8/17/2019 Freeman 1996

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F r equ en cy o f B o l ton too th size d isc r epan c ies amon g

or thodon t ic pa t i en ts

J o h n E . F r e e m a n D D S a A . J . M a s k e r o n i D D S b a n d L e w i s L o r to n D D S M S D c

Fort George G. Meade Md.

The purpose of this study was to determine th e percentage of orthodontic patients who present

with an interarch tooth-size discrepancy l ikely to affect treatment planning or results. The Bolton

tooth-size discrepancies of 157 patients accepted for treatment in an orthodontic residency program

were eva luated for the frequency and the ma gnitude o f deviation from Bolton s mean.

Discrepancies outside of 2 SD were considered as potential ly significant with regard to treatment

planning and treatment results. Although the m ean of the sam ple was nearly identical to that of

Bolton s, the range and standard deviation varied considerably with a large percentage of the

orthodontic patients having discrepancies outside of Bolton s 2 SD. W ith such a high frequency of

significant discrepancies it would seem prudent to routinely perform a tooth-size analysis and

incorporate the findings into orthodontic treatment planning. (Am J Orthod D entofac Orthop

1996;110:24-7.)

On e of the goals in comprehensive ortho-

dontic treatment is to obtain an optimal final oc-

clusion, overbite, and overjet. There are many fac-

tors that will influence the attainability of this goal,

one o f which is the relationship of the total mesio-

distal width of the maxillary teeth to that of the

mandibular teeth. A significant variation in this

relationship should be compensated for in the

treatment planning by considering esthetic bond-

ing, prosthetic recontouring, stripping of enamel,

extraction, leaving spaces, or changing the desired

anterior overjet or overbite. The alternative to not

doing any of these may result in compromising the

occlusion in the buccal segments, an undesirable

result.

There has long been an understanding that a

certain maxilla ry-to-mandibular tooth size relation-

ship was important for proper occlusal relation-

ships. Over the years many investigators have at-

tempted to quantify this relationship. In 1923 Gil-

patric calculated that the total mesiodistal tooth

diameters in the maxillary arch exceeded that in

the mandibular arch by 8 to 12 ram. a Ballard, in

1944, evaluated 500 sets of models of orthodontic

patients and found that 90% possessed mesiodistal

From the U.S. Army Orthodontic Residency Program Fort Meade Md.

The views expressed in this article are those of the authors and do not

reflect the official policy of the Department of Defense or other Depart-

ments of the United States Government.

aLieutenant Commander Dental Corps Unit ed States Navy; Senior

Resident.

bCommander Denta l Corps United States Navy; Clinical Instructor.

CConsultant Statistics and Research Design.

Repri nt requests to: Dr. John E. Freeman Denta l Department U.S.

Naval Hospital Grea t Lakes IL 60088.

8/1/58926

4

crown discrepancies of at least 0.25 mm between

one or more pairs of teeth from opposite sides of

the arch, whereas 80% revealed discrepancies of at

least 0.5 mm. 2 In 1949, Neff developed the ante-

rior coefficient, '3 a method to compare the widths

of the anterior teeth in opposing arches. Neff

concluded, tha t everything else being normal an

orthodontic or nonorthodontic normal will settle to

the degree of overbite indicated by the anterior

coefficient. '3 Ballard reported in 1956 that, in a

study of 400 orthodontic cases, over 50% revealed

an excess of at least 2 mm of mesiodistal tooth

width in the mandibular anterior segment when

compared to the maxillary anterior teeth.4

Bolton's introduction of his analysis in 1958

included comparisons of total mesiodistal widths of

dental arches up to the distal surfaces of the first

molars, as well as segments of the arches. 5 Bolton

evaluated 55 cases with excel lent occlusions; 44

had been treated orthodontically without extrac-

tions and 11 were untreated. The following ratios

were established by Bolton:

Sum mandibular 12

Overall ratio = × 100

Sum maxillary 12

Sum mandibular 6

Anterio r ratio = x 100

Sum maxillary 6

The overal l rat io was calculated from the greatest

mesiodistal measurements of the tee th in each arch

from first molar to first molar. The anter ior rat io

was calculated from the greatest mesiodistal mea-

surements of the six anterior teeth in each arch.

The results of Bolton's study are summarized in

Tables I and II. From Bolton's results it can be

8/17/2019 Freeman 1996

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American Journal of Orthodontics and Dentofacial Orthopedics Freeman, Maskeroni, and Lort on 5

Volume 110,No. 1

Table I S t a ti s ti c a l c o m p a r i s o n B o l t o n s t u d y v e r s u s F o r t M e a d e s t u d y . O v e r a l l 1 2 r a t io

Bolton Fort Meade

Samp le size 55 157

Mea n 91.3 91.4

Median No t available 91.3

Range 87.5-94.8 82.8-99.4

Standa rd deviation 1.91 2.57

Standard error of mean 0.26 0.21

Coefficient of variation 2.09% 2.81%

a b l e I I, S t a ti s ti c a l c o m p a r i s o n B o l t o n s tu d y v e r s u s F o r t M e a d e s tu d y . A n t e r i o r 6 r a t io

Bolton

Fort Meade

Sample size 55 157

Mean 77.2 77.8

Median Not available 77.9

Ra nge 74.5-80.4 68.4-87.9

Stand ard deviation 1.65 3.07

Standard error of mean 0.22 0.25

Coefficient of variation 2.14% 3.95%

s e e n t h a t t h e r e i s a re l a t iv e l y s m a l l r a n g e i n w h i c h

t o o t h s i ze r a ti o s s h o u l d f a ll t o b e a b l e t o a c h i e v e

o p t i m a l o c c l u s a l r e l a t io n s h i p s , s t i r r e r e v a l u a t e d

B o l t o n ' s s t u d y a n d a r r i v e d a t s i m i la r r e s u lt s . 6

C r o s b y a n d A l e x a n d e r f o u n d a l a r g e n u m b e r o f

o r t h o d o n t i c p a t i e n t s p r e s e n t e d w i t h a s i g n i f i c a n t

B o l t o n t o o t h - s i z e d i s c r e p a n c y . 7

T h e p u r p o s e o f th i s s tu d y w a s t o e v a lu a t e t h e

p e r c e n t a g e o f p a t i e n ts w h o p r e s e n t e d w i t h a s ig n if -

i c a n t t o o th - s i z e d i s c r e p a n c y a t t h e U . S . A r m y

O r t h o d o n t i c R e s i d e n c y P r o g r a m a t F o r t G e o r g e G .

M e a d e , M d . A s i g n if i c a n t d i s c r e p a n c y w a s d e f i n e d

a s o n e w h o s e v a l u e w a s o u t s i d e o f 2 S D f r o m

B o l t o n ' s m e a n , 7' 8 a s a p p r o x i m a t e l y 9 5 % o f B o l t o n ' s

c a s e s w e r e w i t h in t h is r a n g e . F o r th e o v e r a l l 1 2

r a ti o , a s i g n if i c a n t d i s c r e p a n c y i s t h e r e f o r e d e f i n e d

a s a r a t i o b e l o w 8 7 . 5 o r a b o v e 9 5 . 1 , w i t h r a t i o s

i n - b e t w e e n f a ll in g w i th i n 2 S D o f B o l t o n ' s m e a n .

L i k e w i s e , a n y r a t i o b e l o w 7 3 . 9 o r a b o v e 8 0 . 5 is

c o n s i d e r e d t o b e a s ig n i f ic a n t d i s c r e p a n c y f o r t h e

a n t e r i o r 6 r a t i o .

M A T E R I A L S A N D M E T H O D S

T h e d a t a f o r t h is s t u d y w e r e o b t a i n e d f r o m r e c o r d s

t a k e n a t t h e F t . M e a d e R e s i d e n c y P r o g r a m , w h e r e a

B o l t on t oo t h - s i z e a na l ys i s i s pe r f o r m e d r ou t i ne l y on a l l

p a t i e n t s a c c e p t e d i n t o th e p r o g r a m . O n l y re c o r d s o f

t h o s e p a t i e n t s w i t h p e r m a n e n t d e n t i t i o n s w e r e c o n s i d -

e r e d f o r e v a l u a ti o n t o e l i m i n a t e e r r o r s t h a t m a y b e

i n c o r p o r a t e d f r o m t h e p r e d i c t i o n o f si z es o f u n e r u p t e d

t e e t h . Thos e w i t h a ny s i gn i f i c a n t a t t r i t i on o r t hos e m i s s -

i n g a n y p e r m a n e n t t e e t h o t h e r t h a n s e c o n d o r t h ir d

m o l a r s w e r e n o t c o n s i d e r e d . A t o t a l o f 4 5 9 r e c o r d s w e r e

e v a l u a t e d a t r a n d o m , a n d 1 5 7 m e t t h e e s t a b li s h e d c r i t e ri a

a n d w e r e u s e d f o r t h i s s t u d y .

T h e 1 5 7 r e c o r d s a l l c o n t a i n e d a B o l t o n t o o t h - s i z e

a n a ly s is p r e v i o u sl y c o m p l e t e d b y a F o r t M e a d e r e s id e n t .

T h e a n a l y se s h a d b e e n c o m p l e t e d b y 2 4 d i ff e r e n t r e si -

d e n t s . T h e s a m p l e c o n s i s t e d o f 8 9 f e m a l e a n d 6 8 m a l e

pa t i e n t s . The r e w e r e 115 w h i t e pa t i e n t s , 27 b l a c k pa -

t i e n ts , a n d 15 pa t i e n t s o f o t he r e t hn i c o r i g i n s .

T h e B o l t o n t o o t h - s i z e a n a l y s i s p e r f o r m e d a t F o r t

M e a d e c o n s is t s o f t w o p a r t s a s d e s c r i b e d i n B o l t o n ' s

pub l i c a t i on . 5 Th e f i rs t pa r t i s t he i nd i v i dua l m e s i od i s t a l

m e a s u r e m e n t s o f a l l t e e t h f r om t he f i r s t m o l a r s m e s i a l l y .

T o o t h - s i z e m e a s u r e m e n t s w e r e t y p i c a ll y t a k e n w i th

s h a r p - p o i n t e d B o l e y g au g e s , m e a s u r i n g t h e w i d e s t m e -

s i o d is t al d i m e n s i o n o f e a c h t o o t h a s d e s c r i b e d b y B o l t o n .

T h e s e c o n d p a r t i s th e c a l c u l at i o n o f a r c h l e n g t h c o m -

p a r i s o n s a n d d e t e r m i n a t i o n o f to o t h - s i z e d i sc r e p a n c y

a c c o r d i n g t o t h e m e t h o d o u t l i n e d b y B o R o n ? T h i s d i s -

c r e p a n c y i n c l u d e s a c o m p a r i s o n o f t h e o v e r a l l a rc h e s ( u p

t h r o u g h f ir st m o l a r s ) a n d a l so a c o m p a r i s o n o f t h e

a n t e r i o r s e g m e n t s .

T h e d a t a c o l l e c t e d f r o m t h e r e c o r d s w e r e e v a l u a t e d

t o d e t e r m i n e t h e p e r c e n t a g e o f p a t i e n t s w h o h a d t o o t h -

s i z e d i s c r e pa nc i e s w h i c h w e r e w i t h i n one , w i t h i n t w o , o r

g r e a t e r t h a n t w o s t a n d a r d d e v i a t io n s f r o m B o l t o n ' s

m e a n . A m e a n , m e d i a n , r a n g e , s t a n d a r d d e v i a t i o n , s t a n -

d a r d e r r o r o f t h e m e a n , a n d c o e f f ic i e n t o f v a r i a t io n w e r e

c a l c u l a t e d f o r b o t h t h e o v e r a ll 1 2 r a t io a n d a n t e r i o r

6 r a t i o . The no r m a l i t y o f t he va r i a b l e s w a s i nve s t i ga t e d

by c a l c u l a t i ng t he s ke w ne s s a nd ku r t o s i s o f t he va r i a b l e s .

I n a d d i t i o n , a P e a r s o n ' s c o r r e l a t i o n b e t w e e n t h e v a r i -

a b l e s w a s p e r f o r m e d .

R E S U L T S

T h e m e a n o v e r a ll 1 2 r a ti o f o r t h e o r t h o d o n t i c

p a t i e n t s w a s f o u n d t o b e 9 1 . 4 ( T a b l e I ) , w i t h a

s t a n d a r d d e v i a t i o n o f 2 .5 7 . T h e v a l u e s r a n g e d f r o m

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2 6 Fr ee m an M as ke ro ni an d L or to n American Journal of Orthodontics and Dentofacial Orthopedics

July 996

FORT ME DE ORTHODONTICC SES

No, of

C a s e s

50

4

20 I ~ ~ l

19

< 87 .5 87 .5-89 .3 89 .4-91 .2 91 .3 91 .4-9 3 .2 93 .3-95 .1 > 95.1

OVERALL "12" RATIO

91.3 = Bo l ton s mean .

89.4-91.2 a nd 91.4-93.2 are wi th in 1 stan dar d deviation.

87.5 .89.3 and 93.3-95.1 a re outs ide 1 s tanda rd dev iat ion , bu t w i th in 2

standard deviat ions.

< 87.5 an d > 95.1 are outs ide 2 s tand ard dev iat ions .

F i g .

1 . F o rt M e a d e o r t h o d o n t i c c a s e s . O v e r a ll " 1 2 " r a ti o : 9 1 . 3 = B o l t o n ' s m e a n . 8 9 . 4 t o 9 1 . 2 a n d

9 1 . 4 t o 9 3 , 2 a r e w i t h i n 1 S D . 8 7 . 5 t o 8 9 . 3 a n d 9 3 . 3 to 9 5 . 1 a r e o u t s i d e 1 S D , b u t w i th 2 S D . < 8 7 . 5

a n d > 9 5 . 1 a r e o u t s i d e 2 S D .

No. of

C a s e s

FORT ME DE ORTHODONTICC SES

< 73.9

73.9-75.4 75.5-77.1

7 ; ~ . 2 7 7 . 3 7 8 . 8 7 8 . 9 8 0 .5

ANTERIOR "6" R ATIO

80.5

7 z 2 = B o l t o n s m e a n .

75.5-7Z 1 an d 7Z3-78.8 are w i th in I s tan dard dev ia t ion .

73.9.75.4 an d 78.9-80.5 are outs ide I s tanda rd dev iat ion , bu t w i th in 2

standard deviat ions.

< 73.9 and > 80.5 r e o u t s i d e 2 standard deviat ions.

F i g . 2 . F o r t M e a d e o r t h o d o n t i c c a s e s . A n t e r io r " 6 " r a ti o : 7 7 . 2 = B o l t o n ' s m e a n . 7 5 . 5 to 7 7 .1 a n d

7 7 . 3 t o 7 8 . 8 a r e w i t h i n 1 S D . 7 3 . 9 t o 7 5 . 4 a n d 7 8 . 9 t o 8 0 . 5 a r e o u t s i d e 1 S D , b u t w i th i n 2 S D . < 7 3 . 9

a n d > 8 0 . 5 a r e o u t s i d e 2 S D . a n d > 9 5 . 1 a r e o u t s i d e 2 S D .

a l o w o f 82 . 8 t o a h i g h o f 9 9 .4 , a n d t h e m e d i a n w a s

9 1 .3 . T h e s t a n d a r d e r r o r o f t h e m e a n w a s 0 . 21 a n d

t h e c o e f f i c i e n t o f v a r i a t i o n w a s 2 . 8 1 % . O f t h e 1 5 7

c a s es , 2 1 ( 1 3 . 4 % ) h a d o v e r a l l 1 2 r a t i o s o u t s i d e o f

2 S D f r o m B o l t o n ' s m e a n ( F i g . 1 ) .

T h e m e a n a n t er i o r 6 r a ti o f o r t h e o r t h o d o n t i c

p a t i e n t s w a s f o u n d t o b e 7 7 . 8 ( T a b l e I I ) , w i t h a

s t a n d a r d d e v i a t io n o f 3 .0 7 . T h e v a l u e s r a n g e d f r o m

6 8 .4 t o 87 . 9, a n d t h e m e d i a n w a s 7 7 .9 . T h e s t a n d a r d

e r r o r o f t h e m e a n w a s 0 . 25 a n d t h e c o e f f ic i e n t o f

v a r i a t i o n w a s 3 .9 5 % . F o r t y - e i g h t ( 3 0 . 6 % ) c a s e s h a d

a n t e r i o r 6 r a t i o s t h a t fe l l o u t s i d e o f 2 S D f r o m

B o l t o n ' s m e a n v a l u e ( s e e F i g . 2 ) .

T h e c o r r e l a t i o n s w e r e h i g h a n d s t a ti s ti c a ll y s ig -

n i f i c a n t b u t t h e r e i s t h e i n d i c a t i o n t h a t t h e o v e r a l l

1 2 r a t io a n d a n t e r i o r 6 r a t io w o u l d n o t p r e d i c t

t h e o t h e r c o n s i s t e n t l y . B o t h g r a p h i n g t h e d a t a a n d

m e a s u r i n g t h e s k e w n e s s a n d k u r t o s i s i n d i c a t e d t h a t

t h e d a t a s e t s w e r e n o t n o r m a l l y d i s t ri b u t e d a n d

t h u s t h e u s e o f 2 S D u n i t s t o in d i c a t e th e n o r m a l

r a n g e is n o t a p p r o p r i a t e .

D I S U S S I O N

A l t h o u g h t h e m e a n s o f t h e o r t h o d o n t i c p a t i e n t s

i n th i s s tu d y a n d t h o s e o f t h e B o l t o n s t u d y a r e

n e a r l y id e n t i c a l , t h e r a n g e s a n d s t a n d a r d d e v i a t i o n s

o f t h e o r t h o d o n t i c p a t i e n t s a r e s i g n if i ca n t ly la r g e r .

S i m i l a r f i n d in g s w e r e f o u n d b y C r o s b y a n d A l e x -

a n d e r i n e v a l u a t i n g o r t h o d o n t i c p a t i e n t s i n a c iv il -

i a n p r a c t i c e ? I f t h o s e c a s e s w i t h r a t i o s g r e a t e r t h a n

8/17/2019 Freeman 1996

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American Journal of Orthodontics and Dentofacial Orthopedics Freeman M askeroni and Lorton 7

Volume 110, No 1

2 S D a w a y f r o m B o l t o n ' s m e a n s t r ul y r e p r e s e n t a

s i g n i f i c a n t d i s c r e p a n c y , t h e n a l a r g e p e r c e n t a g e o f

o r t h o d o n t i c p a t i e n t s p r e s e n t w i t h r e l a t i v e t o o t h

s i z e s t h a t c o u l d p o t e n t i a l l y c a u s e p r o b l e m s i n a t -

t a i n i n g a n o p t i m a l o c c l u s a l r e l a t i o n s h i p . W h i l e

1 3 . 5% o f t h e o r t h o d o n t i c c a s e s p r e s e n t e d w i t h a

s i g n i f ic a n t d i s c r e p a n c y o f t h e o v e r a l l 1 2 r a t i o ,

3 0 . 6 % p r e s e n t e d w i t h a s i g n if i ca n t a n t e r i o r 6

d i s c r e p a n c y . T h e o v e r a l l d i s c r e p a n c y w a s e q u a l l y

l i ke l y t o b e a n e x c e s s in t h e m a x i l l a o r t h e m a n -

d i b le , w h e r e a s t h e a n t e r i o r d i s c r e p a n c y w a s n e a r l y

t w i c e a s li k e ly t o b e a m a n d i b u l a r e x c e s s ( 1 9 .7 % )

t h a n a m a x i l l a r y e x c e s s ( 1 0 . 8 % ) .

A p o s s ib l e s o u r c e o f e r r o r m a y b e i n t r o d u c e d b y

u s i ng t h e m e a s u r e m e n t s f o u n d b y 24 d i f f er e n t e x-

a m i n e r s . O f t h e 1 5 7 r e c o r d s u s e d i n t h is s t u d y t h e

m o s t f r o m a n y si n g l e e x a m i n e r w a s 1 5 , t h u s t h e

i m p a c t f r o m e r r o n e o u s d a t a f r o m a n y o n e p e r s o n

w o u l d b e m i n i m a l . I t w a s n o t f e a s i b l e to t e s t

i n d i v i d u a l e r r o r a s t h e e x a m i n e r s a r e n o w a t v a r i -

o u s l o c a t io n s a r o u n d t h e w o r l d . A n a l t e r n a t iv e

o p t i o n i n t h is s t u d y w o u l d h a v e b e e n f o r o n e p e r s o n

t o d o a l l o f t h e m e a s u r e m e n t s , t h e n i f t h e r e w a s a n y

c o n s i st e n t e r r o r, i t w o u l d h a v e b e e n d e m o n s t r a t e d

t h r o u g h o u t t h e d a t a .

O N L U S I O N S

Thes e f ind ings sugges t tha t a l a rge num ber o f pa -

t i e n t s p r e s e n t i n g f o r o r t h o d o n t i c t r e a t m e n t p o s s e s s a

Bol ton too th-s ize d i s c repancy tha t m ay in f luence t rea t -

m ent goa l s and re su l t s . Th i s s tudy found 30 . 6% of

or thod ont ic p a t i en t s to have a s ign i fi can t an te r io r too th-

s i z e d i s c r e p a n c y c o m p a r e d w i t h t h e 2 2 . 9 % f o u n d b y

C r o s b y a n d A l e x a n d e r . 7 P e r h a p s t h e d i f f e re n c e m a y b e

expla ined by the pa t i en t s e lec t ion p roces s in a m i l i t a ry

res idency program ve rsus a p r iva te p rac t i ce . Because o f

l im i ted re sources , pa t i en t s in m i l i t a ry o r thodont ic p ro-

gram s a re typ ica lly those wi th the m ore s eve re m a locc lu-

s ions , even though those re fused t rea tm ent cou ld ve ry

of ten de r ive bene f i t s i f they were to b e t rea ted . I t i s a l so

p o s s ib l e t h a t t h e p o p u l a t i o n o f p a t i e n t s m a y b e m o r e

d ive rse in th e m i l it a ry p rac t i ce wi th rega rd to race and

e thn ic background . Thus , i t would s eem log ica l tha t the

pe rce n tage o f pa t i en t s wi th s ign if icant d i s c repanc ies m ay

b e s o m e w h a t d e p e n d e n t o n t h e s e l e c ti o n p r o c e ss o r t h e

cha rac te r i s t i c s o f the popu la t ion f ro m which the pa t i en t s

a re d rawn.

As a re su l t o f our f indings , i t would s eem p rud en t fo r

cl inic ians to rout inely include a tooth-s ize analys is in

the i r in i t i a l case workup . Iden t i fy ing such a d i s c repancy

before f ina l too th a l ignm ent would p rove bene f ic ia l in

b o t h t r e a t m e n t p l a n n i n g a n d f i n a l e x p e c t a t i o n s o f b o t h

the c l in ic ian and the pa t i en t . Al though such an ana lys i s

m a y a p p e a r t o b e t i m e - c o n s u m i n g , t h e b e n e f i t s w o u l d

seem to ou twe igh th i s m inor inconvenience by a l lowing

m o re e f f i c ien t d iagnos is o f p ro b lem s , m ore spec if ic ity in

t rea tm ent p lann ing , and a h ighe r succes s ra te in ach iev-

ing opt im al occlusions, overb i te , and o verje t .

REFEREN ES

1. Gilpatric WH. Arch prede term inati on-i s it practical? J Am Dent Assoc, July,

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2. Ballard ML. Asymmetry in tooth size: a factor in the etiology, diagnosis and

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3. Ne ff CW. Tailored occlusion with the anterior coefficient. Am J Ort hod 1949;35:

309-13.

4. Baltard ML. A fifth column within normal dental occlusions. Am J Orthod

1956;42:116-24.

5. Bolton WA. Disharmony in tooth size and its relation to the analysis and treatment

of malocclusion. Am J Orthod 1958;28:113-30.

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different malocclusion groups. Am J Or thod Dentofac Ortho p 1989;95:457-61.

8. Thurow RC. A tlas of orthodontic principles. 2nd ed. St Louis: CV Mosby,

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