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THE EFFECT OF FOUR FIRST PREMOLAR EXTRACTIONS
ON THE POSTERIOR BOLTON RATIO
Anthony D. Mongillo, B.S., D.M.D.
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
2015
© Copyright by
Anthony David Mongillo
ALL RIGHTS RESERVED
2015
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COMMITTEE IN CHARGE OF CANDIDACY:
Professor Eustaquio A. Araujo, D.D.S, M.S.D.
Chairperson and Advisor
Assistant Clinical Professor Patrick F. Foley, D.D.S., M.S.
Associate Professor Ki Beom Kim, D.D.S, M.S.D., Ph.D.
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DEDICATION
“WHAT E'ER THOU ART, ACT WELL THY PART." —William Shakespeare
Son. Brother. Husband. Dentist. Father. Orthodontist. I dedicate this work
to All who gives role to my life.
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ACKNOWLEDGEMENTS
A debt of gratitude is owed to all at Saint Louis University and the Center for
Advanced Dental Education who allowed me to be a part of such a storied orthodontic
program. To my thesis committee: Dr. Eustaquio Araujo, Dr. Ki Beom Kim, and
Dr. Patrick Foley, I owe special thanks for your patience, encouragement, and guidance
on this thesis topic. Thank you, Dr. Heidi Israel, for your assistance with the statistical
analysis. Acknowledgements are due to the many faculty members who have played a
role, whether major or minor, in my specialty education and professional development.
May you all find contentment and satisfaction in knowing that you have touched
innumerable others by sharing your time and talents with a rising generation. Thank you.
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TABLE OF CONTENTS
List of Tables .................................................................................................................... vii
List of Figures .................................................................................................................. viii
CHAPTER 1: INTRODUCTION ....................................................................................... 1
CHAPTER 2: REVIEW OF THE LITERATURE ............................................................. 5
Seekers of Truth ...................................................................................................... 5
Occlusion ................................................................................................................ 5
Interarch Tooth Size Discrepancy........................................................................... 7
The Whole is Equal to the Sum of its Parts ............................................................ 8
Clinical Implications of an Interarch Tooth-Size Discrepancy............................... 9
The Significance of a Tooth-Size Discrepancy: ................................................... 12
The Great Debate: To Extract or Not to Extract? ................................................. 14
The Role of Extractions in A Tooth-Size Discrepancy ........................................ 16
Statement of Thesis ............................................................................................... 19
References ............................................................................................................. 22
Chapter 3: JOURNAL ARTICLE ..................................................................................... 25
Abstract ................................................................................................................. 25
Introduction ........................................................................................................... 27
Materials and Methods .......................................................................................... 30
Sample........................................................................................................... 30
Statistical Analysis ........................................................................................ 39
Reliability ...................................................................................................... 41
Results ................................................................................................................... 41
Discussion ............................................................................................................. 49
Interpretation of Results ................................................................................ 49
Present Outcomes and Past Studies .............................................................. 53
Clinical Significance and Implications ......................................................... 57
Conclusion ............................................................................................................ 62
Literature Cited ..................................................................................................... 63
Appendix A ....................................................................................................................... 65
Appendix B ....................................................................................................................... 68
Appendix C ....................................................................................................................... 69
Appendix D ....................................................................................................................... 71
Appendix E ....................................................................................................................... 74
Appendix F........................................................................................................................ 79
v
Vita Auctoris ..................................................................................................................... 81
vi
LIST OF TABLES
Table 2.1- Ideal ratios and average tooth widths from Bolton's thesis. .............................. 9
Table 3.1- Comparison of Bolton's original thesis sample and this study’s sample. ........ 42
Table 3.2- Paired t-test comparing widths of corresponding upper
and lower posterior teeth. ................................................................................ 42
Table 3.3- Ratios and measurements describing non-extraction
and four first premolar extraction cases. ......................................................... 43
Table 3.4- Comparison of non-extraction and extraction Bolton ratios
as well as expected and observed Bolton ratios. ............................................. 44
Table 3.5- Linear regression of variables explaining variation in net residual space. ...... 49
Table A- List of Abbreviations ......................................................................................... 65
Table B- Significant variable from NRS2Grp ANOVA ................................................... 68
Table C- Significant variables from NRS3Grp ANOVA ................................................. 69
Table D- Linear regression output of all significant variables from
NRS2Grp and NRS3Grp ANOVA ................................................................. 71
Table E- Backward regression of all significant variables from
NRS2Grp and NRS3Grp ANOVA. ................................................................ 74
Table F- Individual regression for U5vsL5 and U5sWidth. ............................................. 79
vii
LIST OF FIGURES
Figure 2.1- Ambiguity inherent in interpreting the overall Bolton ratio. ......................... 11
Figure 3.1- Measuring the mesiodistal widths and defining the clinical
crown margin of each tooth. .......................................................................... 32
Figure 3.2- “Ideal 3-3" digital setup. ................................................................................ 34
Figure 3.3- Occlusion schemes for digital setups. ............................................................ 36
Figure 3.4- Example "Ideal 4's" digital setup. .................................................................. 37
Figure 3.5- Example of measuring residual space in the mandibular arch. ...................... 38
Figure 3.6- Scatterplot of NetResSpc and NetPBDiscrep for each case
with the regression line and equation. ........................................................... 45
Figure 3.7- Frequency of cases grouped by net residual space......................................... 46
Figure 3.8- Two scenarios resulting from prioritizing space closure
over ideal occlusion ....................................................................................... 60
Figure 3.9- Regression equation for predicting residual space ......................................... 61
Figure D- Charts from linear regression of all sig variables from
NRS2Grp and NRS3Grp ANOVA ................................................................ 73
Figure E- Charts for backward regression of all sig variables from
NRS2Grp and NRS3Grp ANOVA ................................................................ 78
viii
CHAPTER 1: INTRODUCTION
The Bolton tooth-size discrepancy analysis is a diagnostic tool employed to help
identify potential limitations in detailing and finishing a patient’s final occlusion before
as much as one bracket is placed. Take, for example, the anterior Bolton ratio which is
most commonly used as a reference against which a patient’s anterior tooth-size ratio is
compared. A mismatching anterior Bolton ratio will indicate whether the anterior teeth
are too large, too small, or just right for proper anterior overjet and overbite. Armed with
this knowledge, the orthodontist is able to inform the patient and plan for restorative
build-ups or selective interproximal reduction in teeth of one arch or the other at the pretreatment consultation. However, little is known about the posterior Bolton ratio, how it
is affected by extracting posterior teeth, and its application in the orthodontic setting.
Many factors contribute to ideal dental occlusion. Perfect occlusion, as defined in
textbooks, takes into account the intercuspation of maxillary and mandibular buccal and
lingual cusps within the fossae or on the marginal ridges of the opposing arch. The
maxillary lingual cusp tips should occlude in the fossae or on the marginal ridges of
mandibular teeth. The maxillary buccal cusp tips are non-occluding, but should fit within
the embrasures or buccal grooves of the mandibular teeth. Mandibular buccal cusps tips
should occlude in the fossae or on the marginal ridges of maxillary teeth. While the
mandibular lingual cusps are non-occluding they should fit in the lingual embrasures or
lingual grooves of maxillary teeth.
Prominent contributors to the orthodontic specialty, Angle and Andrews, cite the
relative molar positions as “keys” to occlusion.1,2 Other major factors influencing dental
1
occlusion include rotations, tip, torque, the occlusal plane, and interdental spacing. When
all factors are in harmony, textbook-perfect occlusion is possible to achieve.
Studying cases deemed to have “excellent” occlusion, Bolton’s landmark study3
published in 1958 included models of 55 patients. The aim was to describe “excellent”
occlusion using a mathematical ratio of the sum widths of bottom teeth versus top teeth.
He found that excellent occlusion can be described as having an anterior ratio of 77.2%
and an overall ratio of 91.3%. Bolton did not report a posterior ratio. Applying the ratios
derived from cases with excellent occlusion to a case prior to orthodontic treatment could
help indicate whether the top or bottom teeth are too large, too small, or just right for
excellent occlusion.
An analogy helpful for understanding the Bolton ratio would be aligning fence
posts and post holes. If the posts of a prefabricated section of a fence are spaced every 10
feet, the post holes in the ground should be spaced every 10 feet for the fence posts to fit
in the holes. This represents an ideal 1:1 ratio. However, if the ratio is changed to 1:1.2,
for example, the fence posts are spaced every 10 feet and the post holes are spaced every
12 feet. The result is that the fence will not fit in the holes. The same goes for teeth in
excellent occlusion.
However, orthodontic treatment often requires extraction of teeth for various
reasons. Although the popularity of extracting teeth for orthodontic purposes has varied
over time, the first premolar teeth have continued to be those most commonly extracted
as part of orthodontic treatment. Extracting teeth may alter the excellent occlusal
relationship found in a full complement of teeth as described by Bolton’s overall ratios.
One can easily understand that by extracting posterior teeth the anterior ratio would not
2
change, but the overall and posterior ratios of teeth would change—especially when the
maxillary and mandibular teeth are not equal sizes. Bolton4 predicted a new expected
overall ratio resulting from the extraction of four premolars. He predicted that the new
overall ratio should be between 87-89% based on average premolar tooth widths. Many
investigators have used the overall ratio that Bolton predicted for cases involving
premolar extractions to study the effect of different extraction patterns on occlusion.
However, Bolton’s predicted ratio was based on mathematical calculation that
simply omits the average widths of extracted teeth. This does not take into consideration
the articulation of the cusps, fossae, and marginal ridges of the remaining teeth as did his
original sample. For accuracy, any newly described ratios for extraction cases should be
calculated in the same way that the original anterior and overall ratios were calculated
from Bolton’s non-extraction cases—that is, from cases treated with extraction and
resulted in excellent occlusion.
A recent study by Kayalioglu et al.5 measured 53 post-treatment models from
patients treated with four first premolar extractions that resulted in good occlusion and
reported a new ideal overall ratio based on this sample. The newly reported ideal overall
ratio was slightly, but significantly larger than Bolton’s predicted value. This may
indicate that many studies using Bolton’s predicted value for cases treated with premolar
extraction may have made erroneous assumptions and/or conclusions about the occlusal
consequences of different premolar extraction patterns.
Using a novel method utilizing digital extractions and setups, this study seeks to
add to the existing literature related to the Bolton ratios by: First, reporting a posterior
Bolton ratio that can be expected from full dentition cases with excellent occlusion as
3
described by Bolton’s anterior and overall ratios; Second, describing the effect of four
first premolar extractions on the posterior Bolton ratio including any compromises in the
ability to finish such cases with excellent occlusion.
4
CHAPTER 2: REVIEW OF THE LITERATURE
SEEKERS OF TRUTH
Although the paradigms for orthodontic treatment have shifted, ebbed, and flowed
from maximizing dental and oral health, masticatory efficiency, temporomandibular joint
function, post-treatment stability, and simple esthetics, what is sure is that humans have
been moving teeth for millennia. Some have even attributed the natural masticatory
system to “the work of the great Creator, who could design and construct such a
marvelous and simple piece of mechanism.”6
Many have studied the dental ‘mechanism’, searching for immutable laws in
occlusal design and function. Notable contributors include Bonwill6 for using
mathematics and geometry to describe the articulation of human teeth, EH Angle1 for
describing the “key to occlusion” and developing the edgewise technique, Bolton3 for
describing excellent occlusion using a mathematical ratio of lower versus upper tooth
widths, and Andrews2 for identifying several specific variables, or keys, contributing to a
normal occlusion as well as developing the straight wire appliance that is so ubiquitous
today.
OCCLUSION
Bonwill’s contribution to dentistry includes the articulator which mimics the
ginglymoarthrodial function of the mandible in the Glenoid fossa and upon which full
and partial dentures are able to be constructed and adjusted extraorally. Speaking toward
those dentists who failed to see his articulator’s potential, he stated, “A tooth may be
elegantly shaped and colored, yet if it lacks the proper shape…and unskillfully set in the
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arch, it is a failure.”6 Skillfully setting natural, living teeth in the arch is the task of an
orthodontist.
EH Angle ushered in the modern era of orthodontics. Aside from inventing the
edgewise technique that is still employed in variants today, he is credited with describing
the most simple and enduring dental system for classifying malocclusion and
normocclusion in orthodontics. He said, “The key to occlusion is the relative position of
the first molars. In normal occlusion the mesiobuccal cusp of the upper first molar is
received in the sulcus between the mesial and distal buccal cusps of the lower…”1
Specifically, a normocclusion exists when the mesiobuccal cusp tip aligns with the
mandibular buccal groove. When positioned anteriorly a Class II is designated, and Class
III when posteriorly positioned. With the “key to occlusion” orthodontists can effectively
identify, classify, communicate, and plan treatment to accomplish orthodontic correction.
However, simplifying the treatment of malocclusions to the correction of merely
one tooth does injustice to the complexity of treatment facing specialists daily. EH Angle
recognized this, stating, “The sizes, forms, interdigitating surfaces, and positions of the
teeth in the arches are such as to give one another, singly and collectively, the greatest
possible support in all directions.”1 Andrews’ “The Six Keys to Normal Occlusion” is a
seminal paper describing ideal dental positions.2
As did Angle, Andrews ascribed a similar importance to molar position, with the
modification that the maxillary first molar’s distal slope of the distobuccal cusp should
contact the mandibular second molar’s mesial slope of the mesial marginal ridge. He
also listed crown angulation (tip), crown inclination (torque), rotations, spaces, and
occlusal plane as the other factors affecting normal occlusion. So accurate and thorough
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was his description of a ‘normal’ occlusion that the now-ubiquitous straight-wire
appliance was developed largely from of his contributions. However, much is left to
chance by assuming that all the teeth will intercuspate ideally and occlude merely by
placing molars in the ideal position. For teeth to properly occlude and intercuspate each
tooth must not only be in the proper position, but must also occupy the proper amount of
space mesiodistally to be in proximal contact with its neighbor.
INTERARCH TOOTH SIZE DISCREPANCY
While acknowledging Ballard’s7 and Neff’s8 pioneering work, Dr. Wayne A.
Bolton studied 55 pre and post-treatment models with ‘excellent’ occlusion as a master’s
candidate at the University of Washington in 1952.9 Among other factors such as
interincisal angle and overbite, he measured the mesiodistal widths of maxillary teeth and
mandibular teeth and compared them in terms of a ratio. Six years later he published his
thesis.3 The interarch ratios are calculated as follows from Bolton’s 1958 paper:
Anterior Ratio:
Sum Mandibular "1s, 2s, 3s"
x 100 = Anterior Ratio
Sum Maxillary "1s, 2s, 3s"
Overall Ratio:
Sum Mandibular 12 teeth
x 100 = Overall Ratio
Sum Maxillary 12 teeth
Bolton found that for teeth with excellent intercuspation, the ratio of anterior
mandibular tooth widths versus the anterior maxillary tooth widths has a mean proportion
of 77.2 ± 0.22%, with a standard deviation of 1.65%. The average overall ratio from
Bolton’s cases is 91.3 ± 0.26%, with a standard deviation of 1.91%.
7
Ratios higher than the ideal indicate that the teeth in the mandibular arch are
larger (or teeth in the maxillary arch are smaller) than what is found to describe for
excellent occlusion. A lower ratio indicates that teeth in the mandibular arch are smaller
(or maxillary teeth are larger) than what was found to describe excellent occlusion.
When anterior or overall ratios do not match the ratios Bolton found, an interarch toothsize discrepancy—hereafter referred to as an “ITSD”—can be diagnosed.
THE WHOLE IS EQUAL TO THE SUM OF ITS PARTS
According to Bolton, “The dental arches must be thought of as consisting of two
components, the anterior and posterior.”4 It must be noted, however, that Bolton does not
report in published literature a ratio that describes the proportion posterior teeth (the first
and second premolars and first molars) found in excellent occlusion. He only states,
The buccal segments were divided into units in an attempt to analyze the cuspal
interdigitation and possibly localize tooth size discrepancy. It is felt that the findings lack
clinical significance; therefore, the buccal measurements are being omitted from this
paper. 3
Why this would lack clinical significance is unclear. Would not ‘excellent’
occlusion depend on the intercuspation of posterior teeth just as much as the anterior
teeth? Why then, report an overall ratio for ‘excellent’ occlusion—one that includes all
teeth, anterior teeth and posterior—if a possible ITSD in the posterior would “lack
clinical significance”? The answer is that it does not, in fact, lack clinical significance.
Bolton had the data to report an anterior and posterior ideal ratio of teeth. In his
thesis9 published at the University of Washington in 1952, Bolton reports the average
tooth widths and standard deviations of each tooth type from central incisors to first
molars. To reveal the ideal posterior Bolton ratio from his sample of cases with
‘excellent’ occlusion, a simple calculation can be made as follows:
8
Posterior ratio:
Sum Mandibular "4s, 5s, 6s"
x 100 = Posterior Ratio
Sum Maxillary "4s, 5s, 6s"
Applying this formula to the tooth widths reported in Bolton’s thesis would have
allowed him to arrive at an ideal posterior ratio (see Table 2.1 for tooth widths, and Table
3.1 for the posterior ratio). One can only speculate why Bolton failed to report the ideal
posterior ratio. Perhaps he truly felt it, “lacked clinical significance.”
Table 2.1- Ideal ratios and average tooth widths from Bolton's thesis.
Ratios
Maxillary
Mandibular
Bolton’s Original Sample
Mean
77.20%
Anterior
91.30%
Overall
8.82 mm
Central
6.96 mm
Lateral
7.91 mm
Canine
7.04 mm
1st Premolar
6.84 mm
2nd Premolar
10.4 mm
1st Molar
5.42 mm
Central
5.94 mm
Lateral
6.93 mm
Canine
7.15 mm
1st Premolar
7.27 mm
2nd Premolar
11.14 mm
1st Molar
SD
1.65
1.91
0.42
0.48
7.91
0.46
0.39
0.58
0.31
0.26
0.37
0.38
0.39
0.62
N
55
55
110
110
110
110
110
110
110
110
110
110
110
110
CLINICAL IMPLICATIONS OF AN INTERARCH TOOTH-SIZE DISCREPANCY
Given an ideal anterior Bolton ratio and an ideal overall ratio, the posterior Bolton
ratio must be ideal and the occlusion should be ‘excellent.’ An alternate way of looking
at it is the ratio of anterior teeth resulting in excellent occlusion is equally important as
9
the ratio of posterior teeth resulting in excellent occlusion. Together, they create an
overall ratio of teeth with excellent occlusion. Conversely, for any given case, an
exaggerated or deficient anterior or posterior ratio can have one of two effects on the
overall Bolton ratio. It could either derange the overall ratio, or compensate for the other,
creating an ideal overall ratio.
This begs the question, what would happen in a case with a large anterior Bolton
ratio and a small posterior Bolton ratio, or small anterior and large posterior ratio,
resulting in an ideal overall Bolton ratio? The answer reveals the insignificance of the
overall Bolton ratio. A large anterior Bolton ratio would indicate that the maxillary
anterior teeth are small in comparison to the mandibular anterior teeth—most likely due
to small maxillary laterals or large mandibular centrals. Either way, when midlines are
matched, canines intercuspate ideally, and the mandibular anterior teeth are ideally
aligned, spacing would be evident somewhere between the maxillary anterior teeth.
Now, considering the small posterior Bolton ratio in this case, one would see the
maxillary first and second premolars and first molars well aligned and in proximal
contact from the distal of the maxillary canine through the maxillary first molar. Yet,
there would be spacing somewhere between the mandibular posterior teeth.
The result of an ideal overall Bolton ratio with a large anterior and small posterior
ratio is a case with spacing in the maxillary anterior and mandibular posterior teeth. The
importance, then, of Bolton ratios seems to lie in the anterior segments and posterior
segments separately, not collectively as the overall ratio. Figure 2.1 is a diagram
illustrating three possible variations of a normal overall Bolton ratio.
10
Large anterior
Small posterior
Ideal overall
Ideal anterior
Ideal posterior
Ideal overall
Small anterior
Large posterior
Ideal overall
Figure 2.1- Ambiguity inherent in interpreting the overall Bolton ratio. Reduced tooth sizes exaggerated
for illustrative purposes. Darkened teeth reduced to 75% of original size. Sketch by present author.
Other researchers have acknowledged the posterior segment is a factor to
consider. While determining the ideal Bolton ratios for a Peruvian population, Bernabè
et al.10 noticed that the anterior segment was not significantly different from Bolton’s
sample but that the overall ratio was significantly different. They report that “the toothwidth discrepancy would be more of a concern in the posterior segment than in the
anterior” in his population.
An anterior ITSD is common. The prevalence of a clinically significant anterior
ITSD has been reported to range from 22 – 33.7% in the orthodontic population.3,4,11,12
Indeed, it has long been recognized that an anterior ITSD can adversely affect finishing a
case. The maxillary lateral incisors are recognized as one of the most widely varying
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teeth in terms of width in the entire dental arch. A lateral that is looks small in
comparison to the width of the central is usually the first suspect as the culprit
contributing to an ITSD. However, Sharma et al.13 have shown that the visual method of
screening for an ITSD has been shown to be unreliable.
Options for addressing an anterior ITSD include restorative build-ups or veneers
to increase the mesiodistal widths, or interproximal reduction of the incisors. Another
option is to leave diastema between the laterals and centrals or laterals and canines. It
may be assumed that similar options exist for cases with a posterior ITSD. Bulked
restorations or prostheses can increase the mesiodistal widths of teeth if necessary.
Interproximal reduction of enamel may reduce tooth mass if necessary. Alternately,
intentionally leaving a diastema is an option to treat a posterior ITSD.
Although the maxillary laterals are generally accepted as the cause of an anterior
ITSD, the lateral incisor actually takes second place in width variability. The maxillary
lateral incisors variability is preceded only by the mandibular second premolars, and
followed by maxillary second premolars, then mandibular central incisors. In fact, Smith
et al.14 report that these four groups of teeth account for half of the variation Bolton
analyses. But, how much ITSD is too much?
THE SIGNIFICANCE OF A TOOTH-SIZE DISCREPANCY
There seems to be no consensus as to what magnitude, whether statistical,
millimetric, or proportional, is clinically significant. Many epidemiological studies have
used 2 standard deviations, or “2-3 mm,” from the normal ratios as the cutoff to describe
a clinically significant proportion of patients within populations with a tooth size
discrepancy.11,15-17 While this may be appropriate for determining the prevalence of
12
populations with a large deviation from what is normal for that population, it says
nothing of the chairside clinical significance.
Ascribing clinical significance to a linear, millimetric measurement allows the
orthodontist to plan prior to treatment if restorative or operative measures may be
necessary, and to what degree, in order to finish the case with excellent occlusion. Proffit
et al.18 and Bernabè et al.10 claim that 1.5 mm of discrepancy is clinically significant.
Othman and Harradine,19 however, claim this amounts to 0.75 mm per side—possibly
“too small a potential error to be clinically significant.” They, Sharma et al.,13 and
Gaidyte and Baubiniene20 offer 2 mm (or 1 mm per side) as a tooth size discrepancy more
likely to cause occlusal problems. It is interesting to note that the American Board of
Orthodontics, though not directly, has weighed in on the matter by assessing one point for
interproximal spaces greater than 0.5 mm.21
Another method of designating clinical significance that has been proposed is to
consider any ratio outside of an acceptable range from the norm as significant. After all,
average tooth sizes vary from person to person. Therefore, a 1 mm discrepancy, for
example, may represent a larger issue for a person with generally small teeth than
someone with generally large teeth. Bolton4 recommends ± 1 standard deviation from the
values he reports as a point at which re-evaluation of clinical treatment is needed. Endo
et al.16 and Othman and Harradine19,22 recommend that an overall tooth-size discrepancy
greater than or equal to 2 standard deviations from the norm is the threshold for the
amount of discrepancy that is clinically significant enough to exhibit noticeable occlusal
compromise or require treatment.
13
Though consensus is lacking, studies generally recommend 2 SD from the norm
or 1.5 to 2 mm as a tooth size discrepancy significant enough to affect the occlusion and
merit treatment consideration.
THE GREAT DEBATE: TO EXTRACT OR NOT TO EXTRACT?
Historically, trends in treating an orthodontic malocclusion with or without
extractions have come full circle. The early pioneers of modern orthodontics, such as
Angle,1 believed that the human jaws were capable of housing all 32 teeth within the
arches. They expanded dental arches to fit teeth into ideal occlusal relationship,
believing that bone would follow based on Wolff’s Law.23
Angle’s contemporary, and most ardent opponent, Case, published articles and
participated in heated debates supporting extractions in orthodontic treatment.24 Among
the principle reasons for extractions included crowding relief and post-treatment stability.
Thus began the Great Debate of 1911 on extraction.25 Though posting a higher extraction
rate, even Case rarely extracted in comparison to the height of later extractionist’s
extraction rates.
Tweed, a respected pupil of Angle, followed his master’s non-extraction
philosophy until he came to terms with the fact that his best efforts were frustrated in
post-treatment retention. Citing Brodie’s research26 demonstrating the impossibility of
interstitial basal bone growth as well as his own patient’s lip fullness and bimaxillary
protrusion, Tweed attributed his cases’ failure to expansion’s tendency to cause
proclination of the mandibular incisors, leaving them unsupported and not upright over
basal bone. Rather than flaring incisors out, his solution was to extract premolar teeth
and use the space to keep the mandibular incisors upright over basal bone.27
14
In a classic story that changed orthodontic history and reversed the aversion to
premolar extraction, Tweed re-treated 100 of his previous “failures” at no charge with
premolar extractions and presented his work for all to see at the AAO convention.
Initially regarded as heresy,28 the extraction pendulum swung the other way, and
premolar extraction became the accepted norm.
According to Proffit,29 extraction rates at the orthodontic residency program at
UNC went from 30% of all cases in 1953 to 76% in 1968, then back down to 28% in
1993. Reasons for the decline in extraction rate after the Tweed years include improved
application and acceptance of functional and extra-oral appliances,30,31 bonded brackets
eliminate the thickness of bands,32 space preservation in the transitional dentition,33 as
well as general risk-and litigation reduction policies.34-36
Although modern extraction rates may not be as high as they once were,
Baumrind’s study37 indicates that when faced with crowding or dentoalveolar protrusion,
up to 2/3rd of current orthodontists agree upon extraction treatment. Baumrind’s followup study38 asking orthodontists why they chose to extract, the four most common reasons
for extracting teeth are: First, to reduce excessive crowding (49% of responses); Second,
to reduce incisor protrusion (14% of responses); Third, the need to correct the profile
(8% of responses; Fourth, due to Class II severity (5% of responses).
Many extraction patterns can address the above problems and are employed
depending on each patient’s initial diagnostic presentation. For Class II patients
requiring extractions, upper first and lower second premolar extractions can optimize
correction to Class I. Occasionally, molars are left in Class II and canines are corrected
to Class I by extracting upper first premolars only. For Class III patients, lower first
15
premolars can be extracted to camouflage the skeletal discrepancy and achieve Class I
canine relationship.
According to Proffit,29 first premolar extractions are the most common extraction
pattern orthodontists choose to correct excessive crowding, reduce protrusion, and to
eliminate or prevent adverse profile appearances.
Lopatiene39 has shown that ITSD do not show predilection to any one Angle
Classification over another. Therefore, given an ITSD, extraction decisions should not be
based on Angle Classification, but should be based on the ability to treat to maximum
ideal intercuspation. Bolton4 advocated for the selective extraction of teeth, not based on
biomechanical efficiency for treating a specific Class of malocclusion, but based on
satisfying ideal a ratios found from his studies so that ‘excellent’ anterior and overall
occlusion can result. In the ideal orthodontic world, teeth can be moved in any direction
without side-effects. Traditionally, extra-oral and intra-oral anchorage such as headgear
and elastics, and more recently, endosteal anchorage such as miniscrews have permitted
orthodontists to move teeth in any direction with less anchorage loss.
THE ROLE OF EXTRACTIONS IN A TOOTH-SIZE DISCREPANCY
Adding intrigue to Bolton’s claim that tooth size discrepancies affecting buccal
segment intercuspation may “lack clinical significance,” one of Bolton’s main
conclusions in his 1958 publication is the “need for considering premolar sizes on an
individual basis before the final decision is made in extraction cases.”3 He offers that the
first premolars are the teeth of choice to remove because their widths are most similar.
The second extraction pattern of choice is the maxillary first premolar and mandibular
second premolar. The least ideal extraction pattern is the second premolars. It can be
16
inferred from these claims that maintaining ‘excellent’ occlusion of posterior teeth is only
possible when similar sized teeth are extracted—the idea being that, given ideal tooth size
ratios, closing similar sized extraction sites on top and bottom will maintain the ideal
tooth-width ratios posterior to the extraction site and their potential for ideal occlusal
relationship.
Many investigators have attempted to reveal an ideal overall Bolton ratio of cases
treated with extractions. In his 1962 paper, Bolton4 reported that a premolar extraction
case removing equally sized premolars should result in an 89% overall ratio, while an
87% ratio should be expected in a case where extracted mandibular premolars were larger
than the maxillary premolars. In fact, using the average tooth widths from his thesis as
shown in Table 2.1, a four first premolar extraction case should result in an 89.67%
overall Bolton ratio. This range of predicted ideal overall ratios in premolar extraction
cases was derived by mathematical calculation that simply omits the average size of the
extracted premolars from the overall ratio equation. It has been shown that any premolar
extraction pattern results in a decreased post-treatment overall Bolton compared to the
pre-treatment overall ratio.40
Gaidyte & Baubiniene,20 grouped pre-treatment cases into small, normal, and
large overall Bolton categories, then simulated different premolar extraction patterns by
omitting that premolar’s width in the overall Bolton ratio measurement. This was done to
see which extraction pattern came closest to Bolton’s reported ideal 88% (average of
87% - 89%. They advocate that the best post-treatment results, judged by attaining an
overall Bolton ratio of 88%, is attained by extracting all first premolars or maxillary first
premolars and mandibular second premolars in small pre-treatment overall Bolton cases,
17
and all second premolars in normal and high pre-treatment Bolton cases. However, much
hangs on the assumption that 88% is the magic number that results in ideal occlusion and
that omitting premolar widths from the calculation will guarantee excellent occlusion.
Also, because they don’t report the anterior ratio one cannot interpret what the reported
overall Bolton ratio in this sample truly means.
Perhaps the most thorough and important study of the effect of premolar
extraction on the Bolton ratios was undertaken by Kayalioglu et al.5 They calculated
Bolton ratios of 53 post-treatment cases treated with four first premolar extractions and
good occlusion as judged by the Peer Assessment Review scores. They found that the
overall Bolton ratio should be 89.28% in a four first-premolar extraction case and
explained that this ratio is only achievable when the pre-treatment overall ratio was small.
This closely matches the ideal overall Bolton ratio of 89.67% for a four first premolar
extraction case deduced from the data in Bolton’s thesis.
An overarching major weakness of all of these studies is the lack of standardizing
the anterior Bolton ratios of cases included in these studies. It is unknown what factors
the anterior Bolton ratio played in the calculated pre-and post-simulation overall Bolton
ratios. Most of these studies simply omit a tooth measurement in calculating the overall
ratio and do not take into consideration the case’s actual finished quality. To reiterate,
just because an overall Bolton ratio is near the ‘ideal’ mean ratio doesn’t mean that
‘excellent’ occlusion is achieved. Excellent occlusion is most likely to be achieved with
both an ideal anterior ratio and ideal posterior ratio. None of these studies report a pretreatment posterior Bolton ratio for their sample.
18
While studying gender and racial differences in the Bolton ratio, Smith et al.14
reported that the posterior Bolton ratio for a non-extraction case ranges from 104% in
Caucasians to 107% in blacks. However, these describe population averages, not the
posterior ratio for cases with excellent occlusion.
One final study by Akinci and Uysal41 deserves mention. When evaluating cases
treated with non-extraction, two, or four premolar extractions according to the ABO
grading criteria,21 they noticed that four premolar extraction cases were assessed
significantly more points for compromised occlusal contacts and occlusal relationships
than non-extraction cases. The points assessed for compromised occlusion could be due
to an ITSD created by extracting teeth, and then forcing closed the spaces resulting from
the tooth-size discrepancy.
STATEMENT OF THESIS
The anterior and overall Bolton ratios and their clinical use are widely known.
However, the overall Bolton is not as informative as the individual anterior and posterior
Bolton ratios separately. Bolton did not report an ideal ratio for posterior teeth in nonextraction cases, nor did he report an ideal ratio for posterior teeth in extraction cases
even though he had the data to do so. Instead, he offered a predicted overall ratio for
cases with excellent occlusion based on the assumption that extracting teeth of similar
size would maintain excellent occlusion. Other studies used his predicted overall ratio
for extraction cases, possibly erroneously. Also, some of these studies did not ensure that
their sample was similar to Bolton’s sample by selecting cases whose anterior Bolton
ratios were within the range reported by Bolton to describe cases with ‘excellent’
occlusion.
19
Considering that extraction treatment is currently a viable treatment option and
first premolars are the most commonly extracted teeth, one should know the effect of a
treatment plan involving the extraction of first premolars on the posterior tooth ratio.
Employing a novel method utilizing digitized models that undergo virtual
extraction of the four first premolars and virtual setups into ‘excellent’ occlusion, this
study seeks to add to the existing literature related to the Bolton ratios by: First,
reporting a posterior Bolton ratio that can be expected for non-extraction cases with
excellent occlusion as described by Bolton’s ideal anterior and overall ratios; Second,
describing the effect of the extractions on the expected posterior Bolton ratio; Third,
describing the effect of the extractions on the observed posterior Bolton ratio through
performing digital setups with ‘excellent’ occlusion; Fourth, correlating discrepancies
between expected and observed posterior Bolton ratios to tooth size factors.
The results of this study can be used by orthodontists as follows: By simply
omitting the width of the first premolars, an orthodontist can calculate his expected posttreatment posterior Bolton ratio. Then, by comparing his expected post-treatment
posterior Bolton ratio to an ideal posterior Bolton ratio for first premolar extraction cases,
the orthodontist should be able to gauge whether an ITSD exists in the remaining
posterior dentition and judge its clinical significance.
This study will also show which teeth tend to have the greatest influence on the
post-extraction occlusion result. The orthodontist will be able to compare his patient’s
tooth widths and ratios to the ideal widths and ratios reported herein in order to help him
determine the effect of extracting four first premolars on his patient’s occlusion.
20
Armed with this diagnostic tool, the orthodontist can inform the patient of
potential compromises to the final occlusion or ability to close extraction spaces, alter
extraction patterns, plan for necessary interproximal reduction or restorative buildups, or
opt to leave interproximal spaces.
21
REFERENCES
1.
Angle EH. Classification of Malocclusion. The Dental Cosmos: a monthly record of
dental science. 1899;41(3):248-64.
2.
Andrews LF. The six keys to normal occlusion. Am J Orthod. 1972;62(3):296-309.
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Bolton WA. Disharmony In Tooth Size And Its Relation To The Analysis And
Treatment Of Malocclusion. Angle Orthod. 1958;28(3):113-30.
4.
Bolton WA. The clinical application of a tooth-size analysis. Am J Orthod.
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5.
Kayalioglu M, Toroglu MS, Uzel I. Tooth-size ratio for patients requiring 4 first
premolar extractions. Am J Orthod Dentofacial Orthop. 2005;128(1):78-86.
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Bonwill WG. The Scientific Articulation of the Human Teeth as Founded on
Geometrical, Mathematical, and Mechanical Laws. The Dental Cosmos: a monthly
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7.
Ballard ML. Asymmetry in Tooth Size: A Factor in the Etiology, Diagnosis and
Treatment of Malocclusion. Angle Orthod. 1944;14(3):67-70.
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Neff CW. Tailored occlusion with the anterior coefficient. Am J Orthod.
1949;35(4):309-13.
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Bolton WA. Disharmony in tooth size and its relation to the analysis and treatment of
malocclusion. Seatle, WA: University of Washington; 1952.
10. Bernabé E, Major PW, Flores-Mir C. Tooth-width ratio discrepancies in a sample of
Peruvian adolescents. Am J Orthod Dentofacial Orthop. 2004;125(3):361-5.
11. Freeman JE, Maskeroni AJ, Lorton L. Frequency of Bolton tooth-size discrepancies
among orthodontic patients. Am J Orthod Dentofacial Orthop. 1996;110(1):24-7.
12. Richardson ER, Malhotra SK. Mesiodistal crown dimension of the permanent
dentition of American Negroes. Am J Orthod. 1975;68(2):157-64.
13. Sharma R, Kumar S, Singla A. Prevalence of tooth size discrepancy among North
Indian orthodontic patients. Contemp Clin Dent. 2011;2(3):170-5.
14. Smith SS, Buschang PH, Watanabe E. Interarch tooth size relationships of 3
populations: “Does Bolton’s analysis apply?”. Am J Orthod Dentofacial Orthop.
2000;117(2):169-74.
15. Araujo E, Souki M. Bolton Anterior Tooth Size Discrepancies Among Different
Malocclusion Groups. Angle Orthod. 2003;73(3):307-13.
16. Crosby DR, Alexander CG. The occurrence of tooth size discrepancies among
different malocclusion groups. Am J Orthod Dentofacial Orthop. 1989;95(6):457-61.
17. Johe RS, Steinhart T, Sado N, Greenberg B, Jing S. Intermaxillary tooth-size
discrepancies in different sexes, malocclusion groups, and ethnicities. Am J Orthod
Dentofacial Orthop. 2010;138(5):599-607.
22
18. Proffit W, Ackerman J. Contemporary orthodontics. St Louis, MO: C.V. Mosby;
1986.
19. Othman S, Harradine N. Tooth Size Discrepancies in an Orthodontic Population.
Angle Orthod. 2007;77(4):668-74.
20. Gaidyte A, Baubiniene D. Influence of premolar extractions on tooth size
discrepancy. Part two: Analysis of Bolton values. Stomatologija. 2006;8(1):25-9.
21. Casko JS, Vaden JL, Kokich VG, Damone J, James RD, Cangialosi TJ, et al.
Objective grading system for dental casts and panoramic radiographs. Am J Orthod
Dentofacial Orthop. 1998;114(5):589-99.
22. Endo T, Uchikura K, Ishida K, Shundo I, Sakaeda K, Shimooka S. Thresholds for
Clinically Significant Tooth-Size Discrepancy. Angle Orthod. 2009;79(4):740-6.
23. Wolff J. The Law of bone remodelling: Berlin ; New York : Springer-Verlag,
c1986.; 1986.
24. Case CS. The question of extraction in orthodontia. Am J Orthod. 1911;50(9):66091.
25. Pollock HC. The extraction debate of 1911 by Case, Dewey, and Cryer. Am J
Orthod. 1964;50(9):656-8.
26. Brodie AG. Some recent observations on the growth of the face and their
implications to the orthodontist. Am J Orthod Oral Surg. 1940;26(8):741-57.
27. Tweed CH. Indications for the extraction of teeth in orthodontic procedure. Am J
Orthod Oral Surg. 1944;30(8):405-28.
28. Hellman M. Fundamental principles and expedient compromises in orthodontic
procedures. Am J Orthod. 1944;34(1):18-26.
29. Proffit WR. Forty-year review of extraction frequencies at a university orthodontic
clinic. Angle Orthod. 1994;64(6):407-14.
30. Fränkel R. The treatment of Class II, Division 1 malocclusion with functional
correctors. Am J Orthod. 1969;55(3):265-75.
31. Kloehn SJ. Guiding Alveolar Growth and Eruption of Teeth To Reduce Treatment
Time and Produce A More Balanced Denture and Face. Angle Orthod.
1947;17(1):10-33.
32. Oftedal B, Wisth J. Residual extraction sites after orthodontic treatment: Part 1. At
debanding1982 1982-02-01 00:00:00. 11-9 p.
33. Brennan MM, Gianelly AA. The use of the lingual arch in the mixed dentition to
resolve incisor crowding. Am J Orthod Dentofacial Orthop. 2000;117(1):81-5.
34. Machen DE. Orthodontic treatment and facial appearance. Am J Orthod Dentofacial
Orthop. 1991;99(2):185-6.
35. Perry CK, Jr. TMJ dysfunction litigation--Pandora's Box opens up. J Mich Dent
Assoc. 1988;70(11-12):533-8.
36. Wheeler PW. Risk preclusion. Am J Orthod Dentofacial Orthop. 1992;101(2):194-5.
23
37. Baumrind S, Korn EL, Boyd RL, Maxwell R. The decision to extract: Part 1—
Interclinician agreement. Am J Orthod Dentofacial Orthop. 1996;109(3):297-309.
38. Baumrind S, Korn EL, Boyd RL, Maxwell R. The decision to extract: Part II.
Analysis of clinicians' stated reasons for extraction. Am J Orthod Dentofacial
Orthop. 1996;109(4):393-402.
39. Lopatiene K, Dumbravaite A. Relationship between tooth size discrepancies and
malocclusion. Stomatologija. 2009;11(4):119-24.
40. Tong H, Chen D, Xu L, Liu P. The effect of premolar extractions on tooth size
discrepancies. Angle Orthod. 2004;74(4):508-11.
41. Akinci Cansunar H, Uysal T. Comparison of orthodontic treatment outcomes in
nonextraction, 2 maxillary premolar extraction, and 4 premolar extraction protocols
with the American Board of Orthodontics objective grading system. Am J Orthod
Dentofacial Orthop. 2014;145(5):595-602.
24
CHAPTER 3: JOURNAL ARTICLE
ABSTRACT
Introduction: The anterior and overall Bolton ratios and their clinical use are
widely known, but a normal overall Bolton ratio may be comprised of compensating
interarch tooth size discrepancies between the anterior and posterior teeth. Therefore, the
anterior and posterior Bolton ratios may be more useful separately. No ideal posterior
ratio is reported in the literature. As four first premolars are the most commonly
extracted teeth in orthodontics, it may be important to know how the posterior occlusion
could be affected when they are extracted. The aim of this study is to investigate how the
posterior Bolton ratio is affected by extracting four first premolars. Methods: Bolton’s
sample was matched by selecting 55 Class I occlusion cases within one standard
deviation of ideal anterior and overall Bolton ratios. Models were digitized, and tooth
widths measured. Models underwent virtual extraction of four first premolars and setup
of anterior and remaining posterior teeth in ideal occlusion. Where space closure
compromised occlusion, preference was given to occlusion. Ideal setups were measured
for residual interproximal spacing. ANOVA and linear regression tests were used to
identify factors contributing to interproximal spacing. Results: The ideal non-extraction
posterior Bolton ratio is 105.77 +/- 1.99%. The ideal expected posterior Bolton ratio for
four first premolar extraction cases is 107.29 +/- 2.23%. Cases finished with an average
of 1.1 mm net residual spacing between mandibular second premolars and first molars.
27% of cases finish with at least 1.5 mm of residual space and 16% of cases finish with at
least 2 mm of residual space. The ratio of the upper second premolars to the lower
second premolars and the width of the upper second premolars best explain residual
25
space (R = 0.554, R square = 0.307). A regression equation for predicting residual space
is offered. Conclusion: A case with ideal anterior, posterior, and overall Bolton ratios
treated with four first premolar extractions and ideal occlusion will likely finish with
some spacing in the mandible. Closing spaces may compromise the occlusion. The best
occlusion results when the maxillary second premolars are small in relation to the lower
second premolars.
26
INTRODUCTION
Like the ratio describing the ideal distances between fence posts versus distances
between fence post holes that result in excellent post and post-hole alignment, Bolton’s1
anterior and overall ratios describe tooth proportions that result in “excellent occlusion.”
Many factors contribute to ideal dental occlusion. Angle2 and Andrews,3 cite the
relative molar positions as “keys” to occlusion. Other major factors influencing dental
occlusion include rotations, tip, torque, the occlusal plane, and interdental spacing.3
Interdental spacing is one manifestation of an interarch tooth size discrepancy (ITSD), or
“Bolton discrepancy.”
While acknowledging the pioneering work accomplished by Ballard4 and Neff,5
Dr. Wayne A. Bolton developed the Bolton tooth-size discrepancy analysis as a
diagnostic tool to be employed to help identify potential limitations in detailing and
finishing a patient’s final occlusion before as much as one bracket is placed.6 Comparing
Bolton’s ideal ratios and the ratios describing a patient’s dentition could indicate whether
teeth are too large, too small, or just right for proper intercuspation, and whether
treatment aimed at reducing the discrepancy may be warranted to improve the occlusion.
Bolton attributes clinical significance to a discrepancy more than one standard
deviation away from his reported ideal ratios.6 The American Board of Orthodontists
Cast-Radiograph Examination assesses points for any spaces greater than 0.5 mm.7
Others recommend that 1.5 to 2 mm is the threshold for clinical significance.8-12 With
this knowledge, the orthodontist is able to recognize an ITSD, inform the patient, and
plan for restorative build-ups or selective interproximal reduction of appropriate teeth at
the pre-treatment consultation.
27
Bolton’s landmark thesis study from 1952,13 later published in 1958,1 included a
sample of models from 55 patients with ‘excellent’ occlusion. Using ratios of lower teeth
to upper teeth, ‘excellent’ occlusion can be described as having an anterior ratio of 77.2%
and an overall ratio of 91.3%. The overall ratio is comprised of the anterior and the
posterior teeth. It is important to note that an anterior tooth size discrepancy may be
masked by a compensating posterior tooth size discrepancy, resulting in a normal overall
tooth size ratio. As the sum of its parts, the overall ratio may be less important than the
anterior and posterior tooth size ratios individually. However, little is known about the
posterior Bolton ratio, how it is affected by extracting posterior teeth, and its application
in the orthodontic setting.
According to Proffit,14 nearly 28% of current orthodontic patients undergo
extractions. Orthodontists often agree on the need to utilize extraction treatment.15
Reasons for prescribing extractions as part of orthodontic treatment include the need to
reduce excessive crowding and incisor protrusion, the need to correct the profile, and to
correct a Class II malocclusion.16 Extracting teeth may alter the excellent occlusal
relationship found in a full complement of teeth as described by Bolton’s ratios. Bolton
predicted a new expected overall ratio resulting from the extraction of four premolars by
omitting the average widths of the first premolars.6 He predicted that the new overall
ratio should be between 87-89% based on average premolar tooth widths. Many
investigators have used 88% as the ideal overall ratio based on this predicted range.
Curiously, the data from his thesis13 shows that the ideal overall Bolton ratio for a four
first premolar extraction case should be 89.67%.
28
Regardless, Bolton’s predicted ratio was based on mathematical calculation that
simply omits the average widths of extracted teeth, but does not take into consideration
the articulation of the cusps, fossae, and marginal ridges of the remaining teeth as did his
original sample. For accuracy, any newly described ratios for extraction cases should be
calculated in the same way that the original anterior and overall ratios were calculated
from Bolton’s non-extraction cases—that is, from cases which undergo premolar
extraction and result in excellent finished occlusion.
A recent study by Kayalioglu et al.17 measured 53 post-treatment models from
cases treated with four first premolar extractions that resulted in good occlusion and
reported a new ideal overall ratio, 89.28 ± 1.07%, based on this sample. With no
reported knowledge of the data included in Bolton’s thesis, the newly reported ideal
overall ratio was strikingly similar to the ideal overall ratio one would expect to find
(89.67%) if four first premolars were extracted in Bolton’s cases.13 However, the
difference is statistically different from the 88% overall ratio predicted by Bolton for
premolar extraction cases. This may indicate that many studies using Bolton’s predicted
value of 87-89% for cases treated with premolar extraction may have made erroneous
assumptions and/or conclusions about the occlusal consequences of different premolar
extraction patterns.
Employing a novel method utilizing digitized models subject to virtual extraction
of the four first premolars and virtual setups into ‘excellent’ occlusion, this study seeks to
add to the existing literature related to the Bolton ratios by: First, reporting a posterior
Bolton ratio that can be expected for non-extraction cases with excellent occlusion as
described by Bolton’s ideal anterior and overall ratios; Second, describing the effect of
29
the extractions on the expected posterior Bolton ratio; Third, describing the effect of the
extractions on the observed posterior Bolton ratio through performing digital setups with
‘excellent’ occlusion; Fourth, correlating discrepancies between expected and observed
posterior Bolton ratios to various combinations of tooth widths, proportions, and
differences.
MATERIALS AND METHODS
Sample
This is a retrospective study approved by the Institutional Review Board at Saint
Louis University. The sample was obtained from archived physical models from patients
who had completed orthodontic treatment at the Center for Advanced Dental Education at
Saint Louis University. In an attempt to match Bolton’s sample, after all screening and
inclusion criteria were met, a final sample of 55 cases within 1 standard deviation of
Bolton’s reported ideal anterior and overall ratios were used in this study.
The preliminary inclusion criteria for the physical models were:
1. Full set of permanent dentition from first molar to contralateral first-molar.
2. Post-treatment case with good Class I occlusion.
3. No obvious signs of interproximal alteration such as restorations or stripping.
Physical models passing the preliminary screening were subject to the manual
screening phase of the process. The manual phase of screening physical models for
inclusion was performed by:
1. Measuring individual maxillary and mandibular tooth widths using an electronic
digital caliper, rounded to the nearest 0.05 mm. Teeth were measured at the widest
point parallel to the central groove or incisal edge when viewed from the occlusal.
30
2. Performing an anterior and overall Bolton Analysis.
3. Physical models were included in the sample a when the anterior and overall Bolton
ratios were found to be within 1 standard deviation of Bolton’s reported ideal values.
Physical models passing the manual screening were subject to the digital phase of
the screening process. The physical models were scanned using a 3D scanner (R700,
3Shape A/S, Copenhagen, Denmark) and OrthoAnalyser (3Shape A/S) software was used
for digital processing. The digital phase of screening physical models for inclusion was
performed by:
1. Calibrating the scanner prior to each scanning session.
2. Scanning the physical maxillary arch, mandibular arch, articulated models, and then
adding a digital base and creating a digital STL file for the model.
3. Measuring individual maxillary and mandibular tooth widths and delineating the
clinical crown margin using the “Preparation” function of the software. Teeth were
measured at the widest point parallel to the central groove or incisal edge when
viewed from the occlusal and rounded to the nearest 0.01 mm (Figure 3.1). The tooth
width data found in the “Analysis” tab (Fig 3.1) was then entered into a Microsoft
Excel® 2010 spreadsheet.
4. Digital models were included in the final sample when the anterior and overall Bolton
ratios were found to be within 1 standard deviation of Bolton’s reported ideal values.
31
Figure 3.1- Measuring the mesiodistal widths and defining the clinical crown margin of each tooth.
32
Models passing the digital screening were subject to the virtual treatment phase of
the process using the “VirtualSetup” function of the software. The virtual treatment
process included:
1. Adding a new setup, titled, “Ideal 3-3” in the list of setups. The collision detection
threshold was set to 0 mm under the “Miscellaneous” tab of the “Move Teeth”
function. The maxillary and mandibular anterior 3-3 teeth were moved into ideal
anterior relationship, meaning coincident midlines, excellent alignment and coupling,
and Class I canine position (Figure 3.2). The setup was renamed, “Ideal 3-3” setup.
33
34
Figure 3.2- “Ideal 3-3" digital setup.
2. Creating an “Ideal 4’s” setup by renaming a copy of the “Ideal 3-3” setup. Using the
“Extraction” function, the four first premolars were extracted. In the “Move Teeth”
function, the contact tolerance threshold was set to 0 mm under the “Miscellaneous”
tab. The Virtual Setup treatment objectives for “Ideal 4’s” setup were to achieve
Andrew’s six keys of occlusion3—tip, torque, rotation, flat curve of Spee, no spaces,
and Class I molar position. Maxillary molars were rotated so that a ray drawn from
the maxillary first molar’s distobuccal cusp tip passes through the mesiolingual cusp
tip and contralateral canine. Also, the buccolingual inclinations of maxillary
posterior teeth were set so that the transverse occlusal plane was flattened. The
process of “Ideal 4’s” setup involved moving teeth posterior to the extraction sites
mesially to be in proximal and occlusal contact in the following sequential order:
mandibular second premolars, maxillary second premolars, maxillary first molars,
and finally mandibular first molars. If complete space closure was not possible
without compromising Class I ideal cusp-fossa or cusp-marginal ridge occlusal
relationships as described by Ash18 then the final tooth position was determined by
ideal occlusal intercuspation in preference over space closure. For example, if the
mandibular or maxillary first molar was found to be lacking ideal occlusal
intercuspation with all proximal spaces closed, then the appropriate tooth was moved
distally until ideal occlusal intercuspation was achieved. See Figure 3.3 for the
occlusion scheme used for the digital setups and Figure 3.4 for an example of an
“Ideal 4’s” digital setup.
35
Ideal cusp-marginal ridge or cusp-fossa
relationship.
Figure modified from Ash, M. Wheeler’s
Dental Anatomy. 8th Ed. Pg. 456, Fig. 16-36.18
Schematic of ideal occlusal contacts. Molars
are rotated so that a ray drawn from the
maxillary first molar’s distobuccal cusp tip
passes through the mesiolingual cusp tip and
contralateral canine.
Figure modified from Ash, M. Wheeler’s
Dental Anatomy. 8th Ed. Pg. 463,
Fig 16-29.18
Transverse occlusal plane flattened.
Figure 3.3- Occlusion schemes for digital setups.
36
37
Figure 3.4- Example "Ideal 4's" digital setup.
3. The “Ideal 4’s” setup was exported as a model and saved.
Maxillary and Mandibular residual spaces (MaxResSpc and MandResSpc) were
measured in the “Ideal 4’s” model by measuring the gap between the two teeth parallel to
the alveolar ridge when viewed from the occlusal using the “Digital Calipers” option in
the “Measurements” pop-up menu from the “Inspection” tools (see figure 3.5 for an
example of mandibular residual space measurement).
Figure 3.5- Example of measuring residual space in the mandibular arch.
All measurements including individual maxillary and mandibular anterior and
posterior tooth widths, interproximal spaces, and various combinations of tooth widths,
proportions, and differences were recorded in a Microsoft Excel® 2010 spreadsheet for
analysis. Appendix A contains a list of abbreviated variables, their definitions, and the
formulas used to derive them.
38
Statistical Analysis
The data recorded in Microsoft Excel® 2010 was exported into IBM SPSS
Statistics 23.0 (SPSS Inc., Chicago, Illinois). The alpha level for all statistical tests was
set at 0.05.
To test for the accuracy of the screening process in matching the experimental
sample to Bolton’s original sample,13 an independent T-test was performed comparing
the anterior Bolton ratio, overall Bolton ratio, and individual posterior tooth widths
between samples. The null hypothesis was that the there was no difference between the
anterior ratio, overall ratio, and individual posterior tooth widths.
Descriptive and frequency statistics were calculated for data in the sample. Data
described, which has not been previously reported include: First, the non-extraction
posterior Bolton ratio (reported as PostBolt), the overall Bolton ratio and posterior Bolton
ratios that could be expected based on a mathematical calculation that omits the widths of
the extracted first premolars (reported as ExpOB and ExpPB, respectively); Second, the
overall Bolton ratio and posterior Bolton ratios observed after four first premolar
extractions and setting the teeth in ideal occlusion (reported as NetOB and NetPB,
respectively).
Paired t-tests were employed to test the null hypothesis that: First, the width of
the individual premolars in the upper arch are not different than the width of the
corresponding premolars in the lower arch; Second, the overall and posterior Bolton
ratios are not altered by extracting teeth; Third, the Bolton ratios determined by
mathematical omission of first premolar widths are not different from Bolton ratios
observed as determined by ideal occlusion after extracting four first premolars.
39
Correlation and regression was used to determine the relationship between the
amount of residual space (NetResSpc) and the discrepancy between the posterior Bolton
ratio determined by mathematical omission of the widths of the first premolars (ExpPB)
and the posterior Bolton ratio observed when ideal occlusion is achieved in preference
over complete space closure (NetPB).
In an attempt to reduce the numerous variables describing tooth widths,
proportions, and differences in each case (see Appendix A) and isolate only those which
may most affect the amount of observed residual spaces after extractions and setups in
ideal occlusion, one-way analysis of variance was performed. Cases were grouped
according to the amount of residual spaces identified (NetResSpc) after the extractions
and setup in ideal occlusion. Two variations of net residual space groupings were used.
The first variant was cases with net residual space below 1.0 mm, and cases with
1.0 mm or more of net residual space, called NRS2Grps. This grouping scheme was
chosen because it is close to the mean and nearly splits the sample into two equal groups.
The second NetResSpc grouping variant was cases with net residual space below
0.75 mm, from 0.75 mm to 1.49 mm, and 1.5 mm and above, called NRS3Grps. This
grouping scheme was chosen because some authors8,9 have suggested that the upper
group’s limit, 1.5 mm, is the threshold for a clinically significant Bolton discrepancy and
because the groups included generally similar numbers of cases. For each case,
numerous factors, or variables, of tooth widths, proportions, and differences were
recorded as listed in Appendix A. The average for each factor within a group was
compared to the averages of that factor within other groups to test the null hypothesis that
the averages of the variables are the same for all groups of net residual space.
40
Multiple (backward stepwise) regression analysis of factors deemed significant
from each the NRS2Grp and NRS3Grp ANOVA tests was used to isolate variables with
the greatest predictive power of the residual spaces.
From these tests, a regression equation was derived that could be used to predict
the amount of the residual space (NetResSpc) remaining in a four first premolar
extraction case treated to ideal occlusion.
Reliability
All manual and digital measurements as well as virtual setups were performed by
the same investigator. Six of the 55 cases were randomly selected using a number
generator (random.org) to assess the intra-examiner reliability. Using OrthoAnalyser
software, the six cases were digitally re-measured with the “Preparation” function and
new setups from 3-3 and 6-6 with extraction of the four first premolars were performed
as described previously. The new models were labeled “Validity Ideal 4’s”. Cronbach’s
alpha set at a level of 0.8 was used to determine the measurement reliability.
RESULTS
Cronbach’s alpha test for intra-examiner reliability between original and repeated
measurements was above 0.8 for all variables except the NRS2Grp variable (Cronbach’s
alpha = 0.76), showing that, generally, the process for obtaining original measurements
and repeated measurements were acceptably reliable for accuracy.
The anterior Bolton ratio and overall Bolton ratio for this sample was
77.23 ± 0.93% and 91.75 ± 0.97%, respectively. Individual tooth widths for the
maxillary first premolar, second premolar, and first molar , respectively, was
7.07 ± 0.48 mm, 6.88 ± 0.46 mm, and 10.42 ± 0.54 mm. Individual tooth widths for the
41
mandibular first premolar, second premolar, and first molar was
7.22 ± 0.46 mm, 7.35 ± 0.51 mm, and 11.20 ± 0.63 mm, respectively. Table 3.1 shows
the descriptive statistics for the anterior Bolton ratio, overall Bolton ratio, and individual
posterior tooth widths from this study’s sample and Bolton’s13 original sample.
Independent t-tests comparing the mean ratios and individual tooth sizes from these
samples do not differ significantly. Therefore, the null hypothesis that the tooth widths
and ratios in the present study’s sample and Bolton’s sample do not differ is not rejected.
Table 3.1- Comparison of Bolton's original thesis sample and this study’s sample.
Anterior Ratio
Overall Ratio
Posterior Ratio
U4
U5
U6
L4
L5
L6
Bolton’s Original Sample
Mean
SD
N
77.20%
1.65
55
91.30%
1.91
55
105.27% a
55
7.04 mm
0.46
110
6.84 mm
0.39
110
10.40 mm
0.58
110
7.15 mm
0.38
110
7.27 mm
0.39
110
11.14 mm
0.62
110
Experimental Sample
Mean
SD
N
77.23%
0.93
55
91.75%
0.97
55
105.77%
1.99
55
7.07 mm
0.48
110
6.88 mm
0.46
110
10.42 mm
0.54
110
7.22 mm
0.46
110
7.35 mm
0.51
110
11.20 mm
0.63
110
P-value
0.904
0.125
0.592
0.499
0.792
0.243
0.174
0.463
a Not reported by Bolton. Calculated from the average individual tooth widths reported in Bolton's original thesis. 13
When comparing widths of corresponding posterior teeth between the upper and
lower arch (for example, upper first premolars versus lower first premolars), paired t-tests
confirm that the widths corresponding teeth are significantly different (See Table 3.2).
Therefore, the null hypothesis that corresponding tooth widths do not differ is rejected.
Table 3.2- Paired t-test comparing widths of corresponding upper and lower posterior teeth.
Paired Samples Test (2-tailed)
U4sWidth - L4sWidth
U5sWidth - L5sWidth
U6sWidth - L6sWidth
Mean Diff
-0.29
-0.95
-1.56
SD
0.49
0.48
0.59
SEM
0.07
0.06
0.08
Widths include left and right sides.
42
Low
-0.42
-1.08
-1.72
Up
-0.15
-0.82
-1.40
t
-4.31
-14.67
-19.74
df
54
54
54
P=
0.000
0.000
0.000
For non-extraction cases, the ideal posterior Bolton ratio is 105.77% ± 1.99 SD.
For four first premolar extraction cases, the expected posterior Bolton ratio is
107.29% ± 2.23 SD and the observed posterior Bolton ratio is 110.48% ± 3.12 SD. The
discrepancy between the expected and observed Bolton ratios for four first premolar
extractions is 3.18% ± 2.59 SD. After extracting four first premolars and setting
posterior teeth in ideal occlusion, an average of 0.04 mm of space was found between the
maxillary posterior teeth (MaxResSpc), 1.16 mm of space was found between the
mandibular teeth (MandResSpc), leaving 1.11 mm of net residual space (NetResSpc) in
the mandible. Table 3.3 shows the various ratios derived and spaces measured from this
study’s sample.
Table 3.3- Ratios and measurements describing non-extraction and four first premolar extraction cases.
Descriptive Statistics
1 Anterior Ratio (%)
Overall Ratio (%)
Posterior Ratio (%)
Mean
77.23
91.75
105.77
SD
0.93
0.97
1.99
N
55
55
55
Range
3.10
3.69
8.15
2 Exp Anterior Ratio (%)
Exp Overall Ratio (%)
Exp Posterior Ratio (%)
3 Max Residual Space (mm)
Mand Residual Space (mm)
Net Residual Space (mm)
Net Post Bolton Discrep (%)
Net Posterior Ratio (%)
Net Overall Ratio (%)
77.23
89.97
107.29
0.04
1.16
1.11
3.18
110.48
91.33
0.93
0.97
2.23
0.19
0.86
0.92
2.59
3.12
1.32
55
55
55
55
55
55
55
55
55
3.10
4.49
8.55
1.13
3.55
4.30
12.06
12.73
5.29
Minimum Maximum
75.58
78.69
89.44
93.13
102.02
110.17
75.58
87.70
103.31
0.00
0.00
-0.75
-2.25
104.15
88.59
78.69
92.19
111.86
1.13
3.55
3.55
9.80
116.88
93.88
1.Non-extraction
2.As calculated by omitting width of extracted first premolars.
3.As observed when four first premolars are extracted and teeth digitally set in ideal occlusion.
Comparison of non-extraction Bolton ratios with expected and observed
extraction Bolton ratios, as shown in Table 3.4 section 1, reveals that the pairs differ
significantly. Therefore, the null hypothesis that the non-extraction, expected, and
43
observed ratios do not differ is rejected. Table 3.4 section 2 shows that expected and
observed Bolton ratios also differ significantly.
Table 3.4- Comparison of non-extraction and extraction Bolton ratios as well as expected and observed
Bolton ratios.
Paired Samples Test (2-tailed)
Mean
Difference
1.78
1 OvrlBolt - ExpOB
0.42
OvrlBolt- NetOB
-1.52
PostBolt - ExpPB
-4.71
PostBolt - NetPB
-1.36
2 ExpOB - NetOB
-3.18
ExpPB - NetPB
SD
SEM
Low
Up
t
df
P<
0.50
1.26
1.15
2.90
1.09
2.59
0.07
0.17
0.16
0.39
0.15
0.35
1.65
0.08
-1.83
-5.49
-1.66
-3.88
1.92
0.76
-1.21
-3.92
-1.07
-2.48
26.45
2.48
-9.81
-12.06
-9.25
-9.12
54
54
54
54
54
54
0.0001
0.016
0.0001
0.0001
0.0001
0.0001
1. Comparison of non-extraction ratios and extraction ratios
2. Comparison of extraction ratios between what is expected by mathematics and what is observed after setups.
Results show an extremely strong positive relationship between the net residual
space and the net posterior Bolton discrepancy. The correlation is 0.997 and R-squared is
0.994. The slope of the regression equation is 2.80% and the constant is 0.06%.
Figure 3.6 shows a scatterplot graph of each case’s net residual space and net posterior
discrepancy along with the regression equation.
44
Relationship Between Residual Space and the
Posterior Bolton Discrepancy
Net Posterior Bolton Discrepancy (%)
12.0
10.0
y = 2.80x + 0.059
R² = 0.994
8.0
6.0
4.0
2.0
0.0
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
-2.0
-4.0
Net Residual Space (mm)
Figure 3.6- Scatterplot of NetResSpc and NetPBDiscrep for each case with the regression line and
equation.
The residual spacing, whether present in the maxillary arch, mandibular arch, or
both, was observed almost exclusively between the second premolar and first molar.
Residual spacing in this study’s sample was observed in 54 of 55 cases. Only one case
finished with no spacing in either the maxillary or mandibular arches. Although
extremely infrequent, three of 55 cases finished with spacing in the maxilla. The average
maxillary spacing for the sample was 0.04 mm. The majority (52 of 55, or 94.5%) of
cases finished with 0 mm of or more spacing in the mandibular arch to the amount of
1.16 mm on average.
When grouping the cases according to the amount of net residual space, 15 cases
(27.3%) had less than 0.5 mm, and 40 cases (72.7%) had 0.5 mm or more of net spacing.
26 cases (47.3%) had less than 1 mm, and 29 cases (52.7%) of cases had 1 mm or more
45
of net spacing. 15 cases (27.3%) had 1.5 mm of spacing or more. Nine cases (16.4%) had
at least 2 mm of residual spacing, and three cases (5.45%) had at least 3mm of net
residual spacing. Figure 3.7 shows the frequency of cases with different amounts of net
residual space.
Frequency of Cases by NetResSpace
60
3
9
50
15
29
Number of Cases
40
40
30
52
52
46
20
40
26
10
15
0
NRS ≥
NRS <
3
0 mm
52
3
0.5 mm
40
15
1 mm
29
26
1.5 mm
15
40
2 mm
9
46
3 mm
3
52
Figure 3.7- Frequency of cases grouped by net residual space.
The next question to be answered was which factors or variables, if any, may
contribute to finishing a four first premolar extraction case with residual space when teeth
are set in ideal occlusion? One-way analysis of variance (ANOVA) was used to
determine if, in some cases, the observed residual spacing could be “filled in” with extra
tooth mass in the mandibular posterior. Cases were divided into groups based on the size
46
of the net residual space (NRS2Grp and NRS3Grp) and tested for differences within nonextraction (PostBolt) and expected posterior Bolton ratios (ExpPB). There were no
significant differences. Therefore, the null hypothesis that the mean for non-extraction
and expected posterior Bolton ratios is the same for all groups of net residual space is not
rejected.
Various combinations of tooth widths, their proportions, and their differences
were next evaluated using one-way ANOVA in an attempt to isolate factors which may
contribute to or reduce net residual spacing. In the NRS2Grp ANOVA, significant
differences within variables exist between the two groups. Five factors with significant
differences were found. Therefore, the null hypothesis that the means of the factors is the
same for all groups of net residual space is rejected. The factors with different means
include the difference in width between the lower second premolar and upper second
premolar (L5minU5), the upper second premolar width as a fraction of the lower second
premolar width (U5vsL5), the upper second premolar as a fraction of the upper posterior
tooth widths (U5PerU456), the lower second premolar as a fraction of the upper posterior
tooth widths (L5PerU456), and the upper second premolar as a fraction of the lower
posterior tooth widths (U5PerL456). See Appendix B for the NRS2Grp ANOVA output
from SPSS.
The NRS3Grp ANOVA test reveals that significant differences within four
variables exist between the three groups. Therefore, the null hypothesis that the means of
the factors is the same for all groups of net residual space is rejected. The four variables
with significant differences include the upper second premolar width (U5sWidth), the
difference in size between the lower second premolar and upper second premolar
47
(L5minU5), the upper second premolar width as a fraction of the lower second premolar
width (U5vsL5), and the upper second premolar as a fraction of the lower posterior
segment (U5PerL456). See Appendix C for the NRS3Grp ANOVA output from SPSS.
When comparing the means of variables from cases in the smaller net residual
space group to those in the larger net residual space group, it is evident that the
U5sWidth, U5vsL5, U5PerU456, and U5PerL456 averages are smaller and the L5minU5
and L5PerU456 averages are greater. Refer to Appendix B and C for the SPSS output for
the ANOVA tests.
All six of the above-mentioned variables were entered into a multiple linear
regression analysis, and it was found that R was 0.586, and R square was 0.343, and the
null hypothesis that there is no significant linear correlation is rejected (See Appendix D
for SPSS output of the regression analysis). Backward linear regression revealed that two
of the six variables were deemed to significantly affect the variability in the observed net
residual space. Again, the null hypothesis that there is no significant linear correlation is
rejected. Excluding the other variables from the regression equation was statistically
deemed to not alter the R square. The two variables with significant correlation were the
proportion of upper second premolars to lower second premolars (U5vsL5) and the upper
second premolars’ width (U5sWidth). Both variables combined for a correlation (R) of
0.554 and a regression (R square) amounting to 0.307. See Appendix E for the SPSS
output of the backward regression for all significant variables from the NRS2Grp and
NRS3Grp ANOVA tests). Individually, the respective R and R square for U5vsL5 was
0.474 and 0.224, and 0.337 and 0.142 for U5sWidth (see Appendix F). Table 3.5 shows
a summary of the R and R square values as well as the regression equation from the
48
multiple, backward, and individual regression analyses for predicting the net residual
space in a given case.
Table 3.5- Linear regression of variables explaining variation in net residual space.
Linear Regression of Variables from ANOVA Contributing to Net Residual Space
Model
R
R
Squared
Adj R
Squared
Regression Equation for Predicting NetResSpc
1
0.586
0.343
0.261
139.18(a) + 0.59(b) - 4.06(c) - 621.33(d) + 589.86(e) - 13.08(f) - 132.54
2
0.554
0.307
0.281
12.43(a) + 0.29(b) - 14.56
3
0.474
0.224
0.210
14.18(a) -12.16
4
0.377
0.142
0.126
0.376(b) - 4.06
1 Multiple reg of six sig factors: U5vsL5 (a), U5sWidth (b), L5minU5 (c), U5PerU456 (d), L5PerU456 (e), U5PerL456 (f)
2 Backward regression results: U5vsL5 (a), U5sWidth (b)
3 Individual regression for U5vsL5 (a)
4 Individual regression for U5sWidth (b)
DISCUSSION
Interpretation of Results
As the anterior ratio, posterior ratio, nor individual tooth widths from this study’s
sample were not found to be significantly different from Bolton’s original sample (see
Table 3.1), it can be inferred that this sample matched Bolton’s sample very closely. This
attests to the accuracy of the two-step screening process utilized in obtaining the sample
for this study.
Table 3.2 and the significance of the statistical test indicate a high confidence that
corresponding maxillary and mandibular tooth sizes are not the same. First premolars
have the least difference in linear width while first molars have the greatest difference in
linear width. The lower posterior teeth are wider than the corresponding upper teeth.
Therefore, maintaining the ideal pre-treatment posterior ratio, and occlusion, may be
impossible to maintain after extracting four corresponding teeth (four first premolars,
four second premolars, or four first molars).
49
The overall Bolton ratio decreases from 91.75% in ideal non-extraction cases to
an expected 89.97% after omitting the width of the four first premolars from the overall
Bolton ratio equation. Even if premolars were equally sized, the expected overall Bolton
is smaller than the non-extraction overall Bolton because the extracted upper premolar is
just a small proportion of all of the top teeth compared with the extracted lower premolar,
which is a larger proportion of all of the bottom teeth. The result is a greater reduction in
the numerator and a smaller reduction in the denominator of the equation for the overall
Bolton ratio. The same reason can explain the reduction from the non-extraction overall
Bolton ratio to the overall Bolton ratio observed when teeth are set to ideal occlusion
(91.33%).
However, when comparing the non-extraction ideal posterior Bolton ratio
(105.77%) and the posterior Bolton ratio expected by omitting the widths of the first four
premolars (107.29%), it is evident that extracting four first premolars increases the
posterior Bolton ratio. Likewise, the posterior Bolton ratio observed when teeth are set in
ideal occlusion (110.48%) is also increased compared to the non-extraction ideal
posterior Bolton ratio. Lower second premolars and first molars are larger than the
corresponding upper premolars and molars. Even if the first premolars were similar in
size, after being extracted the size discrepancy between the remaining upper and lower
second premolars and first molars results in a smaller proportional reduction of the
numerator and greater proportional reduction of the denominator of the equation for the
posterior Bolton ratio.
It is noted, however, that the expected and observed Bolton ratios are not
equivalent (see Table 3.4). The discrepancy between the expected and observed ratios
50
(1.36% for overall ratios and 3.18% for posterior ratios) is due to an average of 1.11 mm
of net residual spacing between the mandibular second premolar and first molar after
performing digital setups in ideal occlusion (see Table 3.3). Regression analysis (see
Figure 3.6) shows with an extremely strong positive relationship that each millimeter of
net residual space accounts for a posterior Bolton discrepancy between the expected and
the observed posterior Bolton ratios amounting to 2.8%. At 0 mm of spacing, the net
posterior Bolton discrepancy is effectively 0% and the expected posterior Bolton ratio
matches the observed posterior Bolton ratio.
When considering the frequency at which net residual spacing or net posterior
Bolton discrepancy is observed in these cases after setup, results in Figure 3.6 can be
interpreted to mean that the majority of cases finished by prioritizing ideal occlusion will
have least some space remaining between mandibular second premolars and first molars.
The chart also shows that a large portion of these cases will finish with potentially large
amounts of residual space. Therefore, many cases with ideal pre-treatment Bolton ratios
undergoing four first premolar extractions cannot finish with ideal occlusion as well as
complete space closure of mandibular extraction sites. The clinical tradeoff between
treating to ideal occlusion versus complete space closure will be covered in greater detail
in a later section.
It should be noted, however, that some cases treated to ideal occlusion after
extracting four first premolars finish closer to achieving complete space closure and more
closely match the expected posterior Bolton ratio than other cases as is evident by the
regression line in table 3.5. The regression line shows that some cases finished with less
net residual spacing and less discrepancy between its expected and observed posterior
51
Bolton ratios than other cases. One-way ANOVA tests of NRS2Grp and NRS3Grp
reveal that cases with larger pre-treatment or expected posterior Bolton ratios do not
appear to finish with less net residual spacing. This is unexpected as one would presume
that wider-than-normal mandibular teeth would occupy the net residual spaces in the
mandible.
Further ANOVA tests of NSR2Grp and NRS3Grp (Appendix B and C) reveal six
unique factors, or variables, that appear to be different depending on the amount of net
residual space. The six factors are all related to the width of the second premolars.
Generally, when the upper premolars are small or the lower premolars are large, the
residual spacing after ideal setups is reduced.
Table 3.5 is a summary of the results of regression analysis of the variables found
to be significant from the above-mentioned ANOVA tests. All six factors together show
a strong positive correlation with net residual spacing in the mandible, but when adjusting
for the number of variables considered and the size of the sample, the adjusted R square
falls off. Some of the variables in the group may not be very good predictors of net
residual space, even though they were found to be statistically significant by ANOVA.
Backward regression narrowed the six variables down to only two: the proportion of the
upper second premolars width versus the lower second premolars with (U5vsL5) and the
linear width of the upper second premolars (U5sWidth). Although the correlation and
regression coefficients are slightly lower, the adjusted R squared is higher, indicating that
the two variables may be better predictors of net residual space than all six variables
combined. Individually, the fraction of upper second premolars width versus lower
52
second premolars width (U5vsL5) is the strongest predictor of net residual space,
followed by the width of the upper second premolars (U5sWidth).
Present Outcomes and Past Studies
This study is the first of its kind to report an ideal posterior Bolton ratio by
matching its sample within one standard deviation of Bolton’s reported ideal anterior and
overall ratios derived from 55 non-extraction cases with ‘excellent’ occlusion.1 The ideal
posterior Bolton ratio calculated from average posterior tooth widths obtained from
Wayne A. Bolton’s original thesis13 was found to be 105.27%. Although arguably more
useful than the overall ratio when used in conjunction with the anterior ratio, Bolton
never explicitly reported this posterior ratio in his thesis or in the literature he published.
Smith et al.19 reported that the posterior Bolton ratio for his sample ranged from 104 –
107% while evaluating whether Bolton’s ratios could be applied equally to all genders
and ethnicities. This range fits nicely around the ideal posterior Bolton ratio for nonextraction cases derived from this study, which is 105.77 ± 1.99%.
Numerous past studies have investigated the effect of premolar extractions on the
Bolton ratios, but only report the effect of extractions on the overall ratio.6,11,17,20-22
Generally, these studies calculate the expected overall ratio by omitting the widths of the
four premolars to be extracted from the overall Bolton ratio equation. From this study,
the expected overall ratio derived by omitting the widths of the extracted four first
premolars is 89.97 ± 0.97%. This is larger than the 87-89% overall ratio that Bolton6
predicted and closer to the 89.28% ratio that Kayalioglu et al.17 derived from a sample of
53 post-treatment models of patients treated with four first premolars finished in ideal
occlusion. Bolton’s thesis13 data, had it been published, reveals an ideal expected overall
53
ratio of 89.67% which is between the 89.28% ratio from the study by Kayalioglu et al.
and the 89.79% ratio from the present study. In spite of the clinical similarity between
the present study and Kayalioglu et al., an independent t-test comparing the mean overall
Bolton ratios reveals that the two means are statistically different. The smaller ratio that
they report could be partially explained by the fact that their study’s inclusion criteria did
not require that the cases in their sample match Bolton’s pre-treatment ideal anterior and
posterior ratios within one standard deviation as was the case in the present study. In
fact, they report that the overall Bolton ratio from the pre-treatment models were
90.61 ± 1.08%, which is smaller than Bolton’s ideal overall ratio.
The present study is the first to investigate and describe how the posterior Bolton
ratio changes with the extraction of four first premolars. The present study used the
mathematical methodology employed in past studies investigating the effect of
extractions on the overall Bolton ratio, but applied to the posterior teeth. That is, the
widths of the four first premolars were omitted from the equation used to derive the
expected posterior Bolton ratio for four first premolar extraction cases. The expected
posterior Bolton ratio for four first premolar extraction cases is 107.29 ± 2.99%.
Unlike past studies, this study acknowledges that extracting teeth in the maxillary
arch of different widths than those in the mandibular arch may derange the potentially
ideal pre-treatment occlusion as defined by ideal anterior, posterior, and overall Bolton
ratios and recognizes the importance of performing setups in ideal occlusion to identify
ideal post-extraction ratios. This study is also the first to investigate and describe the
posterior Bolton ratio when four first premolars are extracted and the remaining posterior
teeth are finished with preference given to ideal occlusion rather than complete space
54
closure. The observed posterior Bolton ratio (NetPB) was 110.48 ± 3.12% when
interproximal spaces remaining after ideal setups were included in the equation for
calculating the posterior Bolton ratio.
The 3.18% Bolton discrepancy between the expected and observed posterior
Bolton ratios and 1.11 mm of net residual space in the mandible could be explained in at
least three ways. First, as is shown in this study, the size differences between extracted
maxillary and mandibular teeth as well as other differences between remaining teeth
seem to account for at least a portion of the discrepancy. Another possibility is that
‘excellent’ occlusion could have been defined differently between Bolton and the present
study’s author. The present study’s author focused on finishing each tooth with ideal
cusp-fossa and cusp-marginal ridge relationship, and standardizing molar rotation as well
as buccolingual inclination of each posterior tooth. Bolton may have focused, more
generally, on Class I molar and canine positions. It is uncertain how the differences in
defining ‘excellent’ occlusion may affect the ratios. Lastly, it is possible that although
non-extraction cases with excellent occlusion are found to have an anterior ratio of
77.2%, an overall ratio of 91.3%, and a posterior ratio of 105.77%, pre-treatment cases
with those ideal ratios do not necessarily have ideal occlusion due to variations in crown
morphology. Using this study’s sample and performing setups to simulate non-extraction
treatment resulting in ideal occlusion would be one way to improve upon this study.
Comparing the residual spaces in the non-extraction group to the residual spaces from
this study would make it more directly possible to isolate the effect of extracting four first
premolars on the posterior Bolton ratio and validate or refute Bolton’s ideal ratios
describing ‘excellent’ occlusion.
55
If the discrepancy between expected and observed posterior Bolton ratios
represents an interarch tooth size discrepancy (ITSD), then the frequency at which the
ITSD occurs in this sample needs to be considered. The sample had, on average,
0.04 mm of spacing between the maxillary second premolar and first molar and 1.16 mm
of spacing between the mandibular second premolar and first molar. When the average
spaces were closed in the maxillary arch and the average mandibular space were reduced
correspondingly, 1.11 mm of net space remains in the mandibular arch between the
second premolar and first molar (or 0.555 mm per side). As the most aggressive estimate
of a clinically significant ITSD in the literature8,9 is 1.5 mm total (or 0.75 mm per side) it
would appear that the ITSD in this sample as a whole is generally not considered
clinically significant.
However, the incidence of a clinically significant ITSD in this sample is not to be
dismissed. In this study’s sample of 55 cases, 15 (27.3%) had at least 1.5 mm spacing—a
level that some authorities deem to be at least borderline clinically significant.3,4 Nine
cases (16.4%) had at least 2 mm—a level that has been described as clinically significant
by several authors.8-12 Three cases had at least 3 mm of net residual spacing.
The American Board of Orthodontics currently assesses one point for each
0.5 mm of interproximal space discovered in a case.7 Therefore, roughly half of the
finished cases from this sample would have two points assessed on the ABO castradiograph examination for finishing with an average of 1.11 mm of spacing after
extracting four first premolars and finishing with preference given to ideal occlusion.
The other half of the cases would be assessed less than two points because they finished
with less residual spacing in ideal occlusion.
56
Conversely, it appears that a no-win situation exists because leaving spaces is not
ideal, but on the contrary, completely closing spaces can compromise the occlusion.
Akinci and Uysal’s study23 provides evidence for this idea. They noticed that four
premolar extraction cases were assessed significantly more points on the ABO
examination for compromised occlusal contacts and occlusal relationships than nonextraction cases. The points assessed for compromised occlusion could be due to an ITSD
created by extracting teeth, and then forcing closed the spaces resulting from the toothsize discrepancy. More on the clinical significance of closing net residual space is
discussed in the next section.
This study was also the first to investigate which tooth widths, differences, and
proportions have the greatest role in finishing with less residual spacing in ideal
occlusion. In these cases, expected and observed posterior Bolton ratios matched more
closely. The proportion of the widths of the upper second premolars compared to the
widths of the lower second premolars (U5vsL5) has the greatest influence on finishing
with ideal occlusion while maximizing space closure. The next most influential factor is
simply the width of the upper second premolars. Together, they account for 30% of the
variation in residual spacing.
Clinical Significance and Implications
The interpretation of a normal overall Bolton ratio is ambiguous. A case found to
have an ITSD in the anterior but normal overall ratio means that the posterior teeth
compensated for the discrepancy in the anterior teeth. It is possible that the
compensation is significant enough to cause occlusal discrepancies in the posterior,
resulting in an anterior and posterior ITSD in spite of a normal overall ratio. A more
57
direct interpretation and more clinically useful application may be attained from knowing
and applying the ideal anterior and posterior ratios to a case separately. As no ideal
posterior Bolton ratio has been reported in the literature against which to check a case for
a posterior ITSD, the results of this study are immediately of use to the orthodontist.
Orthodontists may use 105.77% ± 1.99 SD as the ideal non-extraction posterior
Bolton ratio against which to compare their patients’ posterior Bolton ratio prior to
commencing treatment in order to anticipate if an ITSD may prevent their case from
finishing with ideal occlusion.
Two in three orthodontists agree whether a case should be treated with
extractions, and currently 28% of all orthodontic cases undergo extractions.14-16 As the
four first premolars are reportedly8 the most commonly chosen extraction patterns,
knowing the ideal posterior ratio for four first premolar extraction cases could help an
orthodontist foresee a potential posterior ITSD in their patient’s case. Also the ability to
convert this posterior ITSD percentage into an actual linear, millimetric size discrepancy
could help an orthodontist plan and execute appropriate corrective measures that could
enable him to finish the posterior occlusion as close as possible to ideal.
For a case with pre-treatment ideal anterior, posterior, and overall Bolton ratios,
an orthodontist should expect the posterior Bolton ratio to be 107.29% after extracting
four first premolars. However, should be aware that, based on the sample from this
study, his case has a roughly 50% chance of finishing with 1.1 mm of spacing bilaterally,
a 27% chance of finishing with 1.5 mm of spacing bilaterally, and 16% chance of
finishing with 2 mm of spacing bilaterally between mandibular second premolars and
first molars if ideal occlusion is given preference over complete space closure.
58
Conversely, if complete space closure of any net residual spacing between the
lower second premolar and first molar is given preference over maintaining ideal
occlusion, then a spectrum of occlusal outcomes exist with two potential extremes. On
one end of the spectrum, a case could finish with the canines in ideal Class I occlusion,
while the mandibular first molars would be moved mesially into the residual spacing
toward Class III molar relationship. On the other end of the spectrum, a case could finish
with the molars in ideal Class I occlusion, while the mandibular canine and second
premolar would be moved distally into the residual spacing toward Class II relationship.
Both possible outcomes could also have numerous adverse effect of varying severity
including, but not limited to opening the bite, accelerating occlusal wear, or interfering
with anterior guidance.
Figure 3.8 shows the digital setup illustrating both extreme occlusal outcomes on
the same model. This supports findings by Akinci and Uysal23 showing that cases treated
with four premolar extractions were assessed significantly more points than nonextraction cases on the ABO exam due to compromised occlusal contacts and occlusal
relationships. The patient’s right side shows Class I canine and premolar relationship
with mesial movement of the lower first molars toward Class III. The patient’s left side
shows Class I molar relationship with distal movement of the lower canine and second
premolars toward Class II relationship as explained above. The occlusal markings show
non-ideal contacts on the right molars and left canine and second premolars which could
indicate areas of potentially accelerated tooth wear or occlusal interferences that could
open the bite and/or alter anterior guidance.
59
60
Figure 3.8- Two scenarios resulting from prioritizing space closure over ideal occlusion
Surprisingly, cases with a larger than ideal expected posterior Bolton ratio were
not shown to finish with less interproximal spacing. Therefore, it may be advised to wait
to perform interproximal reduction or buildup of proximal surfaces with the aim to alter
the posterior Bolton ratio until treatment is nearing the finish and pending occlusal
relationships can be assessed chairside.
Or, given a case with an ideal expected posterior Bolton ratio, an orthodontist
could use the regression equation in Figure 3.9 to help predict, with some caution, the
amount of residual spacing present in the case at finish and then decide if interproximal
reduction or buildups are indicated:
𝐍𝐞𝐭 𝐑𝐞𝐬𝐢𝐝𝐮𝐚𝐥 𝐒𝐩𝐚𝐜𝐞 = 𝟏𝟐. 𝟒𝟑(
𝐔𝟓𝐬 𝐖𝐢𝐝𝐭𝐡
) + 𝟎. 𝟐𝟗(𝐔𝟓𝐬 𝐖𝐢𝐝𝐭𝐡) − 𝟏𝟒. 𝟓𝟔
𝐋𝟓𝐬 𝐖𝐢𝐝𝐭𝐡
Figure 3.9- Regression equation for predicting residual space. Predictive power is 0.307.
A positive number indicates spacing in the mandible and a negative number
indicates spacing in the maxilla. If the residual space predicted by the regression
equation is deemed insignificant, then it may be possible to proceed with the treatment
plan to extract four first premolars as usual without any additional treatment
considerations. However, if the residual space is deemed clinically excessive, then
interproximal reductions, buildups, or even an alternate extraction pattern may be
indicated. If interproximal reduction is indicated, it is most likely indicated in the
maxillary arch between the second premolars and first molars. If buildups or an overcontoured restoration are indicated, it is most likely needed in the mandibular arch
between the second premolars and first molars.
61
CONCLUSION
Based on the results obtained from this study showing the effect of four first
premolar extractions on the posterior Bolton ratio, one can conclude that in a case with
pre-treatment ideal anterior and overall Bolton ratios:
1. The non-extraction ideal posterior Bolton ratio is 105.77 ± 1.99%.
2. The expected ideal posterior Bolton ratio is 107.29 ± 2.23% for these cases
treated with four first premolar extractions. However, this is a not a good
predictor of ‘excellent’ post-treatment final occlusion.
3. Cases that undergo four first premolar extractions and are finished with
preference given to occlusion over complete space closure have an average of
0.04 mm of residual spacing in the maxillary arch, 1.16 mm in the mandibular
arch, resulting in 1.11 mm (0.55 mm each side) of net residual spacing
between the mandibular second premolar and first molars.
4. 27% of cases may finish with at least 1.5 mm (0.75 mm each side) of residual
space, and 16% of cases may finish with at least 2 mm (1 mm each side) of
residual space.
5. In cases with a clinically significant posterior interarch tooth-size discrepancy,
interproximal reduction, a bulked restoration, or alternative extraction pattern
should be considered. Alternately, opting to completely close the residual
space may compromise the finished occlusion and occlusal relationships.
6. Cases with small maxillary second premolars tend to finish with less
interproximal spacing. A regression equation is offered to assist in predicting
potential residual space for a given case and aid in treatment plan decisions.
62
LITERATURE CITED
1.
Bolton WA. Disharmony In Tooth Size And Its Relation To The Analysis And
Treatment Of Malocclusion. Angle Orthod. 1958;28(3):113-30.
2.
Angle EH. Classification of Malocclusion. The Dental Cosmos: a monthly record of
dental science. 1899;41(3):248-64.
3.
Andrews LF. The six keys to normal occlusion. Am J Orthod. 1972;62(3):296-309.
4.
Ballard ML. Asymmetry in Tooth Size: A Factor in the Etiology, Diagnosis and
Treatment of Malocclusion. Angle Orthod. 1944;14(3):67-70.
5.
Neff CW. Tailored occlusion with the anterior coefficient. Am J Orthod.
1949;35(4):309-13.
6.
Bolton WA. The clinical application of a tooth-size analysis. Am J Orthod.
1962;48(7):504-29.
7.
Casko JS, Vaden JL, Kokich VG, Damone J, James RD, Cangialosi TJ, et al.
Objective grading system for dental casts and panoramic radiographs. Am J Orthod
Dentofacial Orthop. 1998;114(5):589-99.
8.
Proffit W, Ackerman J. Contemporary orthodontics. St Louis, MO: C.V. Mosby;
1986.
9.
Bernabé E, Major PW, Flores-Mir C. Tooth-width ratio discrepancies in a sample of
Peruvian adolescents. Am J Orthod Dentofacial Orthop. 2004;125(3):361-5.
10. Othman S, Harradine N. Tooth Size Discrepancies in an Orthodontic Population.
Angle Orthod. 2007;77(4):668-74.
11. Gaidyte A, Baubiniene D. Influence of premolar extractions on tooth size
discrepancy. Part two: Analysis of Bolton values. Stomatologija. 2006;8(1):25-9.
12. Sharma R, Kumar S, Singla A. Prevalence of tooth size discrepancy among North
Indian orthodontic patients. Contemp Clin Dent. 2011;2(3):170-5.
13. Bolton WA. Disharmony in tooth size and its relation to the analysis and treatment of
malocclusion. Seatle, WA: University of Washington; 1952.
14. Proffit WR. Forty-year review of extraction frequencies at a university orthodontic
clinic. Angle Orthod. 1994;64(6):407-14.
15. Baumrind S, Korn EL, Boyd RL, Maxwell R. The decision to extract: Part 1—
Interclinician agreement. Am J Orthod Dentofacial Orthop. 1996;109(3):297-309.
16. Baumrind S, Korn EL, Boyd RL, Maxwell R. The decision to extract: Part II.
Analysis of clinicians' stated reasons for extraction. Am J Orthod Dentofacial
Orthop. 1996;109(4):393-402.
17. Kayalioglu M, Toroglu MS, Uzel I. Tooth-size ratio for patients requiring 4 first
premolar extractions. Am J Orthod Dentofacial Orthop. 2005;128(1):78-86.
18. Ash MM N, SJ. Wheeler's Dental Anatomy, Physiology, and Occlusion. 8th ed.
Philadelphia: W.B. Saunders; 2003. 520 p.
63
19. Smith SS, Buschang PH, Watanabe E. Interarch tooth size relationships of 3
populations: “Does Bolton’s analysis apply?”. Am J Orthod Dentofacial Orthop.
2000;117(2):169-74.
20. Tong H, Chen D, Xu L, Liu P. The effect of premolar extractions on tooth size
discrepancies. Angle Orthod. 2004;74(4):508-11.
21. Endo T, Ishida K, Shundo I, Sakaeda K, Shimooka S. Effects of premolar extractions
on Bolton overall ratios and tooth-size discrepancies in a Japanese orthodontic
population. Am J Orthod Dentofacial Orthop. 2010;137(4):508-14.
22. Saatçi P, Yukay F. The effect of premolar extractions on tooth-size discrepancy. Am
J Orthod Dentofacial Orthop. 1997;111(4):428-34.
23. Akinci Cansunar H, Uysal T. Comparison of orthodontic treatment outcomes in
nonextraction, 2 maxillary premolar extraction, and 4 premolar extraction protocols
with the American Board of Orthodontics objective grading system. Am J Orthod
Dentofacial Orthop. 2014;145(5):595-602.
64
APPENDIX A
Table A- List of Abbreviations
Differences, fractions, and measurements obtained from study sample
1
AntMand
2
AntMax
3
HalfL4s
4
HalfL5s
5
HalfL6s
6
HalfU4s
7
HalfU5s
8
HalfU6s
9
L4minU4
10
L4PerL456
11
L4PerU456
12
L4sWidth
13
L4vsU4
14
L5minU5
15
L5PerL456
16
L5PerL56
17
L5PerU456
18
L5PerU56
19
L5sWidth
20
L5vsU5
21
L6minU6
22
L6PerL456
23
L6PerL56
24
L6PerU456
25
L6PerU56
26
L6sWidth
27
L6vsU6
Anterior mandibular width: Sum of mandibular centrals, laterals, canines
L1s + L2s + L3s
Anterior maxillary width: Sum of maxillary centrals, laterals, canines
U1s + U2s + U3s
Half of the lower 4s width: Average width of a mandibular first premolar
L4s Width / 2
Half of the lower 5s width: Average width of a mandibular second premolar
L5s Width / 2
Half of the lower 6s width: Average width of a mandibular first molar
L6s Width / 2
Half of the upper 4s width: Average width of a maxillary first premolar
U4s Width / 2
Half of the upper 5s width: Average width of a maxillary second premolar
U5s Width / 2
Half of the upper 6s width: Average width of a maxillary first molar
U6sWidth / 2
Lower 4s minus upper 4s: The size difference between the premolars
L4sWidth - U4sWidth
Lower 4s width as a fraction of the Lower 4s, 5s, and 6s
L4sWidth / L4s + L5s + L6s widths
Lower 4s width as a fraction of the Upper 4s, 5s, and 6s
L4sWidth / U4s + U5s + U6s widths
Lower 4s width: Sum widths of both mandibular first premolars
Left L4 + Right L4
Lower 4s width versus Upper 4s width: Ratio of corresponding premolars
L4sWidth / U4sWidth
Lower 5s minus Upper 5s: The size difference between the premolars
L5sWidth - U5sWidth
Lower 5s width as a fraction of the Lower 4s, 5s, and 6s
L5sWidth / L4s + L5s + L6s widths
Lower 5s width as a fraction of the Lower 5s, and 6s
L5sWidth / L5s + L6s widths
Lower 5s width as a fraction of the Upper 4s, 5s, and 6s
L5sWidth / U4s + U5s + U6s widths
Lower 5s width as a fraction of the Upper 5s, and 6s
L5sWidth / U5s + U6s widths
Lower 5s width: Sum widths of both mandibular second premolars
Left L5 + Right L5
Lower 5s width versus Lower 5s width: Ratio of corresponding premolars
L5sWidth / U5sWidth
Lower 6s minus Upper 6s: The size difference between the premolars
L6sWidth - U6sWidth
Lower 6s width as a fraction of the Lower 4s, 5s, and 6s
L6sWidth / L4s + L5s + L6s widths
Lower 6s width as a fraction of the Lower 5s, and 6s
L6sWidth / L5s + L6s widths
Lower 6s width as a fraction of the Upper 4s, 5s, and 6s
L6sWidth / U4s + U5s + U6s widths
Lower 6s width as a fraction of the Upper 5s, and 6s
L6sWidth / U5s + U6s widths
Lower 6s width: Sum widths of both mandibular first molars
Left L6 + Right L6
Lower 6s width versus Lower 6s width: Ratio of corresponding premolars
L6sWidth / U6sWidth
65
28
OvrlMand
29
OvrlMax
30
PostMand
31
PostMax
32
U4PerL456
33
U4PerU456
34
U4sWidth
35
U4vsL4
36
U5PerL456
37
U5PerL56
38
U5PerU456
39
U5PerU56
40
U5sWidth
41
U5vsL5
42
U6PerL456
43
U6PerL56
44
U6PerU456
45
U6PerU56
46
U6sWidth
47
U6vsL6
Overall mandibular width: Sum of mandibular anterior and posterior teeth
L1s + L2s + L3s + L4s + L5s + L6s
Overall maxillary width: Sum of maxillary anterior and posterior teeth
U1s + U2s + U3s + U4s + U5s + U6s
Posterior mandibular width: Sum of mandibular first premolar, second premolar, and first molar
L4s + L5s + L6s
Posterior maxillary width: Sum of maxillary first premolar, second premolar, and first molar
U4s + U5s + U6s
Upper 4s width as a fraction of the Lower 4s, 5s, and 6s
U4sWidth / L4s + L5s + L6s widths
Upper 4s width as a fraction of the Upper 4s, 5s, and 6s
U4sWidth / U4s + U5s + U6s widths
Upper 4s width: Sum widths of both maxillary first premolars
Left U4 + Right U4
Upper 4s width versus Lower 4s width: Ratio of corresponding premolars
U4sWidth / L4sWidth
Upper 5s width as a fraction of the Lower 4s, 5s, and 6s
U5sWidth / L4s + L5s + L6s widths
Upper 5s width as a fraction of the Lower 5s, and 6s
U5sWidth / L5s + L6s widths
Upper 5s width as a fraction of the Upper 4s, 5s, and 6s
U5sWidth / U4s + U5s + U6s widths
Upper 5s width as a fraction of the Upper 5s, and 6s
U5sWidth / U5s + U6s widths
Upper 5s width: Sum widths of both maxillary second premolars
Left U5 + Right U5
Upper 5s width versus Lower 5s width: Ratio of corresponding premolars
U5sWidth / L5sWidth
Upper 6s width as a fraction of the Lower 4s, 5s, and 6s
U6sWidth / L4s + L5s + L6s widths
Upper 6s width as a fraction of the Lower 5s, and 6s
U6sWidth / L5s + L6s widths
Upper 6s width as a fraction of the Upper 4s, 5s, and 6s
U6sWidth / U4s + U5s + U6s widths
Upper 6s width as a fraction of the Upper 5s, and 6s
U6sWidth / U5s + U6s widths
Upper 6s width: Sum widths of both maxillary first molars
Left U6 + Right U6
Upper 6s width versus Lower 6s width: Ratio of corresponding premolars
U6sWidth / L6sWidth
Expected: Calculated by omitting first premolar widths
48 ExpAB
49 ExpMand
50 ExpMax
51 ExpOB
52 ExpPB
Anterior Bolton ratio
AntBolt
Expected mandibular posterior: Width of remaining mandibular posterior teeth
PostMand - L4sWidth
Expected maxillary posterior: Width of remaining maxillary posterior teeth
PostMax - U4sWidth
Expected overall Bolton ratio: Expected overall Bolton ratio after omitting first premolar widths
(AntMand + PostMand - L4sWidth / AntMax + PostMand - U4sWidth) x 100
Expected posterior Bolton ratio: Expected posterior Bolton ratio after omitting first premolar widths
(PostMand - L4sWidth / PostMand - U4sWidth) x 100
Non-extraction: Ideal ratios for permanent dentition from first molar to first molar
53 AntBolt
54 OvrlBolt
55 PostBolt
Anterior Bolton ratio
(AntMand / AntMax) x 100
Overall Bolton ratio
(AntMand + PostMand / AntMax + PostMax) x 100
Posterior Bolton ratio
(PostMand / AntMax) x 100
66
Observed: Four first premolar extractions and setup in ideal occlusion
56 MandResSpc
57 MaxResSpc
58 NetOB
59 NetPB
60 NetPBDisc
61 NetPMand
62 NetPMax
63 NetResSpc
64 NRS2Grp
65 NRS3Grp
Mandibular residual space: Spacing between mandibular teeth
Directly measured from mandibular digital model
Maxillary residual space: Spacing between maxillary teeth
Directly measured from maxillary digital model
Net Overall Bolton Ratio: Observed overall Bolton ratio
AntMand + NetPMand / AntMax + NetPMax
Net Posteiror Bolton Ratio: Observed posterior Bolton ratio
NetPMand / NetPMax
Net Posterior Bolton Discrepancy: The difference between expected and observed posterior Bolton ratios
NetPB - ExpPB
Net posterior mandibular width: Widths of mandibular posterior teeth and residual spaces
ExpMand + MandResSpc
Net posterior maxillary width: Widths of maxillary posterior teeth and residual spaces
ExpMax + MaxResSpc
Net residual space: The difference between maxillary and mandibular residual space
MandResSpc - MaxResSpc
Net residual space in two groups
Group "0", NetResSpc < 1 mm
Group "1", NetResSpc ≥ 1 mm
Net residual space in three groups
Group "0", NetResSpce < 0.75mm
Group "1", NetResSpc is from 0.75mm to < 1.5mm
Group "2", NetResSpc ≥ 1.5mm
Segment method: Not used in this study
66 PSegMand
67 PSegMax
68 SegOB
69 SegPDisc
70 SegPostB
Posterior Segment Mandible: Length of posterior segment in the mandible
Sum of direct measurements of right and left distance between distal of L3 to distal of L6
Posterior Segment Maxilla: Length of posterior segment in the maxilla
Sum of direct measurements of right and left distance between distal of U3 to distal of U6
Segment Overall Bolton Ratio:
AntMand + PSegMand / AntMax + PSegMax
Segment Posterior Bolton Discrepancy: The difference between expected and segment posterior ratios
SegPostB - ExpPB
Segment Posterior Bolton Ratio: Posterior segment Bolton ratio
PSegMand / PSegMax
67
APPENDIX B
Table B- Significant variable from NRS2Grp ANOVA. Output modified from SPSS.
Descriptives
N
L5minU5
U5vsL5
U5PerU456
L5PerU456
U5PerL456
Mean
Minimum
Maximum
26
1.1819
0.4478
0.0878
1.0011
1.3628
.130
2.010
1
29
0.7369
0.4077
0.0757
0.5818
0.8920
.050
1.500
Total
55
0.9473
0.4789
0.0646
0.8178
1.0767
.050
2.010
0
26
0.9206
0.0279
0.0055
0.9093
0.9319
.873
.990
1
29
0.9501
0.0265
0.0049
0.9401
0.9602
.904
.996
Total
55
0.9362
0.0308
0.0041
0.9279
0.9445
.873
.996
0
26
0.2800
0.0082
0.0016
0.2767
0.2833
.266
.298
1
29
0.2841
0.0063
0.0012
0.2817
0.2865
.274
.298
Total
55
0.2821
0.0075
0.0010
0.2801
0.2842
.266
.298
0
26
0.3043
0.0092
0.0018
0.3005
0.3080
.278
.319
1
29
0.2992
0.0088
0.0016
0.2958
0.3025
.285
.317
Total
55
0.3016
0.0093
0.0013
0.2991
0.3041
.278
.319
0
26
0.2641
0.0099
0.0019
0.2601
0.2681
.246
.286
1
29
0.2695
0.0086
0.0016
0.2662
0.2728
.253
.289
Total
55
0.2669
0.0096
0.0013
0.2643
0.2695
.246
.289
Between Groups
Within Groups
U5PerU456
L5PerU456
U5PerL456
Mean
Square
2.715
1
2.715
.182
9.667
53
12.382
54
Between Groups
.012
1
.012
Within Groups
.039
53
.001
Total
.051
54
Between Groups
.000
1
.000
Within Groups
.003
53
.000
Total
.003
54
Between Groups
.000
1
.000
Within Groups
.004
53
.000
Total
.005
54
Between Groups
.000
1
.000
Within Groups
.005
53
.000
Total
.005
54
Total
U5vsL5
Std. Error
0
ANOVA
Sum of
Squares
df
L5minU5
Std.
Deviation
95% Confidence
Interval for Mean
Lower
Upper
Bound
Bound
F
Sig.
14.886
.000
16.191
.000
4.413
.040
4.395
.041
4.703
.035
68
APPENDIX C
Table C- Significant variables from NRS3Grp ANOVA. Output modified from SPSS
Descriptives
95% Confidence
Interval for Mean
N
U5sWidth
0
1
2
Total
L5minU5
0
1
2
Total
U5vsL5
0
1
2
Total
U5PerL456
0
1
2
Total
Mean
Std.
Deviation
Std.
Error
Lower
Bound
Upper
Bound
Minimum
19
13.401
0.769
0.176
13.030
13.771
12.260
15.580
21
13.761
1.008
0.220
13.303
14.220
11.850
16.100
15
14.207
0.824
0.213
13.751
14.663
12.260
15.290
55
13.758
0.922
0.124
13.509
14.008
11.850
16.100
19
1.084
0.425
0.098
0.879
1.289
.130
1.870
21
1.059
0.432
0.094
0.862
1.256
.460
2.010
15
0.618
0.475
0.123
0.355
0.881
.050
1.500
55
0.947
0.479
0.065
0.818
1.077
.050
2.010
19
0.926
0.029
0.007
0.912
0.939
.873
.990
21
0.929
0.025
0.006
0.918
0.941
.878
.967
15
0.959
0.030
0.008
0.942
0.976
.904
.996
55
0.936
0.031
0.004
0.928
0.944
.873
.996
19
0.265
0.011
0.003
0.260
0.270
.246
.286
21
0.265
0.007
0.002
0.262
0.268
.253
.276
15
0.272
0.009
0.002
0.267
0.277
.256
.289
55
0.267
0.010
0.001
0.264
0.270
.246
.289
ANOVA
U5sWidth
L5minU5
U5vsL5
U5PerL456
Between
Groups
Within
Groups
Total
Between
Groups
Within
Groups
Total
Between
Groups
Within
Groups
Total
Between
Groups
Within
Groups
Total
Maximum
Sum of
Squares
df
Mean
Square
F
Sig.
5.457
2
2.728
3.507
.037
40.455
52
.778
45.912
54
2.242
2
1.121
5.749
.006
10.140
52
.195
12.382
54
.011
2
.005
7.072
.002
.040
52
.001
.051
54
.001
2
.000
3.652
.033
.004
52
.000
.005
54
69
Multiple Comparisons
Tukey HSD
Mean
Difference (IJ)
Dependent Variable
U5sWidth
95% Confidence Interval
Lower Bound
Upper Bound
1
-.360902
.279272
.4059
-1.03467
.31287
2
*
-.806807
.304650
.0283
-1.54180
-.07181
0
.360902
.279272
.4059
-.31287
1.03467
2
-.445905
.298181
.3014
-1.16529
.27348
0
*
.806807
.304650
.0283
.07181
1.54180
1
.445905
.298181
.3014
-.27348
1.16529
1
.024637
.139816
.9830
-.31268
.36196
2
*
.465684
.152522
.0098
.09771
.83366
0
-.024637
.139816
.9830
-.36196
.31268
2
.441048*
.149283
.0128
.08089
.80121
0
-.465684*
.152522
.0098
-.83366
-.09771
1
-.441048*
.149283
.0128
-.80121
-.08089
1
-.003662
.008801
.9091
-.02490
.01757
2
-.033379*
.009601
.0029
-.05654
-.01022
0
.003662
.008801
.9091
-.01757
.02490
2
*
.009397
.0072
-.05239
-.00705
*
.009601
.0029
.01022
.05654
1
*
.029716
.009397
.0072
.00705
.05239
1
-.000070
.002892
.9997
-.00705
.00691
2
-.007511
.003155
.0538
-.01512
.00010
0
.000070
.002892
.9997
-.00691
.00705
2
-.007441
.003088
.0504
-.01489
.00001
0
.007511
.003155
.0538
-.00010
.01512
1
.007441
.003088
.0504
-.00001
.01489
0
Std. Error
Sig.
1
2
L5minU5
0
1
2
U5vsL5
0
1
0
-.029716
.033379
2
U5PerL456
0
1
2
*. The mean difference is significant at the 0.05 level.
70
APPENDIX D
Table D- Linear regression output of all sig. variables from NRS2Grp and NRS3Grp ANOVA from SPSS.
Descriptive Statistics
Mean
NetResSpc
Std.
Deviation
N
1.11491
.921062
55
13.75836
.922070
55
L5minU5
.94727
.478851
55
U5vsL5
.93618
.030763
55
U5PerL456
.26694
.009573
55
U5PerU456
.28214
.007468
55
.30158
.009299
55
U5sWidth
L5PerU456
Correlations
Pearson
Correlation
Sig. (1tailed)
N
NetResSpc
U5sWidth
L5minU5
1.000
.377
-.431
U5sWidth
.377
1.000
-.067
.199
L5minU5
-.431
-.067
1.000
-.988
U5vsL5
.474
.199
-.988
1.000
.666
U5PerL456
.389
.529
-.613
.666
U5PerU456
.338
.583
-.404
.470
L5PerU456
-.207
.291
.704
.002
NetResSpc
NetResSpc
U5vsL5
U5PerL456
U5PerU456
L5PerU456
.389
.338
-.207
.529
.583
.291
-.613
-.404
.704
.470
-.658
1.000
.860
.026
.860
1.000
.355
-.658
.026
.355
1.000
.001
.000
.002
.006
.065
.314
.072
.000
.000
.016
.000
.000
.001
.000
.000
.000
.000
.000
.424
.474
U5sWidth
.002
L5minU5
.001
.314
U5vsL5
.000
.072
.000
U5PerL456
.002
.000
.000
.000
U5PerU456
.006
.000
.001
.000
.000
L5PerU456
.065
.016
.000
.000
.424
.004
NetResSpc
55
55
55
55
55
55
55
U5sWidth
55
55
55
55
55
55
55
L5minU5
55
55
55
55
55
55
55
U5vsL5
55
55
55
55
55
55
55
U5PerL456
55
55
55
55
55
55
55
U5PerU456
55
55
55
55
55
55
55
L5PerU456
55
55
55
55
55
55
55
71
.004
Variables Entered/Removed
Model
1
Variables
Entered
Variables
Removed
L5PerU456,
U5PerL456,
U5sWidth,
U5PerU456,
L5minU5,
b
U5vsL5
a
Method
Enter
a. Dependent Variable: NetResSpc
b. All requested variables entered.
b
Model Summary
Change Statistics
Model
1
R
Adjusted R
Square
R Square
.586a
.343
Std. Error of
the Estimate
.261
R Square
Change
.791559
F
Change
.343
df1
4.186
6
a. Predictors: (Constant), L5PerU456, U5PerL456, U5sWidth, U5PerU456, L5minU5, U5vsL5
b. Dependent Variable: NetResSpc
ANOVAa
Sum of
Squares
Model
1
Regression
Mean
Square
df
15.736
6
2.623
Residual
30.075
48
.627
Total
45.811
54
F
Sig.
4.186
.002b
a. Dependent Variable: NetResSpc
b. Predictors: (Constant), L5PerU456, U5PerL456, U5sWidth, U5PerU456, L5minU5, U5vsL5
Coefficientsa
Unstandardized Coefficients
Model
1
(Constant)
B
Std. Error
-132.544
99.127
.590
.301
U5sWidth
L5minU5
Standardized
Coefficients
Beta
t
Sig.
-1.337
.187
.590
1.958
.056
-4.052
3.748
-2.106
-1.081
.285
U5vsL5
139.178
104.827
4.648
1.328
.191
U5PerL456
-13.080
27.731
-.136
-.472
.639
U5PerU456
-621.332
423.667
-5.038
-1.467
.149
589.857
397.804
5.955
1.483
.145
L5PerU456
a. Dependent Variable: NetResSpc
Residuals Statisticsa
Minimum
Predicted
Value
Residual
Maximum
Mean
Std.
Deviation
N
.29040
2.74836
1.11491
.539821
55
-1.613278
2.133616
.000000
.746289
55
.000
1.000
55
.000
.943
55
Std.
Predicted
-1.527
3.026
Value
Std.
-2.038
2.695
Residual
a. Dependent Variable: NetResSpc
72
df2
48
Sig. F
Change
.002
a
b
c
Figure D- Histogram (a), P-P Plot (b), and Scatterplot with regression (c) charts from linear
regression of all sig variables from NRS2Grp and NRS3Grp ANOVA. Output from SPSS.
73
APPENDIX E
Table E- Backward regression of all significant variables from NRS2Grp and NRS3Grp ANOVA. Output
from SPSS.
Descriptive Statistics
Mean
NetResSpc
Std.
Deviation
N
1.11491
.921062
55
13.75836
.922070
55
L5minU5
.94727
.478851
55
U5vsL5
.93618
.030763
55
U5PerL456
.26694
.009573
55
.28214
.007468
55
.30158
.009299
55
U5sWidth
U5PerU45
6
L5PerU456
Correlations
NetResSpc
Pearson NetResSpc
Correlation
U5sWidth
L5minU5
Sig. (1tailed)
N
U5sWidth
L5minU5
U5vsL5
U5PerL456
U5PerU456
L5PerU456
1.000
.377
-.431
.474
.389
.338
-.207
.377
1.000
-.067
.199
.529
.583
.291
-.431
-.067
1.000
-.988
-.613
-.404
.704
U5vsL5
.474
.199
-.988
1.000
.666
.470
-.658
U5PerL456
.666
1.000
.860
.026
.389
.529
-.613
U5PerU456
.338
.583
-.404
.470
.860
1.000
.355
L5PerU456
-.207
.291
.704
-.658
.026
.355
1.000
.002
.001
.000
.002
.006
.065
.314
.072
.000
.000
.016
.000
.000
.001
.000
.000
.000
.000
.000
.424
NetResSpc
U5sWidth
.002
L5minU5
.001
.314
U5vsL5
.000
.072
.000
U5PerL456
.002
.000
.000
.000
U5PerU456
.006
.000
.001
.000
.000
L5PerU456
.065
.016
.000
.000
.424
.004
NetResSpc
55
55
55
55
55
55
55
U5sWidth
55
55
55
55
55
55
55
L5minU5
55
55
55
55
55
55
55
U5vsL5
55
55
55
55
55
55
55
U5PerL456
55
55
55
55
55
55
55
U5PerU456
55
55
55
55
55
55
55
55
55
55
55
55
55
55
L5PerU456
74
.004
Variables Entered/Removed
Variables
Entered
Model
1
a
Variables
Removed
Method
L5PerU456,
U5PerL456,
U5sWidth,
U5PerU456
, L5minU5,
b
U5vsL5
Enter
2
U5PerL456
Backward
(criterion:
Probability of F-toremove >= .100).
L5minU5
Backward
(criterion:
Probability of F-toremove >= .100).
L5PerU456
Backward
(criterion:
Probability of F-toremove >= .100).
U5PerU456
Backward
(criterion:
Probability of F-toremove >= .100).
3
4
5
a. Dependent Variable: NetResSpc
b. All requested variables entered.
Model Summaryf
Change Statistics
Model
1
2
R
R Square
Adjusted R
Square
Std. Error of the
Estimate
R Square
Change
F Change
df1
df2
Sig. F
Change
.586a
.343
.261
.791559
.343
4.186
6
48
.002
b
.340
.273
.785254
-.003
.222
1
48
.639
3
.583
c
.571
.326
.272
.786075
-.015
1.105
1
49
.298
4
.556d
.309
.268
.787922
-.017
1.240
1
50
.271
5
e
.307
.281
.781160
-.002
.111
1
51
.740
.554
a. Predictors: (Constant), L5PerU456, U5PerL456, U5sWidth, U5PerU456, L5minU5, U5vsL5
b. Predictors: (Constant), L5PerU456, U5sWidth, U5PerU456, L5minU5, U5vsL5
c. Predictors: (Constant), L5PerU456, U5sWidth, U5PerU456, U5vsL5
d. Predictors: (Constant), U5sWidth, U5PerU456, U5vsL5
e. Predictors: (Constant), U5sWidth, U5vsL5
f. Dependent Variable: NetResSpc
75
a
Coefficients
Unstandardized Coefficients
Model
1
(Constant)
U5sWidth
L5minU5
2
.590
.301
t
Sig.
-1.337
.187
.590
1.958
.056
3.748
-2.106
-1.081
.285
139.178
104.827
4.648
1.328
.191
U5PerL456
-13.080
27.731
-.136
-.472
.639
U5PerU456
-621.332
423.667
-5.038
-1.467
.149
L5PerU456
589.857
397.804
5.955
1.483
.145
(Constant)
-136.469
97.990
-1.393
.170
.566
.295
.567
1.922
.060
-3.891
3.702
-2.023
-1.051
.298
U5vsL5
143.041
103.674
4.777
1.380
.174
U5PerU456
-641.180
418.214
-5.199
-1.533
.132
L5PerU456
598.433
394.223
6.042
1.518
.135
(Constant)
-121.597
97.064
-1.253
.216
U5sWidth
.297
.145
.297
2.043
.046
127.275
102.691
4.251
1.239
.221
U5PerU456
-383.966
339.487
-3.113
-1.131
.263
L5PerU456
357.488
321.048
3.609
1.114
.271
(Constant)
-13.626
4.406
-3.093
.003
.321
.144
.321
2.229
.030
3.279
.002
U5vsL5
U5sWidth
U5vsL5
5
Beta
99.127
-4.052
L5minU5
4
Std. Error
-132.544
U5vsL5
U5sWidth
3
B
Standardized
Coefficients
13.014
3.969
.435
U5PerU456
-6.582
19.728
-.053
(Constant)
-14.559
3.376
.294
.118
12.426
3.526
U5sWidth
U5vsL5
a. Dependent Variable: NetResSpc
76
-.334
.740
-4.312
.000
.294
2.496
.016
.415
3.524
.001
Excluded Variables
a
Collinearity
Statistics
Model
2
U5PerL456
3
Beta In
U5PerL456
Tolerance
-.472
.639
-.068
.165
c
-.375
.710
-.053
.166
c
-1.051
.298
-.148
.004
U5PerL456
-2.023
d
-.144
-.504
.617
-.071
.168
L5minU5
-.324d
-.204
.839
-.029
.005
d
1.114
.271
.156
.001
-.109
e
-.586
.561
-.082
.393
-.262
e
-.167
.868
-.023
.006
-.051
e
-.269
.789
-.038
.382
-.053
e
-.334
.740
-.047
.530
L5PerU456
5
Partial
Correlation
Sig.
-.136b
-.108
L5minU5
4
t
3.609
U5PerL456
L5minU5
L5PerU456
U5PerU456
a. Dependent Variable: NetResSpc
b. Predictors in the Model: (Constant), L5PerU456, U5sWidth, U5PerU456, L5minU5, U5vsL5
c. Predictors in the Model: (Constant), L5PerU456, U5sWidth, U5PerU456, U5vsL5
d. Predictors in the Model: (Constant), U5sWidth, U5PerU456, U5vsL5
e. Predictors in the Model: (Constant), U5sWidth, U5vsL5
Residuals Statisticsa
Minimum
Predicted
Value
Residual
Maximum
Std.
Deviation
Mean
N
.07060
2.18301
1.11491
.510632
55
-1.706587
1.986473
.000000
.766558
55
2.092
.000
1.000
55
2.543
.000
.981
55
Std.
Predicted
-2.045
Value
Std.
-2.185
Residual
a. Dependent Variable: NetResSpc
77
a
b
c
Figure E- Histogram (a), P-P Plot (b), and Scatterplot regression (c) charts for backward
regression of all sig variables from NRS2Grp and NRS3Grp ANOVA. Output from SPSS.
78
APPENDIX F
Table F- Individual regression for U5vsL5 and U5sWidth. Output modified from SPSS.
Descriptive Statistics
Std.
Deviation
Mean
NetResSpc
.921062
55
.93618
.030763
55
13.75836
.922070
55
U5vsL5
U5sWidth
N
1.11491
Correlations
NetResSpc
Pearson
Correlation
Sig. (1tailed)
NetResSpc
.474
U5vsL5
.474
1.000
U5sWidth
.377
1.000
NetResSpc
.000
U5vsL5
N
.000
NetResSpc
55
U5vsL5
2
55
55
Variables Entered/Removed
Model
1
U5vsL5
1.000
Variables
Entered
55
a
Variables
Removed
b
U5vsL5
Method
Enter
b
U5sWidth
Enter
a. Dependent Variable: NetResSpc
b. All requested variables entered.
Model Summaryb
Change Statistics
Model
1
R
2
R Square
Adjusted R
Square
Std. Error of
the Estimate
R Square
Change
F Change
.224
.210
.818810
.224
15.329
1
53
.000
a
.142
.126
.861198
.142
8.768
1
53
.005
.377
b. Dependent Variable: NetResSpc
ANOVAa
2
Sum of
Squares
Regression
Mean
Square
df
10.277
1
10.277
Residual
35.534
53
.670
Total
45.811
54
6.503
1
6.503
39.308
53
.742
45.811
54
Regression
Residual
Total
Sig. F
Change
df2
.474a
a. Predictors: (Constant), U5vsL5, U5sWidth
Model
1
df1
79
F
Sig.
15.329
.000b
8.768
.005b
a. Dependent Variable: NetResSpc, b. Predictors: (Constant), U5vsL5, U5sWidth
a
Coefficients
Unstandardized
Coefficients
Model
1
B
(Constant)
U5vsL5
2
(Constant)
U5sWidth
Standardized
Coefficients
Std. Error
-12.161
3.393
14.181
3.622
-4.063
1.753
.376
.127
Beta
t
.474
.377
Sig.
-3.585
.001
3.915
.000
-2.318
.024
2.961
.005
a. Dependent Variable: NetResSpc
Residuals Statistics
Model
1 U5vsL5
Minimum
Predicted
Value
Residual
Std.
Predicted
Value
2 U5sWidth
Std.
Residual
Predicted
Value
Residual
Std.
Predicted
Value
Maximum
a
Std.
Deviation
Mean
N
.22086
1.96929
1.11491
.436258
55
-1.834508
2.136065
.000000
.811193
55
-2.049
1.958
.000
1.000
55
-2.240
2.609
.000
.991
55
.39668
1.99620
1.11491
.347028
55
-1.696164
2.128661
.000000
.853186
55
-2.070
2.540
.000
1.000
55
.000
.991
55
Std.
-1.970
2.472
Residual
a. Dependent Variable: NetResSpc
80
VITA AUCTORIS
Anthony D. Mongillo was born in Tallahassee, Florida on January 2, 1985 to
Mark and Renee Mongillo. He has one younger brother, David.
His early childhood years were spent mostly in Safety Harbor, Florida. Being in
an adventurous family, he moved with his family to Geneva, Switzerland in 2000 where
he spent his high school years learning French and playing rugby. He graduated from
the International School of Geneva with an International Baccalaureate Diploma in 2003.
After living in Europe, Anthony spent one year attending Brigham Young
University in Provo, Utah where he met his love, Elise Tateoka. However, in 2004 they
parted ways while Anthony took a two-year sabbatical to serve a church mission to
Seoul, Korea where he also learned Korean. Anthony and Elise were reunited again
after Elise returned from her mission to Hawaii, and they were eventually married in
Bern, Switzerland in 2008. Anthony graduated with a Bachelor of Science degree in
Physiology and Developmental Biology in 2009.
Dr. Mongillo attended Nova Southeastern University in Ft. Lauderdale, Florida
where completed his Doctor of Medicine in Dentistry degree in 2013, but not before
adding two sons, Oliver and Nikolas, to his family.
Dr. Mongillo plans to receive his Master of Science degree from Saint Louis
University in 2015.
81