Cite as: Archiv EuroMedica. 2022. 12; 3: e1. DOI 10.35630/2199-885X/2022/12/3.11

Received in revised form 28 April 2022;

Accepted 29 April 2022

One of the most complex problems in forensic medical expertise is the process of identification of unknown corpses and their parts, which very often include bone remains. Sometimes it is practically impossible to collect the data needed for police investigation because the most important parts of the skeleton such as skull, pelvic bones and long trabecular bones are absent. The aim of the study was to develop new methods for sex determination from the clavicle of an adult person based on the mathematical and statistical analysis of their osteometric properties. For this purpose bone samples from three skeletal collections were used: collection of the Department of Anthropology of Lomonosov Moscow State University; collection of the Department of Physical Anthropology of the Peter the Great Museum of Anthropology and Ethnography (St. Petersburg), and the The Robert J. Terry Anatomical Skeletal Collection stored at the Department of Physical Anthropology of the Smithsonian’s National Museum of Natural History (Washington). The study demonstrated the possibility of correct sex determination from the clavicle using the five-interval diagnostic table suitable for quick sex assessment and multiple discriminant models with an accuracy of correct sex estimation between 85% and 97.5%. The methods described in the article can be applied not only in forensic context (especially when working with a limited set of isolated skeletal elements or their fragments), but also in the physical and medical anthropology for reconstructing an unidentified individual’s biological profile.

**Keywords
– **clavicle,
sex estimation, multivariate
discriminant analysis, forensic
anthropology, human identification.

Forensic examination of unidentified corpses and skeletal remains found in a variety of circumstances (e.g., mass disasters, homicide, infanticide etc.) present a significant problem for a medical examiner. The use of DNA analysis, osteological and radiological methods provides substantiated answers to a fairly wide range of questions related to the common and specific features of the victim’s personality. The methods of forensic anthropology are widely used in forensic human identification around the world; unlike the methods of molecular genetics, they do not require complex equipment, expensive consumables, and much time for data processing. If bones are well preserved, sex determination generally does not pose significant difficulties. According to Iscan et al. [1], the accuracy of sex determination reaches almost 100% when all the skeletal elements are present. However, it should be noted that the forensic expert often has to deal with an incomplete set of fragmented remains, where such skeletal objects, significant for identification, as the skull, the pelvic bones, and even the long bones may be missing. In such cases, a valuable importance is given to the methods that involve teeth and such bones as vertebrae, ribs, hyoid bone, scapula, small bones of hands and feet. This list can be expanded if we mention the clavicle as one of the least studied (from the anthropological and forensic perspectives) human skeletal elements.

Currently, there is a significant increase in the number of research papers dedicated to sex identification from the clavicles, and most of them apply up-to-date mathematical statistics, which is of great importance for the forensic practice [2-7]. Thus, the accuracy of sex determination using the stepwise linear discriminant analysis in different populations varies from 70% to 95%.

was
to** **develop
new methods for sex** **determination
from skeletonized clavicles using their osteometric measurements with
subsequent mathematical and statistical processing of the measured
data.

Bone samples (right clavicles) from
three skeletal series were used: series 1 – a collection of
skeletons from the Department of Anthropology of Lomonosov Moscow
State University (Russians, mid-20th century, N=83); series 2 –
«Staraya Ladoga» (Russians, late 18^{th} century, N=35) from the osteological collection belonging to the
Department of Physical Anthropology of Peter the Great Museum of
Anthropology and Ethnography (the Kunstkamera); series 3 – The Robert J. Terry Collection (Caucasian Americans, 20^{th} century, N=114) from the Department of Physical Anthropology of the
Smithsonian’s National Museum of Natural History, Washington, USA. The total number
of bone samples examined was 232. The definitions of clavicle
measurements follow
the standard methodology [8]:

СLМ-1. The total length of the clavicle: the distance between the most medial point of the sternal end of the clavicle and the most lateral point of its acromial end.

СLМ-2. The length of the clavicle diaphysis at the posterior edge: the straight distance between the most medial point of the shoulder end at the posterior edge and the most dorsal point of the epiphysis.

СLМ-3. The length of the diaphysis along the posterior surface: the length along the surface of the posterior edge of the bone from the most medial point of the humeral end to the most dorsal point of the epiphysis.

СLМ-4. The length of the clavicle shaft: the distance from the sternal end of the clavicle to the most forward-protruding point of its diaphysis. The value is measured in parallel with the total length of the clavicle (CLM-1).

СLМ-5. The clavicle circumference: the perimeter of the clavicle in the middle of the shaft. The measurement site is defined as half the total length of the clavicle.

СLМ-6A. The sagittal diameter of the clavicle: the straight distance between the anterior and the posterior edges of the mid-shaft of the clavicle.

СLМ-7A. The vertical diameter of the clavicle (clavicle thickness): the distance between the cranial and the caudal surfaces of the mid-body of the clavicle.

СLМ-6. The largest diameter of the clavicle: the empirically determined maximum size at the mid-shaft of the bone.

СLМ-7. The smallest diameter of the clavicle: the empirically determined minimum size at the mid-shaft.

СLМ-8. The height of the clavicle shaft arc: the height of the most forward-protruding point of the anterior side of the clavicle shaft edge above the straight line connecting the most retracted points of the sternal and the acromial ends of the clavicle at its posterior side.

СLМ-9. The height of the arc of the clavicle acromial end: the height of the most forward-protruding point of the anterior side of the clavicle acromial end above the straight line connecting the most retracted points of the sternal and the acromial ends of the clavicle at its posterior side.

СLМ-8A. The depth of the sternal end arc: the projection distance from the deepest point of the sternal end arc to the tangent passing through the apex of the acromial end arc and the posterior edge of the sternal end.

СLМ-9A. The depth of the acromial end arc: the projection distance from the deepest point of the acromial end arc to the tangent passing through the apex of the sternal end arc and the anterior edge of the acromial end.

СLМ-10. The length of the deltoid tuberosity: the straight distance between the most anterior point of the clavicle acromial end to the most medial point of its deltoid tuberosity.

СLМ-11. The width of the clavicle acromial end: the projection distance between the most protruding points of the ventral and the dorsal edges of the clavicle acromial end.

Osteometric measurements were collected using a standard sliding caliper, osteometric board, and millimeter measuring tapes. Computer data processing was performed using the StatSoft STATISTICA 10 and Microsoft Excel 2007.

**Sex
determination using the univariate discriminant analysis. **Univariate
discriminant analysis (UDA) involves creation of a five-interval
evaluation scale (chart) based on a certain number of differential
osteometric parameters calculated by descriptive statistics using the
following formulas:

- Reliably
male interval: >Х
_{♀}+ 3,3σ_{♀}; - Probably
male interval: Х
_{♀}_{♀}_{ }– Х_{♀}_{ }≤Х +3,3σ_{♀}; - Indefinite
interval: Х
_{♂}_{♂}_{ }– Х_{♀}+1,54σ_{♀} - Probably
female interval: Х
_{♂}-3,3σ_{♂}– Х_{♂}-1,54σ_{♂} - Reliably
female interval: <Х
_{♂}- 3,3σ_{♂}

Table 1 shows a one-dimensional model for sex determination, using 13 standardized measurements of the right clavicle. This model is configured as a simple-to-use diagnostic chart and can be regarded as a «quick» method, which does not require any time-consuming calculations. Sex determination using this model implies three types of solutions:

- Practically reliable (correct classification accuracy – 85%): applies when one or more measurements fall within the reliable intervals of the scale, or when 9 and more measurements fall within one of the probable intervals of the scale.
- Probable (correct classification accuracy<85%): applies if none of the requirements listed in clause 1 apply or if the difference between the number of measurements in the «probably male» and the «probably female» intervals is 4 and more. If all the measurements qualify as probable, the sex is determined based on their absolute count.
- Indefinite: applies if all the measurements fall within the indefinite interval or if the difference between the number of measurements in the «probably male» and the «probably female» intervals is three and less. In this case, the model should be refused, and it is recommended to continue the procedure using a larger set of measurements or applying a multivariate discriminant analysis (MDA).

Table 1. Sex estimation from the clavicle using the univariate discriminant analysis

Measurements | Female | Undetermined intervals, mm | Male | ||

Reliable intervals, mm | Probable intervals, mm | Probable intervals, mm | Reliable intervals, mm | ||

CLM1 |
≤127,4 | 127,5-140,6 | 140,7-147,5 | 147,6-160,0 | ≥161,0 |

CLM4 |
≤33,9 | 34,0-44,9 | 45,0-57,0 | 57,1-67,1 | ≥67,2 |

CLM5 |
≤28,5 | 28,6-34,0 | 34,1-38,8 | 38,9-44,1 | ≥44,2 |

CLM6 |
≤9,2 | 9,3-11,6 | 11,7-13,3 | 13,4-15,4 | ≥15,5 |

CLM6A |
≤7,6 | 7,7-10,4 | 10,5-12,8 | 12,9-14,9 | ≥15,0 |

CLM7 |
≤6,5 | 6,6-8,4 | 8,5-10,0 | 10,1-11,7 | ≥11,8 |

CLM7A |
≤7,1 | 7,2-9,3 | 9,4-11,6 | 11,7-13,9 | ≥14,0 |

CLM8 |
≤19,5 | 19,6-25,7 | 25,8-32,0 | 32,1-37,3 | ≥37,4 |

CLM8A |
≤9,3 | 9,4-14,1 | 14,2-21,2 | 21,3-26,3 | ≥26,4 |

CLM9 |
≤20,3 | 20,4-27,7 | 27,8-34,1 | 34,2-39,1 | ≥39,2 |

CLM9A |
≤2,4 | 2,5-8,8 | 8,9-16,7 | 16,8-20,6 | ≥20,7 |

CLM10 |
≤30,0 | 30,1-38,9 | 39,0-50,8 | 50,9-60,0 | ≥61,0 |

CLM11 |
≤14,1 | 14,2-19,7 | 19,8-25,7 | 25,8-30,5 | ≥30,6 |

The data obtained supplement the available information on the individual variability of the clavicle osteometrics [6]. It should be noted that the accuracy of sex determination using the UDA method is lower than with the multivariate methods. However, if the skeletal remains are very fragmented, this method is the only available so far. To establish the degree of correlation between the sex constant and the measured osteometric parameters, a correlation analysis was conducted that showed a statistically significant correlation (P-value = 0.01) for all the measurements studied, except for CLM-9A. Later on, these measurements were selected to plot multi-dimensional diagnostic models.

**Sex determination using the
multiple discriminant analysis**.
Using the multiple discriminant analysis (MDA), 6 diagnostic models
for sex determination were calculated. They can be divided into two
groups: models with an extended and a reduced set of measurements
that have the maximum achievable accuracy from 96.3% to 97.5%. In all
cases, the models for which the Wilks' lambda value does not exceed
0.27 were selected. The coefficients of the discriminant functions
(models) are presented in Table 2.

Table 2. Sex estimation from the clavicle using the multiple discriminant analysis

Measurements |
Coefficients | |||||||||||

Model 1 | Model 2 | Model 3 | Model 4 | Model 5 | Model 6 | |||||||

♂ | ♀ | ♂ | ♀ | ♂ | ♀ | ♂ | ♀ | ♂ | ♀ | ♂ | ♀ | |

CLM-1 |
4,303 | 4,055 | 4,329 | 4,088 | 4,339 | 4,096 | 3,320 | 3,047 | 3,622 | 3,330 | 3,615 | 3,323 |

CLM-2 |
-1,082 | -1,145 | -0,941 | -0,972 | -0,960 | -0,989 | ||||||

CLM-3 |
0,178 | 0,216 | ||||||||||

CLM-4 |
0,843 | 0,692 | 0,845 | 0,694 | 0,848 | 0,697 | 0,850 | 0,699 | 0,685 | 0,544 | 0,685 | 0,543 |

CLM-5 |
0,429 | 0,360 | 0,448 | 0,383 | ||||||||

CLM-6 |
-0,198 | -0,577 | -0,234 | -0,622 | 0,416 | -0,066 | 1,086 | 0,624 | 1,991 | 1,474 | 2,543 | 2,002 |

CLM-6A |
-1,488 | -0,994 | -1,566 | -1,089 | -1,674 | -1,182 | -2,622 | -2,157 | -2,656 | -2,190 | -3,691 | -3,179 |

CLM-7 |
8,833 | 7,974 | 8,882 | 8,034 | 9,418 | 8,492 | 9,585 | 8,664 | 9,339 | 8,433 | 10,048 | 9,111 |

CLM-7A |
3,831 | 3,464 | 3,822 | 3,452 | 3,974 | 3,583 | 4,824 | 4,458 | 3,692 | 3,394 | 2,781 | 2,524 |

CLM-8 |
6,899 | 6,020 | 6,919 | 6,045 | 7,020 | 6,131 | 7,388 | 6,509 | 6,948 | 6,096 | 6,421 | 5,592 |

CLM-8A |
-5,781 | -5,106 | -5,699 | -5,006 | -5,764 | -5,061 | -5,907 | -5,209 | -5,591 | -4,912 | -4,875 | -4,227 |

CLM-9 |
1,613 | 1,304 | 1,644 | 1,341 | 1,642 | 1,339 | 1,563 | 1,258 | 1,684 | 1,372 | 2,713 | 2,356 |

CLM-9A |
2,735 | 2,650 | 2,753 | 2,672 | 2,768 | 2,685 | 2,213 | 2,113 | 2,045 | 1,956 | ||

CLM-10 |
0,587 | 0,543 | 0,582 | 0,537 | 0,602 | 0,555 | 0,732 | 0,688 | ||||

CLM-11 |
2,239 | 2,005 | 2,201 | 1,959 | 2,218 | 1,974 | 2,354 | 2,114 | 2,329 | 2,090 | 1,927 | 1,706 |

Constant |
-494,562 | -403,006 | -494,502 | -402,916 | -494,351 | -402,806 | -487,752 | -395,804 | -483,737 | -392,259 | -474,957 | -384,232 |

Correct
classification accuracy,
% |
97,5 | 96,3 |

To work with
these models, the researcher needs to substitute the values of
the measured variables into the equations and solve them. For
example, the Model 1, written in a linear form, will look as:
Y=CLM-1*4,303+CLM-2*(-1,082)+CLM-3*0,178+CLM-4*0.843+...+(-494,562).
The highest value of the function determines the sex of the bone. The
probability of referring the studied case to the male or the female
population is determined by the value of the Pl=1/(1+e^{-l})
function relative to l. To do this, one should select the maximum of
the two obtained values of the discriminant Y-function and
subtract the minimum one from it. The resulting difference will
correspond to l, knowing which it is possible to determine the
reliability level of the solution by the table of P1 function values
[9, *248-277*].

Expert conclusions can be formulated as one of three options:

- The solution is reliable if: 1,0>Pl≥0,95
- The solution is probable if: 0,95>Pl≥0,75
- The solution is rejected if: Pl<0,75

**Sex
determination using canonical discriminant analysis.** Calculations of diagnostic canonical functions (Table 3) were carried
out on a combined sample of clavicles from Series 1 and 3. They solve
the problem of discrimination within the same equation and are more
labor-efficient. The probability of attributing an expert case to
male or female groups is done in two stages: first approximately,
focusing on the values of the group centroids (GC), then by the
values of the Pl function. To do this, it is necessary to subtract
the values of the indicator SP (Section Point, the value of the
dividing plane of male and female groups) from the resulting function
value, which is the arithmetic mean of two GC in each function. The
resulting difference corresponds to l, by which the probability level
of the Pl function is searched for and the corresponding expert
conclusion is accepted (similar to the one described above).

Table 3. Sex estimation from the clavicle using the multiple canonic discriminant analysis

Measurements |
Diagnostic Coefficients |
|||

CDA 1 |
CDA 2 |
CDA 3 |
||

CLM-1 |
-0,10675 | 0,0990 | -0,10565 | |

CLM-5 |
-0,19195 | 0,1386 | -0,11495 | |

CLM-8 |
0,1299 | -0,22107 | ||

CLM-8A |
0,13548 | |||

CLM-9 |
-0,11820 | 0,1386 | -0,13424 | |

Constant |
26,15485 | -27,5511 | 27,80095 | |

Canonic
correlation |
0,808 | 0,829 | 0,837 | |

Group
centroids |
♂ ≥ | -1,276 | 1,383 | -1,426 |

♀ ≤ | 1,439 | -1,560 | 1,608 | |

Correct
classification accuracy,
% |
♂ | 88,63 | 93,18 | 95,4 |

♀ | 94,87 | 94,87 | 97,5 |

The study showed the possibility of sex determination from clavicles using osteometric approach. The methods described above make it possible to determine the sex using an extended or a reduced set of measurements, which is especially crucial when working with a limited number of bones or their fragments.

Dmitry Sundukov designed the study; Askold Smirnov collected, analysed, interpreted data and provided the tables. Askold Smirnov and Dmitry Sundukov prepared the manuscript for submission.

- Iscan M. Y., Steyn M. The Human Skeleton in Forensic Medicine. Charles C. Thomas Publishers, Springfield. 2013.
- Akhlaghi M., Moradi B., Hajibeygi M. Sex determination using anthropometric dimensions of the clavicle in Iranian population // J. Forensic Leg. Med. – 2012. Vol. 19, No 7. – P. 381-385. DOI: https://doi.org/10.1016/j.jflm.2012.02.016
- Demir U., Etli Y., Hekimoglu Y. , Kartal E., Keskin S., Yavuz А., Asirdizer M. Sex estimation from the clavicle using 3D reconstruction, discriminant analyses, and neural networks in an Eastern Turkish population // Leg Med (Tokyo) – 2022. Vol. 56. – P. 102043. DOI: 10.1016/j.legalmed.2022.102043
- Koukiasa A.E., Eliopoulos C., Manolis S.K. Biometric sex estimation using the scapula and clavicle in a modern Greek population // Anthropol Anz. – 2017. Vol. 74, N3. – P. 241-246. DOI: 10.1127/anthranz/2017/0658
- McCormick W.F., Stewart J.F.I., Greene I.T. Sexing of human clavicles using length and circumference measurements // Am. J. Forensic. Med. Pathol. – 1991. Vol 12, No 2. – P. 175-181. DOI: 10.1097/00000433-199106000-00017
- Sehrawata J.S., Pathakb R.K. Variability in anatomical features of human clavicle: Its forensic anthropological and clinical significance // Translational Research in Anatomy. – 2016. Vol. 3–4, P. 5-14. DOI: https://doi.org/10.1016/j.tria.2016.08.001
- Shirley N.R. Age and Sex Estimation from the Human Clavicle: An Investigation of Traditional and Novel Methods. Dissertation, University of Tennessee, Knoxville. 2009.
- Voroncova E.L. Morfologicheskaja izmenchivost' kostej plechevogo pojasa i grudiny cheloveka. Avtoreferat dissertacii kand. nauk. М., 2005. [In Russ.].
- Urbah V. Ju. Statisticheskij analiz v biologicheskih i medicinskih issledovanijah. М., 1975: 297 p. [In Russ.]