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Age-specific angulation of unerupted human third molar teeth in a cross-sectional sample
Archs oral Bid. Vol. 30, N~J. 5, pp. 44-444, Printed in Great Britain. All rights reserved
1985 Copyright
AGE-SPECIFIC ANGULATION OF UNERUPTED THIRD MOLAR TEETH IN A CROSS-SECTIONAL
0
0003-9969/85 $3.00 + 0.00 1985 Pergamon Press Ltd
HUMAN SAMPLE
M. EL.COHEN, R. G. WALTER, J. J. HYMAN and PATRICIA K. TOMBASCO Naval Dental Research Institute, Naval Training Center, Building I-H, Great Lakes, IL 60088, U.S.A. Summary-For .males aged 18 to 21, the angulation of unerupted third molars was unrelated to age. A counterbalancing: loss of data resulting from tooth eruption and extraction accounted for this null finding. The value of age-specific angulation in determining whether a tooth will eventually erupt may be limited.
INIRODUCrION Eruption of third molars can be characterized, in part, by tooth growth and tilting relative to the vertical axis. Over time, mandibular and maxillary teeth show decreases in mesial and distal tilting, respectively. Although Shiller (1979) found that mesio-angular impacted human mandibular third molars generally decreased in angulation over a one-year period, this was not true when crosssectional rather than longitudinal data were examined. There were no differences in angulations of unerupted third molars among independent groups of 18, 19, 20 and 21-year-olds. Our object was to investigate the methodological basis of Shiller’s finding in a cross-sectional study that age is unrelated to angulation. Because this finding may have been affected by loss of teeth from the arch by extraction and other factors, epidemiological information pertaining to various conditions was collected and data were collected in respect of both maxillary and mandibular teeth.
plane, with the top of the third molar nearest and parallel to the occlusal line, was set equal to 0” and angulation was increased as a tooth was rotated mesially through to the distal positions. This methodology was designed to provide reliable measurements although the values do not necessarily have a linear relationship to those produced by other radiographic and cephalometric procedures and no attempt was made to determine such a relationship. To assess measurement reliability, the angulations of a random sample of 56 unerupted third molars were determined on two separate occasions. Each replication included measurements made on radiographs presented in different random orders. The mean of the absolute differences was 3.52” (SD _+3.07”; range O-13”). Statistical considerations For each age by arch group, the mean angle, 4, must be defined (Batschelet, 1981) as: arctanb/x)
if
x >O,
180” + arc tanb/x) MATERL4LS AND METHODS
x = C cos(x)/n
The third molar siks on panoramic radiographs of 18, 19, 20 and 21-year-old male naval recruits were examined. Data pertaining to the presence or absence, eruption or non-eruption, and angulation of third molars were recorded. For each age group, subject records were examined until at least 60 unerupted maxillary and 60 unerupted mandibular teeth were identified. This approach permitted age-specific data on third molar absence (for any reason), noneruption and eruption prevalence to be obtained, in addition to that on angulation. A non-erupted tooth was defined as one that was radiographically present but not visible in the mouth. For these teeth an occlusal line was drawn on the radiograph as a tangent to the cusps of the first and second molars, or to the cusps of one of these teeth if the other was absent. If the cusps of the first and second molars were not on a straight line (as due to the curve of Spee, for example) the line was drawn tangentially from the most mesial cusp of the first molar to the most distal cusp of the second molar. A tangent was also drawn throught the cusps of the third molar. Angulation of the third molar in relation to the occlusal line was calculated using an X-Y digitizer and microc#Dmputer. The vertical reference
if and
or x c 0,
where
y = Z sin(x)/n.
The angular deviation, which is equivalent standard deviation in linear statistics, is,
to the
s(degrees) = (180/n),/-, where r is a measure of angular concentration with a range of 0 to 1, equal to Jm. For the data from each arch, statistical comparisons were made of mean angulation and angular dispersion using parametric tests developed by Watson and Williams (1956) and described by Batschelet (1981). The four age groups were compared in a pair-wise fashion, resulting in six non-orthogonal comparisons. To maintain a two-tailed overall alpha level of 0.05 for each set of comparisons, the F statistics of the Watson-Williams tests were converted to Bonferroni t statistics (Gill, 1978). RESULTS Figure maxillary parisons persions Table each age
441
1 shows the mean angles (for age groups) of and mandibular teeth. Pairwise comof mean angulations and angular disshowed no significant effects of age. 1 gives the percentage of teeth present for group and Table 2 shows the percentage of
M. E.
442
(a)
Maxll,lory
A
COHEN
et al.
Maxlilary
0
(b) Mondlbulor
0
Mandlbulor
0
90
Mandfbular
90
It30
Fig. 1. Distributions of angles of unerupted maxillary (a) and mandibular age groups. The line drawn in the centre of the smallest circles represents a proportion of the distance from the centre to the 00 circle corresponding to statistic, r. S is the measure of angular deviation. The lines identified 00, 05,
(b) third molars within four the mean angle and traverses the value of the concentration 10 and 15 indicate frequency.
Angulation Table
1. Third
molar
Age
Present
Absent
18 19 20 21
256 304 332 369
56 52 68 119
sites for which absent*
teeth are present
Percentage present
Total 312 3.56 400 488
82.1 85.4 83.0 75.6
of unerupted vs
Percentage absent 17.9 14.6 17.0 24.4
p < 0.01; x* = 15.04, p < 0.01; ;I* slope = 7.96, linear = 7.08, p < 0.05; (df = 3, I, 2, respectively). *Absent for any reason including past extraction.
x2
teeth that were present. Chi-square tests (Fleiss, 1981) for gradients in proportions of qualitatively-ordered samples (viz. ordered by age) revealed significant age-specific effects. Significant Chi-squares for slope indicated that age was associated with increased percentages of erupted and absent teeth. The null hypothesis of a linear age effect could not be rejected for the eruption/non-eruption data but was rejected for the presence/absence dichotomy, indicating the necessity of a more complex model. Table 1 suggests a discontinuity in the data such that in the oldest group there was an extraction rate that was different from the other three groups. erupted
DISCUSSION
Previous longituditral studies found that third molar angulation decreases with age. However, this was not true when data are collected and analysed crosssectionally. A counterbalancing loss of data associated with tooth eruption and extraction appears to be responsible for this methodological effect. Teeth removed from the sample because of eruption would show fewer average angulations whereas it is a reasonable assumption that extracted teeth might have greater than average values. However, the effect of these two factors may not necessarily be equally balanced and would depend on the magnitude of the underlying trend within the remaining observations, and the number and extent of angulation among missing observations of each type. In our study, as well as in Shiller’s (1979), the combined effects result in a more or less constant mean angle despite the assumed underlying changes. The effect of missing data is important in patient care because the angulation of unerupted third molars is frequently an important consideration in deciding whether they should be extracted. The clinician must decide whether the angulation evident at a particular age would preclude eventual rotation to the vertical and evemual eruption. Thus, an approTable
2. Third
Age
Erupted
18 19 20 21
82 135 160 235
molar
sites for which teeth are erupted unerupted
Unerupted 174 169 172 134
Total 256 304 332 369
Percentage erupted 32.0 44.4 48.2 63.7
vs
Percentage unerupted 68.0 55.6 51.8 36.3
x2= 54.21, p
x2
teeth
443
priate sample includes those persons with asymptomatic unerupted third molars. Data loss due to eruption is therefore a natural outcome which does not distort age/angulation norms for remaining subjects. Similarly, the existence of disease makes the consideration of eruption probabilities a moot point and extractions due to disease do not affect the validity of the estimates in relation to the target population. Asymptomatic extractions, however, do distort these estimates. As teeth with a high angulation are removed in disproportionately greater numbers the mean angulation of the sample would be artificially reduced. Missing data may also have an effect on longitudinal studies in that asymptomatic extractions may occur before or during the course of the study. Subjects who have had teeth extracted cannot be considered for inclusion and other subjects are removed from the study when extractions take place. The sample is therefore limited to those persons who have avoided such procedures. That longitudinal studies more frequently identify agelangulation relationships indicate that less data are lost. However, this is a relative difference and such studies may incorporate substantial, but unmeasured, levels of distortion. Asymptomatic extractions, based upon abnormal angulation, may establish a cycle of continued intervention within the population. Once the process of extraction of highangulation teeth begins, those teeth with lesser angulations would appear to be atypical in comparison to those teeth remaining. Thus valid angulation-by-age norms may not be available; because of lost data, cross-sectional studies reveal little age related variability. Unfortunately, this may be misinterpreted to mean that tilting ceases at the age of 18 years. Longitudinal information might also be misleading because of a bias related to extraction. These factors may account, in part, for the lack of agreement on appropriate criteria for extraction (e.g. Weiss, Yablon and Glatzer, 1984), and for the charge that clinical impressions about eruption probabilities are inaccurate (Friedman, 1983). Acknowledgements-The opinions expressed herein are those of the authors and cannot be construed as reflecting the views of the Navy Department or the Naval Service at large. The use of commercially-available products does not imply endorsement of the products or preference to other similar products on the market. Supported by Naval Medical Research and Development Command Work Unit M0095003-3028. REFERENCES
Batschelet E. (1981) Circular Statistic in Biology. Academic Press, London. Fleiss J. L. (1981) Statistical Methodsfor Rates and Proportions, 2nd edn. Wiley, New York. Friedman J. W. (1983) Containing the cost of third molar extractions: A dilemma for health insurance. Public Healih Rep. 98, 376-384. Gill J. L. (1978) Design and Analysis of Experiments in the Animal and Medical Sciences. The Iowa State University Press, Ames, Iowa. Shiller W. R. (1979) Positional changes in mesio-angular impacted third molars during a year. J. Am. dent. Ass. 99, 460-464.
444
M. E. COHENet al.
Watson G. S. and Williams E. J. (1956) On the construction of significance tests on the circle and the sphere. Biometrika 43, 344352.
Weiss J., Yablon P. and Glatzer M. J. (1984) The third molar question: To extract or not to extract. J. dent. Child. 51, 277-281.
1985 Copyright
AGE-SPECIFIC ANGULATION OF UNERUPTED THIRD MOLAR TEETH IN A CROSS-SECTIONAL
0
0003-9969/85 $3.00 + 0.00 1985 Pergamon Press Ltd
HUMAN SAMPLE
M. EL.COHEN, R. G. WALTER, J. J. HYMAN and PATRICIA K. TOMBASCO Naval Dental Research Institute, Naval Training Center, Building I-H, Great Lakes, IL 60088, U.S.A. Summary-For .males aged 18 to 21, the angulation of unerupted third molars was unrelated to age. A counterbalancing: loss of data resulting from tooth eruption and extraction accounted for this null finding. The value of age-specific angulation in determining whether a tooth will eventually erupt may be limited.
INIRODUCrION Eruption of third molars can be characterized, in part, by tooth growth and tilting relative to the vertical axis. Over time, mandibular and maxillary teeth show decreases in mesial and distal tilting, respectively. Although Shiller (1979) found that mesio-angular impacted human mandibular third molars generally decreased in angulation over a one-year period, this was not true when crosssectional rather than longitudinal data were examined. There were no differences in angulations of unerupted third molars among independent groups of 18, 19, 20 and 21-year-olds. Our object was to investigate the methodological basis of Shiller’s finding in a cross-sectional study that age is unrelated to angulation. Because this finding may have been affected by loss of teeth from the arch by extraction and other factors, epidemiological information pertaining to various conditions was collected and data were collected in respect of both maxillary and mandibular teeth.
plane, with the top of the third molar nearest and parallel to the occlusal line, was set equal to 0” and angulation was increased as a tooth was rotated mesially through to the distal positions. This methodology was designed to provide reliable measurements although the values do not necessarily have a linear relationship to those produced by other radiographic and cephalometric procedures and no attempt was made to determine such a relationship. To assess measurement reliability, the angulations of a random sample of 56 unerupted third molars were determined on two separate occasions. Each replication included measurements made on radiographs presented in different random orders. The mean of the absolute differences was 3.52” (SD _+3.07”; range O-13”). Statistical considerations For each age by arch group, the mean angle, 4, must be defined (Batschelet, 1981) as: arctanb/x)
if
x >O,
180” + arc tanb/x) MATERL4LS AND METHODS
x = C cos(x)/n
The third molar siks on panoramic radiographs of 18, 19, 20 and 21-year-old male naval recruits were examined. Data pertaining to the presence or absence, eruption or non-eruption, and angulation of third molars were recorded. For each age group, subject records were examined until at least 60 unerupted maxillary and 60 unerupted mandibular teeth were identified. This approach permitted age-specific data on third molar absence (for any reason), noneruption and eruption prevalence to be obtained, in addition to that on angulation. A non-erupted tooth was defined as one that was radiographically present but not visible in the mouth. For these teeth an occlusal line was drawn on the radiograph as a tangent to the cusps of the first and second molars, or to the cusps of one of these teeth if the other was absent. If the cusps of the first and second molars were not on a straight line (as due to the curve of Spee, for example) the line was drawn tangentially from the most mesial cusp of the first molar to the most distal cusp of the second molar. A tangent was also drawn throught the cusps of the third molar. Angulation of the third molar in relation to the occlusal line was calculated using an X-Y digitizer and microc#Dmputer. The vertical reference
if and
or x c 0,
where
y = Z sin(x)/n.
The angular deviation, which is equivalent standard deviation in linear statistics, is,
to the
s(degrees) = (180/n),/-, where r is a measure of angular concentration with a range of 0 to 1, equal to Jm. For the data from each arch, statistical comparisons were made of mean angulation and angular dispersion using parametric tests developed by Watson and Williams (1956) and described by Batschelet (1981). The four age groups were compared in a pair-wise fashion, resulting in six non-orthogonal comparisons. To maintain a two-tailed overall alpha level of 0.05 for each set of comparisons, the F statistics of the Watson-Williams tests were converted to Bonferroni t statistics (Gill, 1978). RESULTS Figure maxillary parisons persions Table each age
441
1 shows the mean angles (for age groups) of and mandibular teeth. Pairwise comof mean angulations and angular disshowed no significant effects of age. 1 gives the percentage of teeth present for group and Table 2 shows the percentage of
M. E.
442
(a)
Maxll,lory
A
COHEN
et al.
Maxlilary
0
(b) Mondlbulor
0
Mandlbulor
0
90
Mandfbular
90
It30
Fig. 1. Distributions of angles of unerupted maxillary (a) and mandibular age groups. The line drawn in the centre of the smallest circles represents a proportion of the distance from the centre to the 00 circle corresponding to statistic, r. S is the measure of angular deviation. The lines identified 00, 05,
(b) third molars within four the mean angle and traverses the value of the concentration 10 and 15 indicate frequency.
Angulation Table
1. Third
molar
Age
Present
Absent
18 19 20 21
256 304 332 369
56 52 68 119
sites for which absent*
teeth are present
Percentage present
Total 312 3.56 400 488
82.1 85.4 83.0 75.6
of unerupted vs
Percentage absent 17.9 14.6 17.0 24.4
p < 0.01; x* = 15.04, p < 0.01; ;I* slope = 7.96, linear = 7.08, p < 0.05; (df = 3, I, 2, respectively). *Absent for any reason including past extraction.
x2
teeth that were present. Chi-square tests (Fleiss, 1981) for gradients in proportions of qualitatively-ordered samples (viz. ordered by age) revealed significant age-specific effects. Significant Chi-squares for slope indicated that age was associated with increased percentages of erupted and absent teeth. The null hypothesis of a linear age effect could not be rejected for the eruption/non-eruption data but was rejected for the presence/absence dichotomy, indicating the necessity of a more complex model. Table 1 suggests a discontinuity in the data such that in the oldest group there was an extraction rate that was different from the other three groups. erupted
DISCUSSION
Previous longituditral studies found that third molar angulation decreases with age. However, this was not true when data are collected and analysed crosssectionally. A counterbalancing loss of data associated with tooth eruption and extraction appears to be responsible for this methodological effect. Teeth removed from the sample because of eruption would show fewer average angulations whereas it is a reasonable assumption that extracted teeth might have greater than average values. However, the effect of these two factors may not necessarily be equally balanced and would depend on the magnitude of the underlying trend within the remaining observations, and the number and extent of angulation among missing observations of each type. In our study, as well as in Shiller’s (1979), the combined effects result in a more or less constant mean angle despite the assumed underlying changes. The effect of missing data is important in patient care because the angulation of unerupted third molars is frequently an important consideration in deciding whether they should be extracted. The clinician must decide whether the angulation evident at a particular age would preclude eventual rotation to the vertical and evemual eruption. Thus, an approTable
2. Third
Age
Erupted
18 19 20 21
82 135 160 235
molar
sites for which teeth are erupted unerupted
Unerupted 174 169 172 134
Total 256 304 332 369
Percentage erupted 32.0 44.4 48.2 63.7
vs
Percentage unerupted 68.0 55.6 51.8 36.3
x2= 54.21, p
x2
teeth
443
priate sample includes those persons with asymptomatic unerupted third molars. Data loss due to eruption is therefore a natural outcome which does not distort age/angulation norms for remaining subjects. Similarly, the existence of disease makes the consideration of eruption probabilities a moot point and extractions due to disease do not affect the validity of the estimates in relation to the target population. Asymptomatic extractions, however, do distort these estimates. As teeth with a high angulation are removed in disproportionately greater numbers the mean angulation of the sample would be artificially reduced. Missing data may also have an effect on longitudinal studies in that asymptomatic extractions may occur before or during the course of the study. Subjects who have had teeth extracted cannot be considered for inclusion and other subjects are removed from the study when extractions take place. The sample is therefore limited to those persons who have avoided such procedures. That longitudinal studies more frequently identify agelangulation relationships indicate that less data are lost. However, this is a relative difference and such studies may incorporate substantial, but unmeasured, levels of distortion. Asymptomatic extractions, based upon abnormal angulation, may establish a cycle of continued intervention within the population. Once the process of extraction of highangulation teeth begins, those teeth with lesser angulations would appear to be atypical in comparison to those teeth remaining. Thus valid angulation-by-age norms may not be available; because of lost data, cross-sectional studies reveal little age related variability. Unfortunately, this may be misinterpreted to mean that tilting ceases at the age of 18 years. Longitudinal information might also be misleading because of a bias related to extraction. These factors may account, in part, for the lack of agreement on appropriate criteria for extraction (e.g. Weiss, Yablon and Glatzer, 1984), and for the charge that clinical impressions about eruption probabilities are inaccurate (Friedman, 1983). Acknowledgements-The opinions expressed herein are those of the authors and cannot be construed as reflecting the views of the Navy Department or the Naval Service at large. The use of commercially-available products does not imply endorsement of the products or preference to other similar products on the market. Supported by Naval Medical Research and Development Command Work Unit M0095003-3028. REFERENCES
Batschelet E. (1981) Circular Statistic in Biology. Academic Press, London. Fleiss J. L. (1981) Statistical Methodsfor Rates and Proportions, 2nd edn. Wiley, New York. Friedman J. W. (1983) Containing the cost of third molar extractions: A dilemma for health insurance. Public Healih Rep. 98, 376-384. Gill J. L. (1978) Design and Analysis of Experiments in the Animal and Medical Sciences. The Iowa State University Press, Ames, Iowa. Shiller W. R. (1979) Positional changes in mesio-angular impacted third molars during a year. J. Am. dent. Ass. 99, 460-464.
444
M. E. COHENet al.
Watson G. S. and Williams E. J. (1956) On the construction of significance tests on the circle and the sphere. Biometrika 43, 344352.
Weiss J., Yablon P. and Glatzer M. J. (1984) The third molar question: To extract or not to extract. J. dent. Child. 51, 277-281.