Multivariate Analysis of Craniofacial Measurements in Twin and Family Data1

MINORU NAKATA,2 PAO-LO Y U 3 AND WALTER E . NANCE4 Lecturer, Department of Pedodontics, Tokyo Mediccil a n d Dental Uniucr-

sity, Yiishimci, Bunkyo-ku , Tokyo , Japan, and Fogarty Interncztioncil Fellow, Department of Medical Genetics, lnd iana University, Indianapolis, Inditina; 3 Associate Professor of Medical Genet ics , lnd iana University School of Med- icine, Indianapolis, Ind iana , and Professor of Medical Genetics and M F d - iciize, Ind iana Universi ty School of Medicine, Indianapolis, Indiana 46202

KEY WORDS Craniofacial measurements . Factor analysis Human genetics.

ABSTRACT Thirty-three cephalometric variables and height have been measured on each of 630 individuals (316 male and 314 female) from 157 families. After age and sex differences were adjusted for each measurement, a rotated factor analysis was undertaken to account for the variation by a limited number of linear combinations of the adjusted measurements. It was found that most of the variation could be explained by nine independent fac- tors. Finally, correlation coefficients were computed on twins, siblings and parent-offspring data for factor scores. The results suggest that each factor which is measured by a linear combination of a set of variables could result from the interaction of independent sets of genes with the environment.

Craniofacial measurements have often been treated as independent variables in studies of the hereditary aspects of these traits, despite the fact that they are obvi- ously interrelated. Since it is possible that genetic and environmental factors influ- ence multiple craniofacial measurements in a complex manner, an analysis of the correlations among these measurements would seem to be a more logical and rea- sonable approach to understanding the inheritance of those interrelated charac- ters. This approach was first developed by Wright ('32) who applied the technique of path coefficients to evaluate the pair- wise correlations of a system of multiple skeletal measurements in rabbits. Wright showed that a single factor made a major contribution to the overall size of the skel- eton but also found that other factors (not necessarily genetic in nature) had local- ized effects on individual bones. His in- vestigation was a pioneering achievement in the genetic study of interrelated mea- surements that has been extended by the recent development of multivariate sta- tistical analysis with electronic computers.

Howells ('53) applied the technique of factor analysis to the analysis of 20 mul-

AM. J. PHYS. ANTHROP., 41: 423430.

tiple anthropometric measurements in 76 pairs of male siblings. In his study, seven independent factors were identified and the correlations of factor scores in brothers were highest in long bone length and facial length. In a similar approach, Pot- ter et al. ('68) applied factor analysis to measurements of permanent dentition in a sample of Pima Indian families to de- tect genetic influences on tooth size.

The objectives of the present study are to describe the craniofacial complex by a few meaningful factors and to detect ge- netic variability of these factor scores by the covariance of related subjects.

MATERIALS AND METHODS

The lateral cephalometric roentgeno- grams of 630 individuals from 157 fami- lies comprised the sample (table 1). The study families included sibling data on 58 normal control families obtained from the Cleft Palate Clinic of Lancaster, Penn- sylvania, and twin data from 99 families taken from the Indiana University Twin Study. The number of paired family mem-

This work was supported by a grant from the John A. Hartford Foundation and was completed during the tenure of a Fogarty International Fellowship to M. N.

423

424 MINORU NAKATA, PAO-LO Y U AND WALTER E. NANCE

TABLE 1

A g c ~ distribution oj scrmples

Mean age Subjects Number in months (range)

Fa thers 115 4 74 (31 7-8 12) Mothers 115 445 (279459) Sons 20 1 133 (44-245) Daughters 199 139 (38-238)

bers and their relationships are shown in table 2.

Thirty-three cephalometric variables and height were measured on each subject. Whenever there were significant regres- sions on age or sex the variables in the offspring were adjusted using the follow- ing equation:

y .. = y . . - a l j k j ( x i - 216) - bk j (Xj2 - 2162) + (el - Y",)

where Y g = adjusted value of the jth variable in the ith individual; Yij = raw value of the jth variable in the ith individ- ual; Xi = age in months of the ith indi- vidual; akj,bkj = values of the h e a r and quadratic regression coefficients for the jth variable in the kth generation-sex class; (TI - % ) = difference between adjusted mean of the kth generation-sex class and 18 year old males (k = 1).

For parental data, the variables were first adjusted to the mean age of fathers (474 mo.) and mothers (445 mo.) respec- tively and then to the mean value for 18 year old males by- using the appropriate value for (Ti - yk). The variables are shown in table 3 and figure 1 .

Factor analysis of the 34 variables was performed on the entire sample using BMD program 03M (Dixon, '64) and ignoring

TABLE 2

The s n m p l r

Number Family members of pairs

F a ther-mo ther 115 Father-son 84 Father-daughter 80 Mother- son 84 Mother-daughter 80 Full siblings 61 1

Monozygotic twins 67 Dizygotic twins 29

' Number of families with varying sibship sizes from one to six.

TABLE 3

Cephtrlomrtric vrrrittblrJs used iw this study f o r j k t o r ctntrlysis

Nine angular ineasurements measurements

Twenty-four l inear

S-N Me-NL' N-S-B a N-B a Or-NL' N-S-Ar Ba-PNS A-NL' S-N-ANS ANS-PNS B-NL' S-N-A A-PNS S-Ar NSLiFL G e M e S-Gn PNS-S-Ba Ba-FL' S-PNS Me-Go-Ar N-ANS S-GO NSL/NL N-Pog S-B a NSL/ML N-Me Ar-Go N-NL' Ar-Me Pog-NL' Ar-Gn

Note: FL: Facial plane - the l ine through S and Pog; NL: Nasal plane- the l ine through ANS and PNS; NSL: Nasion-sella plane - t he l ine through N and S; and ML. Mandibular plane - the l ine through Go and Me. FL', NL' and ML' are the projection from each point to the respective line. See figure 1 for definition and location of landmarks.

family relationships. Kaiser's varimax ro- tation factor matrix was also performed (Kaiser, '58). Correlations between various family members with respect to the factor scores were then computed. For the parent- offspring relationship, product-moment correlation coefficients were calculated, while intraclass correlations were obtained

\ \

Fig. 1 Diagram of la teral skull x-ray used i n this study. N : Nasion; S : Sella turcica; Or: Orbi- tale; ANS: Anterior nasa l spine; A: Subspinale; PNS. Posterior nasa l spine; B: Supramentale; Pug: Pogonion, Gn: Gnathion; Me: Menton; G o : Gonion, Ar: Articulare; Ba: Basion.

CRANIOFACIAL MEASUREMENTS IN FAMILY DATA 425

for the full-sibling and twin data. Finally, heritability estimates were obtained from twin and from parent-offspring data.

RESULTS

The rotated factor loading matrix ob- tained from the 34 variables of the pooled sample is shown in table 4.

Description of the fuctors Factor I: Factor I had high loadings for

anterior lower face height and consequent- ly for anterior total facial heights. It was also associated with mandibular gonial angle. On these grounds this factor was termed the anterior louier face height fac- tor.

Factor 11: Factor I1 had high loadings on mandibular depth measurements asso- ciated with some loadings for measure- ments which are related to mandibular prognathism. Thus, this factor was inter- preted as the mandibular depth factor.

Factor 111: The highest loadings were ob- tained for maxillary protrusion with nega- tive loading on the cranial base angula- tion. Some loading was also found for the posterior maxillary height. This factor can be termed the anterior cranial inclination factor.

Factor IV: Highest loadings were on the distance between Basion and Posterior Na- sal Spine and its relating angle. Other loadings were found for the measurements

Variable

1 Height 2 S-N 3 N-Ba 4 Ba-PNS 5 ANS-PNS 6 A-PNS 7 Go-Me 8 Ba-FL‘ 9 N-ANS

10 N-Pog 11 N-Me 12 N-NL’

14 Me-NL’ 15 Or-NL’ 16 A-NL’ 17 B-ML‘ 18 S-Ar 19 S-Gn 20 S-PNS

22 S-Ba 23 Ar-Go 24 Ar-Me 25 Ar-Gn 26 N-S-Ba 27 N-S-Ar 28 S-N-ANS 29 S-N-A 30 NSLiFL 31 PNS-S-Ba 32 Me-Go-Ar 33 NSL/NL 34 NSLiML

13 Pog-NL’

21 S-GO

Percent of total variance

Factor loadings 1

I I1

09 07 11 01 05 02

- 02 - 17

24 87 82 25 93 89

- 02 42 31 05 55 17 15 08 11 29 31 04 03

- 11 - 12 - 38 - 10

58 00 75

15.2

33 -05 29 -13 25 -27 21 13 17 10 17 20 88 -02 61 -01 08 -23 12 -15 18 -16 08 -26 13 -03 27 -03

-15 -06 08 18

02 04 20 04 61 27 24 54 19 15 09 13 19 10 82 10 82 12 01 -57 10 -62 03 87 04 89 55 63

- 09 13 05 -17

-14 -51 -26 -25

IV V VI V I I VIII IX

01 24 51 90 04 05 04 58 02

- 01 - 04

02 - 03 - 07 - 08 - 04 - 05 - 20 - 06 -01 - 10

10 22 23 24 66 49

- 00 - 00 - 12

86 14 08

-01

22 12 16 06 08 10 09

- 02 87 33 37 86

- 04 02 76

- 30 14 14 22 30 15 14 01 07 08 02 00

- 12 - 06 -21 - 13 - 05

51 22

47 05 13 15 20 10 26 79 49 08 32 43 21 08 -03 19 16 06 89 11 09 11 89 08 19 -08 15 06 ..

24 14 27 28 17 12 13 04 16 15 20 22 19 12 08 12 11 22 17 -01 32 -01

- 10 44 73 24 25 29 49 22 45 81 83 03 05 88 10 32 11 30

-20 -01 - 02 08

00 03 - 02 08

04 11 -35 -03 -21 -43 -36 -10 -23 -40

04 04 07 09 11 05

- 01 02 02 06 00 09 14 -05 16 36 08 -07 05 20

- 13 29 06 06 12 10 07 00 14 06 14 06 17 -31 18 -46 27 -15 26 -14

-08 -04 - 03 01 - 08 00

08 -09 -05 -05

9.3 9.1 7.7 6.6 4.8 11.7 11.3 9.3

1 Decimals oinitted.

426 MINORU NAKATA, PAO-LO YU AND WALTER E. NANCE

involving Basion. This factor can be inter- preted as the posterior cranial inclination factor.

Factor V: Factor V had high loadings for anterior maxillary heights and the in- clination of nasal plane. Thus this factor is related to the anterior maxillary height factor.

Factor VI: The highest loading of Fac- tor VI was obtained for posterior cranial base length and some loadings on the height. This factor was termed the poste- rior cranial base factor.

Factor VII: Factor VII had high positive loadings for mandibular ramus height and posterior face height and negative loadings for mandibular angular measure- ments. Thus, the seventh factor can be characterized as the mandibular ramus height factor.

Factor VIII: The distinctive loading of the maxillary depth measurements to this factor characterized it as the maxillary depth factor.

Factor IX: This last factor had the high- est loading on the anterior cranial length and was termed the anterior cranial length factor.

Parent-offspring correlations The correlations between the parental

factor scores and the mean offspring fac-

tor scores are shown in table 5. The dif- ferences between father-son and mother- daughter correlations and between father- daughter and mother-son correlations were not statistic ally signifkan t.

Interclass correlations among offspring Intraclass correlations of full-siblings,

monozygotic (MZ) twins and like-sexed dizygotic (DZ) twins are shown in table 6. The larger values were observed in the order of MZ and DZ twins and full-siblings data, except for the first and fifth factors where intraclass correlations in DZ twins were smaller than in full siblings.

Heritability estimates Heritability estimates were carried out

based on Holzinger's formula ('29) for twins and from the regression of offspring on the mean of parental values. The re- sults are shown in table 7. The estimates based on the twin data were larger than those of parent-offspring regressions. The magnitude of heritability estimates which were obtained from the original measure- ments is shown in parentheses.

DISCUSSION

Rotated factor analysis of 33 cephalo- metric measurements and stature showed that these 34 variables can be described

TABLE 5

Compiirisoii of pcirent-offspriiiy corrc,ltrtions

F iic tors

Significance Significance Father Mother of Father Mother of

X X difference X X difference son daughter (z value) daughter son ( z value)

I. Anterior lower face height factor

11. Mandibular depth factor

111. Anterior cranial inclination factor

IV. Posterior cranial inclination factor

height factor VI. Posterior cranial

base factor VII. Mandibular ramus

height factor VIII. Maxillary depth

factor IX. Anterior cranial

length factor

V. Anterior maxillary

0.44 3 0.31 2 - 0.953

0.32 2 0.40 :1 0.578

0.14 0.32 2 1.198

0.22 1 0.18 - 0.262

0.26 1 0.36 2 0.696

0.27 1 0.24 1 - 0.202

0.34 2 0.46 3 0.900

0.18 0.34 2 1.081

0.04 0.26 I 1.420

0.46 :< 0.44 3 -0.158

0.34 2 0.48 :J 1.061

0.37 :I 0.30 2 - 0.496

0.10 0.31 2 - 1.384

0.14 0.36 :I 1.483

0.39 :J 0.16 - 1.573

0.39 3 0.22 1 - 1.182

0.28 1 0.28 2 0.000

0.16 0.25 1 0.591

1 P < 0.05; 2 P < 0.01; P < 0.001

CRANIOFACIAL MEASUREMENTS IN FAMILY DATA

TABLE 6

427

lntrciclnss corrdcitions of M Z twins , DZ t w i m citzd siblings in ftrctor scan's

Intraclass correlations: t = ug/(ug + ( T ~ )

MZ twins DZ twins Siblings ( N = 6 1 ) Factors ( N =67) ( N =29)

I. Anterior lower face height factor 0.83 :I 0.27 0.36 3 11. Mandibular depth factor 0.68 8 0.20 0.17 1

111. Anterior cranial inclination factor 0.87 3 0.53 2 0.17 I IV. Posterior cranial inclination factor 0.61 :I 0.34 1 0.23 2

V. Anterior maxillary height factor 0.56 3 0.25 0.33 :I

VI. Posterior cranial length factor 0.71 3 0.52 2 0.34 3

VIII. Maxillary depth factor 0.64 3 0.49 2 0.25 2

IX. Anterior cranial length factor 0.78 :1 0.55 :j 0.27 2

VII. Mandibular r amus height factor 0.47 0.50 2 0.20 1

P < 0.05; P < 0.01; :I P < 0.001.

TABLE 7

Heritnbility czstimcctes i n fctctor scores

I . 11.

111. IV. V.

VI. VII.

VIII. IX.

Factors

Anterior lower face height factor Mandibular depth factor Anterior cranial inclination factor Posterior cranial inclination factor Anterior maxillary height factor Posterior cranial length factor Mandibulus ramus height factor Maxillary depth factor Anterior cranial length factor

Twinsa Parent-offsgrinyb h '=(s 'DZ- S ~ M Z ) / S ~ D Z hZ=b,,,P

- 0.76 3 (0.63-0.76) 0.54 3 (0.42-0.64) 0.51 (0.53-0.67) 0.53 3 (0.44-0.51) 0.69 3 (0.42-0.62) 0.52 3 (0.44-0.66) 0.48 I (0.51-0.67) 0.31 3 (0.41-0.56) 0.48 I (0.43-0.66) 0.57 3 (0.57-0.73)

0.31 (0.27-0.59) 0.43 8 (0.41-0.48) 0.50 (0.49-0.53) 0.37 :I (0.40) 0.572 (0.73) 0.34 3 (0.41)

0.50 1 (0.47-0.83) 0.44 3 (0.41-0.44)

a sZMZ, sz DZ lntrapair variances of MZ and DZ twins. Significance was estimated from F ratios '~,)Z-lS'MZ ).

bbo,,,: Regression coefficient of offspring on mean value of parents.

I P < 0.05; 2 P < 0.01; SP < 0.001, Heritability estimates obtained on the original ineasurements are shown in parentheses, where the

values indicate the range of the values of measurements which showed the high loadings in rotated factor analysis.

by nine common factors. Furthermore, these factors were shown to be identifiable and meaningful, and comparable in many ways to those of previous studies.

Brown et al. ('65) examined the factors that differentiated eleven cephalometric measurements in two populations of dif- ferent ethnic origin and found that, for each ethnic group, five principal factors were extracted and, of these, four were common to both groups. The authors found that the factors were most readily inter- preted after rotation than by examination of the principal factor loadings. The five rotated factors found in their study were: the mandibular length factor; the anterior nasal factor; the posterior nasal factor; the ramus height factor and the cranial base factor. These factors would appear to correspond respectively to Factor I1

(mandibular depth), Factor V (anterior maxillary height), Factor IV (posterior cranial inclination), Factor VII (mandibu- lar ramus height) and Factor IX (anterior cranial length) in the present study.

A similar study based on more extensive anthropometric measurements was con- ducted by Solow ('66). In this study, nine- teen factors were obtained from a total of 88 variables. As for the cephalometric mea- surements, seven factors were found to describe the 48 variables that were ob- tained from profile films. These seven fac- tors identified by Solow also correspond rather closely to the factors that emerged from our data.

The results of factor analysis of our data are in general agreement with the previ- ous studies of craniofacial morphology and suggest that, in order to understand

428 MINORU NAKATA, PAO-LO YU AND WALTER E. NANCE

the genetic control of craniofacial mor- phology, it may be more appropriate to examine the relevant variables as multi- variate factors rather than to treat them as independent traits.

Comparison of the correlations of father- offspring and mother-offspring provided no evidence for the existence of significant maternal effects on the nine factors. As shown in table 5 , mother-daughter cor- relations had higher values than the father-son correlations for six of the nine factors but in no case was the difference between correlations significant at the 5 percent level. The finding of a higher mother-daughter than father-son corre- lation would be consistent with the possi- bility that x-linked genes have some influ- ence on the trait in question.

Heritability based on regression coeffi- cients of offspring on the parental value estimates the proportion of additive ge- netic variance that influences the trait. As noted by Falconer ('60a), there is a complication in the use of the regression of offspring on mid-parent if the variance is not equal in the two sexes. However, since the differences in the variances of father and mother were not significant and the correlations between father-son and mother-daughter and between father- daughter and mother-son were similar, as shown in table 5, the regression coefficient of offspring on mid-parent would seem to provide a reasonable heritability estimate for the factor scores. The heritability esti- mates ranged from 0.31 to 0.57 and all were significant at the 0.1 percent level.

If it is assumed that the fraternal twins share a common environment to the same extent as identical twins, a heritabil- ity estimate can also be calculated from the twin data. However, this estimate in- cludes dominance variance in addition to the additive variance (Falconer, '60b) and, therefore, is called the coefficient of genetic determination.

In the present study, the heritabilities on twin data (table 7) range from 0.31 to 0.76 and exceed those of parent-offspring regressions except for the second, fifth and seventh factors. These findings sug- gest that dominance effects exist for some factors but not for others.

The heritability estimates derived from the twin data exceeded those based on the

parent-offspring regressions in only six of the nine factors. Thus, with the possi- ble exception of the anterior cranial length (IX) and anterior lower face height (I) factors there was little evidence for possi- ble dominance effects in the data.

A comparison of heritability estimates obtained from the factor scores with esti- mates from those original variables show- ing loadings for each factor is of some interest. As shown in table 7, the herita- bility values obtained for the factor scores generally fall within the range of the high loading individual variables. This is per- haps not surprising since each factor is a weighted sum of all variables.

Howells' ('53) study of factor scores in brothers demonstrated that the correla- tions tend to cluster about r = 0.63 for factors of long bone length and face length and about r = 0.39 for other body measurements. The values of sibling cor- relations in the present study ranged from 0.17 to 0.36 (table 6) and were consider- ably smaller than Howells' results. These differences may reflect the fact that our sibling sample combined male and female offspring, most of whom were still young and growing subjects. The generally high- er correlations that were observed in DZ twins in comparison with siblings pro- vides some indication that the adjustments for age and sex that were used in this study may not have completely corrected for individual variation in the onset of the pubertal growth. In contrast, the sib pairs examined by Howells were all adult males.

The factor which represents a linear combination of a set of variables under a common influence can be determined by the superimposition of environmental vari- ation to the underlying genetic determina- tion. In a previous study using the same cephalometric variables (Nakata et al., '74), nine independent genetic factors were found from the simultaneous solu- tion of intrapair difference covariance matrices from identical and fraternal twins by multivariate methods. Even though the number of dimensions was the same as that found in the present study, the combinations of variables con- tributing to each factor were not neces- sarily identical. For example, measure- ments of both mandibular length and height appeared to be influenced by a

CRANIOFACIAL MEASURE

single genetic factor in the twin study, while in the present analysis, where ge- netic and environmental influence were not clearly separated, two factors were identified as contributing to mandibular morphology. This suggests that, although some traits are determined by a common genetic factor, they may be so greatly modified by two or more independent en- vironmental factors during growth that the component variables appear in dif- ferent factors when an analysis is per- formed on unrelated individuals in the general population. On the other hand, Bailey ('56) found considerable similarity in the sets of variables which were influ- enced by genetic and environmental fac- tors in a study of osseous morphology in mice, a fact suggesting that for some traits both genetic and environmental factors can influence the same morpho- genic pathway. A similar concordance of genetic and environmental effects is also evident in human material (Nakata et al., '74). Clearly, further study of these ef- fects throughout the growth will be re- quired for a complete understanding of the interaction of genetic and environ- mental influences on craniofacial mor- phology.

ACKNOWLEDGMENTS

The authors are grateful to Drs. M. Mazaheri and W. M. Krogman of the

:MENTS IN FAMILY DATA 429

Lancaster Cleft Palate Clinic for providing some of the data used in this analysis.

LITERATURE CITED Bailey, D. W. 1956 A comparison of genetic and

environmental principal components of mor- phogenesis in mice. Growth, 20: 63-74.

Brown, T., M. J. Barrett and J. N. Darroch 1965 Craniofacial factors in two ethnic groups. Growth, 29: 109-123.

Dixon, W. J. 1964 BMD Biomedical Computer Programs UCLA.

Falconer, D. S. 1960a Introduction to Quanti- tative Genetics. Ronald Press Co., New York, pp. 150-164.

1960b Introduction to Quantitative Ge- netics. Ronald Press Co., New York, pp. 165- 185.

Holzinger, K. J. 1929 The relative effect of na- ture and nuture on twin differences. J. Educ. Psychol., 20: 241-248.

Howells, W. W. 1953 Correlations of brothers in factor scores. Am. J. Phys. Anthrop., 11: 121 -140.

Kaiser, H. F. 1958 The varimax criterion for analytic rotation in factor analysis. Psycho- metrika, 23: 187-200.

Nakata, M., P. L. Yu, B. Davis and W. E. Nance 1974 Genetic determinants of craniofacial morphology: A twin study. Ann. Hum. Genet., 37: 431-443.

Potter, R. H. Y., P. L. Yu, A. A. Dahlberg, A. D. Merritt and P. M. Conneally 1968 Genetic studies of tooth size factors in Pima Indian families. Am. J. Hum. Genet., 20: 89-100.

Solow, B. 1966 The pattern of craniofacial as- sociations. Acta odont. scand., 24: suppl. 46, pp. 1-174.

Wright, S. 1932 General, group and special size factors. Genetics, 1 7 : 603420 .