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

код для вставкиСкачатьEstimation 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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