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A statistical evaluation of the Ricketts and Johnston growth-forecasting methods
A statistical evaluation of the Ricketts and Johnston growth-forecasting methods R. J. Schulhof,
A&,
M.A., Math.Stat.,
and 1. Bagha,
A.B.Math.
Sherman Oaks, Calif.
I
n their classic paper of 1938 Brodie and associates1 concluded : “There seems to be a definite correlation between success of treatment and growth. Apparently, growth and development accounts for a considerable part of the changes which take place during orthodontic treatment . . . A comparison of the intended object of treatment and the mechanics used with tooth movement accomplished should give us a keener appreciation of anchorages.” Evidently, from the foregoing, the contribution of growth to treatment and the desirability of evaluating the treatment objective have been 1~11 appreciated ever since the first scientific studies using cephalomctrics. In 1974 a poll of 100 orthodontists attending the Great Lakes Society meeting showed that 90 per cent took growth into account specifically in their treatment plan. Quantitative methods for constructing a treatment objective which includes the likely contribution of growth have been in use since 1 957.2 Holdaway subsequently advocated the use of growth forecasting for determining the mechanics necessary to achieve soft-tissue objectives. For the last 5 years, computerized growth forecasting with treatment planning aids has been available through more than 40,000 cases processed. Because of this impact, it is appropriate that methods of growth forecasting available to the clinician today should be analyzed as to their relative merits. Such evaluation is the purpose of this article. What is a growth
forecast
used for?
Before proceeding with the scientific how a growth forecast might be applied and from comments received, it is our treatment, the orthodontist would like to each patient : 258
portion of the article, we should show clinically. From surveys WC have made understanding that, before beginning make some estimate of the following on
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Evdunti,on
Fig. 1. A typical
of growth-forecnstiv~g
Class II malocclusion
with
methods
259
high overjet.
1. Is a change in the vertical or horizontal relationship of the upper to the lower jaw indicated9 2. Should the lower incisor be repositioned both horizontally and vertically? 3. What movement of the upper incisor is required P 4. Should anchorage be prepared or preserved in the lower arch@? 5. Is movement or stabilization required for the upper molars? 6. Will the tooth movement bring about a desired esthetic result which will still be acceptable at maturity? 7. Will posttreatment growth affect retention? 8. Will there be space for the third molars, given a specific treatment? Each orthodontist considers these questions before he begins treatment. Now to illustrate the manner in which growt,h and orthopedic changes affect these questions, an actual case is shown. Fig. 1 shows a patient with a typical Class II, TXvision 1 malocclusion. It is generally agreed that there are four basic possibilities by which such a malocclusion could be corrected, which are illustrated in Fig. 2: 1. The maxilla could be influenced backward with extraoral traction. 2. The upper teeth could be moved posteriorly without altering the growth of the skeletal base. 3. The midfacc could be held while the lower jaw was allowed to grow forward. 4. The lower teeth could be moved forward on the basilar mandibular body. In many cases, combinations of all of the above may be used, which was the intended treatment design for the patient shown (Fig. 3). The dcsircd movement of the maxilla to correct convexity depends upon the amount of convexity that the clinician estimates will be reduced naturally
Fig. 2. The four basic ways of treating a Class II malocclusion. A, Moving the maxilla back. 8, Moving the upper teeth back. C, Allowing the lower jaw to grow forward. D, Bringing
the lower
teeth forward.
with future growth (Fig. 4). Use of headgear to produce a straight profile may be undesirable if considerable future horizontal growth of the mandible (as registered by pogonion) is anticipated. As the incisors are to be positioned reciprocally between the jaws, the relative position at the end of treatment of the upper and lower jaws is estimated in order to determine the requirements of the incisors (Fig. 5). Fig. 6 shows that the required movements of the upper molar and incisor depend on the expected position of the mandible ancl the lower arch at the end of
Evaludzon
of growth-forecasting
will use a combination Fig. 3. In most cases the orthodontist titular case, all four methods were used to some extent.
methods
of the above.
261
In this par-
Fig. 4. In order to determine the required reduction of convexity through maxillary orthopedics, the eventual forward growth of the mandible should be estimated. A, Little forward growth is expected; therefore, considerable treatment is required. B, Much forward growth is expected; therefore, little treatment is required.
treatment. Therefore, in order to estimate the required movement of the upper dentition, an estimate is made for the position of the lower teeth at the end of treatment. This, in turn, requires an estimate of the positions of the upper and lower jaws at the end of treatment which, in itself, requires a long-range estimate of forward growth of the mandible.
Fig. 5. The movement the upper and lower
of the lower incisor depends on the expected treated jaws, as the incisors are placed reciprocally between
positions of the iaws.
Fig. 6. The required movement of the upper teeth depends upon the contribution of forward growth of the mandible. A, No change in lower arch; therefore, much treatment is required in upper arch. B, Great change in lower arch and jaw; therefore, little treatment is required in upper arch.
Fig. 7 shows the importance of the position of the lower incisor and growth of the nose and chin in determining esthetics. The study of results of treated cases has shown as many instances of overtreatment as those in which too little was accomplished. Quite often, in borderline extraction eases, the potential eruption of the third molar plays a part in the decision. Recent research work4 has indicated that the probability of eruption of the third molar is a predictable function of the space available at maturity from the center of the ramus (Xi) to the second molar, as shown in Fig. 8. Hence, the lower third molar may be quantitatively predicted before treatment is started.
Evalurrtion
of growth-forecasting
methods
263
Fig. 7. The position of the incisors can greatly affect esthetics. The above shows the expected result of differing incisor positions in the same patient. A, Ideal incisor position for esthetics. B, Retracted incisor position.
The orthodontist who uses growth forecasts begins with the cephalometric head film and draws up a proposed treatment plan, including expected growth. In this manner, he can deliberately assesseach of the previously described factors. Those who do not use visual designs and diagnose and prognose intuitively may well leave out some factors. A plan without all the factors sooner or later is going to be prone to error. In addition, if the orthodontist has specifically drawn up his objective with expected growth built into it, he is better able to determine the source of problems when progress does not go according to plan. He may answer the question, “Is the problem due to the patient’s lack of cooperation, lack or excessof growth, or unusual physiologic reaction to treatment ?” This is quite difficult if he has not predetermined what he has a right to expect from the patient during the treatment period in terms of amount and direction of growth and how these directly affect his treatment plan. Finally, if the orthodontist has specifically drawn up an objective of treatment which has a good chance of being achieved, he can better assesshis treatment methods by comparing the actual result with his previously stated objective. In this way, he has a ready tool with which to differentiate growth from treatment. As a learning instrument, therefore, this may have the greatest value. The principal proponents of growth forecasting, notably Ricketts and Holdaway, have suggested that the major value of the technique is the compilation of all the treatment factors (mechanics, growth, skeletal, and soft-tissue) together on paper to see how they interrelate. Each factor is considered for its contribution to the final decision. Both proposed initially very simple systems of
Fig. 8. Recent research has shown that the probability of eruption of the third molar can be predicted as function of the space between the center of the ramus (Xi point) and the lower second molar. This space can be predicted at the age of 8 to within 2 mm. A, Adequate space available. 6, Inadequate space available.
forecasting which they believed could be easily performed manually by the individual clinician. Each would agree that the most important function of the procedure to treatment planning comes from having all of the conditions related together on paper. The sophistication of the growth element in a forecast is only a minor consideration, because the treatment effects dominate the picture during treatment. Growth effects are more important in the long range. The “growth” part of forecasting at all levels of concern from manual to computer will be discussed and, therefore, the errors between the various methods will be compared. It is the purpose of this article to provide only a comparison of methods. From this, the clinician may decide which procedure he may prefer. Each level of sophistication in growth and the case “set-up” is an element of time and expense. It is not the purpose of this article to disparage any method, for the previous arguments seem to show conclusively that any cephalometric planning technique which includes a reasonable expecbation of amount and direction of growth is quite preferable to one that does not. All have a place, and the underlying thesis is that several may have a place, depending on discipline. Materials
and method
The material for growth analysis included fifty untreated patients. The sample was selected by James McNamara from the University of Michigan growth study. All cases were included, up to a maximum of fifty, so that cephalometric records for approximately 10 years were available and no orthodontic treatment had been performed. The beginning cephalograms were traced by Rocky Mountain Data Systems, Inc. (RMDS) technicians, digitized by an analog digital converter, and processed through the computer, complete with a growth forecast, before the final
Evaluation
of growth-forecasting
methods
265
Fig. 9. A, The method advocated by Dr. Lysle Johnston, which extends each of the points to be predicted the average amount and direction. The basic reference line for this system is sella-nasion. There is no individualization in this method, in that all patients will grow the same amount horizontally and vertically, irrespective of their facial patterns. This method was accurate enough to be useful (near 70 per cent) but was the least accurate of the methods studied. B, A comparison of point B growth with pogonion. In the first illustration we show one of the patients in the study superimposed on the palatal plane. It can be seen that pogonion grew 16 mm., whereas the change in point B was only 7 mm., or less than half. In vertical relation, this is even more pronounced for superimposing on the A-B plane. We see that there has been no vertical change between points A and B, whereas point A to pogonion has increased 10 mm. Thus, point B was disregarded in the study.
films were submitted for examination. The last films were then traced and processed similarly. Copies of the original tracings, final tracings, and growth forecasts were mailed to Dr. McNamara for his study. The average age at the time of the intial records was 6.25 years, and the range was 5 years to 8.5 years. The average age at the final record was 16, with a range of 13 to 26. There were twenty girls and thirty boys. Methods
Four methods of growth forecasting were compared. The objective was to predict the final position of the points A, pogonion, end of the nose, lower molar,
Ant. J. Orthod. Mavch 1975
Fig. 10. The Ricketts short-range forecast. Here there is individualization, in that the patient is growing along his own previously established growth vectors and thus a vertical facial pattern will grow more vertically, a horizontal pattern more horizontally. The basion-nasion plane is used as the basic reference. This method had about 20 per cent less error than the Johnston method. It has been clinically useful, in that assuming that a patient with a vertical pattern will grow more vertically and a patient with a horizontal pattern will grow more horizontally adds a safety factor to the clinical treatment plan.
and center of the ramus (Xi point) with respect to cranial reference lines. Thus, it would be possible to assess the accuracy with which each method predicted the final position of these points representing the relative position of the upper jaw, lower jaw, nose (for soft-tissue profile), and denture (third molar space). The various methods may be described as follows, proceeding from the least involved to the most sophisticated. Predicting the location of a point with respect to cranial reference is the most revealing method of evaluating a growth prediction. For instance, in predicting the location of pogonion, it is possible to err in form of the mandible, size of the mandible, and relation of the mandible to cranial base. Therefore, the errors shown include all factors. Evaluating a prediction through comparing the normal cephalometric measurements may well omit errors in size or form or position. Method 1. The Johnsto?l forecast grid. The dohnston forecast grid5 shows average increments of growth per year for the points nasion, A, B, nose, and posterior nasal spine. It also gives a method of constructing pogonion, given a B point. For this study, we were interested in the points A, pogonion, and the nose. Point B is of less interest in facial growth because of its dependence upon the position of the lower incisor. There can be considerable changes at pogonion which would have great impact facially but would not affect point B. Fig. 9, B shows one such case in the sample. Here a 10 mm. vertical increase from point A to pogonion was seen, but none was seen from point A to point B. There was a 10 mm. change in horizontal position of pogonion, but only 7.5 mm at point B. For this study, therefore, we used the grid to find point A, the nose, and point B and then constructed pogonion from point B, according to Johnston’s
Evaluation GrOWth
Tissue 2 Upper Face
EN,DT BA,NA,AN,PN,AP,All
1 Soft
3 Lover -Girls
of growth-forecasting
Face
methods 267
O's
X,XI,po
-Boys
3) 4
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
Fig. 11. The computer program is based upon Ricketts’ short-range methods with modifications. One of the modifications is the use of variable growth rates according to the patient’s age and sex. This was one of the weaknesses of the Johnston and Ricketts systems which used the same growth rate for each patient, irrespective of age and sex.
method. Then, superimposing the prediction and the final head film on sellanasion at sella, the error, in millimeters, was measureddirectly. Theseerrors were squared, summed, and divided by the number in the sample to get the meansquared error. Then the square root was taken for the root-mean-squarederror. One may interpret the root-mean-squared(rms) error as follows : 70 per cent of the predictions will be within + 1 rms error. 95 per cent will be within + 2 rms errors. Therefore, once the expected value and the rms error are calculated, a complete probability of direction of growth and its uncertainty is determined. Method 2. Average increments from sellu-nasion. Since we were interested in studying points not covered by the Johnston grid, as well as testing the grid’s applicability to a lo-year growth period, we devised a method of prediction equivalent to the grid using the fifty-case lo-year sample. Average increments for each of the points under consideration were calculated from SN with X as the origin, and these increments were then used in a prediction as follows: Using sella-nasion as a horizontal axis with sella as its center, we merely added the average increment per year in the horizontal and vertical directions times the number of years of the forecast to each of the above points.
Fig. 12. The patient. Here cranial
computer
Where we
see a patient base
program
it shows than
the
the who
will greatest
has
grown
not
greatly
advantage much
more
improve is in
the
forecast
patients
in the
mandible
with
for abnormal
and
much
the
average patterns.
less
in the
average.
For the purposes of both of these average predictions, girls were assumed to grow one unit per year until the age of 15 and boys one unit per year to the age of 19, according to Ricketts’ thesis and experiences on a clinical basis. Method 3. The Ricketts short-range prediction. Ricketts suggested that one can do better than the averages in prediction of the chin position by constructing the chin according to the patient’s own mandibular lines.” He did not intend, however, that this method be used beyond a 2- to 3-year prediction. Here the basionnasion plane is used as the reference; the patient’s pattern is extended down his own condyle axis (Fig. 10) and corpus axis to reach pogonion. Therefore, patients who have vertical patterns will grow more vertically, and patients who have horizontal patterns will grow horizontally. It should be noted that in the previous methods all patients grow the same amount and direction, irrespective of their facial patterns, while the Ricketts method includes information from the facial pattern. Root-mean-squared error for pogonion was calculated by means of this intended short-range method of prediction on the lo-year cases by superimposing on the basion-nasion plane at point CC. Method 4. Computer forecast. The computer growth forecast adds the following data input to Method 3 : A. Individual growth curves are used for the mandible, maxilla, and
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Evaluation
of growth-forecasti?ag methods
269
Fig. 13. The differences in the ramus position, condyle location, and cranial base deflection that the computer evaluates in order to warn the orthodontist of the possibility of this abnormal growth. If the factors are significant, the patient grows more in the mandible and less in the cranial base than average. The computer was 67 per cent more accurate than average increments in patients with Class III tendencies.
cranial base rather than using the same increments for every age group. B. Clinical experience with 40,000 predictions has shown that certain persons grow differently than the averages. The RMDS computer bank has been used to identify those characteristics in these unusual patients (less than 5 per cent) which can be identified to grow differently from the averages. They fall into three groups : 1. Patients who grow abnormally large mandibles with less growth in the cranial base, referred to as abnormal Class III patterns. These are predicted using the variations from normal as shown in Fig. 13. 2. Unusually strong patterns which rotate forward. These characteristics are displayed in Fig. 14, B. 3. Abnormally weak facial patterns. These rotate distally ,and have the characteristics shown in Fig. 14, A. It should be noted that none of the foregoin g factors show high linear correlations. The linear correlation assumes that a small increment in the cause produces a corresponding increment in the effect. It has been found that patients with values in the normal range or those who display some but not all of the abnormal characteristics do not show the abnormal tendencies. Characteristics 2 and 3 were derived using Ricketts’ principle of arcial growth of the mandible as a basis.8 At the present time, a complete computer prediction using the principle of arcial growth is not available and, therefore, was not tested as part of the present article. This would be a possibility in the future. These findings are also in agreement with the work of Odegaard,g which showed a correlation of future mandibular form based on initial mandibular form. The
270 Table
Xchdhof I. The error
Am. J. Orthod. March 1975
Bngha
mad
summary
for fifty
Johnston
I
Point h (Maxilla) PO (Mandible) Nose XI (Ramus) B6 (Molar)
j /
untreated
Acerage groxth 14.6 25.4 20.0 14.2 23.4
/
RdlS Error 5.2” 7.5* 6.2
cases
Average
grid
! Per cent / Accuracy 64 70 69
Aucrage growth 14.6 25.4 20.0 14.2 23.4
increment RMIB .tTYOT
1 Per cent accuracy
4.3” 6.8” 6.2 4.4* 4.4”
71 73 69 69 81
The mean period of growth prediction was 9.42 years. As can be seen, most of the predictions were *Indicates significantly greater error than the RMDS computer prediction at the 5 per cent sig
error calculations were made by superimposing on the Frankfort horizontal and pterygoid vertical, the basic reference lines for the computer system. Results
Results are summarized in Tables I and II and may be stated as follows: Method 1. Johnston grid. Although it provides a very useful prediction, the
Johnston grid was the least accurate of the three methods considered, being based on the most simple premise. Comparing the root-mean-squared error, in millimeters, with the average growth change at each point, that portion of predictable growth can be seen. The Johnston grid was about as accurate as any for predicting growth of the nose and, in fact, was almost 70 per cent accurate. This definitely indicates the potential of evaluating patients’ cases on a long-range basis with regard to softtissue profile, and certainly many of the patients who are considered overtreated today from an esthetic standpoint might have been helped had the long-range growth of the nose been taken into account. Of course, to evaluate the profile completely, it would be necessary to predict the reaction of soft tissue to treatment which has been adequately documented by Ricketts2 and Holdaway. The grid was also 64 per cent accurate on point A and 70 per cent accurate on pogonion, once again illustrating that a useful amount of growth over the long range is predictable. This is an especially good result, considering that the growth rates were derived for use over the 5-year period from the ages of 10 to 15 years, whereas many of the patients in this study were observed between the ages of 6 and 18. Method 2. Sella-Nasion average increments. This method gave a useful improvement over the Johnston grid at both pogonion and point A. This improvement comes from two sources: (1) using growth rates applicable to the lo-year prediction period and (2) predicting pogonion directly rather than by construction from point B. Method 3. Ricketts’ short-range prediction method. The Ricketts short-range prediction has somewhat less rms error, in millimeters, than the Johnston grid or average increments from S-N. Some of the smaller over-all error was due to the fact that point CC, the origin of this growth prediction, is closer to pogonion
Evnluation
of growth-forecastbtg
RMS
growth
error
21.8
5.8
271
RMDS program
Ricketts short range Average
methods
Per cent accuracy
Average growth
RMS error
Per cent accuracy
12.2 21.9 18.0 12.7 20.1
3.2 4.8 5.6 3.5 3.4
74 78 69 72 83
73
accurate in the 70 to 80 per cent range, which must be considered useful as a planning
tool.
nificance level.
Table II. A comparison of chin position RMDS
Samvle Total 50 Class III patterns Vertical patterns (59 degrees)
of errors of the various
computer
methods
with
respect to the prediction
S-N
Ricketts
average increment
short range Per cent of
Per cent of comvuter
R M S error
Per cent of comvzcter
R M S error
compder
4.8
100
6.8
142
5.8
121
4.3
100
7.2
167
6.6
153
4.8
100
8.3
173
7.3
152
R M S error
This shows that the methods using average increments were not nearly so successful in the difficult Class III and vertical patterns as they were on average. However, the computer maintained the same efficiency in all three groups and thus does a much better job on individual patients.
than to sella. There was a 10 to 20 per cent improvement of this method over average increments due to the facial pattern, but some of the potential was not realized, possibly because the growth rates used were derived to be applicable to the period of 8 years to 13 years. Therefore, we have a similar problem with the Johnston grid, that is, applying growth rates for one age group to a different age group. It should be mentioned that there is an advantage in using a prediction in which vertical patterns tend to grow more vertically and horizontal patterns more horizontally. Here the root-mean-squared error does not tell the whole story, as it assumes that an error in one direction is just as bad as an error in the other. This is not the case in orthodontic treatment, assuming that vertical patterns will grow more vertically than horizontal patterns, given a safety margin in treatment. If a horizontal pattern grows more vertically than expected, this will aid in treatment and give a more normal appearance. If the orthodontist had not anticipated horizontal growth and it occurred, too much headgear might have been used ; therefore, he might have overtreated the profile as well as possibly extracting when nonextraction treatment would have sufficed. Many clinicians find that ex-
Fig. 14. A case that the computer horizontally (B) than average.
would
predict
to grow
more vertically
(A) and
more
tracting in a brachyfacial pattern may result in an overly flattened profile because of the difficulty of moving lower molars forward. Some reason that the musculature is strong, while others contend that it is due mostly to growth pattern. A similar argument can be used for assuming more vertical growth in vertical facial patterns. Here extraction is not usually a difficulty, for the anchorage is more easily lost, whereas leaving the dentures protrusive, hoping for growth, is generally to be avoided in this type. This is a possible reason that the Ricketts forecast has served so successfully clinically. It is designed to keep the clinician out of trouble, not merely to minimize root-mean-squared error. Meth’od 4. RMDS c.omputer program. As was discussed previously, this system was essentially based upon the theories of Ricketts. RMDS hoped to individualize further by using growth rates variable for the patient’s age and by recognizing unusual facial patterns. The RMDS program was the most accurate of this study. However, the improvement is not pronounced by statistical comparison of root-mean-squared errors. For example, the computer program was only 21 per cent more accurate than the Ricketts short-range method alone and 56 per cent more accurate than the Johnston method. It should be noted that this was a loyear study and that in a 5-year or 2-year study there would be less advantage to the computer. Hence, it is not surprising that other investigators in small samples have found little difference. In a small sample of twenty, a difference of 20 or 30 per cent would not be statistically significant. The sample size is of essential importance in determining the statistical significance of the rms error. In a sample of twenty the rms error has to be greater by 46 per cent to be statistically significant, whereas in a sample of fifty the rms
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Fig. 15. The factors in the mandible that are used to evaluate this potential. These factors represent the squareness of the mandible and the relative length of the condyle head. The computer was 73 per cent more accurate than average increments in the vertical patterns which are a source of trouble to the orthodontists.
error has to be greater by only 22 per cent. This demonstrates that the larger the sample, the greater the statistical significance it bears. One should look further, however, into the components of this fifty-case sample to appreciate fully the use of the RMDS forecast. As we have stated, the vast majority of these patients have relatively normal facial patterns. The computer did not extend these patterns much differently than an average increment method. However, Table II discusses two subgroups within the fifty-case sample that are somewhat lost among the normal samples. They include Class III skeletal patterns as defined by the computer system and vertical patterns which will be defined as simply having a more negative chin from Frankfort plane. These cases are the most interesting, since they actually represent the two major problem areas of treatment. There were only eight patients of the fifty recognized as potential prognathie patterns by the computer and seven recognized as retrognathic patterns. On the Class III patterns, as was discussed previously, the computer evaluates key factors in the deep structure to determine the growth rates to be used in predicting the mandible. There are certain persons, although relatively rare, who have been tentatively identified as having potential for excessive mandibular growth. These persons can present quite bothersome situations, for some may have Class II malocclusions and are treated with extraoral traction, much to the detriment of the future skeletal profile. Others may be treated with normal Class III mechanics for many years and finally require surgical intervention for skeletal correction, It should be noted that in the eight patients in whom the computer recognized Class III skeletal patterns, the improvement was 53 per cent over the Ricketts short-range method, 6’7 per cent over the sella-nasion method, and, of course, there was greater improvement over the Johnston grid. This is nearly twice the improvement if we include these persons in among the normal samples. The vertical patterns showed an increase of 52 per cent over the Ricketts short-range method and 73 per cent over the average increment method. In fact, the computer
error was not increased on any of the three groups-normals, Class III ‘s, or verticals. This shows it,s applicability to the individual clinical situation, as the average increment methods suffered considerably when applied to these nonaverage patterns. Emphasis must be placed on the fact that normal samples do not usually contain the number and variety of facial patterns that the clinician faces in his office. Hence, a small, normal, untreated sample may contain very few of these problem cases and the computer advantage would be obscured. Comparison
of results with
those of other investigators
Johnston and Greenberg’ found, in their study, that there was no significant difference between the computerized method of prediction as applied in 1972 and the average change in the population. Hence, they concluded that the most sophisticated methods of growth forecasting did not individualize and, therefore, the most simple methods would be just as good. This is clearly in conflict with the results of the present study, which show that as more sophistication is added, the accuracy of the prediction improves. There are several factors which we believe explain this apparent contradiction : 1. Since the above study, performed in 1972, two key factors in individualization were introduced into the computer system. In 1973 individual rotational factors in vertical patterns and increased mandibular growth in Class III patterns were instituted. Some relationships are much easier to predict than others. The majority of the relationships which Greenberg and Johnston showed to be as easily predicted by the averages as the computer involved the relative relationships of points A and B. As points A and B are alveolar points, functionally related to the roots of the upper and lower incisors, their relationships cannot change very much more than the relationships of the incisors themselves. It is well known that, both occlusions and malocclusions remain stable, once the permanent teeth are interlocked in development. However, the facial pattern can change, which would have a definite effect on esthetics without causing a corresponding change in OCelusion. Hence, facial changes would not be reflected in points A and B. The conclusion may be drawn that the relationships of A and B are so stable as to not require a sophisticated prediction method. Many clinicians, however, are more interested in the relationship of point A to pogonion. The available chin is used as an indication of the possible need for forward positioning of the lower incisor. The relation of point A to pogonion is thought by many practitioners to be most critical for esthetics and denture balance. 2. Johnston and Greenberg’s data showed that as pogonion was used (instead of point B-see angle of convexity) the computer did have a positive prediction efficiency over other methods. We have shown that, when predicting the relationship of pogonion to cranial structures, the computer has positive et%ciency, and the reason is that this is much harder to do than to predict the relation of A to B. 3. All of the patients in the Johnston-Greenberg group were 10 years of age at the beginning of the study and 15 years old at the end. This is a period
Evaluati,on
of growth-forecasting
methods
275
during which girls grow much the same as boys, on the average, and the very homogeneity of the group would mean that the average would not be very far off from the individual. However, such homogeneity is not the norm in an orthodontic practice, and the orthodontist must have a prediction which is valid for all age groups, short term and long term. In this study there was a variety of prediction times and a lo-year growth period. Hence, any one grid would not suffice for a great variety of ages and predictions. This could be corrected by using complex tables to determine growth increment, now under consideration by Johnston. 4. Greenberg and Johnston’s sample included only twenty patients. This does not allow a great variety of case types, but more important results which may not appear to be significant statistically in twenty cases would be statistically significant in fifty cases. 5. Use of the rms or average error lumps all patients together. Since most members of untreated samples have normal facial patterns, the averages will suffice. However, the patients causing the orthodontist the most trouble are those with abnormal Class III and vertical patterns. If these are studied separately and not lost in the statistics, the computer has an advantage. 6. Each growth-forecast method is designed for specific superimposition. Therefore, the computer system was designed for superimpostion on the Frankfort horizontal and the pterygoid vertical in order to achieve optimum accuracy. It became apparent, when performing various error analyses, that growth was more orderly when viewed from the Frankfort horizontal and the pterygoid vertical, and some of the improvement in the computer prediction is due to the use of these planes for superimposition. In fact, if sella-nasion or basion-nasion were used for superimposition of the computer prediction, there would be less accuracy. DISCUSSION
Growth forecasts have two purposes : 1. Short range-to plan strategy and anchorage. 2. Long range--to give evaluation of final results: esthetics, facial balance. Because of the limited amount of growth in a P-year treatment period compared to treatment effects, all of the methods of growth forecasting would yield the same accuracy. However, a safer strategy for the orthodontist is a method that assumes vertical growth for vertical patterns and horizontal growth for horizontal patterns although theoretically this is not greatly more accurate than assuming the same growth for everyone. Over the longer term, the majority of the growth experienced is consistent enough to be considered predictable (70 per cent ) . Refined computer methods which take into account the individual facial patterns will not be markedly more accurate in the 70 per cent of the patients in the normal range but will show considerable advantage in 30 per cent of the abnormal patterns, including vertical patterns and Class III tendencies. Repeated comparison of predictions with actual results has enabled the com-
REFERENCES
1. Iirodie, A. G., and others: Cephalometric appraisal of orthodontic results: A preliminary report, Angle Orthod. 8: W-265, 193X. 2 Ricltetts, R. M.: Planning treatment on tlro basis of the facial pattern and an estimate of its growth, Angle Orthod. 27: 14.3T, 1957. 3. Rickctts, H. M., and others: An overview of caomputerizcd cephalometrics, Ax J. ORTHOI). 61: l-28, 1972. 4. Turlcy, I’.: A computerized method of forecasting third molar space in the mandibular arch, to lw presented at the American Association for Dental Research, April, 1975. 5. Johnston, Lysle: Lecture presented at Great Lakes Society of Orthodontics, French Lick, Ind., 1974. 6. Gugino, C. F.: An orthodontic philosophy, Denver, 1971, Rocky Mountain Dental Products Company. 7. Grwnbrrg, I,. Z., and Johnst,on, 1,. $1.: Computerized prediction : The accuracy of a commcrcial long-range forecast, Anl. .J. ORTHOR 67: 243-252, 1975. 8. Ricketts, R. M.: A principle of arcial growth of the mandible, Angle Orthod. 42: 368-386, 197“. i 9 Odegaard, J.: Growth of the mandible studied with the aid of metal implant, AM. J. ORTHOD. 57: 145-157, 1970. 15125 Ventura
Blvd. (91403)
A&,
M.A., Math.Stat.,
and 1. Bagha,
A.B.Math.
Sherman Oaks, Calif.
I
n their classic paper of 1938 Brodie and associates1 concluded : “There seems to be a definite correlation between success of treatment and growth. Apparently, growth and development accounts for a considerable part of the changes which take place during orthodontic treatment . . . A comparison of the intended object of treatment and the mechanics used with tooth movement accomplished should give us a keener appreciation of anchorages.” Evidently, from the foregoing, the contribution of growth to treatment and the desirability of evaluating the treatment objective have been 1~11 appreciated ever since the first scientific studies using cephalomctrics. In 1974 a poll of 100 orthodontists attending the Great Lakes Society meeting showed that 90 per cent took growth into account specifically in their treatment plan. Quantitative methods for constructing a treatment objective which includes the likely contribution of growth have been in use since 1 957.2 Holdaway subsequently advocated the use of growth forecasting for determining the mechanics necessary to achieve soft-tissue objectives. For the last 5 years, computerized growth forecasting with treatment planning aids has been available through more than 40,000 cases processed. Because of this impact, it is appropriate that methods of growth forecasting available to the clinician today should be analyzed as to their relative merits. Such evaluation is the purpose of this article. What is a growth
forecast
used for?
Before proceeding with the scientific how a growth forecast might be applied and from comments received, it is our treatment, the orthodontist would like to each patient : 258
portion of the article, we should show clinically. From surveys WC have made understanding that, before beginning make some estimate of the following on
Vohnae Number
67 3
Evdunti,on
Fig. 1. A typical
of growth-forecnstiv~g
Class II malocclusion
with
methods
259
high overjet.
1. Is a change in the vertical or horizontal relationship of the upper to the lower jaw indicated9 2. Should the lower incisor be repositioned both horizontally and vertically? 3. What movement of the upper incisor is required P 4. Should anchorage be prepared or preserved in the lower arch@? 5. Is movement or stabilization required for the upper molars? 6. Will the tooth movement bring about a desired esthetic result which will still be acceptable at maturity? 7. Will posttreatment growth affect retention? 8. Will there be space for the third molars, given a specific treatment? Each orthodontist considers these questions before he begins treatment. Now to illustrate the manner in which growt,h and orthopedic changes affect these questions, an actual case is shown. Fig. 1 shows a patient with a typical Class II, TXvision 1 malocclusion. It is generally agreed that there are four basic possibilities by which such a malocclusion could be corrected, which are illustrated in Fig. 2: 1. The maxilla could be influenced backward with extraoral traction. 2. The upper teeth could be moved posteriorly without altering the growth of the skeletal base. 3. The midfacc could be held while the lower jaw was allowed to grow forward. 4. The lower teeth could be moved forward on the basilar mandibular body. In many cases, combinations of all of the above may be used, which was the intended treatment design for the patient shown (Fig. 3). The dcsircd movement of the maxilla to correct convexity depends upon the amount of convexity that the clinician estimates will be reduced naturally
Fig. 2. The four basic ways of treating a Class II malocclusion. A, Moving the maxilla back. 8, Moving the upper teeth back. C, Allowing the lower jaw to grow forward. D, Bringing
the lower
teeth forward.
with future growth (Fig. 4). Use of headgear to produce a straight profile may be undesirable if considerable future horizontal growth of the mandible (as registered by pogonion) is anticipated. As the incisors are to be positioned reciprocally between the jaws, the relative position at the end of treatment of the upper and lower jaws is estimated in order to determine the requirements of the incisors (Fig. 5). Fig. 6 shows that the required movements of the upper molar and incisor depend on the expected position of the mandible ancl the lower arch at the end of
Evaludzon
of growth-forecasting
will use a combination Fig. 3. In most cases the orthodontist titular case, all four methods were used to some extent.
methods
of the above.
261
In this par-
Fig. 4. In order to determine the required reduction of convexity through maxillary orthopedics, the eventual forward growth of the mandible should be estimated. A, Little forward growth is expected; therefore, considerable treatment is required. B, Much forward growth is expected; therefore, little treatment is required.
treatment. Therefore, in order to estimate the required movement of the upper dentition, an estimate is made for the position of the lower teeth at the end of treatment. This, in turn, requires an estimate of the positions of the upper and lower jaws at the end of treatment which, in itself, requires a long-range estimate of forward growth of the mandible.
Fig. 5. The movement the upper and lower
of the lower incisor depends on the expected treated jaws, as the incisors are placed reciprocally between
positions of the iaws.
Fig. 6. The required movement of the upper teeth depends upon the contribution of forward growth of the mandible. A, No change in lower arch; therefore, much treatment is required in upper arch. B, Great change in lower arch and jaw; therefore, little treatment is required in upper arch.
Fig. 7 shows the importance of the position of the lower incisor and growth of the nose and chin in determining esthetics. The study of results of treated cases has shown as many instances of overtreatment as those in which too little was accomplished. Quite often, in borderline extraction eases, the potential eruption of the third molar plays a part in the decision. Recent research work4 has indicated that the probability of eruption of the third molar is a predictable function of the space available at maturity from the center of the ramus (Xi) to the second molar, as shown in Fig. 8. Hence, the lower third molar may be quantitatively predicted before treatment is started.
Evalurrtion
of growth-forecasting
methods
263
Fig. 7. The position of the incisors can greatly affect esthetics. The above shows the expected result of differing incisor positions in the same patient. A, Ideal incisor position for esthetics. B, Retracted incisor position.
The orthodontist who uses growth forecasts begins with the cephalometric head film and draws up a proposed treatment plan, including expected growth. In this manner, he can deliberately assesseach of the previously described factors. Those who do not use visual designs and diagnose and prognose intuitively may well leave out some factors. A plan without all the factors sooner or later is going to be prone to error. In addition, if the orthodontist has specifically drawn up his objective with expected growth built into it, he is better able to determine the source of problems when progress does not go according to plan. He may answer the question, “Is the problem due to the patient’s lack of cooperation, lack or excessof growth, or unusual physiologic reaction to treatment ?” This is quite difficult if he has not predetermined what he has a right to expect from the patient during the treatment period in terms of amount and direction of growth and how these directly affect his treatment plan. Finally, if the orthodontist has specifically drawn up an objective of treatment which has a good chance of being achieved, he can better assesshis treatment methods by comparing the actual result with his previously stated objective. In this way, he has a ready tool with which to differentiate growth from treatment. As a learning instrument, therefore, this may have the greatest value. The principal proponents of growth forecasting, notably Ricketts and Holdaway, have suggested that the major value of the technique is the compilation of all the treatment factors (mechanics, growth, skeletal, and soft-tissue) together on paper to see how they interrelate. Each factor is considered for its contribution to the final decision. Both proposed initially very simple systems of
Fig. 8. Recent research has shown that the probability of eruption of the third molar can be predicted as function of the space between the center of the ramus (Xi point) and the lower second molar. This space can be predicted at the age of 8 to within 2 mm. A, Adequate space available. 6, Inadequate space available.
forecasting which they believed could be easily performed manually by the individual clinician. Each would agree that the most important function of the procedure to treatment planning comes from having all of the conditions related together on paper. The sophistication of the growth element in a forecast is only a minor consideration, because the treatment effects dominate the picture during treatment. Growth effects are more important in the long range. The “growth” part of forecasting at all levels of concern from manual to computer will be discussed and, therefore, the errors between the various methods will be compared. It is the purpose of this article to provide only a comparison of methods. From this, the clinician may decide which procedure he may prefer. Each level of sophistication in growth and the case “set-up” is an element of time and expense. It is not the purpose of this article to disparage any method, for the previous arguments seem to show conclusively that any cephalometric planning technique which includes a reasonable expecbation of amount and direction of growth is quite preferable to one that does not. All have a place, and the underlying thesis is that several may have a place, depending on discipline. Materials
and method
The material for growth analysis included fifty untreated patients. The sample was selected by James McNamara from the University of Michigan growth study. All cases were included, up to a maximum of fifty, so that cephalometric records for approximately 10 years were available and no orthodontic treatment had been performed. The beginning cephalograms were traced by Rocky Mountain Data Systems, Inc. (RMDS) technicians, digitized by an analog digital converter, and processed through the computer, complete with a growth forecast, before the final
Evaluation
of growth-forecasting
methods
265
Fig. 9. A, The method advocated by Dr. Lysle Johnston, which extends each of the points to be predicted the average amount and direction. The basic reference line for this system is sella-nasion. There is no individualization in this method, in that all patients will grow the same amount horizontally and vertically, irrespective of their facial patterns. This method was accurate enough to be useful (near 70 per cent) but was the least accurate of the methods studied. B, A comparison of point B growth with pogonion. In the first illustration we show one of the patients in the study superimposed on the palatal plane. It can be seen that pogonion grew 16 mm., whereas the change in point B was only 7 mm., or less than half. In vertical relation, this is even more pronounced for superimposing on the A-B plane. We see that there has been no vertical change between points A and B, whereas point A to pogonion has increased 10 mm. Thus, point B was disregarded in the study.
films were submitted for examination. The last films were then traced and processed similarly. Copies of the original tracings, final tracings, and growth forecasts were mailed to Dr. McNamara for his study. The average age at the time of the intial records was 6.25 years, and the range was 5 years to 8.5 years. The average age at the final record was 16, with a range of 13 to 26. There were twenty girls and thirty boys. Methods
Four methods of growth forecasting were compared. The objective was to predict the final position of the points A, pogonion, end of the nose, lower molar,
Ant. J. Orthod. Mavch 1975
Fig. 10. The Ricketts short-range forecast. Here there is individualization, in that the patient is growing along his own previously established growth vectors and thus a vertical facial pattern will grow more vertically, a horizontal pattern more horizontally. The basion-nasion plane is used as the basic reference. This method had about 20 per cent less error than the Johnston method. It has been clinically useful, in that assuming that a patient with a vertical pattern will grow more vertically and a patient with a horizontal pattern will grow more horizontally adds a safety factor to the clinical treatment plan.
and center of the ramus (Xi point) with respect to cranial reference lines. Thus, it would be possible to assess the accuracy with which each method predicted the final position of these points representing the relative position of the upper jaw, lower jaw, nose (for soft-tissue profile), and denture (third molar space). The various methods may be described as follows, proceeding from the least involved to the most sophisticated. Predicting the location of a point with respect to cranial reference is the most revealing method of evaluating a growth prediction. For instance, in predicting the location of pogonion, it is possible to err in form of the mandible, size of the mandible, and relation of the mandible to cranial base. Therefore, the errors shown include all factors. Evaluating a prediction through comparing the normal cephalometric measurements may well omit errors in size or form or position. Method 1. The Johnsto?l forecast grid. The dohnston forecast grid5 shows average increments of growth per year for the points nasion, A, B, nose, and posterior nasal spine. It also gives a method of constructing pogonion, given a B point. For this study, we were interested in the points A, pogonion, and the nose. Point B is of less interest in facial growth because of its dependence upon the position of the lower incisor. There can be considerable changes at pogonion which would have great impact facially but would not affect point B. Fig. 9, B shows one such case in the sample. Here a 10 mm. vertical increase from point A to pogonion was seen, but none was seen from point A to point B. There was a 10 mm. change in horizontal position of pogonion, but only 7.5 mm at point B. For this study, therefore, we used the grid to find point A, the nose, and point B and then constructed pogonion from point B, according to Johnston’s
Evaluation GrOWth
Tissue 2 Upper Face
EN,DT BA,NA,AN,PN,AP,All
1 Soft
3 Lover -Girls
of growth-forecasting
Face
methods 267
O's
X,XI,po
-Boys
3) 4
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
Fig. 11. The computer program is based upon Ricketts’ short-range methods with modifications. One of the modifications is the use of variable growth rates according to the patient’s age and sex. This was one of the weaknesses of the Johnston and Ricketts systems which used the same growth rate for each patient, irrespective of age and sex.
method. Then, superimposing the prediction and the final head film on sellanasion at sella, the error, in millimeters, was measureddirectly. Theseerrors were squared, summed, and divided by the number in the sample to get the meansquared error. Then the square root was taken for the root-mean-squarederror. One may interpret the root-mean-squared(rms) error as follows : 70 per cent of the predictions will be within + 1 rms error. 95 per cent will be within + 2 rms errors. Therefore, once the expected value and the rms error are calculated, a complete probability of direction of growth and its uncertainty is determined. Method 2. Average increments from sellu-nasion. Since we were interested in studying points not covered by the Johnston grid, as well as testing the grid’s applicability to a lo-year growth period, we devised a method of prediction equivalent to the grid using the fifty-case lo-year sample. Average increments for each of the points under consideration were calculated from SN with X as the origin, and these increments were then used in a prediction as follows: Using sella-nasion as a horizontal axis with sella as its center, we merely added the average increment per year in the horizontal and vertical directions times the number of years of the forecast to each of the above points.
Fig. 12. The patient. Here cranial
computer
Where we
see a patient base
program
it shows than
the
the who
will greatest
has
grown
not
greatly
advantage much
more
improve is in
the
forecast
patients
in the
mandible
with
for abnormal
and
much
the
average patterns.
less
in the
average.
For the purposes of both of these average predictions, girls were assumed to grow one unit per year until the age of 15 and boys one unit per year to the age of 19, according to Ricketts’ thesis and experiences on a clinical basis. Method 3. The Ricketts short-range prediction. Ricketts suggested that one can do better than the averages in prediction of the chin position by constructing the chin according to the patient’s own mandibular lines.” He did not intend, however, that this method be used beyond a 2- to 3-year prediction. Here the basionnasion plane is used as the reference; the patient’s pattern is extended down his own condyle axis (Fig. 10) and corpus axis to reach pogonion. Therefore, patients who have vertical patterns will grow more vertically, and patients who have horizontal patterns will grow horizontally. It should be noted that in the previous methods all patients grow the same amount and direction, irrespective of their facial patterns, while the Ricketts method includes information from the facial pattern. Root-mean-squared error for pogonion was calculated by means of this intended short-range method of prediction on the lo-year cases by superimposing on the basion-nasion plane at point CC. Method 4. Computer forecast. The computer growth forecast adds the following data input to Method 3 : A. Individual growth curves are used for the mandible, maxilla, and
Volume 67 Number- 3
Evaluation
of growth-forecasti?ag methods
269
Fig. 13. The differences in the ramus position, condyle location, and cranial base deflection that the computer evaluates in order to warn the orthodontist of the possibility of this abnormal growth. If the factors are significant, the patient grows more in the mandible and less in the cranial base than average. The computer was 67 per cent more accurate than average increments in patients with Class III tendencies.
cranial base rather than using the same increments for every age group. B. Clinical experience with 40,000 predictions has shown that certain persons grow differently than the averages. The RMDS computer bank has been used to identify those characteristics in these unusual patients (less than 5 per cent) which can be identified to grow differently from the averages. They fall into three groups : 1. Patients who grow abnormally large mandibles with less growth in the cranial base, referred to as abnormal Class III patterns. These are predicted using the variations from normal as shown in Fig. 13. 2. Unusually strong patterns which rotate forward. These characteristics are displayed in Fig. 14, B. 3. Abnormally weak facial patterns. These rotate distally ,and have the characteristics shown in Fig. 14, A. It should be noted that none of the foregoin g factors show high linear correlations. The linear correlation assumes that a small increment in the cause produces a corresponding increment in the effect. It has been found that patients with values in the normal range or those who display some but not all of the abnormal characteristics do not show the abnormal tendencies. Characteristics 2 and 3 were derived using Ricketts’ principle of arcial growth of the mandible as a basis.8 At the present time, a complete computer prediction using the principle of arcial growth is not available and, therefore, was not tested as part of the present article. This would be a possibility in the future. These findings are also in agreement with the work of Odegaard,g which showed a correlation of future mandibular form based on initial mandibular form. The
270 Table
Xchdhof I. The error
Am. J. Orthod. March 1975
Bngha
mad
summary
for fifty
Johnston
I
Point h (Maxilla) PO (Mandible) Nose XI (Ramus) B6 (Molar)
j /
untreated
Acerage groxth 14.6 25.4 20.0 14.2 23.4
/
RdlS Error 5.2” 7.5* 6.2
cases
Average
grid
! Per cent / Accuracy 64 70 69
Aucrage growth 14.6 25.4 20.0 14.2 23.4
increment RMIB .tTYOT
1 Per cent accuracy
4.3” 6.8” 6.2 4.4* 4.4”
71 73 69 69 81
The mean period of growth prediction was 9.42 years. As can be seen, most of the predictions were *Indicates significantly greater error than the RMDS computer prediction at the 5 per cent sig
error calculations were made by superimposing on the Frankfort horizontal and pterygoid vertical, the basic reference lines for the computer system. Results
Results are summarized in Tables I and II and may be stated as follows: Method 1. Johnston grid. Although it provides a very useful prediction, the
Johnston grid was the least accurate of the three methods considered, being based on the most simple premise. Comparing the root-mean-squared error, in millimeters, with the average growth change at each point, that portion of predictable growth can be seen. The Johnston grid was about as accurate as any for predicting growth of the nose and, in fact, was almost 70 per cent accurate. This definitely indicates the potential of evaluating patients’ cases on a long-range basis with regard to softtissue profile, and certainly many of the patients who are considered overtreated today from an esthetic standpoint might have been helped had the long-range growth of the nose been taken into account. Of course, to evaluate the profile completely, it would be necessary to predict the reaction of soft tissue to treatment which has been adequately documented by Ricketts2 and Holdaway. The grid was also 64 per cent accurate on point A and 70 per cent accurate on pogonion, once again illustrating that a useful amount of growth over the long range is predictable. This is an especially good result, considering that the growth rates were derived for use over the 5-year period from the ages of 10 to 15 years, whereas many of the patients in this study were observed between the ages of 6 and 18. Method 2. Sella-Nasion average increments. This method gave a useful improvement over the Johnston grid at both pogonion and point A. This improvement comes from two sources: (1) using growth rates applicable to the lo-year prediction period and (2) predicting pogonion directly rather than by construction from point B. Method 3. Ricketts’ short-range prediction method. The Ricketts short-range prediction has somewhat less rms error, in millimeters, than the Johnston grid or average increments from S-N. Some of the smaller over-all error was due to the fact that point CC, the origin of this growth prediction, is closer to pogonion
Evnluation
of growth-forecastbtg
RMS
growth
error
21.8
5.8
271
RMDS program
Ricketts short range Average
methods
Per cent accuracy
Average growth
RMS error
Per cent accuracy
12.2 21.9 18.0 12.7 20.1
3.2 4.8 5.6 3.5 3.4
74 78 69 72 83
73
accurate in the 70 to 80 per cent range, which must be considered useful as a planning
tool.
nificance level.
Table II. A comparison of chin position RMDS
Samvle Total 50 Class III patterns Vertical patterns (59 degrees)
of errors of the various
computer
methods
with
respect to the prediction
S-N
Ricketts
average increment
short range Per cent of
Per cent of comvuter
R M S error
Per cent of comvzcter
R M S error
compder
4.8
100
6.8
142
5.8
121
4.3
100
7.2
167
6.6
153
4.8
100
8.3
173
7.3
152
R M S error
This shows that the methods using average increments were not nearly so successful in the difficult Class III and vertical patterns as they were on average. However, the computer maintained the same efficiency in all three groups and thus does a much better job on individual patients.
than to sella. There was a 10 to 20 per cent improvement of this method over average increments due to the facial pattern, but some of the potential was not realized, possibly because the growth rates used were derived to be applicable to the period of 8 years to 13 years. Therefore, we have a similar problem with the Johnston grid, that is, applying growth rates for one age group to a different age group. It should be mentioned that there is an advantage in using a prediction in which vertical patterns tend to grow more vertically and horizontal patterns more horizontally. Here the root-mean-squared error does not tell the whole story, as it assumes that an error in one direction is just as bad as an error in the other. This is not the case in orthodontic treatment, assuming that vertical patterns will grow more vertically than horizontal patterns, given a safety margin in treatment. If a horizontal pattern grows more vertically than expected, this will aid in treatment and give a more normal appearance. If the orthodontist had not anticipated horizontal growth and it occurred, too much headgear might have been used ; therefore, he might have overtreated the profile as well as possibly extracting when nonextraction treatment would have sufficed. Many clinicians find that ex-
Fig. 14. A case that the computer horizontally (B) than average.
would
predict
to grow
more vertically
(A) and
more
tracting in a brachyfacial pattern may result in an overly flattened profile because of the difficulty of moving lower molars forward. Some reason that the musculature is strong, while others contend that it is due mostly to growth pattern. A similar argument can be used for assuming more vertical growth in vertical facial patterns. Here extraction is not usually a difficulty, for the anchorage is more easily lost, whereas leaving the dentures protrusive, hoping for growth, is generally to be avoided in this type. This is a possible reason that the Ricketts forecast has served so successfully clinically. It is designed to keep the clinician out of trouble, not merely to minimize root-mean-squared error. Meth’od 4. RMDS c.omputer program. As was discussed previously, this system was essentially based upon the theories of Ricketts. RMDS hoped to individualize further by using growth rates variable for the patient’s age and by recognizing unusual facial patterns. The RMDS program was the most accurate of this study. However, the improvement is not pronounced by statistical comparison of root-mean-squared errors. For example, the computer program was only 21 per cent more accurate than the Ricketts short-range method alone and 56 per cent more accurate than the Johnston method. It should be noted that this was a loyear study and that in a 5-year or 2-year study there would be less advantage to the computer. Hence, it is not surprising that other investigators in small samples have found little difference. In a small sample of twenty, a difference of 20 or 30 per cent would not be statistically significant. The sample size is of essential importance in determining the statistical significance of the rms error. In a sample of twenty the rms error has to be greater by 46 per cent to be statistically significant, whereas in a sample of fifty the rms
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273
Fig. 15. The factors in the mandible that are used to evaluate this potential. These factors represent the squareness of the mandible and the relative length of the condyle head. The computer was 73 per cent more accurate than average increments in the vertical patterns which are a source of trouble to the orthodontists.
error has to be greater by only 22 per cent. This demonstrates that the larger the sample, the greater the statistical significance it bears. One should look further, however, into the components of this fifty-case sample to appreciate fully the use of the RMDS forecast. As we have stated, the vast majority of these patients have relatively normal facial patterns. The computer did not extend these patterns much differently than an average increment method. However, Table II discusses two subgroups within the fifty-case sample that are somewhat lost among the normal samples. They include Class III skeletal patterns as defined by the computer system and vertical patterns which will be defined as simply having a more negative chin from Frankfort plane. These cases are the most interesting, since they actually represent the two major problem areas of treatment. There were only eight patients of the fifty recognized as potential prognathie patterns by the computer and seven recognized as retrognathic patterns. On the Class III patterns, as was discussed previously, the computer evaluates key factors in the deep structure to determine the growth rates to be used in predicting the mandible. There are certain persons, although relatively rare, who have been tentatively identified as having potential for excessive mandibular growth. These persons can present quite bothersome situations, for some may have Class II malocclusions and are treated with extraoral traction, much to the detriment of the future skeletal profile. Others may be treated with normal Class III mechanics for many years and finally require surgical intervention for skeletal correction, It should be noted that in the eight patients in whom the computer recognized Class III skeletal patterns, the improvement was 53 per cent over the Ricketts short-range method, 6’7 per cent over the sella-nasion method, and, of course, there was greater improvement over the Johnston grid. This is nearly twice the improvement if we include these persons in among the normal samples. The vertical patterns showed an increase of 52 per cent over the Ricketts short-range method and 73 per cent over the average increment method. In fact, the computer
error was not increased on any of the three groups-normals, Class III ‘s, or verticals. This shows it,s applicability to the individual clinical situation, as the average increment methods suffered considerably when applied to these nonaverage patterns. Emphasis must be placed on the fact that normal samples do not usually contain the number and variety of facial patterns that the clinician faces in his office. Hence, a small, normal, untreated sample may contain very few of these problem cases and the computer advantage would be obscured. Comparison
of results with
those of other investigators
Johnston and Greenberg’ found, in their study, that there was no significant difference between the computerized method of prediction as applied in 1972 and the average change in the population. Hence, they concluded that the most sophisticated methods of growth forecasting did not individualize and, therefore, the most simple methods would be just as good. This is clearly in conflict with the results of the present study, which show that as more sophistication is added, the accuracy of the prediction improves. There are several factors which we believe explain this apparent contradiction : 1. Since the above study, performed in 1972, two key factors in individualization were introduced into the computer system. In 1973 individual rotational factors in vertical patterns and increased mandibular growth in Class III patterns were instituted. Some relationships are much easier to predict than others. The majority of the relationships which Greenberg and Johnston showed to be as easily predicted by the averages as the computer involved the relative relationships of points A and B. As points A and B are alveolar points, functionally related to the roots of the upper and lower incisors, their relationships cannot change very much more than the relationships of the incisors themselves. It is well known that, both occlusions and malocclusions remain stable, once the permanent teeth are interlocked in development. However, the facial pattern can change, which would have a definite effect on esthetics without causing a corresponding change in OCelusion. Hence, facial changes would not be reflected in points A and B. The conclusion may be drawn that the relationships of A and B are so stable as to not require a sophisticated prediction method. Many clinicians, however, are more interested in the relationship of point A to pogonion. The available chin is used as an indication of the possible need for forward positioning of the lower incisor. The relation of point A to pogonion is thought by many practitioners to be most critical for esthetics and denture balance. 2. Johnston and Greenberg’s data showed that as pogonion was used (instead of point B-see angle of convexity) the computer did have a positive prediction efficiency over other methods. We have shown that, when predicting the relationship of pogonion to cranial structures, the computer has positive et%ciency, and the reason is that this is much harder to do than to predict the relation of A to B. 3. All of the patients in the Johnston-Greenberg group were 10 years of age at the beginning of the study and 15 years old at the end. This is a period
Evaluati,on
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during which girls grow much the same as boys, on the average, and the very homogeneity of the group would mean that the average would not be very far off from the individual. However, such homogeneity is not the norm in an orthodontic practice, and the orthodontist must have a prediction which is valid for all age groups, short term and long term. In this study there was a variety of prediction times and a lo-year growth period. Hence, any one grid would not suffice for a great variety of ages and predictions. This could be corrected by using complex tables to determine growth increment, now under consideration by Johnston. 4. Greenberg and Johnston’s sample included only twenty patients. This does not allow a great variety of case types, but more important results which may not appear to be significant statistically in twenty cases would be statistically significant in fifty cases. 5. Use of the rms or average error lumps all patients together. Since most members of untreated samples have normal facial patterns, the averages will suffice. However, the patients causing the orthodontist the most trouble are those with abnormal Class III and vertical patterns. If these are studied separately and not lost in the statistics, the computer has an advantage. 6. Each growth-forecast method is designed for specific superimposition. Therefore, the computer system was designed for superimpostion on the Frankfort horizontal and the pterygoid vertical in order to achieve optimum accuracy. It became apparent, when performing various error analyses, that growth was more orderly when viewed from the Frankfort horizontal and the pterygoid vertical, and some of the improvement in the computer prediction is due to the use of these planes for superimposition. In fact, if sella-nasion or basion-nasion were used for superimposition of the computer prediction, there would be less accuracy. DISCUSSION
Growth forecasts have two purposes : 1. Short range-to plan strategy and anchorage. 2. Long range--to give evaluation of final results: esthetics, facial balance. Because of the limited amount of growth in a P-year treatment period compared to treatment effects, all of the methods of growth forecasting would yield the same accuracy. However, a safer strategy for the orthodontist is a method that assumes vertical growth for vertical patterns and horizontal growth for horizontal patterns although theoretically this is not greatly more accurate than assuming the same growth for everyone. Over the longer term, the majority of the growth experienced is consistent enough to be considered predictable (70 per cent ) . Refined computer methods which take into account the individual facial patterns will not be markedly more accurate in the 70 per cent of the patients in the normal range but will show considerable advantage in 30 per cent of the abnormal patterns, including vertical patterns and Class III tendencies. Repeated comparison of predictions with actual results has enabled the com-
REFERENCES
1. Iirodie, A. G., and others: Cephalometric appraisal of orthodontic results: A preliminary report, Angle Orthod. 8: W-265, 193X. 2 Ricltetts, R. M.: Planning treatment on tlro basis of the facial pattern and an estimate of its growth, Angle Orthod. 27: 14.3T, 1957. 3. Rickctts, H. M., and others: An overview of caomputerizcd cephalometrics, Ax J. ORTHOI). 61: l-28, 1972. 4. Turlcy, I’.: A computerized method of forecasting third molar space in the mandibular arch, to lw presented at the American Association for Dental Research, April, 1975. 5. Johnston, Lysle: Lecture presented at Great Lakes Society of Orthodontics, French Lick, Ind., 1974. 6. Gugino, C. F.: An orthodontic philosophy, Denver, 1971, Rocky Mountain Dental Products Company. 7. Grwnbrrg, I,. Z., and Johnst,on, 1,. $1.: Computerized prediction : The accuracy of a commcrcial long-range forecast, Anl. .J. ORTHOR 67: 243-252, 1975. 8. Ricketts, R. M.: A principle of arcial growth of the mandible, Angle Orthod. 42: 368-386, 197“. i 9 Odegaard, J.: Growth of the mandible studied with the aid of metal implant, AM. J. ORTHOD. 57: 145-157, 1970. 15125 Ventura
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