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A simplified approach to prediction
A sivnplijied approach to prediction Lysle
E. Johnston,
D.D.S.,
Ph.D.
Cleveland, Ohio
D
espite the fact that cephalometric prediction has been championed enthusiastically for nearly two decades, most orthodontists have adopted a “wait and see” attitude. Such caution is not entirely unwarranted: arcane geometry and “space-age” technology require the expenditure of considerable time and money for even a modest clinical trial. In view of the fact that contemporary schemes are essentially mean-change expansions, this complexity seems curiously inappropriate, both to the simplicity of the problem and to the utility of the end result. It will be the purpose of this article to present a simple alternative based on the addition of mean increments by direct superimposition on a printed grid and to characterize the accuracy of this approach in a series of &year forecasts. Materials
and methods
The “forecast grid” developed for this exercise is reproduced in Fig. 1. Vectors for A, B, and M were inferred from descriptive templates prepared by Harris and associates,2 and the behavior of N and P was patterned after reports by Ricketts.4y 5 The various steps required to effect a complete forecast are depicted in Fig. 2 and are described in the accompanying legend. It may be noted that the grid produces a moderate flattening of the profile and occlusal plane, as well as a slight mesial drift of M. In order to estimate the accuracy with which the landmarks can be repositioned, thirty-two 5-year forecasts (nineteen males and thirteen females; average interval, 7.5 to 12.5 years) were performed on tracings executed a decade ago as part of another study.3 Each point was advanced one grid-unit per year. TJsing a standard S-N orientation (registered at S), the forecasts were superimposed on the outcome, and the prediction errors (horizontal, vertical, and total) measured to the nearest 0.1 mm. The tip of the nose could not be included in the validation because its behavior was inferred from a random subsample (ten males and ten females) of the subjects used in the rest of the study. 253
N .
I Ii /l-lII-HIII-I-I-I-Ii-l-l-4 I-I-ti-1.1 l-l-h-l-l 1-1-1-1-1-1 tt-
-Ages 8 to 13, add 1 unit/year 20 mm
0 1974
1. Johnston
Fig. 1. Forecast grid. M, any point on the and supramentale. A at S. The points are Table II).
Forecasting
5, Sella; N, nasion; P, posterior nasal spine; NOSE, tip of the nose; crown of the maxillary first permanent molars; A and B, subspinale tracing of the landmarks is superimposed along S-N and registered then advanced downward and forward one unit per year (but see
errors seen in the present validation
are summarized in Table I.
Discussion
The forecasting technique presented here is essentially a greatly simplified mean-change expansion and, as might be expected, it performs well when applied to published examples of other schemes (for example, Ricketts’ “Case T.M.“s) or to the Bolton Standards of Case Western Reserve University. Unfortunately, schemes of this type do not fit a random series of patients nearly so well. Nor
Simplified s
approach to prediction
255
.... ,a,’
PROFILEW ITHOUT TREATMENT
D Fig. 2. Forecasting technique. A, On the initial tracing, draw planes M-A and A-B; place a mark 0.5 mm. above B for each year of the forecast (for example, 5 years calls for 2.5 mm.)-“pivot.” B, Superimpose a tracing of just the landmarks on the forecast grid and relocate them one grid-unit per year; draw planes M ’-A’ and A’-B’. C, Center A’-B’ over A-B and trace the incisors; slide the forecast back 0.3 mm. per year and trace the outline of the lips. D, Superimpose B’ on the pivot point, rotate the forecast until M ’-A’ is parallel to M-A, and trace the symphyseal outline; retract the forecast 0.3 mm. per year and trace the soft tissue of the chin. E, Add the desired anatomy by regional superimposition from the original tracing; connect the various parts of the soft-tissue profile. If desired, a slight protraction of the bridge of the nose can be effected by a clockwise rotation of the forecast (rotate until P’ is level with P).
is it easy to evaluate the significance of the forecasting error seen here; equivalent data are generally unavailable for other methods. Moreover, the common use of “best-fit” regional superimposition drains much of the meaning from the few examples which have been published5 : . . . Fig. 9 [p. 771 shows the results of patient T.M. with the prediction compared to the actual 8 years later. A general central location shows all points to be within 2 mm. [Italics mine.]
Table
I. Prediction
error: Total, horizontal,
vertical
(predicted
minus actual,
Landmark B
A Error Average error Males Females Average absolute error Males Females Root mean squared error Males Females Root mean squared technical errora
N
Total
-0.4 -0.4
1.8 1.7
X
Y
T&z
-0.8 -1.6 0.0 -1.7
0.5 1.7
i
in mm.) ---
H Y
-0.4 -0.3 1.5 -0.7
Tot02 k 1.6 2.2
P j Y
Total
Y
Jr’
-0.1 -1.6 1.0 -2.0
0.9 0.4
0.4 0.4
-0.8 -0.2
0.8 0.8
2.6 2.4
1.4 1.4
2.1 1.9
3.3 3.2
2.4 2.8
1.6 0.9
2.7 2.9
1.6 1.8
1.7 2.0
1.5 1.6
0.8 1.1
0.9 1.0
1.1 0.9
3.1 2.8
2.1 1.7
2.3 2.2
3.7 3.6
3.1 3.4
2.0 1.2
3.1 3.2
2.1 2.2
2.3 2.3
1.6 1.8
1.0 1.3
1.2 1.3
0.9
* *
1.6
2.2
* *
2.6 2.6 +X
XX
**
YK
Z*
X*
*Estimated from Baumrind and Frantzl-includes of the calculation will be furnished on request.
error for S and N in two tracings.
Details
In the present study, cranial base superimposition was employed. As a result, the forecasting error for any given landmark reflects not only the technical error for that particular point but also a portion of the error for and final. Thus, X and N. Moreover, a validation requires two tracings-initial even a perfect method would exhibit, at the very least, nearly two times the error variance of three landmarks. Viewed in this light, the grid did not perform too badly. Additional accuracy might obtain if the expansion were modified to reflect differences in age and sex. To this end, suggestions inferred from the literature61 7 are presented in Table II. It is probably safe to assume that any one of a variety of contemporary schemes will allow the clinician to visua.Zizethe individual impact of the most likely pattern of growth and thereby permit him to plan treatment accordingly. Whether or not this would be of long-term benefit remains to be seen. Although it is an obvious fallacy to assume that a diagnostic aid is useful merely because it is used, an informed decision should be based, ideally, on personal experience. For those who are interested, it is hoped that the present communication will make data collection a bit less painful. Summary
and conclusions
A simplified method of generating long-term forecasts by the use of a printed “forecast grid” was described and its accuracy characterized for a series of thirty-two S-year forecasts. Although the predictions were not without error, they were not much worse than would be expected from an analysis of cephalometric error, per se. It was concluded that t.he grid may provide a simple-and perhaps useful-introduction to the subject of growth prediction.
Table
npprocrch to predictzon
Riwplified
Number Volume 637 II. Grid-units
to be added,
10
according
9
to starting
Years of predidion 8 7 6
age, years of prediction,
5
4
3
257
and sex
2 6 7
Starting we Males
16
8
15 14
9 10
13
11
12
12
11
13
10
14
Stnrting age FemnlPs
9 a 7 6
3
14
15
16
17
18
19
10.5 12 10
23456789 Years
12.5 13 11
12
of prediction
Because of technical error, one-year forecasts are not recommended. The author wishes to express his appreciation to B. Holly Broadbent, Jr., for providing a prepublieation copy of the Bolton Standards and to Stuart Duchon for his generous technical assistance. REFERENCES
1. Baumrind, S., and Frantz, R. C.: The reliability of head film measurements. 1. Landmark identification, AM. J. ORTHOD.60: 111-127, 1971. 2. Harris, J. E., Johnston, L., and Moyers, R. E.: A cephalometric template: Its construction and clinical significance, AM. J. ORTHOD.49: 249-263, 1963. 3. Johnston, L. E.: A statistical evaluation of cephalometric prediction, Angle Orthod. 38: 284-304, 1968. 4. Ricketts, R. M.: Planning treatment on the basis of the facial pattern and an estimate of its growth, Angle Orthod. 27: 14-37, 1957. 5. Ricketts, R. M.: The application of ares, polar centers, gnomons, and k factors in facial growth prediction, Foundation Orthod. Res. Proc. 4: 53-78, 1971. 6. Riolo, M. L., Moyers, R. E., McNamara, J. A., and Hunter, W. S.: An atlas of craniofacial growth: Cephalometric standards from the University School Growth Study, the University of Michigan, Ann Arbor, 1974, Center for Human Growth and Development. 7. Woodside, D. G.: Distance curve of mandibular length by age for males, Toronto, 1970, University of Toronto Department of Orthodontics. 81.23 Alhgtm
Rd.
E. Johnston,
D.D.S.,
Ph.D.
Cleveland, Ohio
D
espite the fact that cephalometric prediction has been championed enthusiastically for nearly two decades, most orthodontists have adopted a “wait and see” attitude. Such caution is not entirely unwarranted: arcane geometry and “space-age” technology require the expenditure of considerable time and money for even a modest clinical trial. In view of the fact that contemporary schemes are essentially mean-change expansions, this complexity seems curiously inappropriate, both to the simplicity of the problem and to the utility of the end result. It will be the purpose of this article to present a simple alternative based on the addition of mean increments by direct superimposition on a printed grid and to characterize the accuracy of this approach in a series of &year forecasts. Materials
and methods
The “forecast grid” developed for this exercise is reproduced in Fig. 1. Vectors for A, B, and M were inferred from descriptive templates prepared by Harris and associates,2 and the behavior of N and P was patterned after reports by Ricketts.4y 5 The various steps required to effect a complete forecast are depicted in Fig. 2 and are described in the accompanying legend. It may be noted that the grid produces a moderate flattening of the profile and occlusal plane, as well as a slight mesial drift of M. In order to estimate the accuracy with which the landmarks can be repositioned, thirty-two 5-year forecasts (nineteen males and thirteen females; average interval, 7.5 to 12.5 years) were performed on tracings executed a decade ago as part of another study.3 Each point was advanced one grid-unit per year. TJsing a standard S-N orientation (registered at S), the forecasts were superimposed on the outcome, and the prediction errors (horizontal, vertical, and total) measured to the nearest 0.1 mm. The tip of the nose could not be included in the validation because its behavior was inferred from a random subsample (ten males and ten females) of the subjects used in the rest of the study. 253
N .
I Ii /l-lII-HIII-I-I-I-Ii-l-l-4 I-I-ti-1.1 l-l-h-l-l 1-1-1-1-1-1 tt-
-Ages 8 to 13, add 1 unit/year 20 mm
0 1974
1. Johnston
Fig. 1. Forecast grid. M, any point on the and supramentale. A at S. The points are Table II).
Forecasting
5, Sella; N, nasion; P, posterior nasal spine; NOSE, tip of the nose; crown of the maxillary first permanent molars; A and B, subspinale tracing of the landmarks is superimposed along S-N and registered then advanced downward and forward one unit per year (but see
errors seen in the present validation
are summarized in Table I.
Discussion
The forecasting technique presented here is essentially a greatly simplified mean-change expansion and, as might be expected, it performs well when applied to published examples of other schemes (for example, Ricketts’ “Case T.M.“s) or to the Bolton Standards of Case Western Reserve University. Unfortunately, schemes of this type do not fit a random series of patients nearly so well. Nor
Simplified s
approach to prediction
255
.... ,a,’
PROFILEW ITHOUT TREATMENT
D Fig. 2. Forecasting technique. A, On the initial tracing, draw planes M-A and A-B; place a mark 0.5 mm. above B for each year of the forecast (for example, 5 years calls for 2.5 mm.)-“pivot.” B, Superimpose a tracing of just the landmarks on the forecast grid and relocate them one grid-unit per year; draw planes M ’-A’ and A’-B’. C, Center A’-B’ over A-B and trace the incisors; slide the forecast back 0.3 mm. per year and trace the outline of the lips. D, Superimpose B’ on the pivot point, rotate the forecast until M ’-A’ is parallel to M-A, and trace the symphyseal outline; retract the forecast 0.3 mm. per year and trace the soft tissue of the chin. E, Add the desired anatomy by regional superimposition from the original tracing; connect the various parts of the soft-tissue profile. If desired, a slight protraction of the bridge of the nose can be effected by a clockwise rotation of the forecast (rotate until P’ is level with P).
is it easy to evaluate the significance of the forecasting error seen here; equivalent data are generally unavailable for other methods. Moreover, the common use of “best-fit” regional superimposition drains much of the meaning from the few examples which have been published5 : . . . Fig. 9 [p. 771 shows the results of patient T.M. with the prediction compared to the actual 8 years later. A general central location shows all points to be within 2 mm. [Italics mine.]
Table
I. Prediction
error: Total, horizontal,
vertical
(predicted
minus actual,
Landmark B
A Error Average error Males Females Average absolute error Males Females Root mean squared error Males Females Root mean squared technical errora
N
Total
-0.4 -0.4
1.8 1.7
X
Y
T&z
-0.8 -1.6 0.0 -1.7
0.5 1.7
i
in mm.) ---
H Y
-0.4 -0.3 1.5 -0.7
Tot02 k 1.6 2.2
P j Y
Total
Y
Jr’
-0.1 -1.6 1.0 -2.0
0.9 0.4
0.4 0.4
-0.8 -0.2
0.8 0.8
2.6 2.4
1.4 1.4
2.1 1.9
3.3 3.2
2.4 2.8
1.6 0.9
2.7 2.9
1.6 1.8
1.7 2.0
1.5 1.6
0.8 1.1
0.9 1.0
1.1 0.9
3.1 2.8
2.1 1.7
2.3 2.2
3.7 3.6
3.1 3.4
2.0 1.2
3.1 3.2
2.1 2.2
2.3 2.3
1.6 1.8
1.0 1.3
1.2 1.3
0.9
* *
1.6
2.2
* *
2.6 2.6 +X
XX
**
YK
Z*
X*
*Estimated from Baumrind and Frantzl-includes of the calculation will be furnished on request.
error for S and N in two tracings.
Details
In the present study, cranial base superimposition was employed. As a result, the forecasting error for any given landmark reflects not only the technical error for that particular point but also a portion of the error for and final. Thus, X and N. Moreover, a validation requires two tracings-initial even a perfect method would exhibit, at the very least, nearly two times the error variance of three landmarks. Viewed in this light, the grid did not perform too badly. Additional accuracy might obtain if the expansion were modified to reflect differences in age and sex. To this end, suggestions inferred from the literature61 7 are presented in Table II. It is probably safe to assume that any one of a variety of contemporary schemes will allow the clinician to visua.Zizethe individual impact of the most likely pattern of growth and thereby permit him to plan treatment accordingly. Whether or not this would be of long-term benefit remains to be seen. Although it is an obvious fallacy to assume that a diagnostic aid is useful merely because it is used, an informed decision should be based, ideally, on personal experience. For those who are interested, it is hoped that the present communication will make data collection a bit less painful. Summary
and conclusions
A simplified method of generating long-term forecasts by the use of a printed “forecast grid” was described and its accuracy characterized for a series of thirty-two S-year forecasts. Although the predictions were not without error, they were not much worse than would be expected from an analysis of cephalometric error, per se. It was concluded that t.he grid may provide a simple-and perhaps useful-introduction to the subject of growth prediction.
Table
npprocrch to predictzon
Riwplified
Number Volume 637 II. Grid-units
to be added,
10
according
9
to starting
Years of predidion 8 7 6
age, years of prediction,
5
4
3
257
and sex
2 6 7
Starting we Males
16
8
15 14
9 10
13
11
12
12
11
13
10
14
Stnrting age FemnlPs
9 a 7 6
3
14
15
16
17
18
19
10.5 12 10
23456789 Years
12.5 13 11
12
of prediction
Because of technical error, one-year forecasts are not recommended. The author wishes to express his appreciation to B. Holly Broadbent, Jr., for providing a prepublieation copy of the Bolton Standards and to Stuart Duchon for his generous technical assistance. REFERENCES
1. Baumrind, S., and Frantz, R. C.: The reliability of head film measurements. 1. Landmark identification, AM. J. ORTHOD.60: 111-127, 1971. 2. Harris, J. E., Johnston, L., and Moyers, R. E.: A cephalometric template: Its construction and clinical significance, AM. J. ORTHOD.49: 249-263, 1963. 3. Johnston, L. E.: A statistical evaluation of cephalometric prediction, Angle Orthod. 38: 284-304, 1968. 4. Ricketts, R. M.: Planning treatment on the basis of the facial pattern and an estimate of its growth, Angle Orthod. 27: 14-37, 1957. 5. Ricketts, R. M.: The application of ares, polar centers, gnomons, and k factors in facial growth prediction, Foundation Orthod. Res. Proc. 4: 53-78, 1971. 6. Riolo, M. L., Moyers, R. E., McNamara, J. A., and Hunter, W. S.: An atlas of craniofacial growth: Cephalometric standards from the University School Growth Study, the University of Michigan, Ann Arbor, 1974, Center for Human Growth and Development. 7. Woodside, D. G.: Distance curve of mandibular length by age for males, Toronto, 1970, University of Toronto Department of Orthodontics. 81.23 Alhgtm
Rd.