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Prediction of occlusion by measurements of the deciduous dentition
Prediction of occlusion by measurements of the deciduous den&ion Carlos Sanin, Bhim Don R. Thomas Portland,
S. Savara,
Quentin
C. Clarkson,
and
Ore.
I
t can be assumed that the adult dentition as a whole is related to the dentition at earlier ages. Although individual characteristics in the deciduous dentition are not highly correlated with characteristics in the permanent dentition, it is reasonable to assume that a system in a continuous environment will not have completely independent stages of development. On the basis of this assumption, we decided to explore the possibility of predicting occlusion in the permanent dentition from various characteristics in the deciduous dentition. This article presents the results of our investigation. Review
of the literature
A large portion of the longitudinal research concerning occlusion has been directed toward descriptive analysis and discussion of growth changes.l-* Although a basic aim of dentofacial growth studies is the prediction of future occlusal development, work in this area has been limited mainly to (1) linear c0rrelations,Q-14 (2) linear regression,*’ 15-17 and (3) multiple correlations.18 While a number of correlation coefficients have shown statistical significance, their clinical value is highly questionable. Stating that a correlation is statistically significant merely implies that the relationship did not occur by chance. The clinical value of the relationship is better evaluated by the coefficient squared; that is, a correlation of 0.3, which may be statistically significant, accounts for only 9 per cent of the variability and a correlation as high as 0.7 accounts for 49 per cent, or half, of the variability. The complexity of the development of the dental arches is such that it is highly improbable that any one variable could contain enough information to From
the
Child
This investigation of Child Health
Study
Clinic,
University
was supported in part and Human Development,
of
Oregon
Dental
by
Grant National
HD
School.
00157-09 Institutes
of
from the Health.
Institute
561
562
Xanin
et ul.
be of predictive value. An effective way to evaluate the predictive capacity of variables is through the use of multivariate statistical procedures. This approach has been used successfully by anthropologists for differentiation among racial groups and for the determination of sex from cranial measurements.1s-22 With the advent of cephalometric analysis, many procedures have been proposed for predicting facial growth. Prediction of facial growth by the multiple regression method has been attempted by JohnstonZ3 and Balbach.24 Both seem t,o agree that multiple regressions are more efficient than the addition of mean increments of change to the original values ; however, the difference in prediction is “clinically negligible.” It should be ment.ioncd that neither Johnston nor Balbaeh used a procedure with multiple response variables. The utilization of m&iI-ariate techniques for the study of occlusion, as such, has been limited to indicts of malocclusion.25 Factor analyses were used by GraingeF to study the intcrrelationships of malocclusion manifestations and by SOIOW~~to examine the pattern of associations between jaw mclasurcments and measurements that describe the tlcntition. The literature reviewed suggests that st,atistical procedures with multiple response variables have not been employ4 to attempt prediction 01 occlusion. Material
and
methods
Two samples were employed in this investigation. The first sample consisted of forty-eight children with serial study cast,s of the complete deciduous and permanent dentitions (excluding third molars). The results were tested with a second sample of forty-nine children. All children are Caucasians, born and reared in Oregon, and none had received orthodontic treatment. The study casts of the deciduous and permanent dentitions of each child in the first sample were classified by two orthodontists as malocclusion or acceptable occlusion. In the permanent dentition, a case was classified as a malocclusion when orthodontic treatment was considered desirable for esthetic reasons. In the deciduous dentition, bases for classification were the magnitude of the overjet and overbite, the presence of crowding and cross-bites, and the molar relationship. This classification was considered useful in view of the lack of an objective measure of occlusion. Table I shows the four possible groups and the sample size of each group. All measurements but orerjet and overbite were obtained with a new data acquisition method by Sarara and Sanin.28 Independent landmarks in X and Y Cartesian coordinates were recorded on IBM cards. Essentially, the equipment consists of a modified comparator and a decimal converter connected to an IBM keypunch. This equipment permits the obtaining of distances between any of the landmarks recorded. Measurement errors were studied for accurac? of equipment, reorientation of dental casts, reliability of measurements, and reproducibility of landmark location. Table II shows the variables measured in the deciduous dentition and utilized for the main part of this study. Definitiorb of variables. Mesiodistal crown diameters were defined anthropometrically as the greatest distance between the points of conta.ct or the approximate points where contact would occur. The average between the right and left sides was used.
Prediction Table
I. Distribution
in IWO
developmental Group
Table
of a sample stages
of forty-eight
as having
Decichow
Acceptable Malocclusion Malocclusion Acceptable
II. Measurements
in
the
untreated
occlusion
de&Son
1 2 3 4
1. 2. 3. 4. 5. 6. 7.
orthodontically
acceptable
or
Permanent 2 ____j ____$ -
deciduous
Mesiodistal crown diameter-average Width of the dental arch Length of the dental arch Perimeter of the dental arch Spacing-crowding Overjet Overbite
maxillary
and
of right
of occlusion children
classified
malocclusion dentition
It
Acceptable Malocclusion Acceptable Malocclusion
14 16 12 6
mandibular and
left
563
dental
homologous
arches teeth
Widths of the dental arch were defined as the distances between the cusp tip of the right canine, the lingual cusp of the right first molar, and the lingual cusps of the right second molars to corresponding landmarks on the left side. Length of the dental arch was the sagittal distance between a point midway of the mesio-incisal angles of the deciduous central incisors and a point midway of the right and left most distal landmarks. Circumference of the dental arch was the length of a 4 degree polynomial fitted through the mesial and distal crown landmarks of the maxillary and mandibular arches. Spacing and crowding were determined by subtracting the mesiodistal crown diameter of the teeth from the length of the arch circumference. Overjet was the distance between the linguo-incisal angle of the maxillary left central incisor and a point in the labial surface of a mandibular incisor. The millimeter ruler was held parallel to the occlusal plane. Overbite was defined as the length of the crown of the mandibular incisor overlapped by the left maxillary central incisor. Corresponding variables were measured in the permanent dentition but were used only for correlations. Statistical procedures used in this investigation include (1) simple correlation, a method of examining the relationship between a single X variable and a single Y variable ; (2) multiple correlation, a method of examining the relationship between a set of X variables and a single Y variable ; (3) canonical correlation, a logical extension of the simple correlation allowing one to study the relationships between a set of X variables and a set of Y variables ; (4) discriminant analysis, a method for distinguishing between individuals belonging to different groups on the basis of a weighted combination of several measurements.
564
Sanin et al.
Amer.
J. Orthodont. June 1970
Results
The statistical analysis of the data comprises two parts: (1) exploratoq procedures, such as coefficients of linear correlation, canonical correlation, and multiple correlations that apply to the sample as a whole, and (2) descriptivc and predictive procedures, such as means and standard deviations and stepwisc discriminant analyses that apply to the groups shown in Table I. A matrix of simple correlation coefficients between variables in the deciduous and the permanent dentitions is shown in Table VII. Highest coxrelations were found between maxillary arch width at. the second deciduous molars and maxillary arch width at the second premolars (0.80) and between the sum of the tleciduous maxillary crown diameters and the sum of the permanent mandibular crown diameters (0.77). Simple correlation coefficients furnish basic knowledge of variation, but mainly they point out the obstacles involved in prediction OP growth when single variables are utilized. A canonical correlation of 0.91 between the complex of the deciduous dentition variables and the complex of the permanent dentit,ion variables shows that the deciduous dentition, as a whole, is better correlated with t,he permanent dentition, as a whole, than single variables would suggest. Multiple correlations were, in general, larger when compared to simple correlations, but they do not appear to bc of clinical predictive value. The largest mult,iple correlation (0.81) was found between the dependent variable, maxillaq arch width at the second premolars, and th(a independent variables, the sum of the maxillaqv deciduous teeth, maxillar?. deciduous arch length, maxillary deciduous interdental spacing, maxillary arch width at the second deciduous molars, and mandibular deciduous arch length. However, the simple correlation between ma,xillary arch width at the second deciduous molars and maxillary arch width at the second premolars is of similar magnitude (that is, 0.80). The following results apply to the groups shown in Table I. Descriptive statistics of mcsiodistal crown diameters of the maxillary and mandibular deciduous teeth for each of the four groups arc shown in Table III. Consistent differences were found between the means of Group 1 and Groups 2. 3, and 4, thereby suggesting that acccptablc occlusions in both the deciduous and the permanent dentitions have small deciduous teeth. Table IV shows descriptive stat,istics concerning the width of the maxillary and mandibular deciduous dental arches for each of the four groups. Consistent differences were found between the means of Group 2 and the means of Groups I, 3, and 4, suggesting that malocclusions in both the deciduous and the permanent dentitions have narrower deciduous denta. arches. These results were expected, since a large percentage of malocclusions result from a tooth- and arch-size discrepancy. Large teeth or narrow arches would tend to produce malocclusion, but neither of these variables alone is enough to indica,te the development of a malocclusion. A child may have large teeth, but he may also have wide dental arches. Thus, occlusion must be treated as a multivariate system. As our specific purpose was to predict whether a child would have an acceptable occlusion or a malocclusion in the permanent dentition, a discrimina-
Prediction Table
III.
Mesiodistal
crown
diameters Group
of deciduous
1
Mean (mm.)
Tooth
d
Mean (mm.)
Group
3
1
Malocclusion Acceptable
Malocclusion+ Malocclusion S.D. (mm.)
565
teeth
Group
Acceptable-, Acceptable
of occlusion
S.D. (mm.)
Mean (mm.)
Group
4
Acceptable-+ Malocclusion S.D. (mm.)
Hean (mm.)
S.D. (mm.)
Maxillary Central incisor Lateral incisor Canine First molar Second molar
6.1 5.1 6.5 6.8 8.7
t f ?r + rf:
0.4 0.3 0.4 0.4 0.6
6.4 5.3 6.7 7.2 9.Q
k + + 2 2
0.4 0.4 0.4 0.4 0.5
6.5 5.4 6.7 7.1 8.9
t 2 + r +
0.7 0.5 0.5 0.7 0.6
6.1 5.5 6.7 7.4 9.2
3.9 4.4 5.5 7.6 9.5
f f. f +_ 2
0.5 0.3 0.3 0.4 0.4
3.9 4.7 5.7 7.8 10.0
+ + + 2 r
0.3 0.3 0.4 0.4 0.5
4.1 4.8 5.8 8.0 9.8
r +_ t t 2
0.4 0.4 0.4 0.8 0.7
3.9 4.8 5.7 7.8 10.1
t 2 2 2 rt
0.7 0.7 0.6 0.5 0.4
Manclibub Central incisor Lateral incisor Canine First molar Second molar
Table
IV. Widths
of the
deciduous
dental
Group
1
Acceptable+ Acceptable Mean (mm.)
0.4 0.5 0.4 0.6 0.4
arches Group
8
Malocclusion+ Malocclusion
Group
3
Malocclusion+ Acceptable
S.D.
Mean
S.D.
(mm.)
(mm.)
(mm.)
Mean (mm.)
Group
4
Acceptable+ Malocclusion S.D. (mm.)
Mean (mm.)
S.D. (mm.1
Maxillary Intercanine Inter-first Inter-second
molar molar
29.5 30.0 34.2
+_ f. f.
2.3 2.4 2.4
27.0 27.3 31.6
+ k +
1.8 2.2 2.2
28.3 29.0 33.4
+ r t
1.5 1.9 2.3
29.9 30.2 34.8
k k t
2.6 3.1 3.3
molar molar
22.6 25.7 29.3
2 t 5
2.0 1.9 1.9
22.7 25.1 28.2
C f. I!
1.0 1.7 2.1
22.9 25.6 28.8
+ f. 2
1.6 1.9 2.0
23.1 26.2 29.7
2 ? +
2.1 2.2 2.4
Mandibular Intercanine Inter-first Inter-second
tion procedure was used. This procedure determined a set of weights chosen in such a way that an unknown individual would be placed in a group with a minimum probability of being misclassified. Using the variables measured, we applied a stepwise discriminant analysis to select the most efficient variables. The four variables which accounted for the bulk of the separation between the four groups were (1) arch width at the maxillary second molars, (2) mesiodistal crown diameter of the maxillary first molar, (3) mesiodistal crown diameter of the mandibular first molar, and (4) mesiodistal crown diameter of the mandibular second molar. (Overjet and over-
566
Sani?l.
Table
V.
Discriminant
1 (acceptable Category
to
Amer.
al.
et
J. Orthodont.
June
functions
acceptable,
2 (malocclusion
derived acceptable
from to
the
forty-eight
malocclusion,
cases
grouped
malocclusion
to
into
Category
acceptable)
and
to malocclusion) Coeficients
lliscriminant Discriminant
Function Function
1970
1 2
-
Constant
Maxillary arch w&k E-E
BInxdlary mesiodistal D
Ma.ndibular mesiodistal E
-184.43 -183.19
33.90 24.71
-65.08 -24.37
252.63 283.45
If
Function
1 >
Function
2 =
Category
1.
If
Function
2 >
Function
1 =
Category
2.
Mandibulw mesiodistnl D 70.94 31.87
bite were irrelevant.) Seventy-one per cent of the children were classified correctly. Although 71 per cent is considerably better than one would expect from chance alone, it is of limited clinical value. A major difficulty is the environmental effect upon occlusion. Such factors as caries, habits, and oral and facial musculature have effects on occlusion that cannot be predicted from measurements of the dental arches. Using the four variables mentioned, we made a discriminant analysis between Group 2 (malocclusion at both stages) and a composite group made up of Groups 1, 3, and 4. The reason for grouping the cases in this manner is explained in the discussion. Table V shows the discriminant functions derived from these two groups. Eighty-two per cent of the cases were classified correctly using these functions, thus indicating that in a substantial percentage of the cases we can predict tooth-size-arch-width discrepancies from measurements in the deciduous dentition. We found that children with narrow deciduous arches and large or normal teeth or normal deciduous arches and large teeth often develop malocclusions. Reasons that explain some of the misclassifications of cases are (1) large deciduous teeth are not always indicative of large permanent teeth and (2) occlusion is not a discrete variable, taking on only two values. Subjective classification of occlusion gives ample opportunity for misclassifications, especially in the borderline region between acceptable occlusion and malocclusion. To test the validity of the results, the same four measurements were obtained in a sample of forty-nine different children. The children were classified into two categories according to the permanent dentition, as shown in Table V. The discriminant functions obtained above were applied, and each subject was placed in one of the two groups. Results showed that 65.3 per cent of the children were correctly classified. Discussion
The reason for grouping the forty-eight cases into two major categories( 1) acceptable-acceptable, acceptable-malocclusion, malocclusion-acceptable
Volume Number
57 6
Prediction
Table VI. Hypothesized grouping
the children
simplified genetic-environmental into Categories 1 and 2
Deciduous
model
of occlusion
which
567
was the basis for
Permanent
A.
Favorable favorable
genetics and environment
Acceptable occlusion
Favorable genetics and favorable environment
Acceptable occlusion
Same as Group 1
B.
Favorable unfavorable
genetics and environment
Malocclusion
Favorable genetics and favorable environment
Acceptable occlusion
Same as Group 3
C. Favorable favorable
genetics and environment
Acceptable occlusion
Favorable genetics and unfavorable environment
Malocclusion
Same as Group 4
D.
Favorable unfavorable
genetics and environment
Malocclusion
Favorable genetics and unfavorable environment
Malocclusion
Part of Group 2
E.
Unfavorable genetics any environment
Malocclusion
Unfavorable and any environment
Malocclusion
Part of Group 2
and
genetics
and (2) malocclusion-malocclusion-was that, ideally, we would like to be able to separate the environmental influences from the genetic influences and then predict whether or not a child has the genetic potential for acceptable occlusion. To do this, we have hypothesized the following simplified model. First, we assumed that occlusion is discrete (that is, either it is acceptable or it is a malocelusion). Second, we assumed that malocclusion could be primarily genetic in nature or primarily environmental. Using these assumptions, we can equate each of our four groupings with one or more combination of genetics and environment. Table VI gives these combinations and equalities. Notice that all possible combinations of genetics and environment are given and that each combination is equated with only one of our four groupings. Also notice that all malocclusion due to unfavorable genetics would be contained in Group 2. Thus, our hypothesis is that Group 2 contains all the children who would have genetically determined malocclusion in the permanent dentition. Group 2 also contains some children with favorable genetics but continually poor environment, but the important point is that Groups 1, 3, and 4 contain none of the children with unfavorable genetics. The results of the test on the additional sample tend to confirm the consistency of the above model. Although a rate of 65.3 per cent correct classifications would be of limited clinical value, it is still considerably better than one would expect from chance alone. (Probability of classifying thirty-two or more of the forty-nine correctly by chance alone is 3.14 per cent.) Several suggestions can be made which might improve the accuracy of predictions. First, if the above model is correct, we would expect to misclassify those subjects who had potentially good occlusion but who had malocclusion due to
Sank
568
Table
VII.
A4mer. J. Orthodont. June 1970
et al.
Correlation
coefficients
Deciduous
\
Permanent
between
variables
in the
deciduous
dentition
and
permanent
dentitions
Maxillary
\
dentition
ikfaxillary 1
Sum tooth sizes (11,12, C, Pm Total crowd (perimeter-tooth
0.65 1, Pm
2 -0.11
3
4
5
6
0.36
0.31
0.50
0.08
2)
spat
0.08
0.36
0.49
0.15
0.24
0.38
0.33
0.80
0.71
0.34
-0.10
size) 2
0.11
Arch (cusp
width-Pm tips)
Arch (cusp
width-C tips)
0.52
0.04
0.54
0.52
0.31
Arch length (sagittal distance)
0.51
0.04
0.30
0.29
0.58
0.08
Arch
0.09
0.15
0.18
0.18
0.15
--0.03
0.32
0.23
0.57
0.14
0.30
0 .t‘35
0.33
0.06
.-0.09
perimeter
-0.09
Xandibzclar Sum tooth sizes (I 1, I 2, C, Pm 1, Pm Total crowd (perimeter-tooth
spat
G
0.7i
H
-0.07
-0.22
2)
size) I
0.38
0.21
0.59
0.44
0.36
0.04
width-C tips)
J
0.43
0.13
0.38
0.30
0.45
0.00
Arch length (sagittal distance)
K
,0.46
0.01
0.38
0.38
0.44
0.06
Arch
L
0.09
0.26
0.39
0.35
0.09
0.02
Overjet
M
0.31
-0.31
-0.17
-0.16
0.22
-0.10
Overbite
iv
0.07
-0.26
-0.04
-0.08
-0.14
-0:04
Arch width-Pm (cusp tips) Arch (cusp
perimeter
2
Volume Number
57 6
Prediction
of occlusion
569
Mandibular
8
10
11
12
13
14
0.56
-0.22
0.20
0.18
0.39
0.02
0.17
0.05
0.07
0.25
0.44
0.36
0.40
-0.10
-0.08
-0.03
0.30
0.12
0.67
0.52
0.44
0.08
-80.18
0.04
0.36
-0.06
0.41
0.38
0.33
-0.12
0.06
0.05
0.46
-0.13
0.11
0.14
0.55
0.02
0.16
-0.01
0.09
0.17
0.18
0.17
0.39
-0.01
-0.11
-0.01
0.69
-0.33
0.19
0.24
0.45
0.08
0.28
-0.04
-0.07
0.35
0.40
0.41
0.29
-0.02
-0.20
0.12
0.32
0.07
0.69
0.60
0.38
0.03
0.10
0.03
0.35
0.14
0.41
0.51
0.48
0.03
0.17
-0.14
0.45
-0.01
0.24
0.25
0.55
0.05
-0.02
0.21
0.14
0.18
0.39
0.33
0.34
0.04
-0.26
0.12
0.30
-0.24
-0.24
0.00
0.20
-0.09
0.38
0.06
0.07
-0.01
0.02
0.06
0.02
0.02
-0.02
0.36
7
9
570
Sanin
et
al.
Amer.
J. Orthodont. June 1970
environmental factors. In our subjective classification of the subjects with malocclusion, we made no attempt to determine the cause of malocclusion. One possible approach would be the use of factor analysis to gain insight into genet.ic and environmental factors of malocclusion. Second, the original division into groups must be done subjectively, and there was an appreciable number of borderline cases in which the classification could have gone either way, depending upon the orthodontist. Because of the small sample size, these borderline cases were included and classified by the consensus of two orthodontists after comparison with the more easily classifiect cases. This borderline malocclusion difficulty might be resolved in two ways. With a larger sample, separate groups of borderline cases could be formed and a discriminant analysis performed, with the borderline groups being classified decision.” Alternatively, ;1S “no one could use factor analysis or principle components to obtain a continuous, relatively objective index of occlusion and then form a regressive model with the permanent dentition’s index of occlusion being a function of the measurements made on the deciduous dentition. Third, the four variables used in our discrimination are representative mainly of Class I occlusions. If variables can be found which adequately describe other occlusions, they should be included in the predicting functions. Summary
Dental characteristics of the deciduous dentitions of forty-eight children were used to predict the occlusion of the same children in the permanent dentition. The first portion of this study determined the most useful occlusal characteristics for prediction ; the second portion tested the validity of the results on a different sample. The study casts of the deciduous and permanent dentitions of each person were classified as either acceptable occlusion or malocclusion, resulting in the following four groups: (1) acceptable in the deciduous and permanent dentitions; (2) malocclusion in the deciduous and permanent dentitions; (3) malocclusion in the deciduous dentition and acceptable in the permanent dentition; (A) acceptable in the deciduous dentition and malocclusion in the permanent dentition. Tooth size and arch width in the deciduous dentition were compared among the four groups. It was found that malocclusion in the deciduous and permanent dentitions tend to have narrower deciduous dental arches. Furthermore, acceptable occlusions in the deciduous and permanent dentitions tend to have smaller deciduous teeth. We hypothesized that the group with malocclusion in the deciduous and permanent dentitions contains the children with genetically determined malocclusion in the permanent dentition. Statistical procedures indicated that measurements of deciduous arch width and tooth size could be used to predict the occlusion in the permanent dentitions of 82 per cent of the sample. (Children grouped as follows: A, malocclusion in the deciduous and permanent dentitions ; B, Groups 1, 3, and 4 mentioned above.) This finding suggested that if the sample was representative of the population, a large num-
Prediction
of occlusion
571
ber of children who were going to have malocclusion resulting from tooth- and arch-size discrepancies could be identified from four measurements at as early as 3 or 4 years of age. The validity of this result was tested on a different sample of forty-nine children, and in 65.3 per cent of the children malocclusion or acceptable occlusion in the permanent dentition was predicted correctly. While the use of powerful statistical procedures resulted in findings statistically significant in both experiments, they were not sufficiently strong to be clinically valid. REFERENCES
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J. Orthodont.
June19io
Hanihara, K.: Sex diagnosis of Japanese skulls and scapulae by means of discriminant 1959 (summary in English). function, J. Anthrop. Sot. Nippon 67: 191-197, Johnston, T,. E.: A statistical evaluation of cephalometric prediction, Angle Orthodontist 38: 284-304, 1968. Balbach, D.: The cephalometric relationship between the morphology of the mandible and its future occlusal position, Angle Orthodontist 39: 29-41, 1969. Freer, T. J., an<1 Adkins, B. I,.: New approach to malocclusion and indices, J. D. Res. 48: 1111-1117, lQ68. Grainger, R. M.: Interrelations of malocclusion manifestations (mathematical elucitlation of malocclusion syndromes). In Staple, P. H. (editor): Advances in Oral Bio1og.v~ Sew York, lQ68, Academic Press, Inc., vol. 3. Solow, B.: The pattern of craniofacial associations, Acta odont, scandinav. 24: Suppl. 46, 1966. Savara, B. S., and Sanin, C.: A new data acquisition method for measuring dentitions and tests for accuracy, Am. J. Phys. Anthrop. 30: 315-318, 1969. Birkby, W, H.: An evaluation of race and sex identification from cranial measurements, Am. J. Phys. Anthrop. 24: 21-27, 1966. Giles, E.: Sex determination by discriminant function analysis of the mandible, Am. J. Phys. Snthrop. 22: 129-135, 1964. Maj, G., and Luzi, C.: Longitudinal study of mandibular growth between nine and thirteen years as a basis for an attempt at its prediction, Angle Orthodontist 34: 2% 230, 1964. statistical methods in biometric research, New York, 1952, John Rao, C. R.: Advanced Wiley & Sons, Inc. Sanin, C., and Hixon, B. H.: Axial rotations of maxillary permanent incisors, Anglr, Orthodontist 38: 269-283, 1968. Horowitz, S. L., and Hixon, E. H.: The nature of orthodontic diagnosis, St. Louis, 1966, ‘l’he C. V. Mosby Company. G11 S.W.
Campus
Drive
Normal is so individual that we do not know when we have even treatment. Normal is not confined to form alone. There is a normal form and function are so inseparable, each one constantly modifying other, we must think of normal as embracing both. (Mershon, John lingual arch appliance, Transactions of the First [ 19261 International gress, St. Louis, 1927, The C. V. Mosby Company, pp. 279-303.)
attained it in our of function. Since and changing the V.: The removable Orthodontic Con-
S. Savara,
Quentin
C. Clarkson,
and
Ore.
I
t can be assumed that the adult dentition as a whole is related to the dentition at earlier ages. Although individual characteristics in the deciduous dentition are not highly correlated with characteristics in the permanent dentition, it is reasonable to assume that a system in a continuous environment will not have completely independent stages of development. On the basis of this assumption, we decided to explore the possibility of predicting occlusion in the permanent dentition from various characteristics in the deciduous dentition. This article presents the results of our investigation. Review
of the literature
A large portion of the longitudinal research concerning occlusion has been directed toward descriptive analysis and discussion of growth changes.l-* Although a basic aim of dentofacial growth studies is the prediction of future occlusal development, work in this area has been limited mainly to (1) linear c0rrelations,Q-14 (2) linear regression,*’ 15-17 and (3) multiple correlations.18 While a number of correlation coefficients have shown statistical significance, their clinical value is highly questionable. Stating that a correlation is statistically significant merely implies that the relationship did not occur by chance. The clinical value of the relationship is better evaluated by the coefficient squared; that is, a correlation of 0.3, which may be statistically significant, accounts for only 9 per cent of the variability and a correlation as high as 0.7 accounts for 49 per cent, or half, of the variability. The complexity of the development of the dental arches is such that it is highly improbable that any one variable could contain enough information to From
the
Child
This investigation of Child Health
Study
Clinic,
University
was supported in part and Human Development,
of
Oregon
Dental
by
Grant National
HD
School.
00157-09 Institutes
of
from the Health.
Institute
561
562
Xanin
et ul.
be of predictive value. An effective way to evaluate the predictive capacity of variables is through the use of multivariate statistical procedures. This approach has been used successfully by anthropologists for differentiation among racial groups and for the determination of sex from cranial measurements.1s-22 With the advent of cephalometric analysis, many procedures have been proposed for predicting facial growth. Prediction of facial growth by the multiple regression method has been attempted by JohnstonZ3 and Balbach.24 Both seem t,o agree that multiple regressions are more efficient than the addition of mean increments of change to the original values ; however, the difference in prediction is “clinically negligible.” It should be ment.ioncd that neither Johnston nor Balbaeh used a procedure with multiple response variables. The utilization of m&iI-ariate techniques for the study of occlusion, as such, has been limited to indicts of malocclusion.25 Factor analyses were used by GraingeF to study the intcrrelationships of malocclusion manifestations and by SOIOW~~to examine the pattern of associations between jaw mclasurcments and measurements that describe the tlcntition. The literature reviewed suggests that st,atistical procedures with multiple response variables have not been employ4 to attempt prediction 01 occlusion. Material
and
methods
Two samples were employed in this investigation. The first sample consisted of forty-eight children with serial study cast,s of the complete deciduous and permanent dentitions (excluding third molars). The results were tested with a second sample of forty-nine children. All children are Caucasians, born and reared in Oregon, and none had received orthodontic treatment. The study casts of the deciduous and permanent dentitions of each child in the first sample were classified by two orthodontists as malocclusion or acceptable occlusion. In the permanent dentition, a case was classified as a malocclusion when orthodontic treatment was considered desirable for esthetic reasons. In the deciduous dentition, bases for classification were the magnitude of the overjet and overbite, the presence of crowding and cross-bites, and the molar relationship. This classification was considered useful in view of the lack of an objective measure of occlusion. Table I shows the four possible groups and the sample size of each group. All measurements but orerjet and overbite were obtained with a new data acquisition method by Sarara and Sanin.28 Independent landmarks in X and Y Cartesian coordinates were recorded on IBM cards. Essentially, the equipment consists of a modified comparator and a decimal converter connected to an IBM keypunch. This equipment permits the obtaining of distances between any of the landmarks recorded. Measurement errors were studied for accurac? of equipment, reorientation of dental casts, reliability of measurements, and reproducibility of landmark location. Table II shows the variables measured in the deciduous dentition and utilized for the main part of this study. Definitiorb of variables. Mesiodistal crown diameters were defined anthropometrically as the greatest distance between the points of conta.ct or the approximate points where contact would occur. The average between the right and left sides was used.
Prediction Table
I. Distribution
in IWO
developmental Group
Table
of a sample stages
of forty-eight
as having
Decichow
Acceptable Malocclusion Malocclusion Acceptable
II. Measurements
in
the
untreated
occlusion
de&Son
1 2 3 4
1. 2. 3. 4. 5. 6. 7.
orthodontically
acceptable
or
Permanent 2 ____j ____$ -
deciduous
Mesiodistal crown diameter-average Width of the dental arch Length of the dental arch Perimeter of the dental arch Spacing-crowding Overjet Overbite
maxillary
and
of right
of occlusion children
classified
malocclusion dentition
It
Acceptable Malocclusion Acceptable Malocclusion
14 16 12 6
mandibular and
left
563
dental
homologous
arches teeth
Widths of the dental arch were defined as the distances between the cusp tip of the right canine, the lingual cusp of the right first molar, and the lingual cusps of the right second molars to corresponding landmarks on the left side. Length of the dental arch was the sagittal distance between a point midway of the mesio-incisal angles of the deciduous central incisors and a point midway of the right and left most distal landmarks. Circumference of the dental arch was the length of a 4 degree polynomial fitted through the mesial and distal crown landmarks of the maxillary and mandibular arches. Spacing and crowding were determined by subtracting the mesiodistal crown diameter of the teeth from the length of the arch circumference. Overjet was the distance between the linguo-incisal angle of the maxillary left central incisor and a point in the labial surface of a mandibular incisor. The millimeter ruler was held parallel to the occlusal plane. Overbite was defined as the length of the crown of the mandibular incisor overlapped by the left maxillary central incisor. Corresponding variables were measured in the permanent dentition but were used only for correlations. Statistical procedures used in this investigation include (1) simple correlation, a method of examining the relationship between a single X variable and a single Y variable ; (2) multiple correlation, a method of examining the relationship between a set of X variables and a single Y variable ; (3) canonical correlation, a logical extension of the simple correlation allowing one to study the relationships between a set of X variables and a set of Y variables ; (4) discriminant analysis, a method for distinguishing between individuals belonging to different groups on the basis of a weighted combination of several measurements.
564
Sanin et al.
Amer.
J. Orthodont. June 1970
Results
The statistical analysis of the data comprises two parts: (1) exploratoq procedures, such as coefficients of linear correlation, canonical correlation, and multiple correlations that apply to the sample as a whole, and (2) descriptivc and predictive procedures, such as means and standard deviations and stepwisc discriminant analyses that apply to the groups shown in Table I. A matrix of simple correlation coefficients between variables in the deciduous and the permanent dentitions is shown in Table VII. Highest coxrelations were found between maxillary arch width at. the second deciduous molars and maxillary arch width at the second premolars (0.80) and between the sum of the tleciduous maxillary crown diameters and the sum of the permanent mandibular crown diameters (0.77). Simple correlation coefficients furnish basic knowledge of variation, but mainly they point out the obstacles involved in prediction OP growth when single variables are utilized. A canonical correlation of 0.91 between the complex of the deciduous dentition variables and the complex of the permanent dentit,ion variables shows that the deciduous dentition, as a whole, is better correlated with t,he permanent dentition, as a whole, than single variables would suggest. Multiple correlations were, in general, larger when compared to simple correlations, but they do not appear to bc of clinical predictive value. The largest mult,iple correlation (0.81) was found between the dependent variable, maxillaq arch width at the second premolars, and th(a independent variables, the sum of the maxillaqv deciduous teeth, maxillar?. deciduous arch length, maxillary deciduous interdental spacing, maxillary arch width at the second deciduous molars, and mandibular deciduous arch length. However, the simple correlation between ma,xillary arch width at the second deciduous molars and maxillary arch width at the second premolars is of similar magnitude (that is, 0.80). The following results apply to the groups shown in Table I. Descriptive statistics of mcsiodistal crown diameters of the maxillary and mandibular deciduous teeth for each of the four groups arc shown in Table III. Consistent differences were found between the means of Group 1 and Groups 2. 3, and 4, thereby suggesting that acccptablc occlusions in both the deciduous and the permanent dentitions have small deciduous teeth. Table IV shows descriptive stat,istics concerning the width of the maxillary and mandibular deciduous dental arches for each of the four groups. Consistent differences were found between the means of Group 2 and the means of Groups I, 3, and 4, suggesting that malocclusions in both the deciduous and the permanent dentitions have narrower deciduous denta. arches. These results were expected, since a large percentage of malocclusions result from a tooth- and arch-size discrepancy. Large teeth or narrow arches would tend to produce malocclusion, but neither of these variables alone is enough to indica,te the development of a malocclusion. A child may have large teeth, but he may also have wide dental arches. Thus, occlusion must be treated as a multivariate system. As our specific purpose was to predict whether a child would have an acceptable occlusion or a malocclusion in the permanent dentition, a discrimina-
Prediction Table
III.
Mesiodistal
crown
diameters Group
of deciduous
1
Mean (mm.)
Tooth
d
Mean (mm.)
Group
3
1
Malocclusion Acceptable
Malocclusion+ Malocclusion S.D. (mm.)
565
teeth
Group
Acceptable-, Acceptable
of occlusion
S.D. (mm.)
Mean (mm.)
Group
4
Acceptable-+ Malocclusion S.D. (mm.)
Hean (mm.)
S.D. (mm.)
Maxillary Central incisor Lateral incisor Canine First molar Second molar
6.1 5.1 6.5 6.8 8.7
t f ?r + rf:
0.4 0.3 0.4 0.4 0.6
6.4 5.3 6.7 7.2 9.Q
k + + 2 2
0.4 0.4 0.4 0.4 0.5
6.5 5.4 6.7 7.1 8.9
t 2 + r +
0.7 0.5 0.5 0.7 0.6
6.1 5.5 6.7 7.4 9.2
3.9 4.4 5.5 7.6 9.5
f f. f +_ 2
0.5 0.3 0.3 0.4 0.4
3.9 4.7 5.7 7.8 10.0
+ + + 2 r
0.3 0.3 0.4 0.4 0.5
4.1 4.8 5.8 8.0 9.8
r +_ t t 2
0.4 0.4 0.4 0.8 0.7
3.9 4.8 5.7 7.8 10.1
t 2 2 2 rt
0.7 0.7 0.6 0.5 0.4
Manclibub Central incisor Lateral incisor Canine First molar Second molar
Table
IV. Widths
of the
deciduous
dental
Group
1
Acceptable+ Acceptable Mean (mm.)
0.4 0.5 0.4 0.6 0.4
arches Group
8
Malocclusion+ Malocclusion
Group
3
Malocclusion+ Acceptable
S.D.
Mean
S.D.
(mm.)
(mm.)
(mm.)
Mean (mm.)
Group
4
Acceptable+ Malocclusion S.D. (mm.)
Mean (mm.)
S.D. (mm.1
Maxillary Intercanine Inter-first Inter-second
molar molar
29.5 30.0 34.2
+_ f. f.
2.3 2.4 2.4
27.0 27.3 31.6
+ k +
1.8 2.2 2.2
28.3 29.0 33.4
+ r t
1.5 1.9 2.3
29.9 30.2 34.8
k k t
2.6 3.1 3.3
molar molar
22.6 25.7 29.3
2 t 5
2.0 1.9 1.9
22.7 25.1 28.2
C f. I!
1.0 1.7 2.1
22.9 25.6 28.8
+ f. 2
1.6 1.9 2.0
23.1 26.2 29.7
2 ? +
2.1 2.2 2.4
Mandibular Intercanine Inter-first Inter-second
tion procedure was used. This procedure determined a set of weights chosen in such a way that an unknown individual would be placed in a group with a minimum probability of being misclassified. Using the variables measured, we applied a stepwise discriminant analysis to select the most efficient variables. The four variables which accounted for the bulk of the separation between the four groups were (1) arch width at the maxillary second molars, (2) mesiodistal crown diameter of the maxillary first molar, (3) mesiodistal crown diameter of the mandibular first molar, and (4) mesiodistal crown diameter of the mandibular second molar. (Overjet and over-
566
Sani?l.
Table
V.
Discriminant
1 (acceptable Category
to
Amer.
al.
et
J. Orthodont.
June
functions
acceptable,
2 (malocclusion
derived acceptable
from to
the
forty-eight
malocclusion,
cases
grouped
malocclusion
to
into
Category
acceptable)
and
to malocclusion) Coeficients
lliscriminant Discriminant
Function Function
1970
1 2
-
Constant
Maxillary arch w&k E-E
BInxdlary mesiodistal D
Ma.ndibular mesiodistal E
-184.43 -183.19
33.90 24.71
-65.08 -24.37
252.63 283.45
If
Function
1 >
Function
2 =
Category
1.
If
Function
2 >
Function
1 =
Category
2.
Mandibulw mesiodistnl D 70.94 31.87
bite were irrelevant.) Seventy-one per cent of the children were classified correctly. Although 71 per cent is considerably better than one would expect from chance alone, it is of limited clinical value. A major difficulty is the environmental effect upon occlusion. Such factors as caries, habits, and oral and facial musculature have effects on occlusion that cannot be predicted from measurements of the dental arches. Using the four variables mentioned, we made a discriminant analysis between Group 2 (malocclusion at both stages) and a composite group made up of Groups 1, 3, and 4. The reason for grouping the cases in this manner is explained in the discussion. Table V shows the discriminant functions derived from these two groups. Eighty-two per cent of the cases were classified correctly using these functions, thus indicating that in a substantial percentage of the cases we can predict tooth-size-arch-width discrepancies from measurements in the deciduous dentition. We found that children with narrow deciduous arches and large or normal teeth or normal deciduous arches and large teeth often develop malocclusions. Reasons that explain some of the misclassifications of cases are (1) large deciduous teeth are not always indicative of large permanent teeth and (2) occlusion is not a discrete variable, taking on only two values. Subjective classification of occlusion gives ample opportunity for misclassifications, especially in the borderline region between acceptable occlusion and malocclusion. To test the validity of the results, the same four measurements were obtained in a sample of forty-nine different children. The children were classified into two categories according to the permanent dentition, as shown in Table V. The discriminant functions obtained above were applied, and each subject was placed in one of the two groups. Results showed that 65.3 per cent of the children were correctly classified. Discussion
The reason for grouping the forty-eight cases into two major categories( 1) acceptable-acceptable, acceptable-malocclusion, malocclusion-acceptable
Volume Number
57 6
Prediction
Table VI. Hypothesized grouping
the children
simplified genetic-environmental into Categories 1 and 2
Deciduous
model
of occlusion
which
567
was the basis for
Permanent
A.
Favorable favorable
genetics and environment
Acceptable occlusion
Favorable genetics and favorable environment
Acceptable occlusion
Same as Group 1
B.
Favorable unfavorable
genetics and environment
Malocclusion
Favorable genetics and favorable environment
Acceptable occlusion
Same as Group 3
C. Favorable favorable
genetics and environment
Acceptable occlusion
Favorable genetics and unfavorable environment
Malocclusion
Same as Group 4
D.
Favorable unfavorable
genetics and environment
Malocclusion
Favorable genetics and unfavorable environment
Malocclusion
Part of Group 2
E.
Unfavorable genetics any environment
Malocclusion
Unfavorable and any environment
Malocclusion
Part of Group 2
and
genetics
and (2) malocclusion-malocclusion-was that, ideally, we would like to be able to separate the environmental influences from the genetic influences and then predict whether or not a child has the genetic potential for acceptable occlusion. To do this, we have hypothesized the following simplified model. First, we assumed that occlusion is discrete (that is, either it is acceptable or it is a malocelusion). Second, we assumed that malocclusion could be primarily genetic in nature or primarily environmental. Using these assumptions, we can equate each of our four groupings with one or more combination of genetics and environment. Table VI gives these combinations and equalities. Notice that all possible combinations of genetics and environment are given and that each combination is equated with only one of our four groupings. Also notice that all malocclusion due to unfavorable genetics would be contained in Group 2. Thus, our hypothesis is that Group 2 contains all the children who would have genetically determined malocclusion in the permanent dentition. Group 2 also contains some children with favorable genetics but continually poor environment, but the important point is that Groups 1, 3, and 4 contain none of the children with unfavorable genetics. The results of the test on the additional sample tend to confirm the consistency of the above model. Although a rate of 65.3 per cent correct classifications would be of limited clinical value, it is still considerably better than one would expect from chance alone. (Probability of classifying thirty-two or more of the forty-nine correctly by chance alone is 3.14 per cent.) Several suggestions can be made which might improve the accuracy of predictions. First, if the above model is correct, we would expect to misclassify those subjects who had potentially good occlusion but who had malocclusion due to
Sank
568
Table
VII.
A4mer. J. Orthodont. June 1970
et al.
Correlation
coefficients
Deciduous
\
Permanent
between
variables
in the
deciduous
dentition
and
permanent
dentitions
Maxillary
\
dentition
ikfaxillary 1
Sum tooth sizes (11,12, C, Pm Total crowd (perimeter-tooth
0.65 1, Pm
2 -0.11
3
4
5
6
0.36
0.31
0.50
0.08
2)
spat
0.08
0.36
0.49
0.15
0.24
0.38
0.33
0.80
0.71
0.34
-0.10
size) 2
0.11
Arch (cusp
width-Pm tips)
Arch (cusp
width-C tips)
0.52
0.04
0.54
0.52
0.31
Arch length (sagittal distance)
0.51
0.04
0.30
0.29
0.58
0.08
Arch
0.09
0.15
0.18
0.18
0.15
--0.03
0.32
0.23
0.57
0.14
0.30
0 .t‘35
0.33
0.06
.-0.09
perimeter
-0.09
Xandibzclar Sum tooth sizes (I 1, I 2, C, Pm 1, Pm Total crowd (perimeter-tooth
spat
G
0.7i
H
-0.07
-0.22
2)
size) I
0.38
0.21
0.59
0.44
0.36
0.04
width-C tips)
J
0.43
0.13
0.38
0.30
0.45
0.00
Arch length (sagittal distance)
K
,0.46
0.01
0.38
0.38
0.44
0.06
Arch
L
0.09
0.26
0.39
0.35
0.09
0.02
Overjet
M
0.31
-0.31
-0.17
-0.16
0.22
-0.10
Overbite
iv
0.07
-0.26
-0.04
-0.08
-0.14
-0:04
Arch width-Pm (cusp tips) Arch (cusp
perimeter
2
Volume Number
57 6
Prediction
of occlusion
569
Mandibular
8
10
11
12
13
14
0.56
-0.22
0.20
0.18
0.39
0.02
0.17
0.05
0.07
0.25
0.44
0.36
0.40
-0.10
-0.08
-0.03
0.30
0.12
0.67
0.52
0.44
0.08
-80.18
0.04
0.36
-0.06
0.41
0.38
0.33
-0.12
0.06
0.05
0.46
-0.13
0.11
0.14
0.55
0.02
0.16
-0.01
0.09
0.17
0.18
0.17
0.39
-0.01
-0.11
-0.01
0.69
-0.33
0.19
0.24
0.45
0.08
0.28
-0.04
-0.07
0.35
0.40
0.41
0.29
-0.02
-0.20
0.12
0.32
0.07
0.69
0.60
0.38
0.03
0.10
0.03
0.35
0.14
0.41
0.51
0.48
0.03
0.17
-0.14
0.45
-0.01
0.24
0.25
0.55
0.05
-0.02
0.21
0.14
0.18
0.39
0.33
0.34
0.04
-0.26
0.12
0.30
-0.24
-0.24
0.00
0.20
-0.09
0.38
0.06
0.07
-0.01
0.02
0.06
0.02
0.02
-0.02
0.36
7
9
570
Sanin
et
al.
Amer.
J. Orthodont. June 1970
environmental factors. In our subjective classification of the subjects with malocclusion, we made no attempt to determine the cause of malocclusion. One possible approach would be the use of factor analysis to gain insight into genet.ic and environmental factors of malocclusion. Second, the original division into groups must be done subjectively, and there was an appreciable number of borderline cases in which the classification could have gone either way, depending upon the orthodontist. Because of the small sample size, these borderline cases were included and classified by the consensus of two orthodontists after comparison with the more easily classifiect cases. This borderline malocclusion difficulty might be resolved in two ways. With a larger sample, separate groups of borderline cases could be formed and a discriminant analysis performed, with the borderline groups being classified decision.” Alternatively, ;1S “no one could use factor analysis or principle components to obtain a continuous, relatively objective index of occlusion and then form a regressive model with the permanent dentition’s index of occlusion being a function of the measurements made on the deciduous dentition. Third, the four variables used in our discrimination are representative mainly of Class I occlusions. If variables can be found which adequately describe other occlusions, they should be included in the predicting functions. Summary
Dental characteristics of the deciduous dentitions of forty-eight children were used to predict the occlusion of the same children in the permanent dentition. The first portion of this study determined the most useful occlusal characteristics for prediction ; the second portion tested the validity of the results on a different sample. The study casts of the deciduous and permanent dentitions of each person were classified as either acceptable occlusion or malocclusion, resulting in the following four groups: (1) acceptable in the deciduous and permanent dentitions; (2) malocclusion in the deciduous and permanent dentitions; (3) malocclusion in the deciduous dentition and acceptable in the permanent dentition; (A) acceptable in the deciduous dentition and malocclusion in the permanent dentition. Tooth size and arch width in the deciduous dentition were compared among the four groups. It was found that malocclusion in the deciduous and permanent dentitions tend to have narrower deciduous dental arches. Furthermore, acceptable occlusions in the deciduous and permanent dentitions tend to have smaller deciduous teeth. We hypothesized that the group with malocclusion in the deciduous and permanent dentitions contains the children with genetically determined malocclusion in the permanent dentition. Statistical procedures indicated that measurements of deciduous arch width and tooth size could be used to predict the occlusion in the permanent dentitions of 82 per cent of the sample. (Children grouped as follows: A, malocclusion in the deciduous and permanent dentitions ; B, Groups 1, 3, and 4 mentioned above.) This finding suggested that if the sample was representative of the population, a large num-
Prediction
of occlusion
571
ber of children who were going to have malocclusion resulting from tooth- and arch-size discrepancies could be identified from four measurements at as early as 3 or 4 years of age. The validity of this result was tested on a different sample of forty-nine children, and in 65.3 per cent of the children malocclusion or acceptable occlusion in the permanent dentition was predicted correctly. While the use of powerful statistical procedures resulted in findings statistically significant in both experiments, they were not sufficiently strong to be clinically valid. REFERENCES
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Normal is so individual that we do not know when we have even treatment. Normal is not confined to form alone. There is a normal form and function are so inseparable, each one constantly modifying other, we must think of normal as embracing both. (Mershon, John lingual arch appliance, Transactions of the First [ 19261 International gress, St. Louis, 1927, The C. V. Mosby Company, pp. 279-303.)
attained it in our of function. Since and changing the V.: The removable Orthodontic Con-