer assistance.
0.0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1
-
SP
REFERENCES
Fig.- Area under the receiver operating characteristic (ROC)-curve. SN= Sensitivity, SP= Specificity. Explanation in the text.
Abernathy JR, Graves RC, Bohannan HM, Stamm JW, Greenberg BG, DisneyJA(1987). Development and application of a prediction model for dental caries. Community Dent Oral Epidemiol 15:24-28. Afifi AA, Clark V (1990). Computer-aided multivariate analysis. 2nd ed. New York: Van Nostrand Reinhold Company, 162.
Bader JD, Graves RC, Disney JA, Bohannan HM, Stamm JW, Abernathy JR, et al. (1986). Identifying children who will experience high caries increments. Community Dent Oral Epidemiol 14:198-201. Bermann DS, Slack GL (1973). Caries experience relative to individual
TABLE 6 RESULTS OF SPLIT SAMPLING IN THE 1984 DATA SET [Sensitivity (SN), specificity (SP), and area under ROC curve (A) for "estimation sets" and "validation sets".]
Age7/8
C2
Models Sets
SOUprm*, D2pif Estim. 133/21
C3
SOUprm*, D2pi
SN
76
Val. 46/5 100
SP
69
67
86
62
A
80
86
93
89
nlow/hgh
Age 10/11 Models Sets
nlow/high SN
C2 SOUprm*, D12sm, D12pif Estim. Val. 149/45 51/13 73 92
Estim. 146/8 88
Val. 48/3 100
C3 SOUprm*, D12sm, D12pif Estim. Val. 158/36 60/4
75
75
SP
72
71
70
75
A
79
84
80
86
*The sign of the coefficient is negative. Downloaded from jdr.sagepub.com at UNIVERSITE DE MONTREAL on June 7, 2015 For personal use only. No other uses without permission.
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Primary molars, numbers of sites sound approximal surfaces SOUprmr approximal surfaces with radiolucencies in enamel D12prmr D34Fprmr approximal surfaces with radiolucencies in dentin/ fillings Permanent first molars, numbers of teeth M missing molars Permanent first molars, numbers of sites slightly brown discolored occlusal fissures Difi dark brown/black discolored occlusal fissures D2fi slightly brown/dark brown/black discoloredocclusal D12fi fissures decayed/filled occlusal fissures D34Ffi
and future caries experience. JAm Dent Assoc 74:430-438. Kleinbaum DG, Kupper LL, Muller KE (1988). Applied regression analysis and othermultivariable methods. 2nd ed. Boston (MA): PWS-Kent, 328331. Mock B, Krasse B (1979). A comparison between different methods for prediction of caries activity. Sand JDent Res 87:129-139. Marthaler TM (1966). A standardized system ofrecording dental conditions. Helv Odontol Acta 10:1-18. Marthaler TM, Steiner M (1981). Percentages oflifetime caries experience retained by eight systems of partial DMF-recording. Community Dent Oral Epidemiol 9:22-26. MarthalerTM,SteinerM,BandiA(1990). Werdenverfdrbtemolarenfissuren innerhalb von vier jahren haufiger karios als nichtverfarbte? Beobachtungen aus den jahren 1975 bis 1988. Schweiz Monatsschr
D2pi D12pi D34Fpi
Zahnmed 100:841-846. Marthaler TM, Steiner M, Menghini G, Bandi A (1988). Kariespravalenz bei schulern im Kanton Zurich. Resultate aus dem zeitraum 1963 bis 1987. Schweiz Monatsschr Zahnmed 98:1309-1315. Matthews DE, Farewell VT (1988). Using and understanding medical statistics. Basel (Switzerland): Karger, 142-144. SAS Institute Inc. (1986). SUGI supplemental library user's guide. Cary (NC): SAS Institute, 181-202. Seppa L, Hausen H (1988). Frequencyof initial lesions as predictor offuture caries increment in children. Sand J Dent Res 96:9-13. Steiner M, Marthaler TM, Bandi A, Menghini G (1991). Pravalenz der milchzahnkaries in 16 gemeinden des Kantons Zurich in den jahren 1964 bis 1988. Schweiz Monatsschr Zahnmed 101:738-742. ter Pelkwijk A, van Palenstein Helderman WH, van Dijk JWE (1990). Caries experience in the deciduous dentition as predictor for caries in the permanent dentition. Caries Res 24:65-71. van Palenstein Helderman WH, ter Pelkwijk L, van Dijk JWE (1989). Caries in fissures of permanent first molars as a predictor for caries increment. Community Dent Oral Epidemiol 17:282-284.
Appendix: Explanatory variables, predictors. Primary teeth, numbers of teeth sound primary teeth SOUpr
SOUprm DFprm Mprm
sound primary molars decayed/filled primary molars missing primary molars
SOUpra DFpra Mpra
sound primary anterior teeth decayed/filled primary anterior teeth missing primary anterior teeth
Dlpi
Dlpif D2pif D12pif
D34Fpif DIsm D2sm
D12sm D34Fsm
slightly brown discolored pits (ling. on upper, bucc. on lower molars) dark brown/black discolored pits slightly brown/dark brown/black discolored pits decayed/filled pits
slightly brown discolored pits/fissures dark brown/black discolored pits/fissures slightly brown/dark brown/black discolored pits/ fissures decayed/filled pits/fissures lingual/buccal smooth surfaces with white spots (2mm) lingual/buccal smooth surfaces with white spots decayed/filled lingual/buccal smooth surfaces
Dir
approximal surfaces with radiolucencies in outer enamel D2r approximal surfaces with radiolucencies in inner enamel D12r approximal surfaces with radiolucencies in enamel approximal surfaces with radiolucencies in dentin/ D34Fr fillings Second molars, numbers of sites Dlm2fi slightly brown discolored occlusal fissures D2m2fi dark brown/black discolored occlusal fissures D34Fm2fi decayed/filled occlusal fissures Premolars, numbers of sites slightly brown discolored occlusal fissures Dlpfi dark brown/black discolored occlusal fissures D2pfi slightly brown/dark brown/black discolored occlusal D12pfi fissures decayed/filled occlusal fissures D34Fpfi
approximal surfaces with radiolucencies in outer enamel approximal surfaces with radiolucencies in inner D2pr enamel approximal surfaces with radiolucencies in enamel D12pr approximal surfaces with radiolucencies in dentin/ D34Fpr fillings Anterior teeth, numbers of sites surfaces with white spots (2mm) D2a surfaces with white spots D12a D34Fa decayed/filled surfaces
Dlpr
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Introduction. In recent years, many studies have been concerned with caries prediction on the basis of variables characterizing dental status. However, few authors have tried to predict caries increment by using several caries variables simultaneously (Bader et al., 1986; Abernathy et al., 1987; Sepp and Hausen, 1988). In two of these studies, additional bacteriological, socioeconomic, etc., variables were included. Recently, we made an attempt to predict caries increment by using a set of several caries variables simultaneously without resorting to additional variables (Helfenstein et al., 1991; Helfenstein and Steiner, 1992). In the present paper, the general methodology described in those papers was systematically applied to four sets of longitudinal dental caries data with progressively declining caries prevalence. These data had been collected in fouryear periods since 1972. The main characteristics of the present study are listed below: A comprehensive set of 46 dental predictors was studied. It included pre-cavity lesions as well as radiologically detected lesions and sound primary teeth. Older data sets drawn from data bases from children with "high" caries prevalence were investigated. This allowed for the study of the consistency of predictors and predictability of caries increments at four different levels of prevalence. Three different definitions of "high caries increment" were tested. Received for publication August 6, 1991 Accepted for publication June 8, 1992 This study was supported by the Swiss National Fund for Scientific Research, Grant No. 32-9536.88.
1926
Two age classes, 7/8- and 10/11-year-olds, were analyzed. In order to simplify comparisons of the models, we used the index "Area under the ROC-curve".
Materials and methods. Data sets.-The data were obtained from 16 communities of the Canton of Zurich, where large samples of schoolchildren were regularly examined every four years. The standardized method of partial examination supplies data related to most surfaces of the teeth of the right side and data from one bitewing radiograph of the right side (Marthaler, 1966; Marthaler and Steiner, 1981). Caries prevalence of these children and its continued decline have been described in detail (Marthaler et al., 1988, and unpublished observations). For this investigation, four data sets were studied: (1) children examined in 1972 as well as in 1976 (The children were drawn from a data pool in which the average DMFT of 12-yearold children was 5.30 in 1972.); (2) children examined in 1976 and 1980 (DMFT at age 12: 3.90); (3) children examined in 1980 and 1984 (DMFT at age 12: 3.22); and (4) children examined in 1984 and 1988 (DMFT at age 12: 2.39). In all four data sets, two different age groups were studied, namely, 7/8-year-olds (exact limits: 6.50 to 8.49) and 10/11-year-olds (exact limits: 9.50 to 11.49). Target variable.-The target variable measures the number of new DF sites in the permanent teeth of the right side (the teeth of the left side not having been examined) within four years. Radiological findings were included. "D" includes only lesions with cavitation (lesion grades 3 and 4). Children were classified by this variable in groups "high caries increment" or "low caries increment". "High caries increment" was defined in three different ways: (1) C2: 2 or more new DF sites; (2) C3: 3 or more new DF sites; and (3) C4: 4 or more new DF sites. The resulting proportions of high-risk children varied from 65.1% to 2.0%. The latter proportion is very low, but the sample has been included for the sake of completeness. Explanatory variables,predictors.-In order to predict whether a child would suffer from high caries increment, 46 explanatory variables were tested. All variables and the corresponding abbreviations are listed in the "Appendix". Statistical analyses.-All variables were tested as individual predictors in simple logistic regression analyses. The most promising 22 variables-significant (p < 0.001) in three or more caseswere further studied in stepwise multiple logistic regression analyses. In a first stage, radiological predictors were excluded; in a second stage, they were included. Logistic regression and the area under theROCcurve.-Logistic regression is a regression with a dichotomous dependent variable Y (Matthews and Farewell, 1988). Y takes the value 1 withprobability p ("high caries increment") and the value 0 with probability q = 1 p ("low caries increment"). The logistic regression model is then given by p
=
1/ [1 +
-(P+x++WI e
(1)
where the xk (k= 1 ....... p) represent explanatory variables or "predic
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DENTAL PREDICTORS OF HIGH CARIES INCREMENT
Vol. 71 No. 12
1927
tors". After calculation of estimates bk of the parameters (SAS, 1986; Dixon, 1990), the estimated probability p1 for high caries
the model are tested for possible elimination. When multivariableregression models are developed, great care
increment is calculated for each child (i
hastobetakenwithregardto"multicollinearity". Multicollinearity
1,
,n):
is present when sets ofpredictors are highly dependent. In this case, computed estimates of coefficients may be highly unstable, i.e., standard errors of coefficients may be highly inflated. As a protecIf the estimated probability pi is greater than a critical score or tion against multicollinearity, anewvariable was not entered when "cutpoint" pP, the child is classified as "high-risk", otherwise as it did not pass a tolerance test. The tolerance associated with a new "low-risk". The cutpoint pq, is a quantity (between zero and one) variable is 1 minus the squared multiple correlation ofthat variable with the variables already in the model. When tolerance was which may be chosen freely. Several methods are available for selection of variables for smaller than a critical level, then the variable was not included into inclusion in a model-in particular, "forward selection" (FS), "for- the model (Afifi and Clark, 1990). ward stepwise selection" (SW), and "backward elimination" (BE). The "quality" of prediction may be summarized by the two These and other methods have been described in detail by Draper measures of sensitivity SN = TP/(TP + FN) and specificity SP = TN/ and Smith (1981). Wefollowedtheirrecommendationtouse SW. In (FP + TN), where the abbreviations are defined as: TP, number of this method, after a variable has entered a model, the variables in "true positives"; FN, number of "false negatives"; FP, number of
pi= 1/ [1 + e+bl',1+ abed
(2)
TABLE 1
% high risk
RESULTS OF THE SIMPLE LOGISTIC REGRESSION ANALYSES [Age 7/8. Significance of "individual" predictors, p < 0.05 (+) and p < 0.001 (0).] 1972, n = 586 1976, n = 583 1980, n = 334 1984, n = 205 C2 C3 C4 C2 C4 C3 C2 C2 C4 C3 C4 C3 46.1 25.8 15.4 32.1 15.6 8.6 19.8 10.5 5.4 12.7 5.4 2.0 Primary teeth
SOUpr SOUprm' DFprm SOUprmr' D12prmr D34Fprmr
0 0 0 0 0
0
0
D2fi
0 0
0 0
+
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 +
0 0 0 0
0 0 0 0
0
0
0
0
0
0
+
+
+
+
+
°
+
+
+
+
0 0 0 0
+
0
0 0
+
0 + +
+
+
0
0
+
Permanent first molars
D12fi D34Ffi D2pi D12pi D2pif D12pif Dlsm D12sm
+
0 0 0
+
0 0 0 0
0 0 0 0
+
+
0
0
D2r
D12r
0 0
+
+
+
+
+
+
+
+
+
+
+
+
0 0 0 0
0 0
+ +
+
+
0
+
0 0 0 0
0 0 0
0 0 0
+
+
0
0
+
0
+
+
0
0
0 0 0
+
+
0 0 0
+ + + + +
Premolars
D2pfi D12pfi Dlpr D12pr
+ +
Anterior teeth + D12a 0 0 'The sign of the coefficient is negative. Downloaded from jdr.sagepub.com at UNIVERSITE DE MONTREAL on June 7, 2015 For personal use only. No other uses without permission.
0
+
+ +
1928
J Dent Res December 1992
STEINER et al.
"false positives"; and TN, number of "true negatives". For each prediction, one obtains A = 1 or 100%. The Fig. shows an intermechosen cutpoint pp, one obtains a set offour frequencies TP, FN, FP, diate prediction (A = 0.83 or 83%). The area under the ROC curve and TN, and the corresponding SN and SP. Therefore, SN and SP has a probabilistic interpretation: It is the (conditional) probability that the members of a "high increment/low increment" pair are are functions of p p. The information contained in a prediction model may be con- correctly classified (Hanley and McNeil, 1982). In order to study the performance of a prediction model, we used cisely summarized by means of a so-called "receiver operating characteristic" (ROC) curve: To each cutpoint p, a point (x,y) is the "split-sample approach" (Kleinbaum et al., 1988): The data set plotted into a square where x = 1 SP and y = SN. An illustrative is split into two parts with random assignment of the individuals. example is given in the Fig. The ROC curve displays the effects of The first part is used for model-building (estimation set), and the a particular model. In the context of caries prediction, it has been second is used for the study of model performance (validation set). used by ter Pelkwijk et al. (1990). The ROC curve is equivalent to the plotting of two curves, one for SN and one for SP as functions of p In order to compare different prediction models more easily, one Results. may reduce the information contained in a ROC curve to a single All 46 variables were tested as individual predictors in simple index: the area A under the ROC curve (Hanley and McNeil, 1982). logistic regression analyses. The results for the 22 most promising This concept is depicted in the Fig. The diagonal line corresponds predictors are displayed in Tables 1 and 2. Variables which were to a pure chance prediction (A = 0.5 or 50% resp.). For a perfect found to be significant in all data sets and under the three defini-
TABLE 2 RESULTS OF THE SIMPLE LOGISTIC REGRESSION ANALYSES [Age 10/11. Significance of "individual" predictors, p < 0.05 (+) and p < 0.001 (0).]
% high risk
SOUpr* SOUprm* DFprm SOUprmr* D12prmr D34Fprmr D2fi D12fi D34Ffi D2pi D12pi D2pif D12pif
Dism D12sm D2r D12r
D2pfi D12pfi
Dlpr D12pr
C2 65.1 0 0
1972, n = 372 C4 C3 31.5 46.0 0 0
0 0
1976, n = 650 1980, n = 433 C2 C4 C2 C3 C4 C3 48.0 31.2 20.3 37.6 22.2 15.7 Primary teeth 0 0 0 0 0 0 0 0 0 0 0 0
1984, n = 258 C2 C3 C4 8.1 22.5 15.5 0 0
0 0
+ +
0
0
0
+
+
+
+
+
+
+ 0 0 0 0 0 0 + 0
+ + + + + 0 + +
0 0
+ +
+
0 0
0 0
0 0
0 0
0 0
0 0
0 +
0 0 +
0 + +
Permanent first molars + +
+ 0
+
+ 0 0
+
0 0 0 0
+ 0 0
+
0 0 + +
0 0
+ 0 0 +
+
+ + + 0 0 + 0
+ + 0
0 0 + +
0 0 0 0
0
+
D12a + *The sign of the coefficient is negative.
0 0
0 + + + 0 0
0 Premolars 0 0 0 0 Anterior teeth
0 0 0 0 0 0 0 + 0
0 + + + 0 0 + 0
+ 0 + 0
0 + 0 0 0 0 0 0 0 0
0 0 0
+ 0 0
+ 0 0
0 0
0
0
+
0 0 + 0
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DENTAL PREDICTORS OF HIGH CARIES INCREMENT
Vol. 71 No. 12
tions of high caries increment C2/C3/C4 were regarded as "good" predictors. "Good" predictors were in both age classes: low numbers of sound primary molars (SOUprm), sound primary teeth (SOUpr), sound approximal surfaces of primary molars (SOUprmr), and high numbers of lesions in enamel of first molar approximal surfaces (D12r). Other variables were fairly age-specific. In the children at age 7/8, decayed/filled primary molars (DFprm), decayed/filled approximal surfaces of primary molars (D34Fprmr), and discolored pits and fissures of permanent first molars (D12pif) were "good" predictors. In the children at age 10/11, on the other hand, white spots on buccolingual surfaces of first molars (D12sm) and lesions in enamel of approximal surfaces of premolars (Dlpr/D12pr) predicted well. Variables of second molars and anterior teeth were poor predictors in both age classes and all data sets. (The results are not presented for the sake of brevity.) In Tables 3 and 4, the results of the stepwise logistic regression analyses are presented. The method chosen was forward stepwise selection. The criteria for variable entry and exit were p = 0.025 and p = 0.03, respectively. The Tables show which of the 15 variables (radiological variables excluded) were selected and in which order theyenteredthe models. Mostly, one ofthe predictors ofthe primary dentition entered the model first. The sound primary units were found to be superior to the decayed ones. Coefficients of sound primaryunits showed a negative sign. In the second step, pre-cavity lesions of permanent first molars entered the model: While precavity lesions of pit and fissure sites were superior as predictors in the younger children, white spots on lingual and buccal surfaces
1929
were favorites in the older children.
In the older age class, a further step selected pre-cavity lesions and customary DF-lesions of pits and fissures for the model. Some limited contribution to caries prediction came from premolars and anterior teeth. When radiological variables were included, there was a choice of 22 predictors. (The results are not presented for the sake ofbrevity.) In both age classes, radiological predictors were frequently selected as first or second. The best predictors were sound approximal surfaces of primary (negative correlation) molars and lesions in the
enamel of approximal surfaces of first molars. The ability of different models to predict future caries is presented in Table 5. The multiple-inputmodels with stepwise selected predictors showed the "best" results. Inclusion of radiological variables did not produce a substantial improvement. In order to evaluate model performance, we applied the "splitsample approach" to the most relevant data set (1984), to the two age classes, and the two target variables C2 and C3. Kleinbaum et al. (1988) proposed to split a sample of about 200 units in two parts of unequal size, about 3/4 for the estimation set and 1/4 for the validation set. The results concerning SN, SP, and A obtained bythe application of models constructed in the estimation sets in the validations sets are shown in Table 6. One may see how similar corresponding results are in the two sets. Using the three most frequently selected predictors (SOUprm, D12sm, D12pif), we formed "fixed" three-input models. Prediction quality was not diminished markedly (Table 5). These three-input models were compared with standard one-input models (with DMFT or dmft used as a single predictor). In general, the three-input models were found to be superior to the one-input models. However,
TABLE 3 RESULTS OF THE STEPWISE LOGISTIC REGRESSION ANALYSES [Age 7/8.Order of selected predictors (significant at p < 0.05). Sign of coefficients indicated. Radiological variables excluded.] 1984, n = 205 1980, n = 334 1976, n = 583 1972, n = 586 C4 C3 C2 C3 C4 C2 C4 C2 C3 C4 C3 C2 Primary teeth 11SOUpr 1111111SOUprm 1+ 2+ 1+ DFprm Permanent first molars 2+ 2+ D2fM 3+ 2+ D12fi 3D34Ffi 2+ D2pi 2+ D12pi 2+ D2pif 1+ 2+ 2+ D12pif
Dism 2+ Premolars: no predictors
D12sm
2+
2+
D2pfi D12pfi Anterior teeth
D12a
3+
3+
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STEINER et al.
the models with dm*ft (m*: only missing primary molars included) had nearly the same predictive power as the multiple models in the younger children. Predictability of caries increment was clearly better in the populations with low caries prevalence (1980 and 1984) than in the populations with high caries prevalence (1972 and 1976). In addition, when the threshold for "high caries increment" was raised from 2 (C2) to 4 (C4) lesions in four years, predictability increased somewhat, especially in the younger age class.
Discussion. The present investigations were based on unilateral recording. In view of the diagnostic unreliabilities, it would be preferable for research to be carried out on full-mouth data. It is reasonable to assume that SN, SP, and the area under the ROC curve might improve slightly in bilateral recording, because the variability due to diagnostic errors will be diminished. Variables based on the primary dentition supplied the best information with regard to caries prediction in all four data sets. This was true not only for the younger age group (7/8) but, surprisingly, also for the older age group (10/11). Both sound primary teeth (SOUpr) and sound primary molars (SOUprm) were significant predictors, but with a negative correlation. In the class of younger children, sound primary molars (SOUprm) could be replaced by decayed/filled units (DFprm). One is the complement of the other, as long as no primary molars are lost. For older children, DFprm was no longer a good predictor, probably because the DF count does not take into account missing primary molars and early erupted
J Dent Res December 1992
premolars (owing to extraction of decayed primary molars; Steiner et al., 1991). Bader et al. (1986), Abernathy et al. (1987), and ter Pelkwijk et al. (1990) have already shown the usefulness of dmft,
dmfs, and primary molar dmfs as predictors for younger children. While the present study confirms this finding, low numbers of sound primary molars were revealed to be more consistent predictors. The next important information concerning caries prediction was supplied by permanent first molars. Discolored fissures were already revealed as good predictors (Marthaler et al., 1990). The remarkable predictive potential ofwhite spots on lingual and buccal surfaces was documented by Kiock and Krasse (1979) and Seppa and Hausen (1988). Two other groups of authors (van Palenstein Helderman et al., 1989; Glass et al., 1990) found that the inclusion of pre-cavity lesions improved predictive power. However, Seppa and Hausen (1988) concluded that the inclusion ofpre-cavity lesions added little to the predictive power of conventional DFS scores. The inclusion of radiological predictors increased the predictability only marginally. It is therefore unreasonable to urge that radiographs be used at these ages so that caries prediction can be improved. Model performance was studied by means of the "split-sample approach". The results concerning SN, SP, and A obtained in the validation sets were similar to corresponding results in the estimation sets. However, the sample size of 51 for the validation set (the set 7/8 year old in the 1984 sample and C2) contained only 5 children with "high caries increment". The measures characterizing model performance have therefore to be interpreted with caution. As a simplification and for easy applicability, "fixed" three-input models containing SOUprm, D12pif, and D12sm were computed.
TABLE 4 RESULTS OF THE STEPWISE LOGISTIC REGRESSION ANALYSES [Age 10/11. Order of selected predictors (significant at p < 0.05). Sign of coefficients indicated. Radiological variables excluded.] 1972, n = 372 1976, n = 650 1980, n = 433 1984, n = 258 C2 C3 C4 C2 C4 C3 C2 C3 C4 C2 C4 C3 Primary teeth 1111SOUpr 111111SOUprm 1DFprm 2245Permanent first molars D2fi 4+ D12fi D34Ffi 5+ 2+ 3+ 2+ D2pi D12pi D2pif 4+ 4+ D12pif 3+ 3+ 2+ 3+ 2+ Dlsm 43+ D12sm 3+ 2+ 3+ 2+ 2+ 2+ 2+ 1+ 3+ Premolars D2pfi 2+ 3+ 3+ D12pfi Anterior teeth: no predictors D12a Downloaded from jdr.sagepub.com at UNIVERSITE DE MONTREAL on June 7, 2015 For personal use only. No other uses without permission.
DENTAL PREDICTORS OF HIGH CARIES INCREMENT
Vol. 71 No. 12
Age 7/8 SN SP A SN SP A
SN SP A SN SP A SN SP A
Age 10/11 SN SP A SN SP A
SN SP A SN SP A SN SP A
TABLE 5 SENSITIVITY (SN), SPECIFICITY (SP), AND AREA UNDER ROC CURVE (A) FOR DIFFERENT MODELS 1972, n = 586 1976, n = 583 1980, n = 334 1984, n = 205 C2 C4 C3 C2 C3 C4 C2 C3 C4 C2 C3 C4 Multiple models with stepwise selected predictors excluding radiological predictors 70 58 59 68 70 69 72 65 82 75 59 66 71 75 69 74 85 88 84 98 72 69 70 76 75 78 84 81 92 94 Multiple models with stepwise selected predictors including radiological predictors 64 72 64 70 65 74 74 71 78 65 82 100 66 54 59 65 68 77 72 75 81 88 84 84 69 69 72 73 74 82 78 83 88 81 92 94 "Fixed" 3-input models: SOUprm, D12sm, D12pif 62 74 56 67 66 68 71 69 72 62 82 75 60 53 70 64 66 71 65 71 83 87 88 91 67 68 71 69 70 74 75 76 79 79 92 94 1-input models: DMFT 61 40 42 44 50 54 0 40 39 96 100 100 37 63 63 65 64 63 100 75 74 3 9 9 50 51 52 54 57 61 51 57 55 51 55 54 1-input models: dm*ft 67 60 67 69 64 60 61 66 67 62 82 75 54 66 64 56 67 65 71 81 69 82 80 86 62 65 68 65 66 68 68 71 75 77 90 89 = = = 1972, n 372 1976, n 650 1980, n = 433 1984, n 258 C2 C4 C3 C2 C3 C4 C2 C4 C3 C2 C4 C3 Multiple models with stepwise selected predictors excluding radiological predictors 62 70 65 64 63 78 70 70 72 71 75 81 68 67 58 66 68 71 72 73 69 68 73 60 69 68 70 71 71 77 82 75 79 78 80 80 Multiple models with stepwise selected predictors including radiological predictors 62 66 64 72 71 75 66 67 71 81 75 71 72 72 65 68 59 67 68 71 70 71 76 72 74 71 70 73 78 78 78 80 82 85 70 79 "Fixed" 3-input models: SOUprm, D12sm, D12pif 62 71 65 71 75 76 55 56 59 66 69 73 62 64 71 73 72 66 63 66 63 63 56 65 82 74 75 80 80 67 66 67 69 73 75 65 DMFT models: 1-input 68 67 52 74 53 53 66 62 49 55 63 68 66 63 61 71 69 67 63 53 56 51 50 65 64 65 65 64 66 67 59 61 61 61 61 59 1-input models: dm*ft 64 34 0 59 68 52 28 57 75 71 51 49 64 100 72 48 62 62 54 30 60 60 61 59 56 51 50 60 52 64 54 51 54 58 63 53 67 58 67
72 54 69
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STEINER et al.
J Dent Res December 1992
These models showed nearly the same quality of prediction as models containing predictors selected by stepwise procedures (excluding radiographs). This signifies that (1) predictors within primary teeth and first molars are interchangeable up to a certain point, and that (2) the predictors within premolars and anterior teeth are not essential. A "fixed" model is desirable for practical reasons: It is simpler and probably more reliable in routine application, if the investigator or dentist always examines the same few sites. A comparison was made between the "fixed" three-input models and traditional models with dmft resp. DMFT as predictors. The dmf and DMF indices have been commonly used for measurement of the risk for future dental caries (dmft by Hill et al., 1967, and ter Pelkwijk et al., 1990; DMFT by Berman and Slack, 1973, and Honkalaetal., 1984). The respective predictions were inferior to the "fixed" three-input models, especially in the older age class. It is of course favorable that predictions are better in the lowcaries situation. While selective prevention is primarily indicated in populations with low caries prevalence, there is little need for selective prevention in populations with high caries prevalence, for which collective prevention is indicated.
SN 1.0
0.90.80.70.6 0.5 0.4 0.3 0.2i, . If le
.1
Acknowledgments.
i,
0.0oz
We thank Sandra Semadeni for the review of the manuscript and Adrian Bandi for the linkage of examinations and other computer assistance.
0.0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1
-
SP
REFERENCES
Fig.- Area under the receiver operating characteristic (ROC)-curve. SN= Sensitivity, SP= Specificity. Explanation in the text.
Abernathy JR, Graves RC, Bohannan HM, Stamm JW, Greenberg BG, DisneyJA(1987). Development and application of a prediction model for dental caries. Community Dent Oral Epidemiol 15:24-28. Afifi AA, Clark V (1990). Computer-aided multivariate analysis. 2nd ed. New York: Van Nostrand Reinhold Company, 162.
Bader JD, Graves RC, Disney JA, Bohannan HM, Stamm JW, Abernathy JR, et al. (1986). Identifying children who will experience high caries increments. Community Dent Oral Epidemiol 14:198-201. Bermann DS, Slack GL (1973). Caries experience relative to individual
TABLE 6 RESULTS OF SPLIT SAMPLING IN THE 1984 DATA SET [Sensitivity (SN), specificity (SP), and area under ROC curve (A) for "estimation sets" and "validation sets".]
Age7/8
C2
Models Sets
SOUprm*, D2pif Estim. 133/21
C3
SOUprm*, D2pi
SN
76
Val. 46/5 100
SP
69
67
86
62
A
80
86
93
89
nlow/hgh
Age 10/11 Models Sets
nlow/high SN
C2 SOUprm*, D12sm, D12pif Estim. Val. 149/45 51/13 73 92
Estim. 146/8 88
Val. 48/3 100
C3 SOUprm*, D12sm, D12pif Estim. Val. 158/36 60/4
75
75
SP
72
71
70
75
A
79
84
80
86
*The sign of the coefficient is negative. Downloaded from jdr.sagepub.com at UNIVERSITE DE MONTREAL on June 7, 2015 For personal use only. No other uses without permission.
DENTAL PREDICTORS OF HIGH CARIES INCREMENT
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Primary molars, numbers of sites sound approximal surfaces SOUprmr approximal surfaces with radiolucencies in enamel D12prmr D34Fprmr approximal surfaces with radiolucencies in dentin/ fillings Permanent first molars, numbers of teeth M missing molars Permanent first molars, numbers of sites slightly brown discolored occlusal fissures Difi dark brown/black discolored occlusal fissures D2fi slightly brown/dark brown/black discoloredocclusal D12fi fissures decayed/filled occlusal fissures D34Ffi
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D2pi D12pi D34Fpi
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Appendix: Explanatory variables, predictors. Primary teeth, numbers of teeth sound primary teeth SOUpr
SOUprm DFprm Mprm
sound primary molars decayed/filled primary molars missing primary molars
SOUpra DFpra Mpra
sound primary anterior teeth decayed/filled primary anterior teeth missing primary anterior teeth
Dlpi
Dlpif D2pif D12pif
D34Fpif DIsm D2sm
D12sm D34Fsm
slightly brown discolored pits (ling. on upper, bucc. on lower molars) dark brown/black discolored pits slightly brown/dark brown/black discolored pits decayed/filled pits
slightly brown discolored pits/fissures dark brown/black discolored pits/fissures slightly brown/dark brown/black discolored pits/ fissures decayed/filled pits/fissures lingual/buccal smooth surfaces with white spots (2mm) lingual/buccal smooth surfaces with white spots decayed/filled lingual/buccal smooth surfaces
Dir
approximal surfaces with radiolucencies in outer enamel D2r approximal surfaces with radiolucencies in inner enamel D12r approximal surfaces with radiolucencies in enamel approximal surfaces with radiolucencies in dentin/ D34Fr fillings Second molars, numbers of sites Dlm2fi slightly brown discolored occlusal fissures D2m2fi dark brown/black discolored occlusal fissures D34Fm2fi decayed/filled occlusal fissures Premolars, numbers of sites slightly brown discolored occlusal fissures Dlpfi dark brown/black discolored occlusal fissures D2pfi slightly brown/dark brown/black discolored occlusal D12pfi fissures decayed/filled occlusal fissures D34Fpfi
approximal surfaces with radiolucencies in outer enamel approximal surfaces with radiolucencies in inner D2pr enamel approximal surfaces with radiolucencies in enamel D12pr approximal surfaces with radiolucencies in dentin/ D34Fpr fillings Anterior teeth, numbers of sites surfaces with white spots (2mm) D2a surfaces with white spots D12a D34Fa decayed/filled surfaces
Dlpr
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