Discriminant function analysis for sex assessment in pelvic girdle bones: sample from the contemporary Mexican population

Sex assessment of skeletal remains plays an important role in forensic anthropology. The pelvic bones are the most studied part of the postcranial skeleton for the assessment of sex. It is evident that a population-specific approach improves rates of accuracy within the group. The present study proposes a discriminant function method for the sex assessment of skeletal remains from a contemporary Mexican population. A total of 146 adult human pelvic bones (61 females and 85 males) from the skeletal series pertaining to the National Autonomous University of Mexico were evaluated. Twenty-four direct metrical parameters of coxal and sacral bones were measured and subsequently, sides and sex differences were evaluated, applying a stepwise discriminant function analysis. Coxal and sacra functions achieved accuracies of 99% and 87%, respectively. These analyses follow a population-specific approach; nevertheless, we consider that our results are applicable to any other Hispanic samples for purposes of forensic human identification.     

Sexual Dimorphism of the Arm Bones in a Modern Greek Population

Abstract: Several studies have shown that sex determination methods based on measurements of the skeleton are population specific. Metric traits of the long bones of the arm have been reported as reliable indicators of sex. This study was designed to determine whether the three long bones of the arm can be used for sex determination on a skeletal population from Greece. The material used consists of the arm bones of 204 adult individuals (111 males and 93 females) coming from the Modern Human Skeletal Collection of the University of Athens. The age range is 19–96 years for males and 20–99 years for females. The maximum lengths and epiphyseal widths were measured in the long bones of the arm (humerus, radius, and ulna). The discriminant analysis of the metrical data of each long bone gave very high discrimination accuracies. The rate of correct sex discrimination based on different long bones ranges from 90.30% (ulna) to 95.70% (humerus). In addition, intra‐ and inter‐observer error tests were performed. These indicated that replication of measurements was satisfactory for the same observer over time and between observers. The results of this study show that metric characteristics of the arm bones can be used for the determination of sex in skeletal remains from Greece and that bone dimensions are population specific.     

Discriminant function sexing of fragmentary and complete tibiae from medieval Croatian sites

Previous studies have demonstrated that populations differ from each other in size and proportion and that these differences can affect metric assessment of sex. This paper establishes standards for determining sex from fragmentary and complete tibiae in the medieval Croatian population. The sample is composed of 180 tibiae (96 males and 84 females) from six medieval archaeological sites in Croatia. Three of the sites were located in continental Croatia, three on the eastern Adriatic coast and its immediate hinterland. Six tibial dimensions were measured: (1) length of the tibia; (2) maximum epiphyseal breadth of the proximal tibia; (3) maximum epiphyseal breadth of the distal tibia; (4) maximum diameter of the tibia at the nutritient foramen; (5) transverse diameter of the tibia at the nutritient foramen; and (6) circumference of the tibia at the nutritient foramen. Unifactorial and multifactorial analyses were performed on the collected data. Six discriminant functions were generated, one using six variables, two using two variables, and three employing one variable. Results show that complete tibiae can be sexed with 92.2% accuracy. Slightly lower accuracies (91.7 and 87.8%) were achieved using a combination of two variables, while functions employing one variable were accurate from 85.6 to 81.7%. The results of this study show that the medieval Croatian tibia is a good skeletal component for determining sex. Standardized coefficients of the discriminant functions generated in this study support the results of previous studies that found that breadth dimensions provide better separation of the sexes than length.     

The talus: sex assessment of prehistoric New Zealand Polynesian skeletal remains

Prehistoric Polynesian skeletal remains are frequently being recovered in New Zealand due to the increasing pace of urbanisation. Since such material must often be reinterred quickly, it is important that the sex of individuals be determined from the remains in a relatively short time. For this purpose, discriminant function analysis was utilised for sex determination of prehistoric adult New Zealand Polynesian tali (24 males and 27 females). Five measurements were taken and subjected to Statistical Package for the Social Sciences (SPSS) discriminant function analysis. For the discriminant functions derived, accuracy of sex determination ranged from 85.1 to 93.3%. Reduction in error over random assignment by sex ranged from 70 to 87%.     

Sex Determination by Discriminant Function Analysis of Lumbar Vertebrae

Sex determination is critical for developing the biological profile of unidentified skeletal remains. When more commonly used elements (os coxa, cranium) for sexing are not available, methods utilizing other skeletal elements are needed. This study aims to assess the degree of sexual dimorphism of the lumbar vertebrae and develop discriminant functions for sex determination from them, using a sample of South African blacks from the Raymond A. Dart Collection (47 males, 51 females). Eleven variables at each lumbar level were subjected to univariate and multivariate discriminant function analyses. Univariate equations produced classification rates ranging from 57.7% to 83.5%, with the highest accuracies associated with dimensions of the vertebral body. Multivariate stepwise analysis generated classification rates ranging from 75.9% to 88.7%. These results are comparable to other methods for sexing the skeleton and indicate that measures of the lumbar vertebrae can be used as an effective tool for sex determination.     

Prognosis of sexual dimorphism with unfused hyoid bone: Artificial intelligence informed decision making with discriminant analysis

Depending on the metric and non-metric skeletal features of various bones, forensic experts proposed diverse sex identification methods. The main focus of the present study is to calculate sexual dimorphism in human unfused or disarticulated hyoid bone and compared it with studies conducted by different researchers. For this study, 293 unfused hyoid bones were accumulated and investigated from 173 male and 120 female cadavers of the northwest Indian population from the age of 15 to 80 years. Initially, discriminant analysis was performed on the dataset to predict sex and to get an idea for the crucial variables for sexual dimorphism. Later, significant variables predicted by the discriminant analysis were used for machine learning approaches to improve accuracy for sex determination. The standard scaler method is used for pre-processing of the data before machine learning analysis and to prevent overfitting and underfitting, 70 % of the whole dataset was utilized in the training of the model and the remaining data were used for testing the model. According to the discriminant analysis, body length (BL) and body height (BH) were found to be highly significant for the sex determination and predicted sex with 75.1 % accuracy. However, implementation of machine learning approaches such as the XG Boost classifier increased the accuracy to 83 % with sensitivity, and specificity scores of 0.81 and 0.84, respectively. Moreover, the ROC-AUC score achieved by the XG Boost classifier is 0.89; indicating machine learning investigation can improve the sex determination accuracy up to the appropriate standard.     

Sex assessment from the carpals bones: discriminant function analysis in a 20th century Spanish sample

Sex assessment is one of the first essential steps in human identification, in both medico-legal cases and bio-archaeological contexts. Fragmentary human remains compromised by different types of inhumation or physical insults may frustrate the use of the traditional sex estimation methods, such as the analysis of the skull and pelvis. Currently, the application of discriminant functions to sex unidentified skeletal remains is steadily increasing. However, several studies have demonstrated that, due to variation in size and patterns of sexual dimorphism, discriminant function equations are population-specific [1,2,5,12,61]. In this study, in order to improve sex assessment from skeletal remains and to establish population-specific discriminant functions, the diagnostic values of the carpal bones were considered. A sample of 100 individuals (50 males and 50 females) of known sex and age was analyzed. They belong to a 20th century identified collection from the Municipal Cemetery of "San José", Granada (Spain) and housed in the Laboratory of Anthropology, Faculty of Medicine, University of Granada (Spain). The age of the individuals ranged between 22 and 85 years. Between four and nine measurements of each carpal bone were performed [41,59]. Discriminant function statistics showed a sex assessment accuracy as high as 97.8%. The results suggest that carpal bones can be used for assessing sex in both forensic and bio-archaeological identification procedures.     

Sex assessment from carpals bones: discriminant function analysis in a contemporary Mexican sample

Sex assessment is one of the first essential steps in human identification, in both medico-legal cases and bio-archaeological contexts. Fragmentary human remains compromised by different types of burial or physical insults may frustrate the use of the traditional sex estimation methods, such as the analysis of the skull and pelvis. Currently, the application of discriminant functions to sex unidentified skeletal remains is steadily increasing. However, several studies have demonstrated that, due to variation in size and patterns of sexual dimorphism, discriminant functions are population-specific. In this study, in order to improve sex assessment from skeletal remains and to establish population-specific discriminant functions, the diagnostic values of the carpal bones were considered. A sample of 136 individuals (78 males, 58 females) of known sex and age was analyzed. They belong to a contemporary identified collection from the Laboratory of Physical Anthropology, Faculty of Medicine, UNAM (Universidad Nacional Autónoma de México, Mexico City). The age of the individuals ranged between 25 and 85 years. Between four and nine measurements of each carpal bone were taken. Independent t-tests confirm that all carpals are sexually dimorphic. Univariate measurements produce accuracy levels that range from 61.8% to 90.8%. Classification accuracies ranged between 81.3% and 92.3% in the multivariate stepwise discriminant analysis. In addition, intra- and inter-observer error tests were performed. These indicated that replication of measurements was satisfactory for the same observer over time and between observers. These results suggest that carpal bones can be used for assessing sex in both forensic and bio-archaeological identification procedures and that bone dimensions are population specific.     

Metric Sex Determination of the Human Coxal Bone on a Virtual Sample using Decision Trees

Decision trees provide an alternative to multivariate discriminant analysis, which is still the most commonly used in anthropometric studies. Our study analyzed the metric characterization of a recent virtual sample of 113 coxal bones using decision trees for sex determination. From 17 osteometric type I landmarks, a dataset was built with five classic distances traditionally reported in the literature and six new distances selected using the two-step ratio method. A ten-fold cross-validation was performed, and a decision tree was established on two subsamples (training and test sets). The decision tree established on the training set included three nodes and its application to the test set correctly classified 92% of individuals. This percentage was similar to the data of the literature. The usefulness of decision trees has been demonstrated in numerous fields. They have been already used in sex determination, body mass prediction, and ancestry estimation. This study shows another use of decision trees enabling simple and accurate sex determination.     

A comparison between neural network and other metric methods to determine sex from the upper femur in a modern French population

Forensic anthropologists are frequently asked to assess partial or badly damaged skeletal remains.One such request led us to compare the predictive accuracy of different mathematical methods using four non-standard measurements of the proximal femur (trochanter–diaphysis distance (TD), greater–lesser trochanter distance (TT), greater trochanter width (TW) and trochanter–head distance (TH)). These measurements were taken on 76 femurs (38 males and 38 females) of French individuals. Intra- and inter-observer trials did not reveal any significant statistical differences. The predictive accuracy of three models built using linear and non-linear modelling techniques was compared: discriminant analysis, logistic regression and neural network. The neural network outperformed discriminant analysis and, to a lesser extent, logistic regression. Indeed, the best results were obtained with a neural network that correctly classified 93.4% of femurs, with similar results in males (92.1%) and females (94.7%). Univariate functions were less accurate (68–88%). Discriminant analysis and logistic regression, both using all four variables, led to slightly better results (88.2% and 89.5%, respectively). In addition, all the models, save the neural network, led to unbalanced results between males and females. In conclusion, the artificial neural network is a powerful classification technique that may improve the accuracy rate of sex determination models for skeletal remains.     

Sex estimation in a modern American osteological sample using a discriminant function analysis from the calcaneus

Reliable methods for sex estimation during the development of a biological profile are important to the forensic community in instances when the common skeletal elements used to assess sex are absent or damaged. Sex estimation from the calcaneus has potentially significant importance for the forensic community. Specifically, measurements of the calcaneus provide an additional reliable method for sex estimation via discriminant function analysis based on a North American forensic population. Research on a modern American sample was chosen in order to develop up-to-date population specific discriminant functions for sex estimation. The current study addresses this matter, building upon previous research and introduces a new measurement, posterior circumference that promises to advance the accuracy of use of this single, highly resistant bone in future instances of sex determination from partial skeletal remains. Data were collected from The William Bass Skeletal Collection, housed at The University of Tennessee. Sample size includes 320 adult individuals born between the years 1900 and 1985. The sample was comprised of 136 females and 184 males. Skeletons used for measurements were confined to those with fused diaphyses showing no signs of pathology or damage that may have altered measurements, and that also had accompanying records that included information on ancestry, age, and sex. Measurements collected and analyzed include maximum length, load-arm length, load-arm width, and posterior circumference. The sample was used to compute a discriminant function, based on all four variables, and was performed in SAS 9.1.3. The discriminant function obtained an overall cross-validated classification rate of 86.69%. Females were classified correctly in 88.64% of the cases and males were correctly classified in 84.75% of the cases. Due to the increasing heterogeneity of current populations further discussion on this topic will include the importance that the re-evaluation of past studies has on modern forensic populations. Due to secular and micro evolutionary changes among populations, the near future must include additional methods being updated, and new methods being examined, both which should cover a wide population spectrum.     

Discriminant function sexing of fragmentary femur of South African blacks

When fragmentary and incomplete bones are all that are available to the forensic anthropologist for use in sex determination, non-metric and metric sex discriminating parameters that have been derived from complete bones may be of little use. In such circumstances, sex discriminating metric methods that are of specific application to fragmentary bones will be more useful. Since such studies have not been systematically carried out in bones of South African blacks, the aim of this study was to begin to provide such data. Two hundred and twenty left femurs of black South Africans were obtained from the Raymond A. Dart Collection of African Skeleton, School of Anatomical Sciences, University of the Witwatersrand, South Africa. Five variables from the upper end of the femur and three variables from the lower end of the femur were measured and subjected to univariate and multivariate discriminant function analyses. The vertical head diameter and the medial condylar length were most successful in sex identification from the upper and lower ends of the femur respectively. The combined variables were more useful than the use of variables individually. Discriminant function score equations were derived for individual and combined variables from the upper and lower ends of the femur of the South African blacks.     

Sex determination from the talus and calcaneus measurements

Several studies have demonstrated that discriminant function equations used to determine the sex of a skeleton are population-specific. The purpose of the present research was to develop discriminant function equations for sex determination on the basis of 18 variables on the right and left talus and calcaneus in a modern northern Italian sample. The sample consisted of 118 skeletons (62 males and 56 females) from the Frassetto Collection (University of Bologna). The ages of the individuals ranged from 19 to 70 years. The results indicated that metric traits of the talus (in particular) and calcaneus are good indicators of sexual dimorphism. The percentage of correct classification was high (87.9-95.7%). In view of the differences among current Italian populations, we tested the validity of the discriminant function equations in an independent sample of individuals of different origin (northern and southern Italy). The accuracy of classification was high only for the northern Italians. Most southern Italian males were misclassified as females, confirming the population-specificity of discriminant function equations.     

Mastoid Triangle for Sex Determination in Adult Nigerian Population: A Validation Study

In the quest for a simple, reliable technique to estimate the sex of human remains several novel metric skeletal indices have been reported. Only a few have been examined for utility in populations different from those in which they were developed. In this study, the mastoid process was evaluated for sex determination using 102 lateral cephalograms of a Nigerian sample of known age and sex. The asterion‐mastoidale distance and mastoid triangular area were sexually dimorphic with mean values higher in males compared with females (p = 0.02). On analysis of the discriminant function, overall accuracy for sex classification was 55%. On cross‐validation, the triangular area accurately identified 80% of females and 48% of males. The asterion‐mastoidale distance was slightly more accurate at sexing the sample. The practical utility of the mastoid triangle area technique to differentiate sex in Nigerian populations is not supported by the results of this study.     

Sex Determination Using the Second Cervical Vertebra—A Test of the Method*

Abstract: Sex is one of the critical questions addressed when unidentified skeletal remains are discovered in forensic or archeological contexts. Continuous testing and re‐evaluation of existing techniques is essential to improve accuracy and precision. The Wescott (J Forensic Sci 2000; 45 (2):462–6) method of sex determination from dimensions of the second cervical vertebra was blind‐tested on 153 adult individuals from the Spitalfields documented collection of human skeletal remains held at the Natural History Museum, London. Significant sex differences were determined for all dimensions measured (independent two‐sample t‐test, p < 0.05–0.001). The discriminant functions developed by Wescott were shown to have an overall accuracy of classification of 76.99%. Using stepwise discriminant analysis, a discriminant function based on the Spitalfields data correctly classified sex in 83.3% of individuals and was able to classify males and females with equal accuracy. Additional discriminant functions are presented for use in instances where preservation of the second cervical vertebra is poor.     

舌骨的法医人类学研究

目的建立利用舌骨形态测量值判别性别的方法,并探讨其在法医学应用中的价值。方法对于河北地区收集的108例舌骨样本(男78例,女30例)进行观察研究,确立11个观测指标并进行测量,测量值采用SPSS统计软件进行统计学分析,建立利用舌骨形态测量值判别性别的方程,并进行Fisher判别分析。结果在11项观察指标中,8项测量指标男女性别间存在显著性统计学差异(P<0.01);利用8项测量指标中的任一指标或之中的多个指标组合建立线性性别判别方程,方程判别性别的准确率在66%～92%,其中多指标的方程判别性别准确率较单一指标的方程高,最高达到92%。结论舌骨形态存在着性别差异,利用多个舌骨形态学测量值建立的性别判别方程准确率较高,可用于无名尸骨的性别判别。     

Discriminant function sexing of fragmentary and complete femora: standards for contemporary Croatia

Determining sex is one of the first and most important steps in identifying decomposed corpses or skeletal remains. Previous studies have demonstrated that populations differ from each other in size and proportion and that these differences can affect metric assessment of sex. This paper establishes standards for determining sex from fragmentary and complete femurs in a modern Croatian population. The sample is composed of 195 femora (104 male and 91 female) from positively identified victims of the 1991 War in Croatia. Six discriminant functions were generated. one using seven variables, three using two variables, and two employing one variable. Results show that complete femora can be sexed with 94.4% accuracy. The same overall accuracy, with slight differences in male/female accuracy, was achieved using a combination of two variables defining the epiphyses, and with the variable maximum diameter of the femoral head.     

Morphometrics of the hyoid bone for human sex determination from digital photographs

The identification of unknown remains is very important. When unknown remains are found, anthropologists first determine their sex and age. The sex of most skeletons is determined by their shape. In the hyoid bone, the shape is sex related, so it can be used forensically to determine the sex. This study focused on sex-based morphometry of the hyoid bone in Koreans using digital photographs. Hyoid bones from 52 males and 33 females were examined. For each subject, we took 34 measurements from photographs using a computer program, and the data were analyzed statistically using SPSS 11.0. Twenty-one of 34 measurements had significant sex differences (p<0.05). The discriminant functions based on three measurements (X(1)-X(3)) were as follows: The accuracy of discriminant functions is 88.2% in both groups, so these can be used to distinguish males from females in a statistically significant manner.     

Metric determination of sex from the humerus in a Guatemalan forensic sample

The absence of population-specific standards for sex, age and stature estimation for rural Guatemala is problematic for the forensic analysis of skeletal remains recovered from clandestine graves attributed to the recent armed conflict in that country. In order to increase the reliability of the forensic analyses being undertaken in Guatemala, standards for metric determination of sex were developed. Data was collected on several bones; the results for the humerus are presented here. A sample of 118 complete humeri (68 male and 50 female) was studied; maximum length, maximum diameter of the head, circumference at midshaft, maximum diameter at midshaft, minimum diameter at midshaft and epicondylar breadth were measured and subjected to discriminant function analysis. The classification accuracies for the univariate functions range from 76.8% for the maximum diameter at midshaft to 95.5% for the maximum diameter of the head. The classification accuracy for the stepwise procedure was 98.2%.     

Identification of sex depending on radiological examination of foot and patella

Forensic anthropology involves the building of an antemortem profile of an individual from skeletal remains. This includes sex, race determination, and age and stature estimation. Because most bones that are conventionally used for sex determination are often recovered either in a fragmented or incomplete state, it has become necessary to use denser bones that are often recovered intact, eg, the patella, calcaneus, and talus. The present work was performed to investigate the possibility of estimation of sex from some radiologic measurements among a known cross-section of Egyptian population. In this study lateral and anteroposterior radiographs of the right foot and knee were made on 160 living unfractured and nonpathologic individuals comprising 80 males and 80 females aged 25 to 65 years referred to the Radiology Department of Assiut University Hospital. Two measurements on right patella (maximum height and maximum width) and 2 measurements of metatarsal bones (length and midshaft diameter), were used to determine sex by univariate and multivariate discriminant analysis. Eighty radiographs of foot and patella of individuals not used in the original sample were randomly selected to test the accuracy of this method. The study revealed that significant sex differences were demonstrated based on these measurements taken on metatarsal bones more than on patella. One function associating 2 parameters (length and midshaft) of the third metatarsal bone obtained the highest value of correct sex determination with rate of 100% accuracy. The multivariate function associating length of the first, third, and fifth metatarsal bones and midshaft of first, second, and fifth metatarsal gave 100% accuracy. Test of multivariate function on the independent sample revealed a correct classification of 87.5%.