Download A LONGITUDINAL, MULTIVARIATE ANALYSIS OF ORTHODONTIC RELAPSE Nathan Daniel Mellion, D.D.S.

A LONGITUDINAL, MULTIVARIATE ANALYSIS OF
ORTHODONTIC RELAPSE
Nathan Daniel Mellion, D.D.S.
An Abstract Presented to the Graduate Faculty of
Saint Louis University in Partial Fulfillment
of the Requirements for the Degree of
Master of Science in Dentistry
2011
Abstract
Introduction:
Orthodontic relapse is a complex
problem that has troubled orthodontists throughout the
history of the specialty.
Although many studies have
examined the various proposed causes of relapse, few have
reported correlations that seem to support some sort of
strong causal relationship.
If no single factor can
“explain” much of the variation in relapse, perhaps relapse
can be predicted and/or modeled better by a linear
combination of predictor variables--multiple regression and
correlation.
Subjects and Methods:
Sixty-four
posttreatment orthodontic patients of all four Angle
classifications were recalled from one private practice.
All had been treated with so-called “Tweed” mechanics, and
all but five were treated with varying types of premolar
extraction.
Each subject had lateral cephalograms and
study models taken prior to treatment, at deband/debond,
and an average of 22.7 years posttreatment.
From these
records, various measurements of relapse and the factors
that supposedly cause relapse were obtained.
Backwards
deletion multiple regression was employed to model/predict
various types of relapse.
In this process, posttreatment
change in IMPA, incisal irregularity, maxillary intercanine
width, and mandibular intercanine width served as dependent
1
variables, and ten skeletal and dental characteristics that
are commonly thought to cause relapse served as independent
variables.
Results:
There were five statistically
significant multiple regression equations.
Only one
equation had more than one step of regression, the other
four had only one predictor variable, and all featured
small correlation coefficients (R or r between 0.32-0.48).
During treatment, closing--“counterclockwise”-- rotations
measured as Max-CB and Max-Mand angles were related to
increased posttreatment incisal irregularity.
Posttreatment maxillary or differential mandibular growth,
alone or in combination, was not significantly related to
any of the relapse measures.
Supposed dental etiologies of
relapse--treatment changes in IMPA, buccal-segment
inclination, irregularity, mandibular intercanine width,
and maxillary intercanine width--bore a weak, but
statistically significant relationship to the studied
relapse measures.
Conclusions:
The low correlation
coefficients--both simple and multiple--suggest that the
factors commonly thought to be important to orthodontic
stability do not account for a significant portion of the
variability in orthodontic relapse, at least in a
“conservatively” treated sample.
2
A LONGITUDINAL, MULTIVARIATE ANALYSIS OF
ORTHODONTIC RELAPSE
Nathan Daniel Mellion, D.D.S.
A Thesis Presented to the Graduate Faculty of Saint
Louis University in Partial Fulfillment of
the Requirements for the Degree of
Master of Science in Dentistry
2011
COMMITTEE IN CHARGE OF CANDIDACY:
Professor Emeritus Lysle E. Johnston, Jr.,
Chairperson and Advisor
Professor Eustaquio A. Araujo
Professor Rolf G. Behrents
Associate Clinical Professor Donald R. Oliver
i
DEDICATION
To my wife, Tana, my family and teachers, for dedication
and encouragement throughout my education that has enabled
me to pursue my dreams.
ii
ACKNOWLEDGEMENTS
The author would like to acknowledge:
Dr. Lysle E. Johnston, Jr., for this thesis topic
suggestion, tremendous dedication to all aspects of this
thesis, and his passion to keep our specialty focused on
science;
Dr. Rolf G. Behrents, for assistance with the
nuances of relapse covered in this thesis, and his guidance
throughout my orthodontic education;
Drs. Eustaquio A. Araujo and Donald R. Oliver, for
their assistance with this thesis, and their guidance in my
clinical education;
Dr. Heidi Israel, for her assistance, and
tremendous patience, with the statistical analysis for this
thesis; and
Dr. James Vaden, for the use of his records in this
study, and the ability to examine truly remarkable
treatment results.
iii
TABLE OF CONTENTS
List of Tables. . . . . . . . . . . . . . . . . . . . .
vi
List of Figures . . . . . . . . . . . . . . . . . . . .viii
CHAPTER 1:
CHAPTER 2:
REVIEW OF THE LITERATURE. . . . . . . . . .
Introduction . . . . . . . . . . . . . . .
The Etiology of Relapse . . . . . . . . . .
Soft Tissue Equilibrium . . . . . . . .
Anterior Denture Displacement . . .
Third Molar Eruption. . . . . .
Anchorage Loss. . . . . . . . .
Anterior Component of Occlusal
Force . . . . . . . . . . .
Differential Growth . . . . . . . .
Incisor Procumbency . . . . . . . .
Expansion . . . . . . . . . . . . .
Periodontal Remodeling. . . . . . . . .
Statement of Thesis . . . . . . . . . . . .
Literature Cited. . . . . . . . . . . . . .
JOURNAL ARTICLE . . . . . . . . . . . . .
Abstract. . . . . . . . . . . . . . . . .
Introduction. . . . . . . . . . . . . . .
Subjects and Methods. . . . . . . . . . .
Sample. . . . . . . . . . . . . . . .
Cephalometric Technique and Analysis.
Tracing Technique . . . . . . . .
Digitization. . . . . . . . . . .
Cephalometric Superimposition . . . .
Cranial Base. . . . . . . . . . .
Maxilla . . . . . . . . . . . . .
Mandible. . . . . . . . . . . . .
Measurement of Change . . . . . .
Pitchfork Analysis. . . . . .
Total Molar and Incisor
Correction. . . . . . . .
Skeletal and Molar Angles . . . .
Model Analysis. . . . . . . . . . . .
Error Study . . . . . . . . . . . . .
Data Reduction. . . . . . . . . . . .
Results . . . . . . . . . . . . . . . . .
Cephalometric Data. . . . . . . . . .
Model Data. . . . . . . . . . . . . .
iv
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Results (cont.)
Multiple Regression
Error Study . . . .
Discussion. . . . . . .
Error Study . . . .
Treatment Details .
Skeletal Predictors
Dental Predictors .
Restricted Range. .
Summary and Conclusions
References. . . . . . .
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Appendix A. . . . . . . . . . . . . . . . . . . . . . .
Appendix B. . . . . . . . . . . . . . . . . . . . . . .
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Vita Auctoris . . . . . . . . . . . . . . . . . . . . .
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LIST OF TABLES
Table 1.1.
Table 1.2.
Mesial movement of posterior buccal segments
during Class II treatment (mm). . . . . . .
7
Saint Louis University treatment studies
illustrating differential mandibular growth
(ABCH). . . . . . . . . . . . . . . . . . .
10
Table 2.1.
Angle classification by extraction pattern.
27
Table 2.2.
Sample demographics . . . . . . . . . . . .
29
Table 2.3.
Independent variables: potential causes
of orthodontic relapse. . . . . . . . . . .
44
Angular cephalometric measures: means,
standard deviations, and paired
t-tests . . . . . . . . . . . . . . . . . .
48
Linear cephalometric measures: means,
standard deviations, and paired t-tests . .
49
Fiducial and intermolar angle descriptive
and inferential statistics. . . . . . . . .
53
Skeletal and dental components of molar
and overjet change. . . . . . . . . . . . .
55
Model analysis:
descriptive and
inferential statistics. . . . . . . . . . .
57
Dependent and independent variables: means,
standard deviations, and intra-class
correlations. . . . . . . . . . . . . . . .
58
Table 2.10. Multiple regression analysis equations
separated into proposed skeletal and
dental etiologies of relapse. . . . . . . .
59
Table A.
Customized cephalometric analysis . . . . .
78
Table B.1.
Error Study: intra-class correlations
(Cronbach’s α) for angular cephalometric
measures. . . . . . . . . . . . . . . . . .
79
Table 2.4.
Table 2.5.
Table 2.6.
Table 2.7.
Table 2.8.
Table 2.9.
vi
Table B.2.
Table B.3.
Table B.4.
Table B.5.
Error Study: intra-class correlations
(Cronbach’s α) for linear cephalometric
measures. . . . . . . . . . . . . . . . . .
80
Error study: intra-class correlations
(Cronbach’s α) for the components of molar
and overjet change. . . . . . . . . . . . .
81
Error study: intra-class correlations
(Cronbach’s α) for fiducial and intermolar
angles. . . . . . . . . . . . . . . . . . .
82
Error study: intra-class correlations
(Cronbach’s α) for model analysis . . . . .
82
vii
LIST OF FIGURES
Figure 1.1.
Soft tissue equilibrium pressures during
swallowing and at rest. . . . . . . . . .
3
Anterior component of occlusal force
(ACF) . . . . . . . . . . . . . . . . . .
9
Figure 2.1.
Lateral cephalometric landmarks . . . . .
31
Figure 2.2.
Regional superimpositions . . . . . . . .
36
Figure 2.3.
Basal skeletal (hash mark) and intermolar angles. . . . . . . . . . . . . . .
39
Photocopied occlusal surfaces of a
complete series T1-T3 (T1 on left,
T2 middle, T3 right) with a 100
millimeter calibration rule . . . . . . .
41
Transverse intercanine (3-3) and intermolar (6-6) study model measurements. . .
42
Figure 2.6.
The irregularity index. . . . . . . . . .
42
Figure 2.7.
Mean facial outlines superimposed on the
cranial base fiducial hash marks. . . . .
50
Mean facial outlines superimposed on the
maxillary fiducial hash marks . . . . . .
51
Mean facial outlines superimposed on the
mandibular fiducial hash marks. . . . . .
52
Figure 2.10. Average fiducial and intermolar angles. .
54
Figure 2.11. Pitchfork diagrams. . . . . . . . . . . .
56
Figure 2.12. Range restriction . . . . . . . . . . . .
70
Figure A.
77
Figure 1.2.
Figure 2.4.
Figure 2.5.
Figure 2.8.
Figure 2.9.
Customized “Ricketts 71-point regimen”. .
viii
CHAPTER 1: REVIEW OF THE LITERATURE
Introduction
Over a century of orthodontic evolution has
produced a high level of biomechanical efficiency; however,
after active treatment is completed relapse is, and always
has been, a common, little-understood problem.
Dental
crowding, loss of expansion in either arch, de-rotation,
return of overbite and overjet, loss of molar correction,
among many other untoward changes still plague the 21st
century clinician.
As noted by the historian, Weingberger,1 early
orthodontic publications by Angell (1860), Coleman (1865),
and Marvin (1866) emphasized the need for retention to
prevent relapse.
Because relapse is still a problem in
modern orthodontics, the specialty’s response increasingly
has been some form of permanent retention.
Permanent
retention, however, presents obvious problems.
First of all, permanent retention diverts the
specialty’s focus from understanding the causes of relapse.
Secondly, even if determining the causes of relapse is not
considered worthwhile, the long-term presence of bonded
retainers presumably would increase our liability for
problems such as periodontal disease and decalcification.
It would seem, therefore, that understanding the causes of
1
relapse would be a service both to patients and the
specialty.
It will be the purpose of this study to examine
longitudinally and simultaneously the proposed skeletal and
dental etiologies of relapse in a large sample in which
care was taken to avoid expansion and flaring and to
preserve anchorage.
This sample, in other words, was
“conservatively” treated.
The Etiology of Relapse
Soft Tissue Equilibrium
The dentition exists in an environment of soft
tissue function--moving lips, cheeks, and muscles drape the
outside while the tongue supports the inside of the
dentition.
This intimate contact allows the soft tissue,
especially the muscles, to affect the shape of the alveolar
bone and the position of the dentition, both of which are
thought to be responsive to external forces.
According to
the “equilibrium theory of tooth position” as described by
Weinstein and associates,2 teeth are in a position of
balance in the envelope of motion of surrounding soft
tissue.
Movement of the dentition outside this equilibrium
position/range thus would lead to movement that would serve
to return the tooth to a position of equilibrium.
2
Although the existence and importance of a muscular
equilibrium is a commonly-held belief in orthodontics, it
has not yet been demonstrated experimentally.
In a review
of the equilibrium theory, Proffit3 has argued that the
tongue and lip pressures that supposedly create the dental
equilibrium cannot be shown to balance, either during rest
or swallowing (Figure 1.1).
Similarly, an assessment of
normal subjects between ages 8 and 18 by Posen4 showed
maximum tongue forces to be almost ten times maximum lip
forces.
As a result, Proffit argued that other factors,
such as occlusion, dental eruption forces, and head posture
might be responsible for the difference; as of yet, however,
there has been no quantitative analysis that includes all
of these potential factors.
Figure 1.1. Soft tissue equilibrium pressures during
swallowing and at rest. Lingual pressure is greater than
lip pressure in both instances (units of measure not
specified). Adopted from Proffit.3
3
Regardless of the algebraic sum of dental
equilibrium forces, it is apparent that the soft tissues
affect the position of the dentoalveolar complex.
For
example, to measure the effects of the disruption of the
equilibrium, Weinstein and associates2 placed a 2 mm gold
onlay either lingually or buccally on bicuspids set for
extraction in eight subjects.
They found that the
bicuspids would move bucally when the gold onlay was placed
lingually, and vice versa.
It was concluded that a
disruption of muscular equilibrium had caused the teeth to
move toward a position of equilibrium.
It seems reasonable
to conclude, therefore, that expansion or a forward
displacement of the dentition into the envelope of soft
tissue function could lead to relapse.
Anterior Denture Displacement
Some orthodontic mechanics tend to move the
dentition anteriorly, but the extent of movement is
variable.
Because a stable incisal position may be defined
by the envelope of motion of the lips, cheeks, and
tongue,4,5 anterior displacement might serve to upset the
equilibrium.
Ackerman and Proffit6 reviewed the literature
on the tolerance of the dentition to anterior displacement
and suggested that a movement of more than 2 mm would
4
initiate relapse.
Causes of anterior displacement, however,
are controversial and generally fall into one of three
categories:
third molar eruption, anchorage loss during
treatment, and the anterior component of occlusal force.
Third Molar Eruption
Eruption of third molars is thought by many to push
the dentition anteriorly and thus constitute a cause of
relapse.
The literature, however, does not provide a
definitive causal link between third molar eruption and
relapse, or, more specifically, anterior irregularity.
Bergström and Jensen7 examined a sample with
unilateral third molar agenesis and found more crowding on
the side in which the third molar was present.
Vego8
compared samples of bilateral third molar absence and
presence and found 0.8 mm more crowding in the sample in
which the third molars had erupted.
An increase of 0.8 mm,
however, seems to be too small an effect to explain the
entirety of incisor relapse, were it to be due just to
third molar eruption.
More recent studies of patients with extracted
third molars compared to non-extraction samples have
reported that mandibular anterior irregularity is not
statistically related to third molar eruption and/or
5
presence.
Ades and co-workers9 compared the mandibular
anterior crowding in four third molar samples (impacted,
erupted, agenesis, and extracted).
They found no
statistically significant difference in irregularity among
any of the four groups (F=0.313).
Similarly, Harradine and
co-workers10 reported no statistically significant
difference in irregularity between groups with and without
third molars (0.3 mm more crowding in those with third
molars erupted).
Given that recent, more extensive studies have
failed to show a relationship between third molar eruption
and anterior irregularity, the current consensus is that
third molars are unlikely to be a cause of anterior
dentition-displacement and relapse.11,12
Anchorage Loss
The establishment of “Class I” canines and a
reduction in incisor protrusion in Class II, Div. 1,
extraction treatments commonly require mechanics that
displace the buccal segments mesially.
This mesial
movement commonly is called “anchorage loss” and, if
sufficient, might cause the dentition to encroach on the
envelope of function of the lips and exceed the anterior
6
boundary of basal bone, both of which might lead to relapse
of anterior alignment.
Despite treatment goals of maintaining buccal
segment position, Table 1.113-16 shows that maxillary and
mandibular anchorage loss is a common event in
bicuspid-extraction Class II treatment.
Given that
posttreatment skeletal growth continues throughout
adulthood (vide infra), maxillary dentoalveolar
compensations17 might also be a form of upper anterior
relapse.
The literature, however, has little to say
concerning this possibility.
Table 1.1.
Mesial movement of posterior buccal segments
during Class II extraction treatment (mm).
Source
Year
Upper
Lower
Johnston, Lin, Peng13
1988
2.0
3.1
Harris, Dryer, Vaden14
1991
2.5
3.7
Paquette, Beattie, Johnston15
1992
3.1
4.6
Luppanapornlarp and Johnston16
1993
2.0
4.2
Anterior Component of Occlusal Force
According to Proffit,18 intermittent forces, such as
those from occlusal contact, are not of sufficient duration
to cause tooth movement, let alone relapse.
The obvious
dentoalveolar compensations seen in Class III malocclusions,
7
however, seem to contradict the contention that
intermittent occlusal forces cannot affect tooth position.
It is probable, therefore, that occlusal forces,
specifically those that produce an anterior occlusal vector,
could displace the dentition mesially and thus be a cause
of incisal relapse.
Early orthodontic literature19,20 inferred an
anterior component of occlusal force (ACF) from the mesial
inclination of the buccal segments (Figure 1.2).
Southard,
Behrents, and Tolley21,22 measured changes in interproximal
forces as result of biting on a force transducer and
reported that there is a measureable ACF that is dissipated
exponentially anterior to the second premolars.
Southard’s
group also reported a correlation between ACF and anterior
crowding (r=0.54), although the authors stressed that this
correlation does not prove a cause-and-effect relationship.
To date, however, there are no studies relating the
posttreatment inclinations of the buccal segments to
anterior displacement and subsequent relapse.
Differential Growth
The normal facial skeletal growth pattern features
excess mandibular growth relative to maxillary growth, even
in Class II malocclusions.23
Differential mandibular growth,
8
Figure 1.2. Anterior component of occlusal force (ACF).
Figure modified from Southard, Behrents, and Tolley.21
although helpful during Class II treatment (Table 1.215,16,2430
), is considered by Proffit18 to be a contributor to
posttreatment lower incisor irregularity.
Specifically,
Proffit has suggested that excess mandibular growth would
force the mandibular anteriors against the lingual surfaces
of the maxillary incisors, thus producing lower
irregularity.
If this phenomenon occurs posttreatment, it
would be a form of relapse.18
Schudy31 studied a sample of 74 patients averaging
2.9 years posttreatment and found that condylar growth was
significantly correlated with posttreatment incisal
angulation (IMPA; r=-0.62).
Accordingly, mandibular growth
might tend to retrocline the mandibular incisors.
righting, however, is not the same as increased
9
Up-
irregularity.
Glenn and associates32 went a step further
and found a significant correlation between ANB reduction,
as a measure of excess mandibular growth, and incisal
crowding (r=0.65).
Although these correlations support Proffit’s
contention, differential maxillo-mandibular growth per se
has not yet been shown to be related to incisor relapse.
Table 1.2.
Saint Louis University treatment studies
illustrating differential mandibular growth
(ABCH).
Study
Year
ABCH (mm)
Cohlmia24
1978
2.27
Ellis25
1979
2.25
Atkinson26
1980
3.10
Webb27
1981
2.17
Brown28
1985
2.68 extraction
2.32 nonextraction
Phaerukkakit29
1985
2.68
Harper30
1986
1.75
Paquette et al.15
1992
1.94 extraction
2.51 nonextraction
Luppanapornlarp,
Johnston16
1993
2.74 extraction
1.95 nonextraction
10
Incisor Procumbency
Whatever the cause of forward displacement of the
buccal segments, incisor procumbency can be the end result
following leveling and alignment.
Tweed considered 80% of
his nonextraction treatments failures because the results
proved to be unstable.
He attributed this relapse tendency
to the mandibular incisors ending up too far forward
relative to basal bone.
He thus broke from Angle’s
nonextraction treatment philosophy and re-treated a large
group of his nonextraction cases in conjunction with
premolar extraction.33
As a result of this “experiment,” Tweed concluded
that stable posttreatment occlusions are dependent on the
placement of mandibular incisors “upright over basal bone.”
Numerous other workers agreed,34,35 and upright incisors
remain, at least in theory, a common treatment goal.
Failure to achieve this goal--incisal flaring--therefore
could represent an encroachment on the labial soft tissue
envelope of function and thus constitute a cause of relapse.
Many studies support the contention that incisorflaring caused by treatment is prone to relapse.
In a
study of 56 patients whose incisors were intentionally
flared during treatment, Mills36 showed that they relapsed
lingually 4.8-8.6 degrees.
Boley and associates37 went a
11
step further and found a significant correlation between
incisor flaring during treatment to posttreatment incisal
irregularity (r=0.43).
It appears, therefore, that the
labial muscular envelope of function is intolerant of
incisal flaring; however, given that r2=0.18, treatmentinduced procumbency clearly does not explain much of the
variation in incisor relapse and irregularity.
As with
flaring, transverse widening of the dental arches is also
commonly thought to be a cause of relapse.
Expansion
Strang38 argued that stable posttreatment dentitions
are dependent on the maintenance of the pretreatment
intercanine dimension:
There is no question in my mind that denture expansion
as a treatment procedure in the correction of
malocclusion should be discarded and every effort
should be directed toward preserving the muscular
balance that is the most important factor in
establishing and maintaining tooth position.
Many treatments, especially nonextraction
treatments, commonly lead to transverse widening of the
dental arch.
For extraction treatments, some expansion can
be attributed to canine retraction into a wider portion of
the dental arch and, as such, would not obviously be prone
to relapse, given that the final canine position would not
encroach on the buccal envelope of motion.
12
Nonextraction
treatments, however, often feature expansion that would
displace the dentition into the functional buccal soft
tissue envelope and thus might lead to relapse.
There have been many studies designed to test the
stability of treatment expansion.
Burke and associates39
conducted a meta-analysis of twenty-six longitudinal
clinical studies totaling 1,233 subjects.
They found an
average mandibular intercanine treatment expansion of 1.57
mm followed by a relapse of 1.24 mm posttreatment.
It was
concluded, therefore, that mandibular canine expansion is
not stable.
In an analysis of 28 patients eight years
postretention, Glenn and associates32 reported a correlation
between pretreatment and postretention intercanine and
intermolar widths (r=0.57 and 0.63, respectively).
They
concluded that, although expansion is unstable, it could
“explain” less than 40% of the observed “rebound.”
Indeed,
all orthodontic tooth movement seems prone to this type of
relapse/reversion.
Periodontal Remodeling
In general, teeth moved orthodontically have a
tendency to move back to their original position.
Some
types of “rebound” (especially de-rotation) are commonly
13
thought to be related to periodontal remodeling.
The
principal fibers of the periodontal ligament, specifically
the apical and middle thirds, remodel between 50-80 days
posttreatment.40,41 The supracrestal fibers, however, remodel
much more slowly.
Indeed, these fibers will not have fully
remodeled a year posttreatment.40,42,43
The reason that supracrestal fibers are thought not
to remodel quickly is that they can stretch.
This stretch
has been suggested as a cause of relapse,41 as the gingival
fibers are stretched more in treatments with severe initial
crowding;44 however, the literature is not in complete
agreement with this assertion.
In a study of 65 patients
ten years postretention, Little and associates45 failed to
show pretreatment incisal irregularity to be a predictor of
posttreatment incisal relapse.
Årtun and co-workers,46 on
the other hand, examined a similar sample and found a
statistically significant correlation between pretreatment
and posttreatment incisal irregularity (r=-0.38).
They
noted that, although a statistically significant
correlation was found, it could explain (i.e., it shared)
only about 14% of the variance in posttreatment incisal
irregularity.
Periodontal remodeling and initial
malocclusion severity--like all of the other “causes”
14
examined here--explain only a small portion of incisal
relapse.
Statement of Thesis
Relapse in its various manifestations remains a
phenomenon whose etiologies are still largely ill-defined,
unproved, and thus highly controversial.
There are a
number of hypothesized causes of relapse, many of which
have been shown to bear at least a weak relation to various
types of relapse.
Because of the considerable unexplained
variation, however, it is clear that none of the proposed
causes, when studied in isolation, supply an adequate
explanation.
It will be the purpose of this investigation,
therefore, to examine the various proposed etiologies
jointly in an effort to see if a multivariate approach will
supply a more useful model of posttreatment relapse.
15
Literature Cited
1. Weinberger BW. Orthodontics: An Historical Review of
Its Origin and Evolution. St. Louis: C.V. Mosby;
1926.
2. Weinstein S, Haack DC, Morris LY, Snyder BB, Attaway HE.
On an equilibrium theory of tooth position. Angle
Orthod. 1963;33:1-26.
3. Proffit WR. Equilibrium theory revisited: factors
influencing position of the teeth. Angle Orthod.
1978;48:175-186.
4. Posen AL. The influence of maximum perioral and tongue
force on the incisor teeth. Angle Orthod.
1972;42:285-309.
5. Posen AL. The application of quantitative perioral
assessment to orthodontic case analysis and
treatment planning. Angle Orthod. 1976;46:118-143.
6. Ackerman JL, Proffit WR. Soft tissue limitations in
orthodontics: treatment planning guidelines.
Angle Orthod. 1997;67:327-336.
7. Bergström K, Jensen R. Responsibility of the third
molar for secondary crowding. Dent Abstr. 1961:544.
8. Vego L. A longitudinal study of mandibular arch
perimeter. Angle Orthod. 1962;32:187-192.
9. Ades AG, Joondeph DR, Little RM, Chapko MK. A longterm study of the relationship of third molars to
changes in the mandibular dental arch. Am J Orthod
Dentofac Orthop. 1990;97:323-335.
10. Harradine NW, Pearson MH, Toth B. The effect of
extraction of third molars on late lower incisor
crowding: a randomized controlled trial. Br J
Orthod. 1998;25:117-122.
11. Bishara SE, Andreasen G. Third molars:
J Orthod. 1983;83:131-137.
16
a review.
Am
12. Kandasamy S, Rinchuse DJ [sic], Rinchuse DJ [sic]. The
wisdom behind third molar extractions. Aust Dent J.
2009;54:284-292.
13. Johnston LE Jr, Lin SS, Peng SJ. Anchorage loss: a
comparative analysis. J Charles H. Tweed Int Found.
1988;16:23-27.
14. Harris EF, Dyer GS, Vaden JL. Age effects on
orthodontic treatment: skeletodental assessments
from the Johnston analysis. Am J Orthod Dentofac
Orthop. 1991;100:531-6.
15. Paquette DE, Beattie JR, Johnston LE Jr. A long-term
comparison of nonextraction and premolar extraction
edgewise therapy in “borderline” Class II patients.
Am J Orthod Dentofac Orthop. 1992;102:1-14.
16. Luppanapornlarp S, Johnston LE Jr. The effects of
premolar-extraction: a long-term comparison of
outcomes in “clear-cut” extraction and
nonextraction Class II patients. Angle Orthod.
1993;63:257-272.
17. Solow B. The dentoalveolar compensatory mechanism:
background and clinical implications. Br J Orthod.
1980;7:145-161.
18. Proffit WR, Fields HW, Sarver DM. Contemporary
Orthodontics. 4th ed. St. Louis: Mosby; 2007.
19. Trauner F. The causes of progressive movement of the
teeth toward the front. Am Orthod. 1912;3:144-158.
20. Stallard H. The anterior component of the force of
mastication and its significance to the dental
apparatus. Dent Cosmos. 1923;65:457-474.
21. Southard TE, Behrents RG, Tolley EA. The anterior
component of occlusal force. Part 1. Measurement
and distribution. Am J Orthod Dentofac Orthop.
1989;96:493-500.
22. Southard TE, Behrents RG, Tolley EA. The anterior
component of occlusal force. Part 2. Relationship
with dental malalignment. Am J Orthod Dentofac
Orthop. 1990;97:41-44.
17
23. Bishara SE, Jakobsen JR, Vorhies B, Bayati P. Changes
in dentofacial structures in untreated Class II,
Division 1 and normal subjects: a longitudinal
study. Angle Orthod. 1997;67:55-66.
24. Cohlmia GT. The relative contributions of growth and
treatment in orthodontically corrected Class II
malocclusion. [Unpublished Master’s Thesis] St.
Louis: Saint Louis University; 1978.
25. Ellis CE. A quantitative evaluation of the role of
growth and treatment in the correction of several
Class II malocclusions. [Unpublished Master’s
Thesis] St. Louis: Saint Louis University; 1979.
26. Atkinson BG. The relationship of skeletal morphology
to molar correction in Class II, Division 1
malocclusions. [Unpublished Master’s Thesis] St.
Louis: Saint Louis University; 1980.
27. Webb MA. The quantitative effects of maxillary second
molar extraction in the correction of Class II,
Division 1, malocclusion. [Unpublished Master’s
Thesis] St. Louis: Saint Louis University; 1981.
28. Brown RK. A quantitative analysis of the relative
contributions of maxillary and mandibular molar
movement and growth to both the extraction and nonextraction correction of Class II, Division 1
malocclusions with the Begg technique.
[Unpublished Master’s Thesis] St. Louis: Saint
Louis University; 1985.
29. Phaerukkakit S. The relative effects of growth and
tooth movement in the correction of Class II,
Division 1 malocclusion. [Unpublished Master’s
Thesis] St. Louis: Saint Louis University; 1985.
30. Harper DL. The affects [sic] of pretreatment
morphology, treatment change, and posttreatment
growth in relapse. [Unpublished Master’s Thesis]
St. Louis: Saint Louis University; 1986.
31. Schudy GF. Posttreatment craniofacial growth: its
implications in orthodontic treatment. Am J Orthod.
1974;65:39-57.
18
32. Glenn G, Sinclair PM, Alexander RG. Nonextraction
orthodontic therapy: posttreatment dental and
skeletal stability. Am J Orthod Dentofac Orthop.
1987;92:321-328.
33. Tweed CH. Indications for the extraction of teeth in
orthodontic procedures. Am J Orthod Oral Surg.
1944;30:405-428.
34. Margolis HI. The axial inclination of the mandibular
incisors. Am J Orthod Oral Surg. 1943;29:571-594.
35. Grieve GW. The stability of the treated denture.
Orthod Oral Surg. 1944;30:171-195.
Am J
36. Mills JRE. The long-term results of the proclination
of lower incisors. Brit Dent J. 1966;120:355-363.
37. Boley JC, Mark JA, Sachdeva RC, Buschang PH. Long-term
stability of Class I premolar extraction treatment.
Am J Orthod Dentofac Orthop. 2003;124:277-87.
38. Strang RHW. The fallacy of denture expansion as a
treatment procedure. Angle Orthod. 1949;19:12-22.
39. Burke SP, Silveira AM, Goldsmith LJ, Yancey JM, Van
Steward A, Scarfe WC. A meta-analysis of
mandibular intercanine width in treatment and
postretention. Angle Orthod. 1998;68:53-60.
40. Reitan K. Tissue rearrangement during retention of
orthodontically rotated teeth. Angle Orthod.
1959;29:105-113.
41. Edwards JG. A surgical procedure to eliminate
rotational relapse. Am J Orthod. 1970;57:35-46.
42. Reitan K. Clinical and histologic observations on
tooth movement during and after orthodontic
treatment. Am J Orthod. 1967;53:721-745.
43. Blake M, Bibby K. Retention and stability: a review
of the literature. Am J Orthod Dentofac Orthop.
1998;114:299-306.
19
44. Reitan K. Principles of retention and avoidance of
posttreatment relapse. Am J Orthod. 1969;55:776790.
45. Little RM, Wallen TR, Riedel RA. Stability and relapse
of mandibular anterior alignment-first premolar
extraction cases treated by traditional edgewise
orthodontics. Am J Orthod. 1981;80:349-65.
46. Årtun J, Garol JD, Little RM. Long-term stability of
mandibular incisors following successful treatment
of Class II, Division 1, malocclusions. Angle
Orthod. 1996;66:229-238.
20
CHAPTER 2:
JOURNAL ARTICLE
Abstract
Introduction:
Orthodontic relapse is a complex
problem that has troubled orthodontists throughout the
history of the specialty.
Although many studies have
examined the various proposed causes of relapse, few have
reported correlations that seem to support some sort of
strong causal relationship.
If no single factor can
“explain” much of the variation in relapse, perhaps relapse
can be predicted and/or modeled better by a linear
combination of predictor variables--multiple regression and
correlation.
Subjects and Methods:
Sixty-four
posttreatment orthodontic patients of all four Angle
classifications were recalled from one private practice.
All had been treated with so-called “Tweed” mechanics, and
all but five were treated with varying types of premolar
extraction.
Each subject had lateral cephalograms and
study models taken prior to treatment, at deband/debond,
and an average of 22.7 years posttreatment.
From these
records, various measurements of relapse and the factors
that supposedly cause relapse were obtained.
Backwards
deletion multiple regression was employed to model/predict
various types of relapse.
In this process, posttreatment
change in IMPA, incisal irregularity, maxillary intercanine
21
width, and mandibular intercanine width served as dependent
variables, and ten skeletal and dental characteristics that
are commonly thought to cause relapse served as independent
variables.
Results:
There were five statistically
significant multiple regression equations.
Only one
equation had more than one step of regression, the other
four had only one predictor variable, and all featured
small correlation coefficients (R or r between 0.32-0.48).
During treatment, closing--“counterclockwise”--rotations
measured as Max-CB and Max-Mand angles were related to
increased posttreatment incisal irregularity.
Posttreatment maxillary or differential mandibular growth,
alone or in combination, was not significantly related to
any of the relapse measures.
Supposed dental etiologies of
relapse--treatment changes in IMPA, buccal-segment
inclination, irregularity, mandibular intercanine width,
and maxillary intercanine width--bore a weak, but
statistically significant relationship to the studied
relapse measures.
Conclusions:
The low correlation
coefficients--both simple and multiple--suggest that the
factors commonly thought to be important to orthodontic
stability do not account for a significant portion of the
variability in orthodontic relapse, at least in a
“conservatively” treated sample.
22
Introduction
More than a century of orthodontic evolution has
produced highly efficient treatments.
Advancement in
controlling posttreatment stability, however, as evidenced
by reports from the earliest practitioners1 to those of
today, has failed to keep pace; relapse remains a problem
in modern orthodontics.
Despite the potential problems of
periodontal disease and decalcification, a popular solution
in many of today’s treatments is some form of permanent
retention.
This approach implies that the precise causes
of relapse are unknown or ignored, although many possible
explanations have been presented in the literature.
The dentition is surrounded by functioning soft
tissue.
It has been hypothesized that the dentition is
positioned in equilibrium with the envelope of motion of
these soft tissues.2
Disruption of this equilibrium by
anterior and/or lateral displacement of the dentition
during treatment thus would be a cause of relapse.3-5
Movement of the dentition mesially so that the
incisors impinge on the labial muscular envelope of
function is thought to cause relapse in the form of lingual
tipping and crowding.6-10
Commonly hypothesized causes of
anterior displacement are third molar eruption, anchorage
loss, and the anterior component of occlusal force.
23
Third molar eruption was once generally thought to
be a cause of lower anterior crowding.11,12
More recent
literature, however, argues that the third molars are
probably not a major cause of either anterior displacement
or incisal relapse.13-16
Despite treatment goals of maintaining buccalsegment position, maxillary and mandibular anchorage loss
is a common event in bicuspid-extraction Class II
treatment.17-20
Given that posttreatment skeletal growth
continues throughout adulthood (vide infra), maxillary
dentoalveolar compensations21 might also contribute to
relapse.
The literature, however, has little to say about
this possibility.
The mesial inclination of the posterior occlusion
is another possible cause of relapse.
This inclination
creates an anterior component of occlusal force (ACF).
Southard, Behrents, and Tolley,22,23 however, only found a
moderate correlation (r=0.54) between interproximal forces
as a measure of ACF and incisal crowding.
Although the various causes of displacement of the
lower anterior dentition on basal bone have been shown
individually to be slightly related to incisal relapse,
none can account for a clinically useful portion of the
24
observed variability in posttreatment irregularity and
crowding.
Differential mandibular growth is another commonly
cited cause of lower incisor relapse.24
Studies dealing
with this conjecture, however, have tended to focus on
condylar growth25 or ANB reduction.26
Little research has
been conducted to measure its relation to actual
differential jaw growth.
Lateral displacement into the buccal muscular
envelope of function--expansion--also is thought to be a
cause of orthodontic relapse.3
Although recent studies26,27
are in agreement about its instability, all have concluded
that dental expansion alone does not “explain” all the
variation in the stability of expansion.
Another commonly proposed cause of relapse-especially rotation--is the elastic nature of slowly
remodeling periodontal tissues28-31 in relation to initial
malocclusion severity.32
Severe initial crowding would
likely require more movement during alignment, movement
that would stretch the elastic periodontal fibers.
The
literature, however, has not demonstrated a strong
correlation between initial malocclusion severity and
relapse to be of clinical utility.
25
On balance, the various types of relapse remain
phenomena whose etiologies are still largely unknown and/or
unproved.
There are a number of hypothesized causes, many
of which have been shown to bear at least a weak relation
to various types of relapse.
Because of the considerable
residual unexplained variation, however, it is clear that
none of the proposed causes, in isolation, supply an
adequate explanation.
It will be the purpose of this
investigation, therefore, to examine the various proposed
etiologies jointly in an effort to see if a multivariate
approach will supply a more useful model of posttreatment
relapse.
Subjects and Methods
The purpose of this study was to test the nature of
the relationship, if any, between hypothesized relapse
etiologies and the various measures of relapse.
To this
end, data were obtained both from lateral cephalograms and
study models.
Sample
The present sample consisted of 64 former
orthodontic patients recalled by a single private-practice
26
orthodontist.A
All Angle classifications were represented:
18 Class I; 39 Class II, Division 1; 6 Class II, Division
2; and 1 Class III.
There also were a variety of
extraction patterns, although the sample was predominately
Class II, Division 1, treated in conjunction with the
extraction of four first premolars (Table 2.1).
The
retention protocol was a mandibular bonded retainer from
cuspid-to-cuspid, and a maxillary removable Hawley retainer.
All subjects were out of retention at recall.
Table 2.1.
Angle classification by extraction pattern.
Extraction Pattern
Class
4/4
4/5
5/5
4/
Non-ext.
I
10
1
4
1
2
II/1
16
12
8
2
1
II/2
2
1
2
0
1
III
0
0
0
0
1
There were no exclusion criteria; the subjects
presented at their own discretion and expense between the
years 2005 and 2008.
Because it was assumed that relapse
etiologies would be more or less common to all types of
malocclusion, all Angle classes were included.
The
subjects presented in conjunction with their child’s
A
James L. Vaden
27
orthodontic treatment, during which time they consented to
having follow-up orthodontic records taken.
Because they
had returned with their own children some 20-25 years later,
the sample was presumably biased toward successful
orthodontic treatment, at least as judged by laypersons.
The fact that an outcome was liked by a patient, however,
does not mean that there was no relapse or that the factors
that cause relapse would not be operative.
All had been treated with so-called “Tweed”
mechanics featuring J-hook headgear, tip-back bends, and
Class II elastics as needed.
sample’s demographics.
Table 2.2 summarizes the
At the recall appointment, a
lateral cephalogram, panoramic radiograph, alginate
impressions for plaster study models, and intra-oral and
extra-oral photographs were obtained.
Cephalometric Technique and Analysis
Tracing Technique
Each subject’s treatment was documented by three
lateral cephalograms:
pretreatment, T1; immediate
posttreatment/debond, T2; and long-term recall, T3.
the 64 series was traced at a single sitting with a
drafting pencil (2H lead) on tracing acetate (0.003”
28
Each of
thickness).
A second observerB examined the finished
tracings and superimpositions before cephalometric
digitization and numerical analysis.
Disagreements were
resolved by discussion and/or retracing and re-measurement.
Table 2.2.
Sample demographics (yrs)
Time/Interval
Mean
S.D.
Range
Treatment
T1
13.0
1.84
11-20
T2
15.3
1.84
13-22
2.3
0.40
1.8-3.8
T1-T2
Posttreatment
T3
37.8
3.89
31-51
T2-T3
22.5
3.03
17-29
The tracing protocol of Johnston33 was employed here.
Figure 2.1 shows the anatomical features traced in each
lateral cephalogram.
Johnston’s superimpositions were
based on Björk’s structural method (vide infra).
Specifically, unique trabecular patterns within the cranial
base, maxilla, and mandible were included for each series.
To optimize superimposition reliability, templates specific
to each series were created for the key ridge,
B
L.E. Johnston, Jr.
29
pterygomaxillary fissure, third molar germ (if present),
and the contour of the mandibular canal.
Templates were also constructed for the most
clearly discernable maxillary and mandibular first molars
and incisors in each of the three film series (Figure 2.1).
The incisors were traced as a long axis from apex to
incisal edge.
The molars were traced as a horizontal line
connecting the mesial and distal contact points, and a
vertical line representing the long axis connected to the
midpoint of the horizontal line.
Superimposition revealed that 22 of the 64 series
featured a reduction in magnification between T2 and T3.
This shrinkage probably was the result of a change in
cephalostat and an inadvertent reduction in the object-film
distance.
In order to minimize the effect of this
discrepancy, the T3 tracings were scanned into an image
editing program (Adobe Photoshop CS3 Extended, version 10.0,
Adobe Systems, Inc., San Jose, CA) and magnified an average
of 2.5% so that Sella-Nasion of T3 matched that of T2.
The
T2 average age was 15, so it was assumed that there would
have been relatively little growth between T2 and T3.
enlarged T3 scan was then printed and measured.
30
The
Digitization
The cephalometric tracings were digitized on a
transparent digitizer (Numonics digitizing board, Model
A30Bl.H, Numonics Corporation, Montgomeryville, PA) and
analyzed with a commercial software program (Dentofacial
Planner, version 5.32, Dentofacial Software, Toronto,
Canada).
After the landmarks had been digitized according
to a modified “Ricketts 71-point regimen,” a customized
analysis of both linear and angular measures was executed
(Appendix A).
Figure 2.1.
Lateral cephalometric landmarks.
31
Cephalometric Superimposition
Because the goal of this study was to evaluate the
various proposed causes of orthodontic relapse, it was
necessary to quantify both the skeletal and dental changes
that had occurred during and after treatment.
These
changes were estimated from cranial base, maxillary, and
mandibular regional superimpositions33 based on stable
structures as defined by Björk’s implant studies.34-36
For each regional superimposition, “fiducial hash marks,”
arbitrary horizontal lines with vertical marks at both ends,
were placed in cranial base, maxilla, and mandible of T2 and
then passed through to T1 and T3 based on stable structural
details (vide infra).
hash marks:
There were two purposes for these
to record the regional superimposition,37 and
to determine if vertical skeletal changes during treatment
are a cause of relapse by depicting the pattern of
displacement of the midface and mandibular basal bones
relative to the cranial base and to each other.
Cranial Base
The commonly-utilized S-N cranial base
superimposition was not used here because both landmarks
remodel over time.33,38
Instead, Björk’s structural methods
as implemented by Johnston,33 were used here:
32
1. the
anterior wall of sella turcica, including the intersection
with the anterior clinoid; 2. the cribriform plate; and
3. the greater wings of the sphenoid, especially near the
intersection between it and the cranial base.
An arbitrary
point, the so-called “Wing point” (W),39 defined as the
intersection between planum sphenoidale and the averaged
greater wings of the sphenoid, was located on T2 and
transferred to T1 and T3 by superimposition on the cranial
base fiducial lines (Figure 2.2 A).
Maxilla
The maxillary superimposition was executed based on
the best fit of:
1. the lingual cortical plate of the
maxilla, specifically the anterior curvature; 2. common
internal maxillary trabecula; and 3. the anterior surface
of the key ridge.
Fiducial lines were then placed along
the T2 palatal plane (ANS-PNS), and then transferred to T1
and T3 based on best-fit superimposition (Figure 2.2 B).
For the present study, the functional occlusal
plane (FOP) served as the plane of orientation for the
measurements of some dental and skeletal changes (vide
infra).
FOP (similar to the “average occlusal plane”
described by Jenkins40), the bisection of the maxillary and
mandibular buccal occlusion through the canines, represents
33
the relatively stable buccal occlusion, in contrast to the
commonly used Downs occlusal plane,41 which is sensitive to
changes in incisor position.33
The maxillary fiducial hash
marks of T1 and T3 were superimposed and the FOPs were
averaged by inspection to produce a mean functional
occlusal plane (MFOP).
The MFOP was then transferred to T2,
also by way of a maxillary structural superimposition.
Mandible
The mandibular best-fit superimposition was based
on:
1. trabecular patterns and the lingual endoesteal
surface of the mandibular symphysis; 2. the outlines of the
mandibular canals; and 3. the lower border of the
mandibular third molar germs, if present.
Fiducial hash
marks were scribed on the T2 tracing at Gonion and the
intersection of the mandibular plane with a line
perpendicular to the mandibular plane dropped from Pogonion,
and then transferred to T1 and T3 by way of mandibular
structural superimposition.
Similarly, the so-called “D-
point,”42 the arbitrary center of the mandibular symphysis,
was first marked on T2 and then transferred to T1 and T3
(Figure 2.2 C).
34
Measurement of Change
Pitchfork Analysis
The so-called “pitchfork analysis” was used to
measure the skeletal and dental components of treatment and
posttreatment change.33
These measurements were used to
describe the changes during treatment and posttreatment,
and determine if the tooth movements and the individual
pattern of maxillo-mandibular growth are potential causes
of relapse as well as measures of relapse, itself.
The pitchfork analysis measures A-P changes that
add up to the molar relationship and overjet, and both
skeletal and dental changes are measured parallel to the
MFOP.
Based on the fiducial lines, the tracings were
superimposed (T1 and T2 and T2 and T3) and measurements were
taken to the nearest 0.01 mm with digital calipers under
the control of a small magnifying glass.
Net change (T1 to
T3) was calculated by the algebraic sum of treatment and
posttreatment changes.
A common application of the pitchfork analysis is
to quantify the components of the molar and overjet
correction.
In the present study, the vast majority were
Class II and most underwent some overjet correction.
Accordingly, a sign convention for the components of the
molar and overjet corrections was employed as follows:
35
a
positive sign was given to changes that would tend to
produce a Normal molar occlusion or to reduce overjet in a
Class II patient, and changes that would tend to a Class II
molar relation or increase the overjet would be given a
negative value.
Figure 2.2. Regional superimpositions. T2 fiducial hash
marks were placed along the S-N plane for the cranial base
(A), palatal plane (ANS-PNS) for the maxilla (B), and
Gonion to a line dropped from Pogonion perpendicular to the
mandibular plane for the mandible (C). The hash marks were
transferred to T1 and T3 by structural superimposition.
36
The tracings were superimposed on the maxillary
fiducial hash marks (which would also ensure that each
tracing’s MFOP were coincident) to measure:
1. maxillary
displacement (MAX) relative to cranial base;
2. differential mandibular growth (ABCH); and 3. maxillary
first molar (U6) and incisor (U1) displacement relative to
maxillary basal bone.
Mandibular displacement (MAND)
relative to the cranial base was then determined
algebraically:
MAND=ABCH-MAX.
Changes in position of
mandibular first molar (L6) and incisor (L1) relative to
mandibular basal bone were measured with two tracings
oriented along the MFOP and registered on D-point.
Total Molar and Incisor Correction
Change in molar relationship was seen to be the
algebraic sum of:
1. ABCH, 2. U6, and 3. L6.
Similarly,
the overjet change was calculated as the sum of:
2. U1, and 3. L1.
1. ABCH,
As a check on measurement error, molar
and overjet corrections were calculated directly and
compared to the summed estimates.
If the difference was
greater than + 0.3mm, the measurements were repeated until
the summed components were within these limits.
37
Skeletal and Molar Angles
In order to estimate an anterior component of
occlusal force (ACF) from posttreatment molar angulation
and its effect, if any, on relapse, the intermolar angle
was measured (Figure 2.3).
The intermolar angle was
measured from the long axes of the maxillary and mandibular
molar templates (vide supra).
To measure the effect on relapse of vertical
skeletal change during treatment, the angles between the
cranial base, maxillary, and mandibular fiducial hash marks
were measured (Figure 2.3).
Because fiducial hash marks
represent underlying stable skeletal structures,33,37 these
angles characterize the pattern of skeletal rotation during
and after treatment, and given a “hyper-divergent” pattern,
might have an impact on the A-P position of the dentition
(a skeletal version of ACF).
Model Analysis
Study-models measurements were used to estimate
treatment expansion of the maxillary and mandibular canines
and molars and initial incisal irregularity as potential
causes of relapse.
Posttreatment changes in intercanine
width and posttreatment incisal irregularity served as
dental measures of relapse.
38
Figure 2.3. Basal skeletal (hash mark) and intermolar
angles. 1. Cranial base to maxilla; 2. maxilla to
mandible; 3. cranial base to mandible; and 4. intermolar
angle as the angle between long axes of maxillary and
mandibular first molars.
The occlusal surfaces of the three maxillary and
mandibular models in each series were photocopied (Ricoh
Aficio MP5000, Ricoh Co., Ltd., Japan) along with a 100
millimeter calibration rule (Figure 2.4).
These copies
were then digitized on a transparent digitizer and analyzed
with customized software in Dentofacial Planner version
5.32 (vide supra) to generate arch widths and mandibular
incisor irregularity measures for T1, T2, and T3.
39
Arch width was calculated as the distance between
cusp tips for the canines, and the middle of the central
grooves for the molars (Figure 2.5).
The “irregularity
index” (Figure 2.6; Little43) was calculated as the
cumulative displacements of the five mandibular anterior
contact points from the mesial of the right cuspid to the
mesial of the left cuspid.
To verify the digitization
measurements, arch width and irregularity were calculated
by hand with a digital caliper for many of the T1 mandibular
models.
If the digitization and hand values differed by
more than + 0.3 mm, the digitization was redone.
The
digital measurements were the ones that were used in the
present analysis.
Error Study
To test the reliability of the cephalometric and
model measurements, a random number generator (from
www.random.org44) was used to select ten series (30
radiographs and sets of models) to be re-analyzed.
Intra-
class correlation was estimated by Cronbach’s α.
Reliability is commonly considered “adequate” when the
intra-class correlation coefficients are equal to or
greater than 0.80.
40
Figure 2.4. Photocopied occlusal surfaces of a complete
series T1-T3 (T1 on left, T2 middle, T3 right) with a 100
millimeter calibration rule.
Data Reduction
Statistical analysis was carried out by way of a
commercially-available spreadsheet program (Microsoft Excel
2003) and statistical software (SPSS, version 15.0, SPSS
Inc., Chicago, IL).
41
Figure 2.5. Transverse intercanine (3-3) and intermolar
(6-6) study model measurements. Measurements were from the
cusp tips for the canines, and the middle of the central
grooves for the first molars.
Figure 2.6. The irregularity index: the sum of the
displacements of the five lower anterior contacts A+B+C+D+E.
Modified from Little.43
42
Means and standard deviations were calculated for
all cephalometric and model measurements.
Paired t-tests
were employed to test the null hypothesis that skeletal and
dental changes during treatment (T1 to T2) and posttreatment
(T2 to T3) did not differ significantly from zero--Ho:δ=0.
To compensate for the family-wise error from repeated
t-tests, the type-I error was set at α=0.0167 (α of 0.05
divided by 3 repeated measures, 0.05/3=0.0167) and 0.003
(α=0.01/3).
Backwards elimination multiple regression was
utilized to test the hypothesis that the cumulative effect
of the proposed causes of relapse could explain a
significant portion of the variability in the relapse seen
here.
Four posttreatment changes (T3 minus T2) served as
measures/predictors of relapse (i.e., dependent variables):
1. mandibular incisor to mandibular plane angle (IMPA post
tx∆); 2. Irregularity Index (Irr post tx∆); 3. mandibular
intercuspid width (Mand 3-3 post tx∆); and 4. maxillary
intercuspid width (Max 3-3 post tx∆).
The potential
relapse etiologies (the independent variables) as
characterized by measures of treatment change are defined
in Table 2.3.
Given that the present sample size--N=64--
was too small to permit ten independent variables in one
regression equation (Table 2.3), separate dental and
43
skeletal equations were generated.
Thus, there were a
total of eight equations, each with five potential
independent variables--commonly assumed causes of relapse.
The “probability in” (PIN) was 0.05 and the “probability
out” (POUT) was 0.10, with a maximum of 2 independent
variables to be allowed in each equation.
Table 2.3. Independent variables:
orthodontic relapse.
Measure
potential causes of
Abbreviation
Treatment change (T2 minus T1)
Angularo
Incisor to mandibular plane
Intermolar angle
IMPA tx∆
Intermolar
Mandible to cranial base
Maxilla to cranial base
Mand-CB tx∆
Max-CB tx∆
Maxilla to mandible
Max-Mand tx∆
Linear (mm)
Irregularity Index
IRR tx∆
Mandibular cuspid expansion
Mand 3-3 tx∆
Maxillary cuspid expansion
Max 3-3 tx∆
Posttreatment change (T3 minus T2)
Maxilla to cranial base (mm)
Differential mandibular
Post tx∆ MAX
Post tx∆ ABCH
growth (mm)
44
Results
Cephalometric Data
Means and standard deviations for start, finish,
and recall angular and linear cephalometric measures are
presented in Tables 2.4 and 2.5.
To depict changes between
time points for each regional superimposition (cranial base,
maxilla, and mandible), average tracings created from a
customized utility within Dentofacial Planner version 5.32
(average.exe) are depicted in Figures 2.7-2.9 by
superimposition on their respective fiducial marks.
Descriptive statistics, means and standard
deviations, for the angles amongst fiducial hash marks and
the long axes of first molars are presented in Table 2.6.
Figure 2.10 depicts the mean fiducial and intermolar angles
for T1, T2, and T3.
Means and standard deviations for the skeletal and
dental components of molar and overjet change are presented
in Table 2.7.
The means for both groupings are also
depicted in the “pitchfork” diagrams of Figure 2.11.
To test whether the mean angular and linear
cephalometric changes for all cephalometric data between T1
and T2 and between T2 and T3 differed significantly from
zero (Ho:δ=0), repeated-measures t-tests are presented in
Tables 2.4-2.6.
Because of an increased family-wise error
45
from multiple t-tests, the conventional 0.05 and 0.01
significance levels were adjusted to P<0.0167 and P<0.003.
Model Data
Irregularity index, intercanine width, and
intermolar width descriptive statistics (means and standard
deviations) for T1, T2, T3, treatment change (T2–T1),
posttreatment change (T3–T2), and net change (T3–T1) are
presented in Table 2.8.
Repeated measures t-tests (Ho:δ=0),
with the above-described α-adjustments, for T1 to T2 and T2
to T3 are also summarized in Table 2.8.
Multiple Regression
Means and standard deviations for each dependent
variable (measure of relapse) and independent variable
(commonly proposed causes of relapse) are shown in Table
2.9.
The results of the backwards deletion multiple
regression analysis is presented in Table 2.10.
It is
worth noting here that all of the relapse measures are
significantly related to one or more of the dental
independent variables.
Only one relapse measure, incisal
irregularity, however, was significantly related to any of
the proposed skeletal etiologies.
46
Error Study
Intra-class correlations (Cronbach’s α) for all
duplicate measures are presented in the last column of
Table 2.9 and Appendix B.
47
Table 2.4.
Angular cephalometric measures:
and paired t-tests.
T1
T2
means, standard deviations,
T3
Paired t (Ho:δ=0)
Measure
Mean
S.D.
Mean
S.D.
Mean
S.D.
T1 to T2
SNA
81.43
3.67
79.20
3.52
79.73
3.61
7.19**
SNB
77.28
3.26
77.19
3.21
77.21
3.45
0.44
ANB
4.16
2.29
2.02
2.25
2.52
2.34
9.29**
Y-axis
57.40
3.66
57.31
3.57
56.58
3.51
0.29
2.38
U1-SN
104.59
6.74
104.27
7.00
102.15
6.88
0.28
3.65**
U1-NA
23.15
6.81
25.08
7.37
22.42
6.96
-1.53
4.33**
L1-NB
21.92
5.70
20.29
5.50
19.32
5.92
2.50
1.79
1/1
130.77
9.21
132.62
6.86
135.74
7.85
-1.35
-3.73*
FMA
20.82
6.16
20.22
6.53
18.92
6.51
1.95
3.17**
IMPA
93.16
6.86
91.89
6.43
91.62
5.76
1.91
0.53
FMIA
66.02
6.06
67.92
6.49
69.16
7.05
-2.76*
-2.06
Z
76.06
9.43
82.72
8.53
87.58
8.85
-8.23**
-6.41**
SN-PP
8.19
3.36
8.40
3.15
8.93
3.40
-1.02
-3.01*
SN-FOP
18.16
4.83
17.01
4.43
16.50
4.77
* P<0.0167
** P<0.003
48
2.81*
T2 to T3
-2.40
0.07
-3.25**
1.36
Table 2.5.
Linear cephalometric measures:
and paired t-tests Ho:δ=0.
T1
means, standard deviations,
T2
T3
Paired t (Ho:δ=0)
Measure
Mean
S.D.
Mean
S.D.
Mean
S.D.
T1 to T2
T2 to T3
Wits A/B
2.73
3.34
-1.07
2.75
0.49
3.32
9.46**
-5.37**
PNS-A pt
49.56
2.87
48.53
3.16
49.74
2.82
3.80**
-5.26**
S-Ar
34.81
3.44
35.72
3.80
35.25
3.52
-3.65**
2.66*
S-Go
80.51
5.75
85.77
6.13
86.00
6.52
-10.63**
-0.21
Ar-Gn
108.12
6.27
113.41
5.59
113.45
6.18
-10.06**
0.57
Pg-NB
1.89
1.97
3.07
2.36
3.60
2.26
-6.22**
-2.73*
U6-PTV
16.73
3.74
20.62
3.58
22.68
3.80
-13.55**
-7.50**
U1-NA
4.09
2.85
4.01
2.69
3.23
2.51
0.17
3.25**
L1-APg
0.52
2.22
1.12
2.05
0.05
2.20
-2.60
6.36**
Overjet
6.34
2.60
3.53
0.91
4.10
0.90
8.44**
-4.45**
Overbite
2.39
2.15
1.50
1.10
2.83
1.55
3.30**
-6.96**
N-Me
118.54
6.15
124.44
6.81
123.70
6.52
-10.93**
1.52
N-ANS
53.11
3.02
55.04
3.26
55.12
3.59
-6.64**
0.66
ANS-Me
66.97
5.33
70.30
5.63
69.48
5.43
-8.70**
2.16
UFH (%)
44.85
2.21
44.23
2.22
44.59
2.47
3.52**
-1.77
LFH (%)
56.45
2.78
56.44
2.41
56.13
2.60
0.02
1.62
LL-E
line
-1.24
3.28
-3.98
2.77
-6.29
2.86
9.00**
9.28**
* P<0.0167
** P<0.003
49
Figure 2.7. Mean facial outlines superimposed on the
cranial base fiducial hash marks. Start, black; finish,
red; and recall, green.
50
Figure 2.8. Mean facial outlines superimposed on the
maxillary fiducial hash marks. Start, black; finish, red;
and recall, green. Note the maxillary dentoalveolar
compensations, specifically the maxillary molars continue
to come forward with the mandible.
51
Figure 2.9. Mean facial outlines superimposed on the
mandibular fiducial hash marks. Start, black; finish, red;
and recall, green.
52
Table 2.6.
Fiducial and intermolar angle descriptive and inferential statistics.
T1
T2
T3
Treatment
Measure
Mean
53
Maxilla-CB
S.D.
Mean
S.D.
Mean
Paired t
(Ho:δ=0)
Change
S.D.
T2 minus T1
Posttreatment
T3 minus T2
Net
T3 minus T1
Mean
S.D.
Mean
S.D.
Mean
S.D.
T1 to
T2
T2 to
T3
7.38
2.99
8.01
3.07
7.98
3.16
0.62
1.53
-0.06
2.59
0.34
2.59
-3.26**
-0.47
MaxillaMandible
27.03
6.59
25.84
7.02
25.41
7.16
-1.19
1.99
-0.18
2.56
-1.30
2.56
4.77**
0.85
Mandible-CB
34.40
6.86
33.83
7.43
33.52
7.40
-0.57
2.30
-0.61
5.65
-1.2
5.65
1.95
0.34
Intermolar
170.73
4.86
171.35
4.53
169.74
4.87
0.61
4.14
-1.70
3.91
-1.01
3.91
-1.18
* P<0.0167
** P<0.003
3.89**
54
Figure 2.10.
Average fiducial and intermolar angles.
Table 2.7.
Skeletal and dental components of molar and
overjet change.
Change
Measurement
Treatment
Posttreatment
Net
T2 minus T1
T3 minus T2
T3 minus T1
Mean
S.D.
Mean
S.D.
Mean
S.D.
Skeletal
ABCH
2.50
1.94
1.06
1.70
3.56
2.63
Maxilla
-1.31
1.34
-0.47
1.03
-1.78
1.78
Mandible
3.81
2.68
1.52
1.85
5.33
3.52
Dental
Upper 6
-3.20
1.70
-1.96
1.52
-5.22
2.09
Lower 6
2.44
1.96
1.13
1.22
3.57
2.06
Upper Incisor
2.32
3.10
-0.71
1.48
1.61
3.17
Lower Incisor
-1.74
2.18
-0.98
1.61
-2.72
2.25
Total
Molar correction
1.72
1.56
0.23
1.19
1.95
1.92
Overjet change
3.13
2.65
-0.70
0.97
2.43
2.39
55
Figure 2.11. Pitchfork diagrams. A. Components of molar
and overjet change; B. Treatment change; C. Posttreatment
change; and D. Net change (in mm). Note that the maxillary
molars came forward more than the mandibular molars, ABCH
was greater in the posttreatment interval, and the
maxillary and mandibular incisors moved lingually
posttreatment.
56
Table 2.8.
Model analysis:
descriptive and inferential statistics.
T1
T2
T3
Change
Paired t
Measure
Mean
Irregularity
Mandibular
Intercuspid
Maxillary
57
Intercuspid
Mandibular
Intermolar
Maxillary
Intermolar
* P<0.0167
** P<0.003
S.D.
Mean
S.D.
Mean
S.D.
Treatment
Posttreatment
Net
T2 minus T1
T3 minus T2
T3 minus T1
Mean
S.D.
Mean
S.D.
Mean
S.D.
T1 to T2
T2 to T3
(Ho:δ=0)
4.80
3.12
0.74
0.80
2.57
1.60
-4.10
3.17
1.81
1.71
-2.23
3.23
10.28**
-8.42**
24.95
1.52
26.24
1.44
24.47
1.43
1.29
1.49
-1.76
1.15
-0.48
1.46
-6.83**
12.19**
31.91
2.22
33.34
1.58
32.31
1.76
1.43
1.91
-1.01
1.18
0.40
1.77
-5.95**
6.82**
40.60
2.54
38.21
2.30
37.90
2.66
-2.41
2.36
-0.31
1.39
-2.70
2.06
8.12**
1.76
44.93
2.96
43.79
2.27
43.44
2.55
-1.15
2.20
-0.36
1.32
-1.50
2.11
4.14**
2.16
Table 2.9.
Dependent and independent variables:
standard deviations, and intra-class
correlations.
Item
Abbreviation
Mean
means,
S.D.
Cronbach’s
α
Dependent Variables (Relapse)
Incisor to mandibular
plane
Post tx∆ IMPA
-0.27
3.98
0.71
Post tx∆ IRR
1.81
1.71
0.76
Mandibular intercuspid
width
Post tx∆ Mand 3-3
-1.76
1.15
0.76
Maxillary intercuspid
width
Post tx∆ Max 3-3
-1.01
1.18
0.70
Irregularity Index
Skeletal Independent Variables (Predictors)
Mandible to cranial base
Mand-CB tx∆
-0.56
2.30
0.84
Maxilla to cranial base
Max-CB tx∆
0.62
1.53
0.75
Maxilla to mandible
Max-Mand tx∆
-1.19
1.99
0.81
Maxilla to cranial base
Post tx∆ MAX
-0.47
1.03
0.98
Differential mandibular
growth
Post tx∆ ABCH
1.06
1.70
0.59
Dental Independent Variables (Predictors)
Incisor to mandibular
plane
IMPA tx∆
-1.31
5.46
0.73
Intermolar angle
171.35
4.53
0.89
Irregularity Index
IRR tx∆
-4.10
3.17
0.94
Mandibular cuspid
expansion
Mand 3-3 tx∆
1.29
1.49
0.76
Maxillary cuspid
expansion
Max 3-3 tx∆
1.43
1.91
0.82
Intermolar angle
58
Table 2.10.
Multiple regression analysis equations separated into proposed skeletal and
dental causes of relapse.
Dependent
Variable
Constant
Regression Coefficients
r/R
r2/R2
F-Ratio
Skeletal Predictors
Post tx∆ IMPA
. .
None significant
. .
. .
. .
Post tx∆ IRR
1.76
-0.28 MAX-Mand tx∆ -0.26 CB-MAX tx∆
0.35
0.12
3.91*
Post tx∆ Mand 3-3
. .
None significant
. .
. .
. .
Post tx∆ Max 3-3
. .
None significant
. .
. .
. .
59
Dental Predictors
Post tx∆ IMPA
Post tx∆ IRR
Post tx∆
Mand 3-3
Post tx∆ Max 3-3
* P<0.05
** P<0.01
*** P<0.001
-0.36
-0.32 IMPA tx∆
-0.32
0.10
6.70*
-0.36 Intermolar Angle
-0.36
0.13
8.83**
-1.36
-0.40 Mand 3-3 tx∆
-0.40
0.16
11.41***
-0.59
-0.48 Max 3-3 tx∆
-0.48
0.23
8.81**
1.92
Discussion
Error Study
The intra-class correlations for the double
determinations show that most of the measurements are
acceptably reliable (Cronbach’s α above 0.80).
There were,
however, some measures for which the reliability
correlations were low.
It must be noted at the outset that
a lack of technical reliability may be, in certain
instances, a contributor to the generally low and
clinically non-significant correlations seen here.
Unfortunately, at present there really is no other
source of data than lateral cephalograms and study models.
Another possible reason for the low correlations in the
present study is the method utilized to correct the T3
cephalometric magnification reduction present in 22 of the
64 series.
If, in some subjects, growth was not minimal
between T2 and T3, as was assumed, the resulting T3
measurements may have slightly under-estimated the
posttreatment changes.
Treatment Details
The descriptive statistics imply that the present
sample was treated conservatively in accord with the
precepts of the Tweed technique.
60
Cephalometric data
summarized in Tables 2.4 and 2.5 illustrate relatively
small, often statistically non-significant, treatment
changes:
the mandibular incisors were up-righted 1.27
degrees (IMPA) and retracted 0.60 mm (L1-APg); the
interincisal angle (1/1) was increased 1.85 degrees; and
the common vertical measurements, Y-axis and FMA, each
decreased less than 1 degree.
Linear measures of size
generally showed statistically significant increases, as
did measures of molar movement, overjet reduction, profile
protrusion, and maxillary size/position (SNA).
From the study-model measurements (Table 2.8), it
may be seen that the canines were expanded on average 1.29
mm in the mandible and 1.43 mm in the maxilla.
Both upper
and lower intermolar dimensions were decreased during
treatment (Table 2.8), 2.41 mm in the mandible and 1.15 mm
in the maxilla.
These small changes were statistically
significant and perhaps can be attributed to the fact that,
because of the mechanics of space closure, the canines
moved distally and the buccal segments moved mesially along
a “V-shaped” basal arch (vide infra).
As measured from the fiducial hash mark angles,
there were also minimal, and mostly non-significant,
vertical changes (Table 2.6 and Figure 2.10).
It is
perhaps worthwhile to note that there was a slight closing
61
rotation of the mandible during treatment (Mand-CB angle
treatment change of -0.57o).
This change, however, was not
significantly different from zero.
This finding
contradicts a popular assertion in the Tweed literature
that their approach to vertical control allows the mandible
to auto-rotate upwards and forwards, the so-called
“mandibular response.”45-47
Conversely, the lack of an
opening rotation suggests, at the very least, that the
present treatment mechanics produced results that counter
the common claim that “all orthodontic mechanics are
extrusive.”
Apparently, it need not be so.
From the present descriptive data, it is evident
that care was taken by the treating orthodontist to avoid
many of the classically-proposed causes of relapse.
Despite conservative treatment, however, there were
instances in which there was a relationship between even
these small treatment changes and subsequent relapse.
Further, there were skeletal causes that were beyond the
control of the clinician.
Skeletal Predictors
The multiple regression equations summarized in
Table 2.10 show that most of the hypothesized skeletal
62
causes of relapse did not account for a significant portion
of the actual incisor relapse seen here.
Schudy,25 reported a significant correlation between
condylar growth and a decrease in IMPA.
The skeletal
predictor variables studied here were considerably more
complex--differential maxillo-mandibular relations,
maxillary displacement, and angular measures of basal
rotation (changes in Mand-CB, Max-CB, and Max-Mand angles).
The lack of a significant relationship suggests that
posttreatment incisal inclination is relatively independent
of the overall pattern of skeletal change.
As was noted
earlier, whatever the change in incisor inclination, it is
not the same as change in incisor irregularity, as the two
might be relatively independent.
As shown in Table 2.8, irregularity increased
1.81 mm in the posttreatment interval to a recall value of
2.57 mm, a result that is similar to several other longterm recall studies of similarly-treated patients.19,20,48
Indeed, 51 of the 64 subjects had posttreatment
irregularity below Little’s success/failure borderline of
3.5 mm.49
Although irregularity relapse was small, it was
correlated with posttreatment change in ABCH (r=0.218,
63
P=0.047C) and negatively correlated with treatment changes
in Max-CB (r=-0.340, P=0.004) and Max-Mand (r=-0.238,
P=0.033).
These relationships, although weak, are
statistically significant and thus require comment.
The Pitchfork Analysis (Table 2.7) showed that the
mandible outgrew/out-advanced the maxilla (ABCH) in
treatment and posttreatment intervals, a pattern of change
that is thought by some to be a potential cause of incisal
relapse.24,26
The weak positive correlation between ABCH and
irregularity suggests that excessive mandibular growth is,
at best, a minor factor.
ABCH, however, was not part of
the multiple regression equation, suggesting that
mandibular excess did not supply significant, unduplicated
information beyond that supplied by the skeletal variables
that did enter.
The regression equation for irregularity relapse
was statistically significant and included treatment
changes in the Max-Mand and Max-CB basal-bone angles.
The
multiple correlation coefficient, however, was only 0.35; R2,
only 0.12.
The negative correlation of these angles to
incisal crowding inferred from regression coefficients
(vide supra) suggests that a forward basal rotation during
C
Given the intent to employ multivariate analysis, the simple
correlation matrix was not tabulated.
64
treatment would serve to increase posttreatment
irregularity.
The fact that the model can only account for
12% of the observed variation, however, suggests that this
sample’s favorable pattern of skeletal rotation is not a
clinically significant predictor of irregularity relapse.
Further, regardless of predictive significance,
posttreatment maxillo-mandibular rotations would seem
beyond the control of the clinician.
The proposed dental
etiologies, however, were more significantly related to
relapse and presumably are clinically modifiable.
Dental Predictors
The results summarized in Table 2.10 show that the
multiple regression equation for each measure of relapse
had only one statistically significant dental independent
variable.
In these instances, therefore, multiple
regression was really simple regression.
For posttreatment change in IMPA, treatment change
in IMPA was the only statistically significant predictor
(r=-0.32; r2=0.10; P=0.006; Table 2.10).
The negative
correlation implies that changes in incisor angulation will
have a slight tendency to “rebound.”
This outcome is in
agreement with Tweed,8 Ackerman and Proffit,50 Blake and
Bibby,31 and many others who have argued that the original
65
mandibular incisor inclination is the most stable position.
In the present sample, the incisors were uprighted during
treatment and continued this trend posttreatment.
Both
effects, however, were small and non-significant.
It was
the same with irregularity relapse.
The posttreatment increase in Little’s Irregularity
Index was small and consistent with previous long-term
recall studies of similar treatments (vide supra).
Regression analysis found only a single significant dental
predictor, the intermolar angle at debond; hence, R=r
(Table 2.10; r=-0.36, r2=0.13).
The negative correlation
suggests that more mesially inclined buccal segments will
have a slight tendency to increase the posttreatment
irregularity, perhaps because of an increased anterior
component of occlusal force.
The intermolar angle did not
change significantly during treatment (Table 2.6), the
buccal segments remained mesially inclined, and thus the
occlusal forces in this sample would feature an anterior
component of force (ACF) that might serve to displace the
dentition anteriorly into the labial soft tissue envelope
of function.
The mesially inclined buccal segment as a potential
cause of irregularity is in agreement with a two-part paper
by Southard, Behrents, and Tolley.22,23
66
They found a
correlation between interproximal forces during occlusion,
a measure of anterior occlusal force, and incisor
irregularity (r=0.54).
Their correlation was greater than
seen here, possibly suggesting that a measure of occlusal
force in combination with mesial buccal segment inclination
might have provided an improved prediction in the present
study.
It is also worthwhile to note here that initial
irregularityD was not correlated to posttreatment
irregularity relapse.
This finding disagrees with Årtun
and co-workers,32 a difference that might be due to the
nature of Årtun’s sample, which had both nonextraction and
extraction treatments, as compared to the present sample,
which was almost all extraction.
Presumably, nonextraction
treatments of patients with modest anterior space
deficiencies often would align the dentition by flaring the
incisors into the labial soft tissue envelope of
function.4,5,51
In contrast, extraction treatments probably
would procline the incisors less frequently and thus would
decrease the variation to be predicted.
Canine expansion
is a kind of lateral “flaring,” and it too, was examined
with respect to “dental etiologies.”
D
Because treatment generally reduced irregularity to zero at T2,
treatment change with the sign reversed served as the measurement of
initial irregularity in the regression analysis.
67
Of the five dental independent variables, there was
only one significant predictor of the stability of
mandibular and maxillary canine expansion--the extent of
the expansion during treatment (mandible, r=-0.40. r2=0.16;
maxilla, r=-0.48, r2=0.23).
Thus, even the small, seemingly
unavoidable canine expansion seen here appears to be, to a
degree, unstable.
This outcome is in agreement with
Strang’s classic observation about the “inviolability” of
lower intercanine width.3
The present study’s expansion
relapse is also similar to the results of Little, Wallen,
and Riedel,49 who found an average of 2.02 mm of canine
relapse.
The small r2 values for both expansion equations,
however, suggest that, at least in this sample, canine
expansion during treatment is not a clinically significant
predictor of relapse.
A possible reason for this low
correlation is that retraction of the canines into a wider
portion of the arch would be measured as expansion, but at
the same time might not impinge on the buccal soft tissue
envelope of function.
Another possibility for the small r2
values in the expansion equations is the restricted range
of the treatment changes seen here (Table 2.8; standard
deviations for treatment changes in mandibular intercanine
width was 1.49 mm and for maxillary intercanine width was
1.91 mm).
For the present study, if there is little
68
expansion, there is little relapse; if there is little
relapse there is almost nothing to predict.
Restricted Range
Only one of the five statistically significant
regression equations featured more than one predictor
variable, and all featured weak, seemingly clinically
insignificant correlations.
One possible reason for the
weak correlations is the conservative treatment that was
employed.
For example, there was little expansion and no
incisor flaring.
Correlation measures the covariance of
standard scores, and if one variable is relatively constant,
there is little covariance, and the resulting correlation
coefficients must, of necessity, be small (Figure 2.12 A).
The combination of nonextraction and extraction treatments
might serve to increase the range and perhaps increase the
correlation.
If, say, 70-80% of the sample were to have
been treated with contemporary non-extraction mechanics,
there would be deliberate canine expansion, and an increase
in range.
If such treatments were to be examined 10-20
years posttreatment, this increased range perhaps would
lead to much stronger correlation between expansion and
relapse (Figure 2.12 B).
Time will tell.
69
Figure 2.12. Range restriction. Abscissa is expansion;
the ordinate, the relapse associated with a change in width.
The narrow grouping of results from conservative Tweed
mechanics (A) would tend to obscure any correlation between
expansion and relapse; however, the range of results
produced by a trend to non-extraction/expansion mechanics
(B), might show a more obvious relation between expansion
and relapse.
Summary and Conclusions
The present investigation was a multivariate
statistical evaluation of commonly-hypothesized causes of
relapse in a longitudinal sample of treated cases recalled
over 20 years posttreatment.
Despite conservative
treatments and relatively small changes in many of the
factors thought to cause relapse, a few isolated
relationships proved to be statistically significant:
1. Forward basal rotation of the maxilla and mandible
during treatment was correlated with an increase in
incisal irregularity;
70
2. Treatment change in mandibular incisal angulation
was negatively correlated to posttreatment change in
incisal angulation;
3. Perhaps as a result of the anterior component of
occlusal force, mesial buccal-segment inclination
was negatively correlated to posttreatment
mandibular incisor irregularity; and
4. Maxillary and mandibular canine expansion during
treatment will tend to relapse.
Despite scattered instances of statistical
significance, no clinically significant prediction
equations could be generated from this conservatively
treated sample.
Perhaps the relapse seen here was too
small to be detected by the statistical power of a
conventional cephalometrics study.
If so, future studies
of more marked treatment effects may reveal relationships
that are of greater clinical significance.
Alternatively
perhaps the causes of relapse are more subtle than
contemporary methods and conjectures can address.
71
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76
APPENDIX A
Cephalometric Digitization Regimen
Appendix A depicts a customized “Ricketts 71-point
regimen” from Dentofacial Planner version 5.32 (Figure A),
and the corresponding cephalometric analysis (Table A).
Figure A. Customized “Ricketts 71-point regimen” from
Dentofacial Planner version 5.32. Point 65 defined the
anterior extent of the functional occlusal plane.
77
Table A.
Customized cephalometric analysis.
Measures
Angular
Linear
SNA
Wits A/B
SNB
PNS-A pt
ANB
S-Ar
Y-axis
S-Go
U1-SN
Ar-Gn
U1-NA
Pg-NB
L1-NB
U6-PTV
Interincisal (1/1)
U1-NA
FMA
L1-APg
IMPA
Overjet
FMIA
Overbite
Z
N-Me
SN-Palatal Plane (ANS-PNS)
N-ANS
SN-Functional Occlusal Plane
ANS-Me
UFH (%)
LFH (%)
LL-E line
Wits A/B
PNS-A pt
78
APPENDIX B
Error Study
Appendix B contains the intra-class correlations
(Cronbach’s α) for both cephalometric and model duplicate
measures.
Table B.1.
Error Study: intra-class correlations
(Cronbach’s α) for angular cephalometric
measures.
Measures
T1
T2
T3
SNA
0.91
0.81
0.83
SNB
0.89
0.85
0.74
ANB
0.94
0.97
0.97
Y-axis
0.92
0.83
0.81
U1-SN
0.94
0.72
0.86
U1-NA
0.94
0.82
0.90
L1-NB
0.94
0.95
0.96
Interincisal
0.94
0.84
0.82
FMA
0.93
0.95
0.95
IMPA
0.97
0.92
0.97
FMIA
0.85
0.71
0.77
Z
0.97
0.94
0.96
SN-PP
0.90
0.92
0.79
SN-FOP
0.93
0.96
0.81
79
Table B.2.
Error Study: intra-class correlations
(Cronbach’s α) for linear cephalometric
measures.
Measures
T1
T2
T3
Wits A/B
0.95
0.87
0.87
PNS-A pt
0.86
0.93
0.95
S-Ar
0.93
0.98
0.98
S-Go
0.87
0.98
0.99
Ar-Gn
0.99
0.99
0.98
Pg-NB
0.95
0.96
0.92
U6-PTV
0.85
0.93
0.91
U1-NA
0.93
0.97
0.94
L1-APg
0.86
0.95
0.96
Overjet
0.96
0.89
0.79
Overbite
0.88
0.87
0.70
N-Me
0.96
0.97
0.98
N-ANS
0.88
0.95
0.94
ANS-Me
0.99
0.98
0.99
UFH (%)
0.90
0.88
0.92
LFH (%)
0.83
0.80
0.90
LL-E line
0.92
0.98
0.97
80
Table B.3.
Measure
Error study: intra-class correlations
(Cronbach’s α) for the components of molar
and overjet change.
Treatment
Post-treatment
Net
Skeletal
MAX
0.70
0.98
0.94
ABCH
0.57
0.59
0.69
MAND
0.51
0.80
0.76
Dental
U6
0.88
0.78
0.74
L6
0.93
0.80
0.83
U1
0.99
0.78
0.97
L1
0.90
0.90
0.84
Total
Molar
0.80
0.66
0.90
Overjet
0.97
0.75
0.96
81
Table B.4.
Error study: intra-class correlations
(Cronbach’s α) for fiducial and intermolar
angles.
Measures
T1
T2
T3
Maxilla-CB
0.76
0.84
0.86
Maxilla-Mandible
0.84
0.94
0.94
Mandible-CB
0.95
0.98
0.96
Intermolar
0.59
0.89
0.85
Table B.5.
Error study: intra-class correlations
(Cronbach’s α) for model analysis
Measures
Irregularity
Mandibular
Intercuspid
Maxillary
Intercuspid
Mandibular
Intermolar
Maxillary
Intermolar
T1
T2
T3
0.97
0.95
0.94
0.97
0.97
0.98
0.87
0.96
0.92
0.97
0.98
0.98
0.99
0.98
0.98
82
VITA AUCTORIS
Nathan Daniel Mellion was born on September 13,
1982 in Akron, Ohio.
He received his undergraduate
education at Denison University in Granville, Ohio.
He
received his dental education at The Ohio State University,
and graduated with a degree of Doctor of Dental Surgery in
2008.
Immediately after graduation from dental school, he
began his graduate orthodontic education at the Center for
Advanced Dental Education at Saint Louis University, in St.
Louis, Missouri.
He is currently a candidate for the
degree of Master of Science in Dentistry.
to Tana Marie Mellion on December 27, 2008.
He was married
83