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Estimation of age from the pubic symphysis by means of multiple regression analysis.

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Estimation of Age from the Pubic Symphysis by Means of
Multiple Regression Analysis
KAZURO HANIHARA AND TAKA0 SUZUKI
Department of Anthropology, Faculty
Tokyo 113, Japan
of
Science, The University of Tokyo,
KEY WORDS Age change. Pubic bone. Pubic symphysis Age
estimation . Assessment of age
ABSTRACT
This study has been carried out to assess the age from the pubic
symphysial surface employing a multiple regression analysis and a quantification theory model I analysis. Using partial regression coefficients and/or normalized scores obtained from the analyses, ages of skeletal remains can be quantitatively estimated with a fairly high reliability. The use of this method is, however, limited to the samples between 18 and 38 years of age, because age changes
in the symphysial surface show large variations after about 40 years. The
reliability of this method was also examined.
Ever since Todd ('20-30) described age
changes in the pubic symphysis, it has been
used as a good age indicator of skeletal remains. Because of its usefulness, a number of
studies which applied this method on different
samples, both present and past, have been reported.
Techniques of age estimation have been
improved by several authors. For instance,
Hanihara ('52) applied this method in analyzing 135 pairs of male Japanese pubic bones
and found little difference in assessment of
ages between Caucasians and Japanese. If the
ages of the Japanese pubic bones are estimated by the Caucasian standards, they tend
to be two to three years older than the actual
ages. He also provided a table which supported
age estimation by comparing each item with
corresponding characteristics observed in the
pubic bones.
Brooks ('55) used the Todd method to estimate ages of 470 American Indians. As a result, she found that the correlations between
estimated and actual ages were higher in
males than in females. In addition, she suggested that the Todd's phases V-VIII (27-44
years) should be adjusted to make them
shifted about three years younger. This finding agrees quite well with that of Hanihara.
McKern and Stewart ('57) investigated 450
AM. J. PHYS. ANTHROP. (1978)48: 233-240.
skeletal remains of war dead and developed
a variant of the Todd's scoring method for
assessing of age from the pubic symphysis.
They selected three components which show
relatively large age changes. Each component
is divided into five stages and the combinations of the three scores show a high correlation with the actual ages. This method makes
age estimation easier and more accurate than
the Todd's method because the scoring eliminates a subjective bias in interpretation of
bone metamorphosis.
Krogman ('621 summarized these and other
methods of age estimation from skeletal remains in which the pubic bones as an age
indicator were described in detail.
In the present study, we also adopted the
scoring element of Todd's method, but the
treatment of the scores was somewhat different from that developed by McKern and
Stewart. In our case, scores obtained from the
pubic symphysis were used as raw data for
a multivariate statistical analysis. Through
this method, the age can be estimated by calculating a simple linear function derived from
the regression analysis.
Although still in a preliminary stage of in' A preiiminary report of this article was presented to the Sixtieth
Conference of the Medico-Legal Society of Japan held in 1976 at Sapporo, Japan
233
234
KAZURO HANIHARA AND TAKA0 SUZUKI
vestigation, the method suggested here may
have some advantages over others in assessing
ages from skeletal remains.
assessment of age in older individuals cannot
reliably be made unless age changes in the
other parts are examined in combination.
MATERIALS
METHODS
This study is based on 70 pairs of pubic
bones of recent Japanese, of which 33 belong
to the collection of the Department of Anatomy, the University of Tokyo; and 37 to the
Department of Anatomy, Sapporo Medical
College. Besides these materials, ten samples
of pubic bones selected a t random were used
for a blindfold test to examine the reliability
of age estimation.
Since Todd (‘20) found no clear difference
between sexes in age changes of the pubic
bones, both sexes were combined in this study.
I t is desirable, however, to separate male and
female groups in the future studies, because
assessment of age of females by the pubic symphysis can hardly be as accurate as in the case
of males (Stewart, ’57).
The ages of the specimens ranged from 18 to
38 years. As Todd (‘20) stated that the pubic
symphysis is “a much more reliable age indicator from 20 to 40 than after the latter
age,” the most accurate estimation of age
from this part is limited to the individuals
who are under about 40 years of age. Thus,
Scoring of age changes in the
pubic symphysis
Based on the morphological analysis and
our experience, the following seven morphological features in the pubic symphysis were
selected for assessment of age: horizontal
ridges and furrows, pubic tubercle, lower end,
dorsal margin, superior ossific nodule, ventral
bevelling, and symphysial rim. These features
correspond well with those pointed out by
Todd (’20) as showing evident age changes.
Age changes in each of these morphological
feature were scored on scales of 1 through 4
(table 1).Since morphological differences between adjacent scores are fairly distinct, the
scoring is relatively easy for observers with a
little experience. In the present study, observations were made by each author separately
and the scores obtained were cross-checked to
verify objectivity of the scoring. An inconsistency of 1point in score was found in 42 cases
out of 490 observations (8.57%),so that the
concordance between the two observers was
fairly satisfactory.
TABLE 1
Scoring ofuge changes in the articular surface of the pubis
Variable
Morphological
feature
X,
Horizontal
ridges and
furrows
X2
Pubic tubercle
X3
Lower end
x,
Dorsal margin
X6
Superior
ossific
nodule
Ventral bevelling
x,
Score
Morphological change
1
2
3
4
Distinct
Furrows become shallow
Trace
No longer visible
Attached by cartilage
United
Indistinct
Narrow ridge
Broad ridge
None
Interrupted narrow ridge
Narrow ridge over full length
Broad ridge
None
Present
No longer visible
None
Incomplete
Completed over full length
Upper part no longer visible
Incomplete
Whole symphysial surface bordered
by a broad rim
1
2
1
2
3
1
2
3
4
1
2
3
1
2
3
4
X7
Symphysial rim
1
2
AGE ESTIMATION FROM PUBIC SYMPHYSIS
‘TABLE 2
Partial repression coefficients
Variable
Coefficient
Standard error
of coefficient
X,
1.40
0.48
2 11
1.91
0.27
1.45
0.14
10.14
0.7169
1.1336
0.9029
0.7694
0.9300
0.5666
0.9564
1.6703
X2
X3
x,
X,
XS
~
X?
Constant
Methods
of
statistical analysis
Since there are seven morphological features or variables in the present case, the
assessment of age can be made by employing a
multiple regression analysis, in which the
scores for morphological features correspond
to independent variables and the age to be
assessed to dependent variables.
As is well-known, the basic model of the
multiple regression analysis is
YI=bO+blxil t b ~ x i 2 f. . . +bGip+ei,
where bo is a constant, b,fi -1,Z, . . p ) is a partial regression coefficient of y to x, and e , is a
residual or an error. In the present case, XG
stands for a score for t h e j - t h morphological
feature in the i-th specimen, andyi for the age
of the i-th specimen.
Another model employed in this study is one
called “quantification theory model I” devised
by Hayashi (’52). In this model the independent variables are represented by discrete
numbers and the dependent variables by
continuous numbers. Mathematically, i t is
equivalent to a multiple regression equation
to which the dummy variables are applied.
Also in this case, the scores for each morphological feature and the actual age of each
specimen were used a s raw data for calculation.
The calculation was processed by the 0 s - 7
system of the University of Tokyo Computer
Centre using the programs CMREGl and
CQUANT1. The former is a program for a
multiple regression analysis and the latter for
a quantification theory model I analysis.
Description ofage changes i n the
pubic symphysis
1. Horizontal ridges and furrows
The ridges and furrows on the symphysial
surface are very distinct under 20 years of age,
when the ridges are high and the furrows deep
235
and sharp. In the ages between 20 and 23
years, the furrows become shallow and the
ridges relatively dull. This weakening continues until about 27 years of age. After 28
years, with rare exception, this feature disappears completely and the symphysial surface
becomes flat.
2. Pubic tubercle
In pubic bones under 23 years, this tubercle
is attached through cartilage, so that the
epiphysial line is visible. After 24 years, however, the tubercle unites completely with the
pubic bone without exception.
3. Lower end
Before 22 or 23 years, the lower end of the
symphysial surface is indistinguishable from
the upper end of the inferior pubic ramus.
From about 23 to 30 years, the lower part of
symphysial surface is bordered by a narrow
ridge, and after about 30 years, the ridge is
broadened and, in many cases presents a
triangular swelling.
4. Dorsal margin
Until 19 years of age, no marginal ridge borders the symphysial surface, and a t about 20
years, a trace of the ridge appears a t the dorsal
border of the surface. In individuals older than
27 years, formation of the ridge is nearly completed, though still narrow, over the full
length of the dorsal margin. In about half of
the cases, the ridge is broadened after 33 or 34
years, but varies widely. In the present specimens 12 out of 22 (54.4%)show broadened
margins (score 41, but the remaining ten cases
still show narrow margins (score 3).
5. Superior ossific nodule
This formation appears a t the upper part of
the pubic surface for a limited period. None of
the nodule can be observed in the individuals
under 20 years of age, but from 21 to 27 years,
it is easily recognizable, and then disappears
again. Since age changes of this nodule are
relatively distinct, its appearance or disappearance represents a good age indicator for
the period from early to late twenties.
6. Ventra 1 bevel ling
Until 22 years, the ventral border of the
pubic symphysial surface coincides with the
ventral surface of the pubic bone. In older
ages, however, a narrow surface appears between the two surfaces. Todd (’20) called this
236
KAZURO HANIHARA AND TAKA0 SUZUKI
TABLE 3
Analysis of variance for the regression
Source of
variation
Degrees of
freedom
Sum of
squares
Variance
Value of F
2377.70
339.66
51.50
6.60
Attributable to
regression
Deviation from
regression
62
408.92
Total
69
2786.62
7
intermediate surface ventral bevelling, and
regarded it an useful feature for age estimation. It appears a t about 23 years, but is not
completed until about 27 years. During the
ages between 28 and 33 years, it is completely
formed along the full length of the pubic symphysis. In the individuals older than 33 or 34
years, the upper part of the ventral bevelling
disappears, but variations of this change are
relatively large.
7. Symphysial rim
In older individuals, the symphysial surface
is occasionally bordered by a relatively broad
and dull rim. Such cases can be found among
individuals older than 30, and their frequencies increase after 34 years, although the variation is again quite large. Therefore, the age
of an individual with a distinct rim can be
safely estimated to be in the middle thirties or
older, but an individual without a rim may not
necessarily be young.
TABLE
Variable
XI
X2
X3
X4
XS
XS
RESULTS
Multiple regression analysis (MRA)
The partial regression coefficients for the
seven variables, the constant, and their standard errors are shown in table 2. Based on the
results, the following formula can be used for
estimation of age:
Age=10.14+1.40X1+0.48X2+2.11X3+1.91&
-0.27Xs+1.45&+0.14X7.
The coefficients for the variables X I , XB,X,
and X6 are larger than those for X2, X5 and X7,
and are more useful for estimation of age.
Actually, the latter three variables correspond to the morphological features showing
larger variations.
The results of multiple regression analysis
show that the correlation coefficient between
the observed and estimated ages, or the multiple correlation coefficient, is 0.9237, the
coefficient of determination is 0.8533, and
the standard error of dependent variables is
2.5682. These values show that the formula
above is quite useful for the present purpose.
In addition, an analysis of variance shows that
4
Normalized scores and partial correlation coefficients
derived from quantification theory model Ianalysis
x
7
Morphological
Normalized
score
score
1
2
3
4
1
2
1
2
3
1
2
3
4
1
2
3
1
2
3
4
1
2
18.08
19.36
21.46
21.74
0.00
0.95
0.00
-0.33
3.52
0.00
0.86
2.72
5.25
0.00
1.95
2.88
0.00
0.77
0.37
2.82
0.00
-0.85
Partial
correlation
coefficient
0.25
0.11
0.49
0.37
0.23
0.34
0.12
the regression is highly significant under the
0.1 percent level (table 3).
Quantification theory model Z
analysis (QMI)
As this model was proposed to solve multiple
regression equations with the independent
variables given by dummy variables, the
model is more suitable for the present data
than the usual multiple regression analysis.
As a result of calculation, normalized scores
which give the best estimates of the dependent variables are obtained (table 4). The age
of an unknown individual can be assessed by
adding the normalized scores which correspond t o each score for the morphological features. For example, the age of an individual
who shows the morphological score 3222231 is
assessed by the following formula:
Age=21.46+0.95 -0.33
= 25.26.
+ 0.86+ 1.95+0.37 +O.O
237
AGE ESTIMATION FROM PUBIC SYMPHYSIS
TABLE 5
Reliability in three age groups
Standard error of
estimated ages
Age group
No. of specimens with
large residualq
No. of
specimens
MRA '
(/MI
MRA
&!MI
26
17
27
2.1960
2.1791
2.7408
1.9055
1.9109
2.7832
5 (19.2%
3 (17.69;;)
7 (25.9%)
3 (11.5%)
1 (18-25 yrs)
2 (26-30yrsi
3 (31-38 yrsJ
2 (11.8%)
7 (25.9%)
' Multiple regression analysis
Quanrification theory model 1 analyais.
Number of specimens showing more than 3.0 of residuals.
The multiple correlation coefficient, a correlation coefficient between the actual and
estimated ages, is 0.9332, and the coefficient
of determination is 0.8703. These values are a
little bit higher than those for a multiple
regression analysis, and show the usefulness
of this model for the present purpose.
The partial correlation coefficients in table
4 show the rates of contribution of each variable to estimation of age. Among the seven
variables, the third, fourth and sixth variables
show larger coefficients than the others, so
that they seem to be more useful for assessment of age. This result is fairly parallel with
that obtained from the multiple regression
analysis.
DISCUSSION
Reliability of the two methods is discussed
through analyses of the residuals. Since the
ranges of residuals are expected to be different a t different ages, reliability is examined for three age groups separately.
First, standard errors of dependent variables were calculated to compare the amounts
of residuals between the two models and
among the three age groups (table 5 ) . In the
age groups 1 and 2, the values are smaller in
the quantification theory model I analysis
(QMI) than in the multiple regression analysis (MRA), while in the age group 3, the values
are almost the same in both analyses.
On the other hand, in the former two age
groups, frequencies of the specimens representing residuals of more than 3.0 are higher
in MRA than in QMI, while those in the last
age group are almost the same in both
methods.
These results show that the reliability of
QMI is slightly higher than that of MRA for
the samples belonging to the age groups 1and
2 , while the two methods represent almost the
same reliability for those older than 30 years,
Such a difference between the two methods
may result from a difference in the mathematical models.
TABLE 6
Confidence ranges of the estimated ages at the 5%level
Loweriupper limits
Age
group
MRA
1
2
3
-5.09- +4.04
-5.36-- +3.43
-3.00- 16.46
Kesidual
=
QMI
-3.33-
-2.39-6.51-
+4.48
+4.57
i4.89
(Actual age) - {Estimaced age)
Secondly, rejection limits for residuals a t
the 5% level were calculated for each age
group to estimate confidence range of the estimated ages (table 6). The results again show
that QMI represents higher reliability than
MRA for the first two age groups. In addition,
one can notice the following trends: if MRA is
employed, the ages are apt to be estimated a
little older than the actual ages in the age
groups 1 and 2, but the reverse is the case in
age group 3; when QMI is used, the ages tend
t o be estimated a little younger than the
actual ages in the first two age groups, but
again the reverse is true in the third age
group.
As a result, the confidence range of the estimated age should be determined by drawing
attention to the age group in which the specimen is included, and to the method employed.
Finally, blindfold tests were carried out
using ten samples selected a t random. They
were not included in those used for the present
analysis. Table 7 shows that the ages estimated from QMI are closer to the actual ages
than those from MRA in seven of them. Although the difference is small, reliability of
QMI seems to be slightly higher than that of
MRA as shown by the analysis of residuals.
In conclusion, the following principles are
recommended in assessing ages:
(1) The result of the quantification theory
model I analysis is more reliable than that of
the multiple regression analysis, though the
difference between the two methods is negligible;
238
KAZURO HANIHARA AND TAKA0 SUZUKI
TABLE 7
Blindfold tests of estimation of age
Estimated age
Specimen
No '
Morphological
score
Actual
age
MRA
QMI
T2126
T2161
T 2099
T 2176
s 91
T 2593
T 2086
T2178
T 2158
S 96
1111111
21 1 1 111
2112111
2122111
2121211
4223321
4233331
4233341
3233341
4233341
18
20
20
21
25
28
31
31
33
37
17.2
18.6
20.5
22.7
21.0
28.8
32.3
32.4
32.4
33.8
18.1
19.4
20.2
19.9
21.0
28.7
32.2
34.6
34.4
34.6
' T, University
of Tokyo, S, Sapporu Medical College.
(2) The confidence limits of the estimated
ages should be carefully checked by referring
to table 6 ;
(3) When t h e age of the specimen is expected to be younger than 18 years or older
than 38 years, the methods presented here
cannot be used, and, in such a case, other
methods should be employed.
ACKNOWLEDGMENTS
The authors a r e deeply grateful to Professor
T. Ooe of t h e Department of Anatomy, the
University of Tokyo, and Professor K. Mitsuhashi of the Department of Anatomy, Sapporo Medical College, for their kind permission to investigate t h e pubic bones which
belong to their collections.
LITERATURE CITED
Brooks, S. T. 1955 Skeletal age a t death: reliability of
cranial and pubic age indicators. Am. J. Phys. Anthrop.,
13 567-597.
Hanihara, K. 1952 Age changes in the male Japanese
pubic bone. J. Anthrop. Soc. Nippon, 62: 245-260. (In
Japanese with English summary.)
Hayashi, C. 1952 On the prediction of phenomena from
qualitative data and the quantification of qualitative
data from the mathematico-statistical point of view. Ann.
Inst. Statist. Mathem., 3: 69-98.
Krogman, W. M. 1962 The Human Skeleton in Forensic
Medicine. Charles C Thomas Publisher, Springfield,
Illinois.
McKern, T. W., and T. D. Stewart 1957 Skeletal age
changes in young American males. Headquarters Quartermaster Res. & Develop. Command, Technical Report
EP-45, Natick, Massachusetts.
Stewart, T. D. 1957 Distortion of the pubic symphyseal
surface in females and its effect on age determination.
Am. J. Phys. Anthrop., 15: 9-18.
Todd, T. W. 1920-30 Age changes in the pubic bone.
1920 I. The male white pubis. Am. J. Phys. Anthrop., 3:
285-334.
1921 II. The pubis of the male Negro-white hybrid; 111.
The pubis of the white female; IV. The pubis of the female
Negro-white hybrid. Am. J. Phys. Anthrop., 4: 1-70.
1921 V. Mammalian pubic metamorphosis. Am. J. Phys.
Anthrop., 4: 333-406.
1921 VI. The interpretation of variations in the symphysial area. Am. J. Phys. Anthrop., 4: 407-424.
1923 VII. The anthropoid strain in human pubic symphyses of the third decade. J. Anat., 57: 274-294.
1930 VIII. Roentgenographic differentiation. Am. J.
Phys. Anthrop., 24: 255-271.
PLATE 1
EXPLANATION OF FIGURES
Estimated age
Figure
Morphological
score
Actual
age
MRA
QMI
1 (right)
2211211
20
19.0
22.3
2 (right)
4233331
29
32.4
32.2
3 (left)
4233332
33
32.6
31.3
4 (right)
4234342
37
36.0
36.3
AGE ESTIMATION FROM PUBl(' SYMPtlYSlS
Kazuru Hanihara and Taka" Suzuki
P1.A'L'Y 1
239
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