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Correlations between cephalometric andphotographic measurements of facial

attractiveness in Chinese and US patients afterorthodontic treatment

Hee Soo Oh,a Edward L. Korn,b Xiaoyun Zhang,c Yan Liu,c Tianmin Xu,d Robert Boyd,e and Sheldon Baumrindf

San Francisco, Calif, Bethesda, Md, and Beijing, China

Introduction:Orthodontists rely on esthetic judgments from facial photographs. Concordance between es-

timates of facial attractiveness made from lateral cephalograms and those made from clinical photographs

has not been determined. We conducted a preliminary examination to correlate clinicians rankings of facial

attractiveness from standardized end-of-treatment facial photographs (Photo Attractiveness Rank) with ceph-

alometric measurements of facial attractiveness made for the same subjects at the same time. Methods:

Forty-five Chinese and US orthodontic clinicians ranked end-of-treatment photographs of separate samples

of 45 US and 48 Chinese adolescent patients for facial attractiveness. Separately for each sample, the pho-

tographic rankings were correlated with the values of 21 conventional hard- and soft-tissue measures from

lateral cephalograms taken at the same visits as the photographs. Results: Among US patients, higher

rank for facial attractiveness on the photographs was strongly associated with higher values for profile angle,

chin prominence, lower lip prominence, and Z-angle, and also with lower values for angle of convexity, H-an-

gle, and ANB. Among Chinese patients, higher rank for facial attractiveness on the photographs was strongly

associated with higher values for Z-angle and chin prominence, and also with lower values for angle of con-

vexity, H-angle, B-line to upper lip, and mandibular plane angle. Chinese patients whose %lower face height

values approximated the ethnic ideal (54%) tended to rank higher for facial attractiveness than patients with

either higher or lower values for %lower face height. The absolute values of the correlations for the 7 US mea-

sures noted above ranged from 0.41 to 0.59; those of the 7 Chinese measures ranged from 0.39 to 0.49.TheP

value of the least statistically significant of these 14 correlations was 0.006, unadjusted for multiple compar-

isons. On the other hand, many cephalometric measures believed by clinicians to be indicators of facial attrac-tiveness failed to correlate with facial attractiveness rank for either ethnicity at even the P\0.05 level, including

SN-pogonion angle, lower incisor to mandibular plane angle, and Wits appraisal. Conclusions: In general,

there was less association than expected or desired between objective measurements on the lateral cephalo-

grams and clinicians rankings of facial attractiveness on sets of clinical photographs. (Am J Orthod

Dentofacial Orthop 2009;136:762.e1-762.e14)

Much of the orthodontic literature since Downs

classic 1948 article has focused on the analy-

sis of the lateral cephalograms.1 Combina-

tions of cephalometric measures have been grouped

into many cephalometric analyses (eg, those of

Downs,1,2 Steiner,3 Tweed,4,5 Jarabak andFizzell,6 Sas-

souni,7 Bjork,8 Ricketts,9,10 McNamara,11 Arnett and

Bergman,12 and Arnett et al13). Findings from each of

these analyses are used by orthodontists in diagnosis,

treatment planning, and outcomes research. Almost all

aAssistant professor, Department of Orthodontics, Arthur A. Dugoni School of

Dentistry, University of the Pacific, San Francisco, Calif.bMathematical statistician, Biometric Research Branch, National Cancer Insti-

tute, NIH, Bethesda, Md.cAssistant professor, Department of Orthodontics, PekingUniversity School and

Hospital of Stomatology, Beijing, China.dProfessor and chair, Department of Orthodontics, Peking University School

and Hospital of Stomatology, Beijing, China.eProfessor and chair, Department of Orthodontics, Arthur A. Dugoni School of

Dentistry, University of the Pacific, San Francisco, Calif.fProfessor, Department of Orthodontics, and Director, Craniofacial Research

Instrumentation Laboratory, Arthur A. Dugoni School of Dentistry, University

of the Pacific, San Francisco, Calif.

The authors report no commercial, proprietary, or financial interest in the prod-

ucts or companies described in this article.

Supported by a grant of Orthodontic Faculty Development Fellowship Award

from the American Association of Orthodontists Foundation and in part by

NIHNIDR Grants DE07332 and DE08713.

Reprint requests to: Sheldon Baumrind, 1525 Walnut St, Berkeley, CA 94709-

1512; e-mail,[email protected].

Submitted, January 2009; revised and accepted, April 2009.

0889-5406/$36.00

Copyright 2009 by the American Association of Orthodontists.

doi:10.1016/j.ajodo.2009.04.020

762.e1
mailto:[email protected]:[email protected]

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these analyses contain some measurements that are be-

lieved to quantify facial attractiveness. In recent

years, orthodontists have also come to rely heavily on es-

thetic judgments from semistandardized facial photo-

graphs. These photographs have now becomea component of the orthodontists routine records set

for diagnosis, treatment planning, and outcome analysis.

An examination of the concordance between esti-

mates of facial attractiveness made from lateral cepha-

lograms and those made from clinical photographs is

therefore in order. Some previous studies have probed

this relationship, but the available findings are far

from conclusive.14-16 In our study, we conducted a pre-

liminary examination of this clinically important ques-

tion by correlating clinicians rankings of facial

attractiveness from standardized end-of-treatment fa-

cial photographs (Photo Attractiveness Rank) with

cephalometric measurements of facial attractiveness

made for the same subjects at the same time. Our gen-

eral hypothesis was that thevalues for the cephalometricmeasures would correlate highly with Photo Attractive-

ness Rank. In testing this hypothesis, we sought explicit

answers to the following specific questions.

1. To what extent do conventional hard- and soft-tis-

sue cephalometric measures generally considered

to be related to facial attractiveness correlate with

Photo Attractiveness Rank?

2. To what extent do the data support the idea that the

patients with the highest Photo AttractivenessRanks have cephalometric values close to the ceph-

alometric ideals, whereas patients with cephalo-metric values either higher or lower than the

cephalometric ideals tend to be judged less at-

tractive? (We asked this question because it reflects

the common expectation among orthodontists that,

for many cephalometric measures, the highest rank

for facial attractiveness on photographs would be

closely associated with the ideal value of the ceph-

alometric measures, whereas both higher and lower

values for the cephalometric measures would tend

to be associated with lower Photo Attractiveness

Ranks. To the extent that this condition holds for

any particular cephalometric measure, its presence

will not be detected by conventional linear correla-

tional methods unless the data are transformed.

This problem and its solution will be discussed in

Material and methods.)

3. To what extent does adding together information

from several different cephalometric measures of

facial attractiveness improve our ability to account

for observed differences in Photo Attractiveness

Rank? (We asked this question to test the assump-

tion that the merging of information from different

cephalometric measures improves our ability to

predict Photo Attractiveness Rank.)

Answers to these questions were sought by testing

them in hypothesis form against data from samples oflateral cephalograms and facial photographs comprising

a total of 93 treated Chinese andUS orthodontic patients.

MATERIAL AND METHODS

The data evaluated in this study are from 2 samples

of orthodontic patients of different ethnicities treated by

experienced orthodontists in the United States and

China. They were randomly selected from the records

of patients who had completed treatment at the graduate

orthodontic clinic of the Department of Orthodontics at

Peking University, Beijing, China, and the private prac-tice of the director of the graduate orthodontic clinic of

the New Jersey Dental School, Newark.

At each institution, a stratified random sample of 48

subjects was acquired, comprising 4 groups of 12 pa-

tients each. In each group of 12 patients, 3 were Class

I extraction, 3 Class I nonextraction, 3 Class II extrac-

tion, and 3 Class II nonextraction. The sampling process

was the same at both institutions and is illustrated sche-

matically inFigure 1. Three of the original 48 US sub-

jects were excluded from this study for poor image

quality, yielding a final sample of 45. In addition, sev-

eral of the remaining US subjects hae missing valuesfor some cephalometric measures, but the sample size

for no cephalometric measure was less than 41.

The US sample consisted of late-adolescent whitepatients living in northern New Jersey. The Chinese

sample consisted of late-adolescent patients of Chinese

ethnicity, residing in the Beijing area. Cephalometric

and photographic data were complete for all subjects

in the Chinese sample. Further details of the sampling

process have been supplied in previous articles.17,18

Among the end-of-treatment materials available for

each subject were conventional lateral cephalogramsand standardized triplet facial photographs taken at

the same end-of-treatment visit (Fig 2). The photo-

graphs of the US sample were taken with the patient po-

sitioned in the cephalostat according to the original

standard of the Second Roentgenographic Workshop.19

The triplet photographs from both samples had been

ranked for facial attractiveness by each of 45 orthodon-

tically trained judges (25Chinese, 20 US) using previ-

ously described methods.17,18 Also available for each

patient were the database-stored coordinates of 35

hard- and soft-tissue landmarks located on the end-of-

treatment lateral cephalogram for each subject. Each

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cephalogram had been traced independently by 2 or

more judges, and the average values had been recorded

in a numerical database from which the measures of

almost all standard cephalometric analyses could becalculated by computer operations.

From the coordinate values of a subset of the hard-and

soft-tissue landmarks, 9 cephalometric measures whose

values are conventionally considered to be strong indica-

tors of facial attractiveness were selected by the principal

author (H.O.) for analysis. Later, an informal survey con-

ducted among faculty orthodontists at the Universityof the

Pacific in San Francisco identified 12 additional estheti-

cally related cephalometric variables, which were added

to the analysis. To reduce the complexity of data presenta-tion, the results of the 2 analyses have been combined.

Operational definitions for the 21 measures are

listed below. Among them are 10 hard-tissue measures

(designated [H]), 3 orientation-free soft-tissue measures

(designated [S]), and 8 soft-tissue measures oriented to

the hard-tissue-defined Frankfort line (designated [SF]).

Eleven measures are angular; 9 are linear, and 1 is a ra-

tio. The 9 measures examined in the first pass are iden-

tified by asterisks.

Angular measures (in degrees)

1. ANB angle*: the included anglebetween Point A,

nasion, and Point B (after Riedel20) [H].

2. Angle of convexity: theincluded angle between na-

sion, Point A, and pogonion (after Downs2) [H].

3. Facial plane angle*: the acute angle formed by the

intersection of the line nasion-pogonionwith theFrankfort horizontal line (after Holdaway21) [H].

4. H-angle: the included angle between soft-tissue

nasion, soft-tissue pogonion, and the most anterior

point on the upper lip (after Holdaway22) [S].

5. Lower incisor to A-pogonion angle: the acute

angle formed by the intersection between the

line Point A-pogonion and the long axis of the

lower incisor (after Ricketts23) [H].

6. Lower incisor to mandibular plane angle*: the an-

gle formed by the intersection of the long axis of

the lower central incisor andthe lower border of

the mandible (after Tweed4,5) [H].

7. Mandibular plane angle*: the acute angle formed

by the intersection of the line gonion-menton with

the Frankfort horizontal plane (after Downs2) [H].

8. Nasolabial angle: the included angle between

lower nose tip, soft-tissue subnasale, and the ver-

milion border of the upper lip (after Burstone24)

[S].

9. Profile angle*: the included angle between gla-bella (defined in this study as the most anterior

point on the soft tissue of the forehead), soft-tissue

subnasale, and soft-tissue pogonion, defined in

Fig 1. Schematic showing the procedures for drawing the equivalent Chinese and US samples. Step

1: at each venue, patients who received treatment during a specified time period were identified. Step

2: each patient wasassigned a random number; all subsequent procedures were conducted with the

charts sorted in random order to ensure that the sample was representative of the population (ie,

practice) from which it was drawn. Step 3: proceeding in random order, all charts with complete re-

cords were identified and duplicated for further studies (for the purposes of the general project of

which this study is a part, a complete record was considered to be one in which a lateral cephalo-

gram, study casts, full-mouth intraoral or panoramic x-rays, and a facial photographic triplet were

available at the beginning and end of full-bonded orthodontic treatment). Step 4: parallel stratified

subsets of 48 Chinese subjects and 45 US subjects with complete records were selected; the subset

from each institution comprised the first 48 randomly ordered charts from that venue that satisfied the

Angle Class and extraction and nonextraction criteria for this study, except that 3 subjects were lost

from the US group because their images were technically unsatisfactory.

American Journal of Orthodontics and Dentofacial Orthopedics Oh et al 762.e3Volume136,Number6

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this study as the most anterior point onthe soft-tis-

sue surface of the chin (after Burstone25) [S].

10. SN-pogonion angle*: the included angle between

the landmarks sella-nasion and pogonion (after

Bell et al26) [H].

11. Z-angle: the angle formed by the intersection be-

tween the Frankfort horizontal line and the line

from soft-tissue pogonion to the anterior-most

point on the lower lip (after Merrifield27) [SF].

Linear measures (in millimeters)

12. B-line to lower lip: the distance from the anterior-

most point on the lower lip and the line from soft-

tissue subnasale to soft-tissue pogonion measured

parallel to the Frankfort plane (after Burstone25)

[SF].

13. B-line to upper lip: the distance from the anterior-

most point on the upper lip and the line from soft-

tissue subnasale to soft-tissue pogonion measured

parallel to the Frankfort plane (after Burstone25)

[SF].

14. Chin prominence: the distance from soft-tissue

pogonion to a line perpendicular to the Frankfort

plane and passing through soft-tissue subnasale

(after Arnett et al13) [SF].

15. E-line to lower lip*: the distance from the ante-

rior-most point on the lower lip to the line from

the nose tip to soft-tissue pogonion measured

parallel to the Frankfort plane (after Ricketts23)

[SF].

16. Lower incisor to A-pogonion distance: the dis-

tance between the tip of the lower incisor and

a line from Point A to pogonion measured parallel

to the Frankfort plane (after Ricketts23) [H].

Fig 2. Representative photographic triplets from the US (upper) and Chinese (lower) samples.


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17. Lower lip prominence: the distance from the ante-

rior-most point of the lower lip to a line perpendic-

ular to the Frankfort plane and passing through

soft tissue subnasale (after Arnett et al13) [SF].

18. Nose prominence: the distance from the nose tip to

a line perpendicular to the Frankfort plane and

passing through soft-tissue subnasale (after Arnett

et al13) [SF].

19. Upper lip prominence: the distance from the ante-

rior-most point of the upper lip to a line perpendic-

ular to the Frankfort plane and passing through

soft-tissue subnasale (after Arnett et al13) [SF].20. Wits appraisal*: the distance between the intersec-

tion of a perpendicular line to occlusal plane from

Point A and the intersection of a perpendicular

line to the occlusal plane from Point B (after

Jacobson28) [H].

Ratio

21. %Lower face height*: lower face height times 100

divided by total face height (after Farkas29) [H].

The locations of the anatomical landmarks required

to compute the 21 measures are shown inFigure 3.

Statistical analysis

Since this study was essentially an exploratory in-

vestigation of a new area of interest, we allowed our-

selves to consider more variables than would be

appropriate in a definitive hypothesis test. Rather than

perform a formal multiple comparisons adjustment,

we chose to focus our consideration on measures whose

Pvalues were less than 0.01.For answers to the first question, Pearson correla-

tions (r) were used to calculate the strength of associa-tion between Photo Attractiveness Ranks of the

patients and their scores for each of 21 cephalometric

measures.

Separate tests were performed for the patients of

each ethnicity. However, each patients Photo Attrac-

tiveness Rank was the single mean value for all 45 US

and Chinese judges pooled. The decision to pool the

values of the Chinese and US judges was based on the

previous finding that the correlation between the Photo

Fig 3. Locations of the landmarks used in computing the 21 cephalometric measures. Thedashed

lines show the Frankfort horizontal and a line perpendicular to it passing through subnasale.


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Attractiveness Ranks of the Chinese and US judges was

strong (r 50.92 and P \0.0001 for USpatients; r 50.86 and P \0.0001 for Chinese patients).18

In examining associations between variables, we

have chosen to report Pearson rho values rather than

Spearman rho values that are frequently used for ranked

data. We reasoned that, since Photo Attractiveness Rank

for each patient in this study is the mean of 45 individual

values, they would be expected to be approximately nor-

mally distributed by the central limit theorem. In addi-tion, the cephalometric variables did not appear to

have grossly nonnormal distributions. Therefore, thePearson correlation would be expected to have good

properties for detecting linear associations between

the Photo Attractiveness Rank and the cephalometric

variables. In theory, the Spearman rho might be more

sensitive to nonlinear but monotone associations, al-

though with the small sample sizes this is unclear. Nei-

ther correlation would be sensitive to nonmonotone

associations; this is why we used the absolute-value

transformations to address question 2.

The advantage of using the Pearson correlation over

the Spearman was that its square (r2) can be used as

a measure of explained variance, thus facilitating

a straightforward assessment of increased association

when combinations of cephalometric variables were

considered in question 3.

Question 3 was investigated by using the technique

of stepwise linear regression. A P value less than 0.01

was required for a variable to enter the model for each

ethnicity, and a P value greater than 0.05 was requiredto leave the model. Although a number of alternative

methods of regression analysis were available, we con-

sidered stepwise regression a reasonable approach for

assessing the association with combinations of cephalo-

metric variables, given the relatively small sample sizes

and the exploratory nature of the study.

RESULTS

Table I lists the means and standard deviations for

all 21 cephalometric measures for the US and Chinese

Table I. Means and standard deviations by ethnicity for this sample and means of best available comparable studies

US cohort Chinese cohort

Present sample Best avail able norm Present sampl e Best available norm

Cephalometric measures Mean SD Mean SD Ref Mean SD Mean SD Ref

Angular measures ()

ANB 2.7 1.9 2.0 1.8 20 4.0 2.3 2.5 1.5 30

Angle of convexity 2.4 5.3 0.0 5.1 2 7.9 5.7 5.5 2.9 31

Facial plane angle 83.5 3.4 85.0 3.0 21 83.1 3.5 87.7 3.0 30

H-angle 13.5 3.7 10.0 3.0 22 18.0 3.7 13.6 3.6 30

Lower incisor to A-pogonion line 25.7 5.2 22.0 4.0 23 27.9 6.5 26.9 5.1 2

Lower incisor to mandibular plane 95.6 7.0 90.0 5.8 4, 5 99.0 9.6 94.3 5.5 30

Mandibular plane angle 27.7 6.6 25.0 4.5 4, 5 30.1 7.1 27.2 4.7 30

Nasolabial angle 127.3 8.2 102.0 8.0 24 97.1 9.6 84.0 80-110 31

Profile angle 165.6 5.9 168.7 4.1 25 166.6 5.1 168.6 3.7 31

SN-pogonion angle 77.0 3.7 79.0 3.0 26 76.7 3.7 79.5 3.3 30

Z-angle 71.2 6.9 80.0 9.0 27 66.3 6.2 71.0 32

Linear measures (mm)

B-line to lower lip 2.6 2.5 3.0 1.0 25 5.9 2.3 6.5 1.6 30B-line to upper lip 3.1 1.8 2.0 1.0 25 6.1 1.7 4.9 1.7 30

Chin prominence (F) 12.2 5.4 2.6 1.9 13 11.8 5.2 6.7 3.3 31

(M) 15.6 8.6 3.5 1.9 16.2 4.6 8.5 3.4

E-line to lower lip 2.9 3.2 2.0 2.0 23 0.9 2.4 1.4 1.9 30

Lower incisor to A-pogonion line 2.4 1.6 1.0 2.0 23 4.4 2.0 4.3 1.8 31

Lower lip prominence (F) 4.5 3.1 1.9 1.4 13 0.1 2.8 3.8 2.3 31

(M) 4.3 4.2 1.0 2.2 3.4 3.2 2.6 1.6

Nose prominence 17.1 2.4 16.0 1.4 13 14.9 2.1 13.1 2.0 31

Upper lip prominence (F) 0.5 2.1 3.7 1.2 13 1.8 2.1 6.1 2.2 31

(M) 0.0 2.6 3.3 1.7 0.0 2.3 5.5 2.4

Wits appraisal (F) 2.3 4.0 0.1 1.8 28 0.9 3.1 3.9 2.1 31

(M) 3.2 4.3 1.2 1.9 0.1 2.1 2.6 1.2

Ratio (%)

%Lower face height 53.7 2.3 55.5 1.0 29 53.7 1.9 54.0 1.0 31

Ref, Reference; F, female;M, male.


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samples. For use in later comparisons, it also contains

information on the ideal value for each measure for

each ethnicity.2,4,5,2032

The findings of the study will be presented in terms

of the 3 questions raised in the introduction.

Question 1 was to what extent do conventional hard-

and soft-tissue cephalometric measures generally con-

sidered to be related to facial attractiveness correlate

with clinicians rankings of facial photographs for facial

attractiveness?

To answer this question,Table II lists the correlation

with the Photo Attractiveness Rank of each of the 21cephalometric measures for each ethnicity. Within eth-

nicity, the values are listed in descending order of abso-

lute magnitude.

Seven cephalometric measures for the US sample

and 6 cephalometric measures for the Chinese sample

correlated with the judges rankings of facial photo-

graphs withPvalues less than 0.01. The absolute values

of the correlations for the 7 US measures ranged from

0.41 to 0.59. The corresponding range for the 6 Chinese

measures was 0.39 to 0.49. For each ethnicity, both lin-

ear and angular measures and both hard- and soft-tissue

measures were found among the most highly significant

measures. Four of the most highly significant measures

were the same in the Chinese and US patient samples:

angle of convexity, chin prominence, Z-angle, and

H-angle.

In the US sample, profile angle, chin prominence,lower lip prominence, and Z-angle correlated positively

with Photo Attractiveness Rank. As the value of each of

these measures increased, the patient tended to be

judged more attractive. On the other hand, angle of con-

vexity, H-angle, and ANB angle correlated negatively

with the Photo Attractiveness Rank. As the value ofeach of these measures increased, the patient tended

to be judged less attractive.

In the Chinese sample, Z-angle and chin promi-

nence correlated positively with Photo Attractiveness

Rank. As the value of each of these cephalometric mea-

sures increased, the patient tended to be judged more at-

tractive. On the other hand, angle of convexity, H-angle,

B-line to upper lip, and mandibular plane angle corre-

lated negatively with Photo Attractiveness Rank; as

the value of each of these cephalometric measures in-

creased, the patient tended to be judged less attractive.

Table II. Correlations between Photo Attractiveness Rank and 21 raw cephalometric measures

US patients (n 5 45) Chinese patients (n 5 48)

Order Cephalometric measure

Raw cephalometric value

Order Cephalometric measure

Raw cephalometric value

r P r P

1 Profile angle () 0.59 \0.0001 1 Z-angle () 0.49 0.0004

2 Angle of convexity () 0.51 0.0003 2 Angle of convexity () 0.45 0.002

3 Chin prominence (mm) 0.50 0.001 3 Chin prominence (mm) 0.42 0.003

4 H-angle () 0.48 0.001 4 H-angle () 0.40 0.005

5 ANB () 0.44 0.003 5 B-line to upper lip (mm) 0.40 0.005

6 Lower lip prominence (mm) 0.41 0.005 6 Mandibular plane angle () 0.39 0.006

7 Z-angle () 0.42 0.006 7 ANB () 0.35 0.014

8 Mandibular plane angle () 0.38 0.011 8 Facial plane angle () 0.34 0.02

9 Upper lip prominence () 0.32 0.03 9 E-line to lower lip (mm) 0.34 0.02

10 Lower incisor to A-pogonion line

(mm)

0.29 0.05 10 Lower incisor to A-pogonion line () 0.33 0.02

11 E-line to lower lip (mm) 0.29 0.06 11 Profile angle () 0.32 0.03

12 Nose prominence (mm) 0.25 0.10 12 B-line to lower lip (mm) 0.31 0.03

13 SN-pogonion angle (

) 0.24 0.11 13 Lower incisor to mandibular plane()

0.25 0.09

14 Nasolabial angle () 0.25 0.13 14 Nose prominence (mm) 0.20 0.18

15 Facial plane angle () 0.23 0.14 15 Lower lip prominence (mm) 0.19 0.20

16 Wits appraisal (mm) 0.21 0.16 16 Upper lip prominence (mm) 0.10 0.50

17 B-line to lower lip (mm) 0.19 0.22 17 SN-pogonion angle () 0.10 0.52

18 B-line to upper lip (mm) 0.12 0.43 18 %Lower face height (%) 0.09 0.55

19 Lower incisor to mandibular plane

()

0.07 0.65 19 Nasolabial angle () 0.06 0.69

20 Lower incisor to A-pogonion line () 0.05 0.73 20 Wits appraisal (mm) 0.02 0.87

21 %Lower face height (%) 0.01 0.94 21 Lower incisor to A-pogonion line

(mm)

0.001 0.99

Negative values for r indicate cephalometric measures that decrease as facial attractiveness increases.


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Scatterplots for each of the highly statistically sig-

nificant measures in Table II are given in Figure 4.

They show the distributions of individual case values

for the associations between Photo Attractiveness

Rank on the y-axis and each of the cephalometric mea-sures on the x-axis. Values for the least attractive pa-

tients are at the bottom of each plot, and values for

the most attractive patients are at the top. Within ethnic-

ity, the y-value for each patient is the same in all plots.

On each plot, the ideal value of the cephalometric

measure is represented by the vertical red line. It can

be seen that, for almost all these measures, the ideal

value falls within the distribution, but it is rarely near

the distributions center. For the majority of cephalo-

metric variables, the values for the less attractive pa-

tients tend to be farther from the ideal than the

values for the more attractive patients.

The patterns of the scatterplots for each of the 4 vari-

ables that met our high significance criterion for both

ethnicities (angle of convexity, chin prominence, H-an-

gle, and Z-angle) were quite similar for both ethnicities.

With regard to the goal of clinical prediction, it was

noted that, even though when the correlations are highly

statistically significant, these real-world distributions

showed considerable variability.

We also thought it important that many cephalomet-

ric measures generally considered to be strongly associ-

ated with facial attractiveness failed to correlate

significantly with the judges rankings of facial attrac-

tiveness on photographs. Among these were lower inci-sor to mandibular plane angle, %lower face height, Wits

appraisal, nose prominence, and all other measures in

Table I whose probability of occurring by chance was

greater than 0.05. At this point in the study, it was not

possible to be sure whether the values for these variables

actually had little association with Photo Attractiveness

Rank or whether they had a curvilinear association that

was undetectable by linear correlation unless the data

were transformed. Hence, the relevance of Question 2.

Question 2 was to what extent do the data support

the idea that the patients with the highest Photo Attrac-

tiveness Ranks have cephalometric values close to thecephalometric ideals, whereas patients with cephalo-

metric values either higher or lower than the cephalo-

metric ideals tend to be judged less attractive?

If we correlate Photo Attractiveness Rank with

a cephalometric measure whose facial attractiveness is

highest at its ideal value but lower both above and

below the ideal value (a condition we expected to

encounter for a number of cephalometric measures),

the regression line would tend to approximate a para-

bolic curve rather than the straight line that results

when 2 variables maintain the same relationship to

each other throughout their range.

This is a problem because the Pearson correlation

method as usually used is almost completely insensitive

to this type of nonlinear distribution. To protect our-selves from failing to detect associations of this type be-

tween Photo Attractiveness Rank and one or more of the

cephalometric measures under examination, a new

value was calculated equal to the absolute distance (in

degrees or millimeters) between each patients raw

value for each measure and the ethnic ideal for that

measure. The transformed cephalometric values for

each cephalometric measure are then amenable to con-

ventional linear correlation with the patients Photo

Attractiveness Ranks.

The ideal value for each measure for each ethnicity

from Table I was used to transform the raw value of each

subject by rescaling it in terms of its absolute distance

from the ideal.Table III lists the transformed correla-

tions and P values for the relationships between Photo

Attractiveness Rank and each of the 21 cephalometric

measures for both the Chinese and the US samples.

Also listed is the increment or decrement in the strength

of each correlation as compared withTable II. As can be

seen in the table, only 1 measure that did not satisfy our

P\0.01 criterion for statistical significance inTable II

achieved such significance after transformation. This

was the transformed value of %lower face height in

the Chinese sample. For this cephalometric measure,

the change in r value was dramatic, moving from r 50.09 to r 5 0.44, and from the 18th position among

the 21 Chinese cephalometric variables to first. The ac-

tual distributions of the raw and transformed values for

this correlation are shown inFigure 5. This implies that

%lower face height values that were larger or smaller

than the Chinese ideal of 54% tended to be equally

unattractive.

No other cephalometric measure for either ethnicity

whose correlation with Photo Attractiveness Rank did

not satisfy the P \0.01 criterion before transformation

increased sufficiently to satisfy it after transformation.

B-line to lower lip and B-line to upper lip in the US sam-ple did show substantial improvements in r value after

transformation but still did not reach our criterion for

statistical significance.

In general, the transformations had less effect than

we had expected. Three of the 4 cephalometric mea-

sures that had correlated most highly with Photo Attrac-

tiveness Rank in both the Chinese and US samples in

Table I(chin prominence, angle of convexity, and Z-an-

gle) remained highly significant after transformation,

with only very small changes in r value. For example,


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the transformation increased thevalue of profile angle in

the US sample from 0.59 to 0.61.

It is theoretically possible that a curvilinear relation-

ship might have been missed by our transformation if

the ideal value for that cephalometric measure werefar from the center of the distribution of sampled values.

To control for this possibility, we examined the plots of

all cephalometric measures vs Photo Attractiveness

Rank. (All plots can be viewed on the Internet at

www.cril.org.) Only for lower lip prominence and naso-

labial angle, both for the US sample, were there any in-

dications that this might be true. To explore this

possibility further, we transformed the individual case

values of these 2 measures by computing their absolute

differences from their sample means rather than from

the ideal for the cephalometric measure. The result-

ing correlations were 0.25 (P 50.098) for lower lip

prominence and 0.39 (P 5 0.015) for nasolabial angle.

The value for lower lip prominence represents a decre-

ment with respect to the value inTable II. The finding

for nasolabial angle is more interesting. In the past,

our laboratory found the reliability of this measure to

be low because its landmarks are located near each other

and are ambiguous. The fact that the transformed value

nevertheless came so close to meeting our criterion for

statistical significance makes it a reasonable target for

further investigation.

Question 3 was are the associations made stronger

when combinations of cephalometric variables are com-

pared with the rankings from facial photographs?In clinical orthodontics, practitioners frequently ag-

gregate data from several measures. Hence, we asked in

our third question whether combinations among the sig-

nificant variables in our study can more fully account

for the observed variability in Photo Attractiveness

Rank.

To provide answers to this question, separate step-

wise regression analyses were performed for the US

and the Chinese samples. The dependent variable in

each test was Photo Attractiveness Rank. The indepen-

dent variables in each test were the most highly statisti-

cally significant raw and transformed cephalometricvariables for that ethnicity. We asked whether any com-

bination of these variables yielded a substantial im-

provement in accounting for attractiveness in either

ethnicity. For the US sample, the transformed value of

profile angle was the only variable that entered into

the stepwise regression model. Its r2 value was 0.37, im-

plying that slightly more than 2/5 of the variability in

Photo Attractiveness Rank could be accounted for by

the set of cephalometric variables.

For the Chinese sample, Z-angle entered the modelfirst, followed by the transformed value of %lower face

height. The cumulative r2 value for the 2 variables con-

sidered together was 0.41, implying that here too

slightly more than 2/5 of the variability in Photo Attrac-

tiveness Rank could be accounted for by the pair of

cephalometric variables. (The r2 value for Z-angle con-

sidered alone was 0.24.)

It can be seen that adding together information from

several raw and transformed cephalometric variables

did not greatly improve our ability to explain the clini-

cians rankings of facial photographs for attractiveness.

Although it is true that our sample sizes were small for

conducting multiple regression analyses of this sort, our

results do strongly imply the need for caution in treating

findings from different but related cephalometricmeasures as if information from them can be treated

additively.

DISCUSSION

Lateral cephalograms and facial photographs have

complementary roles in the evaluation of facial attrac-

tiveness by orthodontists. Photographs show the surface

structures of the face in considerable detail, and x-ray

images allow us to understand the relationship between

those surface structures and the skeletal and dental ar-mature that supports them. Certainly, photographs are

much closer to the natural state of the subject than are

lateral cephalograms. However, techniques for quantita-

tive measurement of facial photographs and standardi-

zation of photographic orientation are much less well

advanced in orthodontics.33-38 Ranking methods such

as the one that we used are useful for the conduct of

studies such as this one. But the numerical rank of

each of our subjects was completely dependent on the

judges evaluations of the other patients in our particular

sample. For that reason, it cannot be compared quantita-

tively to the rank of a photograph from any other sam-ple. Clearly, the development of reliable, clinically

useful quantitative and objective measures of facial at-

tractiveness on photographs would be desirable, but

such measures have yet to be developed. Now, only rel-

atively vague sets of rules and principles have been

Fig 4. Distributions of the actual relationship between Photo Attractiveness Rank and A, the 7 US

and B, 6 Chinese cephalometric measures for which highly significant associations are reported in

Table II. The purportedly ideal value for each measure from Table Iis indicated by a vertical red

line. Even though these associations are highly statistically significant, these real-world distributions

are much more scattered than the perfect schematic distributions.

:

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established, mostlyimported from the fields of art (eg,

divine proportions,39-42

and vertical thirds and horizon-tal fifths43-46) and psychology (eg, averageness, 47-50

youthfulness,51,52 and symmetry53,54). Those measureson photographs that have been thus far developed in or-

thodontics (eg, the smile line55-57) have been subjected

to limited critical testing. And when tests have been

done, the results have generally not been statistically

significant.58,59

Lateral cephalograms, on the other hand, are fairly

well understood by the members of the orthodontic

community. Although quantification of facial esthetics

is certainly not the main use of cephalograms in ortho-

dontics, many cephalogrametric measurements have

been proposed as reliable indexes of facial attractive-ness. From the early work of Downs1 to the recent

work of Arnett et al,13 almost every proposed cephalo-metric analysis contains some measures of facial attrac-

tiveness. Hence, it seems reasonable to investigate the

concordance between the objective angular and lin-

ear measurements of x-ray cephalometry and the

subjective but highly reliable ranking of facial

photographs for attractiveness.

The underlying approach of this study was to use

such highly reliable but noninterval and hence only rel-

ative average rankings by clinicians of representative

Table III. Correlations between Photo Attractiveness Rank and 21 transformed cephalometric measures

US patients (n 5 45) Chinese patients (n 5 48)

Transformed value Transformed value

Order Cephalometric measure r P Difference* Order Cephalometric measure r P Difference*

1 Profile angle () 0.61 \0.0001 0.02 1 %Lower face height 0.44 0.002 0.35

2 H-angle () 0.53 0.0002 0.05 2 Chin prominence (mm) 0.43 0.002 0.01

3 Chin prominence (mm) 0.49 0.001 0.01 3 Angle of convexity () 0.38 0.008 0.07

4 Angle of convexity () 0.46 0.002 0.05 4 Z-angle () 0.37 0.009 0.12

5 Z-angle () 0.45 0.003 0.03 5 ANB () 0.36 0.01 0.01

6 Lower lip prominence

(mm)

0.40 0.008 0.02 6 Facial plane angle () 0.35 0.01 0.01

7 B-line to lower lip (mm) 0.37 0.01 0.18 7 H-angle () 0.33 0.02 0.07

8 SN-pogonion angle () 0.35 0.02 0.11 8 Mandibular plane angle

()

0.33 0.02 0.06

9 Upper lip prominence () 0.35 0.02 0.03 9 Nose prominence (mm) 0.31 0.03 0.12

10 Lower incisor

to A-pogonion line

(mm)

0.35 0.02 0.06 10 Profile angle () 0.28 0.06 0.04

11 B-line to upper lip (mm) 0.32 0.04 0.20 11 B-line to upper lip (mm) 0.21 0.16 0.19

12 Mandibular plane angle

()

0.28 0.06 0.10 12 Lower incisor

to mandibular

plane angle ()

0.19 0.19 0.05

13 E-line to lower lip (mm) 0.26 0.10 0.03 13 SN-pogonion angle () 0.19 0.21 0.09

14 Nasolabial angle () 0.25 0.13 0.00 14 Lower lip prominence

(mm)

0.18 0.22 0.01

15 ANB () 0.25 0.10 0.19 15 Lower incisor

to A-pogonion line

angle ()

0.10 0.48 0.23

16 Facial plane angle () 0.20 0.19 0.03 16 E-line to lower lip (mm) 0.10 0.49 0.24

17 Wits appraisal (mm) 0.15 0.31 0.06 17 Upper lip prominence

(mm)

0.08 0.58 0.02

18 %Lower face height 0.12 0.45 0.11 18 Nasolabial angle () 0.08 0.60 0.02

19 Nose prominence (mm) 0.12 0.45 0.13 19 Wits appraisal (mm) 0.04 0.79 0.02

20 Lower incisor to

mandibular

plane angle ()

0.05 0.74 0.02 20 B-line to lower lip (mm) 0.04 0.81 0.27

21 Lower incisor

to A-pogonion line

angle ()

0.04 0.79 0.01 21 Lower incisor

to A-pogonion line

(mm)

0.01 0.92 0.01

*Difference 5 change in r compared toTable II; %Lower face height in the Chinese sample had the largest increase in absolute r value and is the

only measure that increased sufficently after transformation to satisfy our criteria for high statistical significance. Other large increases in absolute r

values were found for B-line to lower lip and B-line to upper lip in the US sample, but these still did not meet our criteria for statistical significance.


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sets of facial photographs as a standard against which to

test the association of 21 widely used quantitative ceph-

alometric measures. The cephalometric variables cho-

sen for this test included classical hard-tissue

measures from Downs,1,2 Steiner,3 Riedel,20 and so

on, as well as soft-tissuemeasures from the morerecentanalyses of Holdaway,21 Arnett and Bergman,12 Arnett

et al,13 and Burstone.24 Separate assessments were

made for samples of treated Chinese and US orthodontic

patients.

Approximately one third of the 21 cephalometric

measures tested for patients of each ethnicity correlated

with the clinicians rankings for facial attractiveness for

at least 1 ethnicity with high statistical significance

(P\0.01). Chin prominence, angle of convexity,

H-angle, and Z-angle correlated significantly with

Photo Attractiveness Rank among patients of both US

and Chinese ethnicities. Some other measures correlatedsignificantly with Photo Attractiveness Rank among pa-

tients of 1 ethnicity but not of the other. Among the US

patients, these measures included profile angle, ANB an-

gle, and lower lip prominence. Among the Chinese pa-

tients, B-line to upper lip and mandibular plane angle

were included.

The statistically significant relationships described

in the previous paragraph were all linear; ie, facial at-

tractiveness tended to increase (or decrease) in a fairly

straight line throughout the full range of available

values for a particular measure. Additional data-trans-

forming tests were performed for all 21 cephalometric

measures for both ethnicities to detect any measures

for which clinicians preferred some ideal value in

the middle of the variable range, but values on either

side of the ideal tended to be found less attractive.We believed at the outset of this study that many ceph-

alometric measures would exhibit this pattern. But we

found this pattern to be of consequential importance

for only 1 measure, %lower face height among the Chi-

nese patients. For this variable, there was substantial ev-

idence that the judges considered values approximating

the ideal of 54% (Table I) to be most attractive, withvalues either above or below 54% tending to be consid-

ered less attractive. This implies that, among the Chi-

nese patients, the vertical orientation of the chin

contributed consequentially to the evaluation offacial

attractiveness (see the study of Johnston et al60 for

comparison).

The limited ability of our data-transforming proce-

dure to increase the number of statistically significant

correlations between the cephalometric measures and

the Photo Attractiveness Rank seems to imply that clini-

cians perception of attractiveness might not be as sym-

metrically distributed around the ideal values of most

cephalometric measures as has been thought. Almost

half of the 21 cephalometric measures commonly con-

sidered markers for facial attractiveness failed to corre-

late with Photo Attractiveness Rank better than chance

in either their raw or transformed form. Among the

poorer measures were E-line to lower lip, lower incisorto mandibular plane angle, and Wits appraisal. And even

among cephalometric measures that did correlate highly

with photographic rank, no single raw or transformed

measure had a higher correlation than 0.61, and no com-

bination of measures accounted for more than 41% of

the variability in the ranking of facial photographs forattractiveness by orthodontists.

In considering the relatively small portion of the to-

tal variance in Photo Attractiveness Rank accounted for

by the cephalograms, it should be recalled that the pho-

tographs used in the ranking process included frontal

and smiling views as well as a profile view. Recent stud-ies of facial photographs of the type examined here have

reported that frontal and frontal smiling images account

for a larger part of a judges conclusions about facial at-

tractiveness than do profile images.14,61,62 In general, it

seems fair to infer that most information that viewers

use in the evaluation of facial attractiveness is not avail-

able in lateral cephalograms.

As in any study, the limitations of the sample must

be considered when generalizing the study results.

The images in this sample were all taken at the end of

the orthodontic treatment of relatively attractive normal

Fig 5. A, Raw cephalometric values from Table II; B,

transformed values from Table III. The high statisticalsignificance of plot B shows that patients who had raw

%lower face height values close to the ethnic mean of

54% tended to have more favorable Photo Attractive-

ness Ranks than patients who had %lower face height

values either higher or lower than the ideal value.


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subjects. The sample had been stratified to make it more

representative of the adolescent population seeking or-

thodontic treatment than of the general population. In

each sample at original presentation, half of the patients

were Class I, and half were Class II; half were treatedwith extractions, and half without extractions; three

quarters were girls, and a quarter were boys. These con-

straints might have tended to make the range of values

of the cephalometric measures smaller than would

have been the case for pretreatment cephalograms.

CONCLUSIONS

In general, correlations between cephalometric

measures and rankings of facial attractiveness were

less strong than had been expected. Soft-tissue profile

angle appeared to be the most important single variable

in accounting for differences in facial attractivenessrank on photographs of US patients, but it was not

nearly as important in ranking the photographs of Chi-

nese patients. In the Chinese patients, a combination

of Z-angle and transformed %lower face height contrib-

uted statistically significantly to the explanation of the

observed variability in Photo Attractiveness Rank.

However, no combination of cephalometric measures

for either ethnicity accounted for more than 42% of

the variance in Photo Attractiveness Rank, thus leaving

more than half of thevariance unexplained. In general, it

seems fair to infer that most of the information that

viewers use in the evaluation of facial attractiveness isnot available in lateral cephalograms.

For both Chinese and US patients, flatter facial pro-

files appeared to be preferred. In both ethnicities,

greater chin prominence in the sagittal direction was

preferred, and lip position was considered important.

With the exception of %lower face height in the Chinese

sample, close approximation to the ethnic ideal did

not appear to be highly correlated with facial attractive-

ness rank.

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