American

Journal

of ORTHODONTICS di~lrrr~r 74. NIU~&T 6

ORIGINAL

December,

1978

ARTICLES

Mandibular plane changes dwing maxillaq retraction Part 2 Sheldon Baumrind, D.D.S., M.S.,* Robert Molthen, D.D.S.,** Eugene E. West, D.D.S.,*** and David M. Miller, B.S., M.S.**** San Frunciscn, Calif.

T

he conventional wisdom of the orthodontic specialty holds that certain morphologic relationships which can be observed on pretreatment head films predispose patients treated with distally directed forces to the maxilla toward an increase in mandibular plane angulation. Most orthodontists also believe that when mandibular plane angulation does increase during treatment, the increase will be associated with characteristic changes in certain other head film measurements. In a recent article’ we reported evidence that the rneun change in mandibular plane orientation associated with the delivery of forces to retract the maxilla during mixeddentition Class II treatment is very much smaller than has been previously supposed. We also inferred that only a small part of the between-patient tw-iubility in observed change in mandibular plane orientation seems to depend upon the precise direction from which the maxillary retractive forces are applied. The present article continues our inquiry into the goodness of contemporary orthodontic theory in accounting for the changes which actually occur following treatment administered by expert clinicians employing methods of their own choice. We again focus our

“Ahsociatr Profebsor of Orthod~,ntica/Radit,lof4-. Department of Growth and Development. University of California-San Franciwo. ‘“Awxiate Research Orthodonttat. Departmsnt uf Grwth end Devclqm~ent. l’ni\er\itk trf California-San Franciwo. “**Professor ot Orthodontics. Department uf Grwth ;tnd Development. I’n~\?!~itq of C.ilifWniaSan Francisco. ““**Assistant Research Engineer. Department of Growth and Development, LlniverGty of California-San Francisco 0002-911hi7XiI~0M7?+18$OI.X0/0

0

lY7X The C. V. Mosbq

Co.

603

Am. J. Orrhod. December I918

Table

I. Variables

investigated

vun’ablrs (measures whose components of variability we are attempting to analyze) D:MPA Change in mandibular plane angle of Downs D:GOGNSN Change in gonion-gnathion to sella nasion angle II. Antrcedenr srare variables (variables defining the subject’s condition at beginning of treatment) II. 1 MPA:FI Original mandibular plane angle of Downs II.2 GOGNSN : Fl Original gonion-gnathion to sella nasion angle II.3 AGE:Fl Age in months II.4 SEX Sex II.5 MOLAR:FI Severity of Class II molar relationship = horizontal distance between mesiobuccal cusp of upper first molar and mesiobuccal cusp of lower first molar measured parallel to occlusal plane of Downs 11.6 PROPU6CX Horizontal U6C proportion = horizontal distance sella to U6C measured parallel to SN line expressed as percentage of distance from sella to nasion 11.7 PROPU6CY Vertical U6C proportion = vertical distance sella to U6C measured perpendicular to SN line expressed as a percentage of distance from sella to nasion II.8 PRPRAMUS Ramus height proportion = distance condyle to gonion expressed as percentage of distance from sella to nasion II.9 PROPBODY Mandibular body length proportion = distance gonion to menton expressed as percentage of distance from sella to nasion 11.10 RAMUSBOD Ramus-body ration = distance condyle to gonion expressed as percentage of distance from gonion to menton II. 11 PRPDYLX Horizontal condyle proportion = horizontal distance sella to condyle measured parallel to SN line expressed as percentage of distance from sella to nasion II. 12 PRPDYLY Vertical condyle proportion = vertical distance sella to condyle measured perpendicular to SN line expressed as percentage of distance from sella to nasion II.13 PROPTFH Total face height proportion = distance nasion to menton expressed as percentage of distance from sella to nasion I. Dependent

1.1 1.2

*Three subjects have been dropped from the original sample because of uncertainty as to age at the onset of treatment. Nore: All angular, linear, and superimpositional variables are defined in terms of the processes by which we actually measured them. For example, our measurements of Class II severity and Class II correction (Molar:Fl and D:MOLAR) make no reference to centric relation or centric occlusion because neither we nor any other investigators possess at this time a valid method for checking these relationships on head films. Our operational definitions for all landmarks, angular measures, and superimpositions used may be found in: The reliability of head film measurements, 1, AM. J. ORTHOD. 60: 11 l-127, 1971. The reliability of head film measurements, 2, AM. J. ORTHOD. 60:505-517, 1971. The reliability of head film measurements, 3, AM. J. ORTHOD. 70~617~ 644. 1976.

attention on changes in mandibular plane orientation and will attempt to develop explicit quantitative answers to the following questions: 1. How much of the between-patient variability of change in mandibular orientation during treatment is predictable on the basis of age, sex, and morphologic factors which can reasonably be known to the clinician before treatment is commenced? 2. What changes in other head film measurements are characteristically associated with increase or decrease in mandibular plane angulation during treatment? 3. How much of the observed variability of change in mandibular plane angulation during treatment can be accounted for solely on the basis of knowledge of the direction of force mnlic~ti-~

V&me Number

14 6

Mandihulcrr

plane

changes

605

Table I. Cont’d III.

IV.

Concurrent change variables (measures of change between the pretreatment film and the end of treatment film; all values in this group are measured in mm. unless otherwise indicated) III. 1 D : MOLAR Class 11 molar correction III.2 D:MOLAR Distal positioning of mesiobuccal cusp of upper first molar measured parallel to sella nasion line of pretreatment film with films superimposed on anterior cranial base III.3 DYU6ACB Vertical displacement of mesiobuccal cusp of upper first molar measured perpendicular to sella nasion line of pretreatment films with films superimposed on anterior cranial base III .4 DW6PAL Vertical displacement of mesiobuccal cusp of the upper first molar measured perpendicular to Film 1 occlusal plane of Downs with films superimposed on best fit of plane of Downs with films superimposed on best fit of palate 111.5 D:MBL Change in mandibular body length increase in length of line segment gonion to menton III.6 DX:DYLSN Horizontal change in position of condyle relative to superimposition on anterior cranial base measured parallel to SN line of first film III.7 DY: DYLSN Vertical change in position of condyle relative to superimposition on anterior cranial base measured perpendicular to SN line of the first film (Note: This value is a valid measure of vertical growth and developmental changes between the anterior cranial fossa and the glenoid fossa.) III.8 DY : DYLSN Horizontal change in position of condyle relative to superimposition on best fit of mandible measured parallel to Downs occlusal plane of pretreatment film (Note: This value is a measure of the anteroposterior change in position of the head of the condyle relative to the rest of the mandible.) 111.9 DY:DYL: M Vertical change in position of condyle relative to superimposition on best fit of mandibular border measured parallel to Downs occlusal plane of pretreatment film (Note: This value is a measure of increase in ramus height.) 111.10 EMONTHS Elapsed time between films (measured in months) Treatment type variables N= IV.1 Cervical gear 104 IV.2 Straight-pull headgear to “j” hooks 16 IV.3 High-pull headgear to upper first molar 53 IV.4 Combi headgear 15 IV.5 Intraoral appliances 61 IV.6 Untreated control cases 53 300*

Materials and method The data presented in this article are the product of further computer-conducted analyses of the same data base examined in our previous article. i The data base is constructed from measurements made on paired lateral head films for 303 subjects. each of whom presented with clinically diagnosed Class II malocclusion in the mid-to-late mixed dentition. Of these, 249 subjects had received treatment for the correction of anteroposterior dysplasia using one of five intraoral or extraoral appliances but not including full orthodontic banding. In general, these treatments can be characterized as the initial phase of a two-phase mixed-dentition treatment. The remaining fifty-four subjects were untreated Class II controls. All tested subjects were patients in the practices of well-known clinicians who are consensually accepted as experts by the orthodontic specialty. Each clinician employed the appliance which was generally used in his practice at the time the patients were

Am. J. Orthod. December 1978

treated. Sample selection was made entirely on the basis of pretreatment criteria and pretreatment records. Within each clinician’s practice, cases were sampled without conscious bias and in a manner as close to statistical randomness as was possible. However, the study is retrospective in the sense that the sampling took place after initial-phase treatment had been completed. In the portion of the study reported in this article, we evaluated the ability of thirteen “measures of antecedent state,” ten “measures of concurrent change,” and six “types of treatment” to account for the observed differences in each of two “measures of change in mandibular orientation” during treatment. The “measures of antecedent state” were sex, age at the beginning of treatment, and eleven morphologic relationships measured on the pretreatment head film. The “measures of concurrent change” were elapsed time between the pretreatment film and the end-of-phase-one film, and nine measures of morphologic change between the two films. The “types of treatment” were cervical traction, straightpull headgear to j hooks, high-pull headgear to the upperj’rst molars, “combi” headgear, various intraoral appliances, and untreated controls. The two “measures of change in mandibular orientation” were (1) change in mandibular plane angle of Downs (D:MPA) and (2) change in the gonion-gnathion to SN angle D:GOGNSN). Both measures of change in mandibular orientation are reported because each is preferred over the other by some clinicians. Our methods of data reduction have been described in our previous article. ’ The list of variables for the present article is defined more fully in Table 1 and illustrated in Fig. 1. Through an inadvertence, Figs. 1, 2, and 3 have been omitted. Space limitations have made it impossible to replace them without delaying publication of this issue. These three illustrations will appear in the January, 1979, issue of the Journal. It may be seen that the variables in Table I are arranged into four groups. Group I consists of the two measures the sources of whose variability we are trying to determine. In the parlance of statistics, these are termed “dependent variables.” The remaining variables are termed “independent variables.” Group II is the group of antecedent state variables. They can be used to answer the first of the three questions listed in the introduction. For statistical purposes, that question may be rephrased as follows: How much of the variance in the dependent variables can be accounted for on the basis of the thirteen antecedent variables alone? And which of the antecedent variables are the most powerful predictors’? Group III is the group of concurrent change variables. They can similarly be used to answer the second question in the introduction, rephrased for these purposes as follows: How much of the variance in the dependent variables can be accounted for on the basis of the concurrent change variables alone? And which of the concurrent change variables are the most powerful predictors? Group IV is the group of treatment types. By segregating the sample according to treatment modality, one can answer the third question in the introduction, now restated in the form: How much of the variance in the dependent variables can be accounted for on the basis of knowledge of treatment type alone?

Volume 74 Number 6

Table

Mmdibttlrrr

changes

607

II. Descriptive statistics Variables Dependent

variables

(Group

Mean

Independent

0.06

-0.01

1.68 1.86

variables

Antecedentstate variables (Group II) MPA:FI GOGNSNFI AGE:Fl SEX* MOLAR:FI PROPU6CX PROPU6CY PRPRAMUS PROPBODY RAMUSBOD PRPDYLX PRPDYLY PROPTFU Concurrentchangevariables(GroupIII) D : MOLAR DXU6ACB DYU6ACB DW6PAL D:MBL DX: DYLSN DY: DYLSN DX:DYL:M DY:DYL:M EMONTHS = I, Female

Standarddeviation

I)

D:MPA D:GOGNSN

*Male

plane

26.14 33.95 114.41 1.53 -1.12 42.04 -89.49 81.57

81.11 100.81 -0.19 -0.21 154.93

5.13 4.99 18.60 0.49 1.71 5.05 4.95 5.29 5.07 7.26 0.04 0.04 7.83

2.81 -0.76 -3.58 1.32 3.08 -1.05 -1.08 -2.81 5.21 27.56

2.68 3.07 3.65 1.85 2.13 1.83 2.26 2.45 3.90 13.40

= 2

Finally, by pooling all the independent variables, we can answer an important related question: How much of the variance in the dependent variables can be accounted for on the basis of knowledge of all the variables of Groups II, III, and IV taken together? The statistical procedure known as multiple regression is typically used by statisticians io answer questions in this form in which the problem is to analyze the degree to which a number of variables taken together “explain” the variability in some other single variable. The variable whose variance is being explained is termed the “dependent” variable, while the other variables are categorized as “independent” variables. The degree to which the independent variables explain the observed variance (that is, deviations from the mean value) in the dependent variables, may be assessed either by analyzing the group of independent variables as a unit or by sequentially adding independent variables one at a time on the basis of their individual predictive power. The method of adding independent variables one at a time on the basis of their individual predictive power is called “stepwise regression.” When this procedure is used, a new linear “estimating equation” is developed after each step so that each independent variable which has been entered (that is,

Am. J. Orthod. December 1978

Ta ble Ill8 (above

double

line). Coeflicicnta

of determination

D : GOGNSN

MPA:FI

-0.04

-0.06

-0.03 0.09 -0.17’ -0.19’ -0.39** -0.09 -0.26*’ 0.07 -0.16* 0.48** -0.00 -0.01 -0.02 -0.01 0.03 -0.04 0.15* -0.1 I 0.05 0.00

D:MPA

(1.‘)) expressed GOGNSNFI

as percentages AGE:FI

D:GOCNSN

MPA:FI GOGNSNF I AGE:FI SEX MOLAR:Fl PROPU6CX PROPU6CY PRPRAMUS PROPBODY RAMUSBOD PRPDYLX PRPDYLY PROPTFH D : MOLAR DXU6ACB DYU6ACB DYU6PAL D:MBL DX : DYLSN DY: DYLSN DX:DYL:M DY:DYL:M EMONTHS

-0.05

-0.01

-0.05 0.08 -0.17** -0.00 -0.16* 0.07 -0.02 -0.06 0.18** -0.39** -0.03 0.17* -0.18** -0.08 0.22** -0.16* -0.10 -0.02

0.01 0.05 -0.10 0.04 -0.14* 0.04 -0.04 -0.05 0.15* -0.31** 0.04 0.1 I -0.22** -0.10 0.24** -0.11 -0.20** -0.07

Table IIIA (below

double

*Indicates “*Indicate5

a relationship a relationship

line). Coefficients of correlation significant at the .Ol level. significant at the ,001 level.

0.04

-0.53 -0.08 -0.38** -0.19** -0.17* -0.06 0.26** 0.54** -0.01 -0.08 0.11 -0.12 -0.00 0.06 0.09 0.05 -0.07 -0.12

0.16* 0.06 -0.35** 0.32** 0.20** 0.10 -0.07 -0.01 0.13 0.05 0.04 -0.00

0.02 -0.16* 0.01 -0.06 -0.07 0.00 -0.02

(r)

introduced) is represented by a single term. In this article we will not concern ourselves with these estimating equations per se but only with the order in which the independent variables are entered and with the amount of the variance in the dependent variables which each independent variable “explains.” Two caveats are in order during the evaluation of output from multiple regression analyses. First, since multiple regressions consider only linear relationships between variables, it is possible that nonlinear relationships may exist but fail to be detected. Second, it is necessary to be aware that when a variable is added to the equation in a stepwise regression, those portions of the variance which it accounts for in common with other variables yet to be added are credited, so to speak, to the variable which is added to the equation earliest. This means that if two variables in an analysis are highly interdependent, the addition of the first one will markedly reduce the apparent predictive power of the other, causing it to be added to the equation only much later, if at all. This principle is explained in Fig. 2. In summary, the general strategy of data analysis for this article was, first, to see how much of the variance in each of the two dependent variables was accounted for by each of the independent variables considered separately. This operation was accomplished by generating a table of conventional Pearson correlations (r’s) for all possible pairs of

Volume 74 Number

~andihular

6

Table 1118. Coefficient\ SEX

D:MPA D:GOGNSN MPA:FI GOGNSNF AGE:FI

of determination MOLAR:FI

I

(1.?) expressed PROPLWX

as percentages

PKOPu6CY

28% 12%

plane changes

609

(continued)

PRPRAMUS

PROPBODY

RAMUSBOD

15% 14% 10%

SEX

MOLAR : F I PROPU6CX PROPU6CY PRPRAMUS PROPBODY RAMUSBOD PRPDYLX PRPDYLY PROmFH D: MOLAR DXU6ACB DYU6ACB DYU6PAL D:MBL DX: DYLSN DY: DYLSN DX:DYL:M DY:DYL:M EMONTHS

-0.00

-0.01 0.07 -0.03 0.09 -0.03 0.12 -0.00 -0.00 -0.03 0.12 -0.09 -0.01 0.06 0.01 0.07 -0.09 -0.05

-0.00 0.08 -0.47** 0.19** 0.00 -0.01 0.02 0.07 0.05 0.13 -0.05 -0.06

-0.37** -0.40** 0.05 0.13* -0.04 -0.01 -0.02 -0.00 0.02 -0.06 0.06 0.11

0.34** -0.77** -0.12 0.00 -0.04 0.08 0.05 -0.05 0.05 -0.01 -0.03 0.03

0.10 0.36** 0.09 0.05 0.00 -0.00 -0.01 0.03 -0.32** 0.11 -0.07 0.01

-0.07 0.39** 0.10 0.06 -0.02 0.00 -0.01 0.01 -0.11 0.02 0.04 0.06

0.16* -0.00 -0.01 0.00 0.01 -0.01 0.00

0.01 -0.19** 0.08 -0.11 -0.04

Table IIIA. Coefficients *Indicates **Indicates

of correlation (r) (continued) a relationship significant at the .Ol level. a relationship significant at the ,001 level.

variables. Next we determined how much of the variance in each dependent variable could be accounted for by each of the three groups of independent variables taken separately. These operations were accomplished by a series of stepwise multiple regressions of the type described above. Finally, we determined, by means of additional stepwise regressions, how much of the variance in each dependent variable could be accounted for by the entire set of independent variables taken as a single group. All calculations were made using the SPSS Statistical Program Package.2 Findings

The tabulated results of the several statistical procedures are presented in this section. As is the case with all experimental findings, they are amenable to more than one interpretation, depending upon the biases of those who examine them. In order to allow the reader to evaluate the data while only minimally influenced by the biases of the authors, we present in this section only the tabulated data while reserving our own comments and interpretation for the discussion. Table II lists the means and standard deviations for the dependent variables, the antecedent state variables, and the concurrent change variables. Angular values are expressed in degrees, linear values are expressed in millimeters, and proportional relation-

Am. .I. Orthod. December I978

Table IllB (above percentages

double

line). Coefticient~

01‘ determination

(r”)

cxprrsaed

as

(continued) PRPD YLX

D:MPA D:GOGNSN MPA:FI GOGNSNF I AGE:FI SEX MOLAR:FI PROPU6CX PROPU6CY PRPRAMUS PROPBODY

PRPDYLY

PROPTFH

D:MOLAR

DXU6ACB

DYU6ACB

16% 23% 29%

22% 11%

14% 12%

16% 59% 13% 15%

0.02 -0.04 0.05 -0.05 -0.17** -0.24** 0.13* -0.05 -0.00 0.03

0.01 -0.00 0.10 -0.10 -0.01 0.06 -0.28** 0.18** -0.16* -0.02

0.09 -0.06 0.04 -0.04 -0.00 0.03 -0.02 0.02 -0.01 -0.08

ggDg D : MOLAR DXU6ACB DYU6ACB DYU6PAL D:MBL DX : DYLSN DY: DYLSN DX:DYL:M DY:DYL:M EMONTHS

Table IIIA (below *Indicates **Indicates

a relationship a relationship

double

line).

Coefficients

of correlation

-0.16* 0.05 0.03 -0.09 0.01 -0.06

0.33** -0.09 -0.24’* -0.13** 0.22** 0.35**

-0.67** 0.23** 0.26** 0.44** -0.70** -0.76**

(r) (continued)

significant at the .Ol level. significant at the ,001 level.

ships are expressed as percentages. For the purposes of this table, the 300 subjects in the sample are pooled with respect to treatment type. Table III presents the Pearson correlation coefficients (r) between all variable pairs. Significance values are listed for each coefficient whose probability of occurring by chance is less than 1 percent. It should be borne in mind that with sample sizes as large as the present one, it is possible to discern differences which are highly significant statistically, even though they account for too small a portion of the total variance in the system to be of clinical importance.3 For this reason, we also provide in Table III a listing of r squared, the coefficient of determination for each variable pair. This statistic, in effect, represents the average ability of either member of a variable pair to predict the other when used for single cases.4 In order to simplify the reading of these tables, values are expressed as percentages accounted for instead of in the usual decimal form. In addition, values are omitted for all variable pairs which account for less than 10 percent of the system variance, whether or not they are statistically significant. It may be seen that no single independent variable in Table III predicts more than 16 percent of the total variance in either D: MPA (change in mandibular plane angle of downs) or DGOCNSN (change in gonion-gnathion to SN angle). For this reason, we next turned to analyses using multiple groupings of variables. Table IV summarizes the out-

Volume 74 Number 6

Table MB.

Coefficients DYU6PAL

D:MPA D:COGNSN MPA:FI GOGNSNF I AGE:Fl SEX MOLAR : F I PROPU6CX PROPUbCY PRPRAMUS PROPBODY RAMUSBOD PRPDY LX PRPDYLY PROPTFH D: MOLAR DXU6ACB DYU6ACB DYU6PAL D: MBL DX : DYLSN DY: DYLSN DX:DYL:M DY:DYL:M EMONTHS

DtMBL

(?)

expresed

DX : D YLSN

as percentages DY: DYLSN

(concluded)

DX:DYL:M

DY:DYL:M

EMONTHS

10%

II%

19% 14% II%

Table IIIA. *indicates “*lndicate~

of determination

Coefficients a relationship u relationship

49% 28% 37%

12% 58% 32% 35%

of correlation (r) (concluded) sipnilicant at the .Ol level. significant at the .OOl level.

comes of multiple regression analyses for the four groupings of independent variables listed above (antecedent state variables, concurrent change variables, treatment type variables, and all independent variables pooled). Summaries are reported separately for each of the two dependent variables. Outcomes for D : MPA (Downs) are summarized in Table IV, 4A. Outcomes for D:GOGNSN are summarized in Table IV, 4B. Discussion This section is an abbreviated verbal presentation of some of the more striking findings presented in numerical form in Tables 11, III, and IV. For the 300 mixed-dentition Class I1 cases considered in this study, which were selected without conscious bias within their respective treatment types, we believe that the following assertions may properly be made: On the basis of Table II. The mean change in mandibular plane angle (Downs) was 0.06 degrees, with a standard deviation of 1.68 degrees. The mean change in GOGNSN angle was -0.01 degrees. with a standard deviation of 1.86 degrees. These mean changes are much smaller than have been previously assumed. They are certainly far below the measurement error for calculating these measures in single cases.5 The other data reported in Table II are primarily of descriptive interest. On the basis of Table III. The power of any single independent variable to predict

612

Baurl7rinci

Table

IV. Summary

A. Dependent

Am. J. Orthod. Decembrr 1978

et trl. of multiple

variable

Independent

= D: MPA

variables

I

(change

= Antecedent (Group II)

Variable name

Rank

regression

New var* (percent)

PRPRAMUS

analyses in mandibular

Cum. L’arf (percent)

3

change

Variable name

Rank

New var* (percent)

3

Cum. vari (percent)

Mult. R

16

0.40

2

DY U6PAL

I

23

0.48

3

D: MBL

5

28

0.53

4

DX:DYL:M

3

31

0.55

5

DYU6ACB

1

32

0.56

6

DY:DYL:M

3

35

0.59

7

DY:DYLSN

6

41

0.64

8

EMONTHS

1

42

0.65

9

DX : DYLSN

1

43

0.66

Variable name All treats

type variables New var* (percent) 4

(Positive

Associations)

additional

contribution

toward

explaining

to in-

the

III)

16

Treatment

Implications

Shorter original ramus height relative original SN distance is associated with crease in mandibular plane angulation

no significant

DXU6ACB

change variability

Clinical

0.18

make

(Group

Mult. R

1

The remaining concurrent explaining the observed

Rank

variables

of Downs)

state variublrs

The remaining antecedent state variables observed variability in D: MPA Concurrent

plane

variable (D: MOLAR) in D: MPA (Group

IV)

Cum. vart (percent) 4

Clinical

Implications

(Positive

Associations)

Distal movement of U6 cusp is associated with increase in mandibular plane angulation Downward movement of U6 cusp is associated with increase in mandibular plane angulation Relative lack of increase in mandibular body length is associated with increase in mandibular plane angulation Distally directed growth of mandible at condyle is associated with increased mandibular plane angulation Downward movement of U6 cusp is associated with increase in mandibular plane angulation Relative lack of increase in ramus height is associated with increase in mandibular plane angulation Relative lack of increase in posterior upper face height (glenoid fossa to SN) is associated with increase in mandibular plane anguiation Shorter treatment times are associated with increase in mandibular plane angulation Posterior remodeling of glenoid fossa is associated with increase in mandibular plane angulation makes no significant

additional

contribution

toward

I Mult. R 0.20

Clinical

implications

(positive

associations)

All treatments are associated mandibular plane angulation .._.__^. -> .~ 1 ~~~ o---r

witt increase as compared

in to

Volume 14 Number

Mandibular

plane

imp[ications

(positive

6

Table

changes

613

IV. Cont’d

All independent

variables

Variable name

Rank

(Groups

II, III,

New, iar* (percent)

and IV pooled)

Cum.

vart

Mult.

(percent)

R

Clinical

I

DXU6ACB

16

0.40

2

DYU6PAL

23

0.48

3

D:MBL

28

0.52

4

DX:DYL:M

31

0.55

5

RAMUSBOD

33

0.57

6

DY:DYL:M

34

0.58

I

DYU6ACB

38

0.61

8

DY: DYLSN

43

0.65

9

EMONTHS

1

44

0.66

10

PRPDYLY

I

45

0.67

11

DX : DYLSN

46

0.67+

No remaining independent variable served variability in D: MPA

B. Dependent Independent

variable variable.\

= D:GOGNSN = Antecedent (Group

Variable name

Rank

1

RAMUSBOD

New

makes a significant

(change stat
,ariables

II) tw*

(percent)

Cum.

vurt

(percent)

2

The remaining antecedent state variables observed variability in D: GGGNSN

2

make

Mult. R

0.14

no significant

Clinical

implications

(positive

associations)

Shorter original ramus height relative to original mandibular body length is associated with increase in mandibular plane angulation additional

contribution

toward

explaining

the

Am. J. Orthod. December 1978

Table

IV. Cont’d change

Concurrent

Variable name

Rank

variables New \,ar* (percent)

(Group

III)

Cum. var? (percent)

Malt. R

1

DXU6ACB

9

9

2

DYU6PAL

5

14

0.37

3

DY:DYL:M

7

21

0.46

4

DY: DYLSN

8

29

0.54

5

EMONTHS

4

33

0.58

6

DYU6ACB

1

34

0.59

7

D : MOLAR

2

36

0.60

8

D:MBL

1

37

0.61

The remaining concurrent change variables the observed variability in D: GOGNSN Treatment

ppe

Variable name

Rank

L,ariable New vat-* (percent)

All treats

All independent

variables

Variable name

Rank

make

(Group

New var* (percent)

(positive

associations)

Distal movement of U6 cusp is associated with increase in mandibular plane angulation Downward movement of U6 cusp is associated with increase in mandibular plane angulation Relative lack of increase in ramus height is associated with increase in mandibular plane angulation Lack of increase in posterior upper face height (glenoid fossa to SN) is associated with increase in mandibular plane angulation Shorter treatment times are associated with increase in mandibular plane angulation Downward movement of U6 cusp is associated with increase in mandibular plane angulation Greater Class II molar correction is associated with increase in mandibular plane angulation Lack of increase in mandibular body length is associated with increase in mandibular plane angulation

no significant

Cum. raart (percent) 2

Malt. R 0.15

additional

contribution

toward

explaining

Clinical

implications

(positive

associations)

All treatments are associated with increase mandibular plane angulation as compared untreated control group

in to

II, III, and IV pooled) Cum. vd (percent)

Mult. R

I

DXU6ACB

9

9

0.31

2

DYU6PAL

5

14

0.37

3

DY:DYL:M

7

21

0.46

4

DY:

8

29

0.54

5

EMONTHS

4

33

0.58

DYLSN

implications

IV)

2

(Groups

0.3 1

Clinical

Clinical

implicalions

(positive

associations)

Distal movement of U6 cusp is associated with increase in mandibular plane angulation Downward movement of U6 cusp is associated with increase in mandibular plane angulation Lack of increase in ramus height is associated with increase in mandibular plane angulation Lack of increase in posterior upper face height (glenoid fossa to SN) is associated with increase in mandibular plane angulation Shorter treatment times are associated with increase in mandibular plane angulation

Volume 14 Number 6

Table

MandihtcIar

phe

615

changes

IV. Cont’d

All independent

Rank

9

10

variables

Variable name

(Groups

II. III,

and IV pooled)

Nrrv \Ylr* (prrcen1)

C1rm. wrt (percent)

Mu/t. R

PROPBODY

2

35

0.59

DYU6ACB

1

36

0.60

D : MOLAR

I

37

0.61

PROPTPH

1

38

0.62

SEX

1

39

0.62+

No remaining independent variable served variability in D: GOGNSN

makes a significant

Clinical

implications

(positive

associations)

Greater original body length relative to original SN distance is associated with increase in mandibular plane angulation Downward movement of U6 cusp is associated with increase in mandibular plane angulation Greater Class II molar correction is associated with increase in mandibular plane angulation Greater total face height relative to SN distance at onset of treatment is associated with increase in mandibular plane angulation Boys show a greater tendency toward increase in mandibular plane angulation than do girls

additional

contribution

toward

explaining

*New var. (percent) = New variance, percentage. The amount of the previously unaccounted-for which is accounted for by the current variable. tCum. var. (percent) = Cumulative variance, percentage. The total amount of the variability counted for by the current variable and all previously entered variables.

the ob-

variability which

is ac-

either of the dependent variables seems disappointingly small. The best individual predictor of D: MPA turns out to be DXU6ACB - the horizontal (sic!) change in position of the upper molar cusp relative to superimposition on anterior cranial base (ACB). None of the other independent variables, considered by itself, accounts for even as much as 10 percent of the variance in either D:MPA (D) or D:GOGNSN. In particular, knowing the mandibular plane angle before treatment tells us, on the average, almost nothing about the direction of changes which will take place during treatment! Among the independent variables themselves, there are stronger paired associations to be found. We will not pursue these relationships far, since they are not central to the present study. However, we do wish to direct attention to three findings of special interest. The first two are the relationships between original MPA (Downs) and original GOGNSN angle and between change in MPA (Downs) and change in GOGNSN angle. It is the generally accepted belief of orthodontists that the two variables in each of these pairs are fairly equivalent and. indeed, almost interchangeable. Hence, it is not surprising to find the within-pair correlations highly significant. However, closer examination reveals that these variables are far from interchangeable, as may be seen in summary (Table V). Here it is demonstrated that more than two fifths of the variance in original MPA (Downs) is not common to original GOGNSN angle, and that one-fourth of the variance in change in MPA (Downs) is not common to change in GOGNSN. This means that to consider these measures to be interchangeable is to be highly imprecise. We consider this finding to be worthy of further study elsewhere. The third finding of special interest in Table III concerns the impact of differences in treatment time (EMONTHS). In a formal prospective experiment, some investigators might have considered it appropriate to strive for between-treatment equality in elapsed

Am. J. Orthod. December 1978

Table

V Relationship

Original MPA (Downs) with original GOGNSN angle Change in MPA (Downs) with change in GOGNSN angle

Correlation

r

Variability accounted for (r2) in percent

Variubility for (I-3)

unaccounted in percent

0.74

56

44

0.86

74

26

time and force magnitude. In practical clinical terms, however, we believe that such standardization would have been inappropriate since different force levels and different treatment durations are, in fact, employed clinically in different types of treatment (Table VI). The goal of our study is not to determine what might hypothetically happen under conditions of formal “equality” but, rather, to determine what actually does happen when competent clinicians treat patients using techniques of their own choosing and therefore with different time durations and force magnitudes. The only way to answer the real-world question of differences in treatment effect, we believe, is to study each type of treatment under the conditions in which it is actually used (in what some investigators call the naturalistic mode). It is certainly true that the increased number of variables one deals with in a naturalistic experiment complicates the problem of drawing valid conclusions from the data. Clearly, for example, differences in treatment time will have some effects. The problem is to determine which effects. This problem can be solved to some extent by studying the relationship between variability in treatment time and the variability of the other parameters measured. In this context, the last row and the last column of Table III report the correlations and coefficients of determination between elapsed time (EMONTHS) and each of the other variables taken individually. These data establish that there is no significant relationship and, in fact, practically no relationship at all between difference in treatment time and change in mandibular orientation as measured by either D:MPA or D:GOGNSN. (For D:MPA, r = -0.02; for D:GOGNSN, r = -0.07.) On the other hand, there are strong and highly significant positive associations between increase in elapsed time and increase in eight of the nine linear measures of concurrent change. These positive associations are probably due, for the most part, to the fact that almost all linear dimensions in the skull and face increase through time in children as part of the processes of growth and development. The one linear measure of change which is not strongly associated with elapsed time is D : MOLAR (correction of Class II molar relationship). We believe that this finding is merely a consequence of the previously noted fact that different types of treatment obtain correction of Class II molar relationship over different intervals of time. On the basis of Table II/. Table IV summarizes the multiple regression analyses. It has two parts (A and B)-one for each of the two dependent variables. Because (as just noted)) changes in MPA (Downs) and in GOGNSN angle are not perfectly correlated, it is not surprising that the multiple regression procedures for the two dependent variables give slightly different results. However, a consistent pattern does emerge for both variables for which we believe that what follows is a fair summary. It will be seen that this summary constitutes a set of answers to the questions asked in the introduction and the section on Materials and Method

Volume 74

Mcrndihulcrr

Number

6

Table

VI. Differences in treatment time for different treatments Elapsed Treatment

type

x

Cervical Straight-pull High-pull * Combi Intraoral Control All cases ‘Always

means

high pull to upper

36.6 34.2 15.9 18.3 23.8 27.6 27.6 first

plane

changes

617

time (in months) s.d. 16.4 15.7 7.1 9.5 1.6 1.3 13.4

molars

So far as antecedent state measures are concerned, the only factors which are significantly predictive of change in mandibular orientation are those involving mandibular ramus proportions (as compared either to mandibular body length or to sella-nasion distance). Persons with relatively short rami tend to have subsequent increases in mandibular plane angle. Once this relationship has been considered, no other remaining antecedent measure makes a statistically significant contribution to explaining the residual variability in D: MPA or in D : GOGNSN. Specifically, the original MPA (Downs) and original GOGNSN angle measures do not contain predictively useful information, considered either by themselves or in combination with other measures. (For graphic representations of the percentages of the variance explained by each group of independent measures, see Fig. 3.) So far as the concurrent measures are concerned, the power of the independent variables examined is considerably better than that of the antecedent variables. The most important single measure in accounting for change in mandibular orientation is DXU6ACB-the horizontal movement of upper first molar cusp. Specifically, the further distally the molar is displaced, the more the mandibular angle will tend to open. Thus, it is implied, at least with respect to the presently evaluated treatments, that the tendency of the angle to open is directly proportional to the effectiveness of restraint of the mesial movement of the upper first molar. In other words, this finding implies that any attempt to correct a Class II malocclusion on a nonextraction basis by the distal movement of the upper first molar or by the restriction of its normal mesial migration will tend to create conditions for mandibular plane opening. To some clinicians, this observation may in itself be a telling argument in favor of extraction therapy in patients who have undesirably high mandibular plane angles at the beginning of treatment. The second most important concurrent association with increase in mandibular plane angle is the downward movement of the upper first molar. The greater the downward displacement of the upper first molar from palatal plane, the more the mandibular plane angle tends to increase. (It must. however, be borne in mind that the upper first molar increases its distance from palatal plane by eruption as well as by extrusion. An attempt to partition the effects of eruption from those of extrusion will be made in a subsequent article. ) The two most important concurrent factors are thus associated to a considerable degree with the treatment process itself. The next three or four measures recruited into the equation are not so associated and are generally considered to be beyond the therapist’s

Am. .I. Orthod. December 1918

Table

VII. Changes

in mandibular

I. Change in MPA with high original

Treatment rype Cervical Straight-pull High-pull Combi Intraoral Control All cases

n

x

S.D.

8 0 8 1 5 4 26

0.34 0.49 -2.02 0.40 -0.02 0.25

2.09 1.07 1.54 1.61 1.57

plane

angulation

(D) for cases MPA ID)* 95 percent confidence interval -1.4to -0.4 -1.5 -2.6 -0.4

+2.1 to to to to

+1.4 +2.3 +2.5 +0.9

in “high-angle”

cases

2. Change in GOGOSNA for CUSPS with high original GOGNSNA **

n

.F

S.D.

5 0 12 0 9 5 31

0.47 0.39 -0.8 0.03 -0.00

1.92 1.78 1.72 1.52 1.74

95 percent confidence interval -1.9

to +2.9 -0.7 to +1.5 -2.1 to +0.5 -1.9to +1.9 -0.6 to +0.6

3. Matched pairs***

n 3 0 7 0 3 3 16

*Minimum original MPA(D) = 30.0; mean original MPA(D) = 36.01; S.D. original MPA(D) = 2.52. **Minimumoriginal GOGNSNA = 40.0; meanoriginal GOGNSNA = 42.71; S.D, OriginalGOGNSNA = 2.14 ***Matched pairs = Cases which are included in both the high MPA(D) and the high GOGNSNA categories as defined above.

control. In general, these factors involve relative lack of growth in ramus height, mandibular body length, and posterior upper face height (that is, the distance from glenoid fossa to SN). Insufficient growth in any of these area will lead to an increase in mandibular plane angulation. Finally, the tables tell us that, other things being equal, shorter treatment time is associated with opening of the angle. This effect is probably a reflection of the well-known spontaneous tendency of mandibular plane angulation to decrease through time. As far as treatment type is concerned, the regression analysis tells us that no single appliance type accounts for a statistically significant part of the variance or differs significantly from the others. However, if we force the computer to consider the effects of all treatment types together, disregarding the question of statistical significance, we find the very small values for treatment effect which appear in Table IV. These show that type of treatment accounts for only 4 percent of the observed variance in D: MPA and only 2 percent of the observed variance in D: GOGNSN. The last sections of Table IV consider the ability of all the independent variables taken together to explain the observed variability in the two dependent variables. We believe that the most important observation to be made here is that the concurrent change variables taken by themselves account for almost all the observed power of the test. Among the antecedent state variables, knowledge of mandibular proportions gives us slightly greater understanding of dependent variable change; knowledge of original MPA(D) or of treatment type adds almost nothing. Some readers may accept results of Tables II through IV for all cases pooled but believe that cases with so-called “high angle” values at the outset of treatment would have displayed a different response pattern. For this reason, additional tests were performed in which we examined successively only those cases which had (1) an original mandibular plane angle in excess of 33 degrees and (2) an original GOGNSN angle above 40 degrees. Results of these tests are summarized in Table VII. We believe that they indicate that mean changes in mandibular plane orientation are not consequentially different for the high-angle cases than for 211 rm=c IJ~WPW~ +hnvn 0’~ ~iffzz.~;; :,; piiGIIlb

Volume 74 Number 6

Mandibular

plune changes

619

of variability and association of high-angle cases which warrant more detailed examination at a later date. Conclusions Before listing our conclusions, we believe that it is desirable that we define again our goals in the present study. We are definitely not attempting to demonstrate the superiority of any one treatment method over any other. Rather, we believe that there is ample evidence, both before this study and from it, that skilled orthodontic clinicians can and do produce excellent results using a wide range of techniques and apparatus systems. It seems clear to us that the standard of quality of orthodontic treatment, that is, the ability of clinicians to arrive at their desired treatment goals, is excellent and that, on the basis of therapeutic results, we need feel no fear of comparison with any other specialty in medicine or dentistry. However, at the level of theory, we believe that the picture is not nearly so favorable. At that level, some of our ideas can stand rigorous testing and some are marginally acceptable, but quite a few are completely inadequate. In sum, orthodontic treatment appears to succeed not because of the predictive power of our theory but, rather, because of the in-course adjustments (modifications of treatment plan) which skilled clinicians make. Deficiencies in theory reduce the efficiency of our progress toward our treatment goals. They require us to invest more time and energy and may cause us to produce more transient and permanent tissue damage than would otherwise be the case. The function of this article, and of the others in this series, is to examine the goodness of contemporary theory, to determine which components of that theory are sustained by data from actual treated cases and which components are revealed to be in need of modification or rejection. In this context, we suggest that the following conclusions flow logically from the findings listed and discussed above. These conclusions deal only with the question of change in mandibular orientation and their applicability is, of course, restricted to situations for which the present sample are representative (that is, for mixed-dentition treatment of Class II malocclusion using distally directed forces to retract the maxilla). 1. Mean change. Mean changes in mandibular plane orientation associated with treatment are much smaller than has been previously assumed (Table II). 2. Vuriability of change. Although change in mandibular plane angle is also less variable than has previously been supposed, it is consequential as well as being statistically significant. Attempts to explain the observed variability of change in mandibular orientation in terms of variability in other measures lead to the following conclusions: A. Among the measures obtainable at the start of treatment (termed herein “antecedent state variables”). the only ones which were predictively important were those which concerned the relative sizes of the parts of the mandible (body and ramus), either in relationship to each other or in relationship to face depth. The smaller the ramus length relative to the body length, the more the mandibular plane will tend to open. The smaller the ramus length relative to the SN distance, the more the mandibular plane will tend to open. With the exception of these measures of mandibular proportion, no other measured antecedent state variables were predictive of change in mandibular plane orientation. In particular and in contrast to the generally accepted belief of clinicians, the original mandibular plane orientation appears to bear no relation-

620

Bnrrrr?rird

rt rrl

Am. J. Orfhod. December 197X

ship to the magnitude of its subsequent change. Age at the onset of treatment and the relative positions in the skull of the condyle and the upper molar cusps at the beginning of treatment are similarly nonpredictive. B. Among the measures of concurrent change, the one which correlates most strongly with opening of the mandibular plane angle is the relative or absolute distal positioning of the upper first molar (DXU6ACB). This factor seems to be about twice as important as the next most important factor, which is eruptionextrusion of the upper first molar (DYU6PAL). The other correlates of upper molar extrusion will be considered in a subsequent article. A number of other measures of concurrent change are associated with opening of the mandibular plane angle, though generally to a smaller degree than the two just mentioned. These other factors include relative failure of the body of the mandible to grow (D:MBL), relative failure of increase in posterior maxillary vertical dimension (DY: DYLSN), relative failure of the ramus to increase in height (DY:DYL:M), and, according to one test, relative shortness (sic) of treatment time until Class II correction is achieved (EMONTHS). C. As far as type of treatment is concerned, all the examined treatments appeared to yield slight increases in the mean value of MPA and GOGNSNA, especially when compared with the small but statistically significant reduction in these values which occurs spontaneously through time in untreated subjects. However, as far as variability of change in mandibular orientation is concerned, the data seemed to establish that, in situations in which skilled clinicians use extraoral treatment modalities of their own choice, the differences in effect between the different types of headgear employed account for only a small and nonsignificant part of the observed variability of change in mandibular plane orientation. Our final comment deals with the question of the clinical use of head film data. It seems to us that information from head films can be used for two purposes. First, data obtainable at the time treatment is initiated can be used forpredicting treatment-associated changes. Second, data which become obtainable after treatment has been conducted can be used to better our understanding of the effects of treatment. In the present article, we believe that we have demonstrated beyond reasonable doubt that the antecedent state and treatment type variables studied have little predictive power with respect to treatmentassociated changes in mandibular orientation. On the other hand, we are encouraged to find that the explanatory power of the concurrent change variables is considerably greater, yielding rigorous identification of the actual sites of morphologic change which account for 40 percent of the variability in opening of the mandibular plane during clinical retraction of the maxilla. Information of this type improves our understanding of treatment dynamics and should aid us in developing better treatment strategies for the future. REFERENCES I. Baumrind, S.. Molthen, R., West, E. E., and Miller, D. M.: Mandibular plane changes during maxillary traction, AM. .I. ORTHOD. 74:32-40, 1978. 2. Nie, N., et al.: Statistical package for the social sciences, ed. 2, New York, 1974, McGraw-Hill Book Company, Inc., pp.320 ff. 3. Horowitz, S., and Hixon, E. H.: The nature of orthodontic diagnosis, St. Louis, 1967, The C. V. Mosby Company. 4. Johnston, L. E.: Statistical evaluation of cephalometric prediction, Angle Orthod. 38~284, 1968. 5. Baumrind. S.. and Frantz. L.: Reliability of head film measurPm-nt~ Am t norunn Gn-Gcc ‘07’