Univariate Discriminant Function Research Articles

Sex estimation from skull measurements of a contemporary Japanese population using three-dimensional computed tomography images.

In this study, we assessed the sexual dimorphism of the contemporary Japanese skull and established sex discriminant function equations based on cranial measurements using three-dimensional (3D) computed tomography (CT) images. The CT images of 263 corpses (142 males, 121 females) that underwent postmortem CT scanning and subsequent forensic autopsy were evaluated. Twenty-one cranial measurements were obtained from 3D CT reconstructed images, which extracted only bone data. We performed descriptive statistics and discriminant function analyses for the measurements. Nineteen measurements were significantly larger in males, suggesting sexual dimorphism of the Japanese skulls. Univariate discriminant function analyses using these measurements showed a sex classification accuracy of 57.8-88.2%, and bizygomatic breadth provided the highest correct prediction rate. Multivariate discriminant function analyses offered the most accurate model using seven variables with an estimation rate of 93.9%. Our results suggest that cranial measurements based on 3D CT images may help in the sex estimation of unidentified bodies in a contemporary Japanese population.

A Cost of Misclassification Adjustment Approach for Estimating Optimal Cut-Off Point for Classification

Classification is one of the main areas of machine learning, where the target variable is usually categorical with at least two levels. This study focuses on deducing an optimal cut-off point for continuous outcomes (e.g., predicted probabilities) resulting from binary classifiers. To achieve this aim, the study modified univariate discriminant functions by incorporating the error cost of misclassification penalties involved. By doing so, we can systematically shift the cut-off point within its measurement range till the optimal point is obtained. Extensive simulation studies were conducted to investigate the performance of the proposed method in comparison with existing classification methods under the binary logistic and Bayesian quantile regression frameworks. The simulation results indicate that logistic regression models incorporating the proposed method outperform the existing ordinary logistic regression and Bayesian regression models. We illustrate the proposed method with a practical dataset from the finance industry that assesses default status in home equity.

Morphometric evaluation of the orbital region for sex determination in a Saudi Arabian population using 3DCT images.

In forensic anthropology, the analysis of variations in the orbitometric features plays a crucial role in identifying the sex of a skull detached from its skeleton. Therefore, it is essential to create population-specific values to maximize the accuracy rate of sex estimation. The objective of this study was to evaluate the orbital region morphometrically for sex determination in a Saudi Arabian population using CT scan images. This study included 456 CT images (228 males and 228 females; age range, 18-58years). Six orbital measurements and the orbital index of both sides were evaluated to determine sexual dimorphism and laterality using an independent t-test. Sex was estimated using discriminant function analysis. Based on the orbital index, the orbit was classified into megasemes, mesosemes, and microsemes. All the measurements were significantly greater in males than females, but the orbital index showed no significant sexual dimorphism. No significant asymmetry was found in all orbital dimensions. The univariate discriminant function of the orbital measurements showed an accuracy rate between 83.8 and 70%. The multivariate analysis classified the orbital dimensions into male (93%) and female (92.1%) to the highest level of accuracy. In Saudis, the megaseme category was the most prevalent form of orbit. The right orbit height (83.8%), left orbit height (80.7%), right orbit width (79.4%), and left orbit height (79.4%) were the most reliable variables that could be used in sex determination. According to multivariate analysis, the overall accuracy rate for determining sex was 92.1%. While the present study data may not be used alone for sexing a complete skull, there must be various occasions in which this new standard will contribute to determining sex in forensic contexts.

Gender Dimorphism in Maxillary Permanent Canine Odontometrics Based on a Three-Dimensional Digital Method and Discriminant Function Analysis in the Saudi Population

The present study aimed to analyze the gender dimorphism in odontometrics of permanent maxillary canines using a three-dimensional digital method and to test the accuracy in gender estimation using discriminant function analysis in a sample of the Saudi population. A total of 120 diagnostic dental casts of patients aged 16–29 years were used in the present study. Plaster models of their maxillary dentition obtained from the archives were scanned and digitally measured using a three-dimensional digital method. The mesiodistal width of the right and left maxillary canines and intercanine distance were measured. Gender dimorphism was established using the Garn method. Data were statistically analyzed using descriptive statistics, the Mann–Whitney U test and discriminant analyses. Males showed larger mean dimensions of canines than females with regard to both mesiodistal width and intercanine distance, and the difference was statistically significant (p < 0.05). The right maxillary canine mesiodistal width showed a higher percentage of gender dimorphism (3.5%). Discriminant function analysis showed that the overall accuracy of gender prediction was 80.5% for the multivariate analysis. The univariate discriminant function equation revealed that intercanine distance was the most accurate predictor of gender (78%), followed by the right canine mesiodistal width (76.3%). The use of three-dimensional technology for odontometrics presents a promising method, and permanent maxillary canine parameters can be used as an acceptable ancillary tool for gender estimation in forensic science.

Evaluation and comparison of linear and diagonal odontometry of first molars as a tool for gender discrimination; assessed in a population from Maharashtra.

Linear odontometry is customarily used in gender determination which can pose difficulties in cases of tooth decay, attrition since they mainly involve the proximal surfaces. The present cross-sectional observation study, estimated the efficacy of alternative measurements, that is, diagonal measurements and cervical measurements in gender determination in comparison to routine odontometry. A total of 200 dental cast models (upper and lower) of 100 individuals (50 male and 50 female) from Maharashtra state were included. Univariate discriminant function analysis showed that, in maxillary molars, MD width gave the highest gender dimorphism of 64%, followed by BL with 62%. In the mandibular teeth, MD gave an accuracy of 75% followed by MB-DL with 73%. Multivariate logistic regression analysis showed that overall diagonal and linear measurements gave the highest dimorphism of 81% with 80% correctly identified as females and 82% as males. The mandibular MD, BL and MB-DL gave an accuracy of 79% with 78% corrected identified as females and 80% correctly identified as males. Mandibular ML-DB and Cervical DB-CML together gave an accuracy of 77% and mandibular MD with75%. Thus, the study proves that diagonal measurements give almost equivalent or better results than linear measurements in gender determination.

The sex difference of the volume and surface area of the human axial skeleton.

We assessed the sex difference in the volume and surface area of the bone using three-dimensional bone models generated from computer tomography images of axial skeletal elements from 110 Korean cadavers. The volume and surface area of all bones were significantly different between females and males. The accuracy of sex determination ranged from 55.6%-93.7% in univariate discriminant function analysis, with the second thoracic vertebra showing the highest accuracy. In discriminant analysis using paired bone combinations, 22 combinations of bone volume and surface area yielded > 90% accuracy in sex determination. The highest accuracy in the stepwise analysis was 94.7% when using the surface area of the ribs, sternum, and vertebrae for determining sex. This result shows a higher or similar accuracy than previous metric and non-metric studies using the axial skeleton, however, it shows lower accuracy than previous study which used volume and surface area of the appendicular skeleton. Nevertheless, this method might have advantage that is possible to determine sex quickly due to base on the computation with medical images.

Ear morphology and morphometry as potential forensic tools for identification of the Hausa, Igbo and Yoruba populations of Nigeria

BackgroundThe human external ear is unique in every individual in terms of shape, size and dimension making it suitable in forensic anthropology for sex estimation and personal identification purposes. The study aimed to evaluate sexual dimorphism and ethnic specificity of the external ear in major Nigerian ethnic populations.ResultsThere was variation in the morphological features of the external ear of the sampled subjects. The external ear features vary in the right and left ears in both sexes of the ethnic groups. All variables were statistically significant (p < 0.05) except ear width. Univariate discriminant function gave sex prediction accuracies between 56.4 and 57.3% for left and right ears, respectively. Population-specific sex prediction accuracy using stepwise discriminant analysis of left ear variables ranged 58–69.7% and 57.5–74.2% for right ear.ConclusionThe ear parameters showed potential for sex estimation, but cannot be solely relied upon for personal identification.

Morphometric analysis of foramen magnum and occipital condyle using CT images for sex determination in a Saudi Arabian population

The objective of this study was to evaluate FM and occipital condyles measurements morphometrically for sex determination by using discriminant function analysis and to note visually the variation in the shape of the foramen magnum in a Saudi Arabian population by using CT scan images. This study included 472 CT scans (236 males and 236 females; age range, 18-72 years). The foramen magnum shapes were classified into 8 types: oval, egg, round, hexagonal, pentagonal, tetragonal, irregular (A) and irregular (B). The intraobserver and interobserver test was done to calculate the reliability of the measurement. Eight dimensions of the FM and occipital condyle were evaluated to determine the sexual dimorphism using an independent t-test. Sex determination was estimated using discriminate function analysis. The commonest shape of FM was hexagonal and the tetragonal shape was the least common type. Coefficient of reliability (R) was high, ranging between 0.89 and 0.99, which indicates the measurements are reliable and sufficiently precise. All the eight measurements, the FM length and width, FM index, FM area, the width and length of right and left occipital condyles were significantly greater in males than the female. Univariate discriminant function showed an accuracy rate varying from 61% to 66.6% based on FM or occipital condyles measurements. The multivariate analysis of FM and occipital condyle measurements increased the overall accuracy rate of sex determination to 71.6%. The univariate analysis of FM and occipital condyle measurements indicates, that the FM area (66.1%), FML (62.5%), FMW (62.5%) and ROCL (62.1%) could be reliable individual variables in sex determination. The multivariate analysis including all the eight variables of FM and occipital condyle increased the accuracy rate of sex determination to 71.6% in determining the sex as male (73.3%) or female (69.9%). The shape of the FM is not useful in sex estimation. The results obtained showed a low degree of sexual dimorphism in the basicranium, the use of this method in forensic anthropology could be helpful for assessment on highly fragmented skull bases.

Sex identification of the ashy-throated parrotbill (Paradoxornis alphonsianus): A species heavily hunted for bird fighting in Guizhou Province, China

The ashy-throated parrotbill ( Paradoxornis alphonsianus) is a sexually monomorphic species with high abundance in Southwest China, which has been widely used as a fighting bird across Guizhou Province, leading it to become one of the most coveted and heavily hunted wild birds in the region at present. Information on the sexes is a fundamental requirement for a wide variety of avian studies. From a conservation perspective, knowledge necessary for quick sexing of this species should be important, as the determination of sex contributes to the understanding of which sexes are used for fighting. Our goal was to develop a quick method that can be used to identify sex of the ashy-throated parrotbill in the field. Seven body traits were measured and compared between the sexes among 124 individual ashy-throated parrotbills, with sex determined by molecular techniques. Data revealed that the male is the larger sex, with significantly greater measurements than the female in bill length, wing length, and middle claw length. The univariate discriminant function based on bill length featured the highest identification accuracy (67.7%). The larger body size of males may have evolved by sexual selection, but additional data are needed to test this hypothesis. This study found that male and female ashy-throated parrotbills are divergent in size, although further efforts are required for a discriminant function with more robust accuracy.

Sex Determination from Sacrum and Coccyx measurements using Magnetic Resonance Imaging in a Sample of Egyptian Population

Background: Estimation of sex is an important step in identification of unidentified persons. The aim of the current work was to evaluate sacrum and coccyx gender differences using magnetic resonance imaging (MRI) in Egyptian population. Subjects and method: 230 Egyptian subjects (115 males and 115 females) were investigated with MRI over the sacrum and coccyx. MRI images of every person were used to get seven length estimations and two angle dimensions in the sacrum and coccyx. Results: Measured lengths including anterior sacral length (ASL), posterior sacral length (PSL), anterior sacrococcygeal length (ASCL), posterior sacrococcygeal length (PSCL) and antero-posterior diameter of S1 vertebra corpus (APD) were higher in males. But, there was no significant variation in maximum breadth of alae sacralis (MBA), maximum lumbo-sacral curve angle (MLSCA) and lumbo-sacral angle (LSA) between males and females. Univariate discriminant function analysis showed that ASL and PSL recorded 71.9% and 71.5% accuracy rates respectively. Stepwise analysis considered that (ASL and PSL) collectively produced 68.9% correct prediction rate. Conclusion: the results of the current work concluded that the sacrum and coccyx are valuable for identification of sex and could be helpful for sex identification of skeletal remnants in the Egyptian population when utilized with other methods as assessment of readily accessible bones

Identification of sex using discriminant function analysis of fingerprint ridge density at three topological areas among North Indian population

The present study attempted to identify sex of an individual using a fingerprint ridge density at three topological areas in the North Indian population. The study population consisted of 134 males and 136 females aged 17 to 25 years (mean age 19.34±2.12). Ridge density (RD) at radial, ulnar and proximal topological areas of the distal phalanges were determined on the surface area of 25mm2. Fingerprint ridge density in a defined area was significantly higher among females as compared to their male counterparts at radial, ulnar and proximal topological areas for both hands. Sexual dimorphic ratio also supported this trend for all three counting areas in right and left hands. Univariate discriminant function analysis explained that the left 2 radial (L2R) (88.1%) had the highest percentage of accuracy for sex identification, followed by the left 3 ulnar (L3U) (82.1%) and the right 2 ulnar (R2U) (81.6%). Multivariate discriminant function analysis showed that the radial topological area of the left hand was the best predictor of sex with the overall accuracy of 84.4%with following discriminant function equation −8.263 − 0.236(L1R) + + 0.321(L2R) + 0.269(L3R) + 0.268(L4R) − 0.067(L5R).&#x0D; It can be inferred that ridge density in the radial topological area of left hand is the most reliable tool for identifying the sex of an individual.

Estimation of Sex from Patella Measurements in Sichuan Han Population Based on CT-Three-Dimensional Volume Reconstruction Technique

Objective To estimate sex based on patella measurements of Sichuan Han population by computed tomography three-dimensional volume reconstruction technique, and to explore the application value of patella in sex estimation. Methods CT three-dimensional volume reconstruction images of patella of 250 individuals were collected, the four measurement indicators including patellar length, patellar width, patellar thickness, and patellar volume were measured. The t-test was used to determine measurement indicators with sex differences. Fisher discriminant analysis was used to establish the sex discriminant function and the prediction accuracy was calculated by leave-one-out cross validation. Results The sex differences of the four measurement indicators had a statistical significance （P<0.05）. The accuracy rate of the univariate discriminant function established by the patellar length was the highest （82.0%）. The accuracy rates of the all indicators discriminant function and the stepwise discriminant function were 80.4% and 81.6%, respectively. Conclusion It is feasible and accurate to estimate sex of Sichuan Han population by patella measurements with CT three-dimensional volume reconstruction technique. The method may be used as an alternative for sex estimation of Sichuan Han population when other bones with higher accuracy are not available.

Sex estimation in a modern Turkish population using the clavicle: a computed tomography study

ABSTRACT Morphometric analysis of the clavicle is a potential source of useful data for the estimation of sex. Clavicle is often retrieved intact from decomposed and scavenged remains when pelvis and skull, essential sex indicators, are often found damaged or missing. The objective of this study is to analyse clavicle morphometric data for sex estimation in a Turkish population. Computed tomography (CT) scans of the thorax of two hundred Turkish adult patients (71 male and 81 female patients with an age range of 22–80 years) were included. Furthermore, morphometric data for the left clavicle using two-dimensional (2D) and three-dimensional (3D) clavicle CT images were obtained, and six variables were measured in the clavicle images. Univariate and multivariate discriminant function analysis (DFA) was used to create population-specific functions for sex estimation. The classification accuracy for the cross-validated data ranged from 75% to 89% in the uni- and multivariate DFA. Stepwise discrimination analysis yielded an 89% accuracy rate for the maximum length and midshaft circumference variables. The study showed that the clavicle can provide useful data for estimating sex in a modern Turkish population and that when there is difficulty accessing bone collections, CT scans can provide useful data for sex estimation.

SEX DETERMINATION FROM DISCRIMINANT FUNCTION ANALYSIS OF CEPHALOMETRIC MEASUREMENTS OF BROKPAS AND PURIGPAS OF LADAKH (UT): A FORENSIC ANTHROPOLOGICAL STUDY

Forensic anthropology involves diverse applications of anthropological knowledge to medico-legal problems like human identification based on sex determination, age estimation, stature reconstruction and deciphering ancestry of unknown living individuals or skeletal remains. Sex can be determined by using different body parts such as extremities (legs and arms) parameters, head, face, clavicle, and others parameters. In present cross-sectional study, cephalometric dimensions of 800 Ladakhi subjects (431 males and 369 females) of Purigpas and Brokpas ancestry were taken. Descriptive statistics of cumulative cephalometrics in two sexes revealed that all the measurements were significantly larger in males than the females (p<0.001). Statistically significant sex differences were found in the various anthropometric, cephalometric and morphological features of Brokpas and Purigpas of Kargil (Ladakh, UT). Univariate discriminant function analysis found head length as the best cephalofacial variable to estimate sex of 73.4% individuals; followed by physiognomic facial length to estimate sex of 71% subjects. From multivariate discriminant function analysis, the physiological facial length, head length, nasal breadth, head circumference, nasal height, bizygomatic breadth, length of right ear and left ear breadth were selected as the best variables to correctly classify sex of 83.8% individuals to their category (81.9% males and 85.9% females). The present study results are the only cephalometric standards which have been suggested for Purigpas and Brokpas of Ladakh (Jammu and Kashmir) which can be used for medico-legal sex determination of unknown individuals of studied population.

Sex estimation from upper limb bones in a Thai population.

Sex estimation from skeletal remains is an important practice for forensic human identification. The aims of this study were to assess sexual dimorphism and to develop discriminant function equations for sex estimation using 12 measurements of upper limb bones (humerus, ulna, and radius) in a Thai population. The sample consisted of 228 Thai skeletons (114 males and 114 females) from the Forensic Osteology Research Center, Chiang Mai University, Chiang Mai, Thailand. All skeletal length variables were measured according to the Standards for Data Collection from Human Skeletal Remains. The values of measurements were used to develop the sex estimation equations using univariate and multivariate discriminant function analyses. The results of sexual dimorphism showed that upper limb bone lengths of males were statistically significantly longer than those of females in all dimensions (P<0.05). For univariate discriminant function analysis, the results showed that the epicondylar breadth of the humerus, the physiological length of the ulna, and the antero-posterior diameter at the midshaft of the radius were the best indicators for sex estimation in the humerus, ulna, and radius, respectively. Moreover, the multivariate discriminant function equation using all variables of the ulna and radius was the best indicator for sex estimation. In conclusion, the discriminant function equations derived from upper limb bone measurements provided highly accurate sex estimation in Thai samples. Therefore, these equations using humerus, radius, and ulna measurements can be applied for sex estimation with good accuracy in Thais.

Sex estimation from handprints in a Croatian population sample

Aim: To test if handprint measurements show sexual dimorphism in the Croatian population, and to develop population-specific sex estimation standards. Methods: A cross-sectional study was conducted on 100 adult volunteers from a Croatian population (50 males and 50 females) aged between 20 and 45 years. Using a fingerprint ink, we collected handprints of both hands on a paper sheet. We scanned handprints and took 13 measurements. Bilateral asymmetry and sexual dimorphism of the measurements was analyzed and sex estimation models were developed using linear discriminant analysis. Results: All measurements exhibited statistically significant sexual dimorphism (P&amp;lt;0.001). Univariate discriminant functions provided sexing accuracy from 75% to 92%. The highest accuracy rate (92%) and the lowest sexing bias (0%) was obtained using the handprint breadth. A multivariate discriminant function could estimate sex with 93% accuracy, but with more pronounced sexing bias (10%). Conclusion: We showed that handprint measurements could be used for sex estimation in the Croatian population with a high accuracy level. Therefore, they could serve as a valuable tool for biological profiling of perpetrators in criminal investigations when other evidence is not conclusive.

Estimation of stature and sex from skull measurements by multidetector computed tomography in Chinese.

The present study is an attempt to estimation of stature and sex from skull measurements by multidetector computed tomography (MDCT) in contemporary Chinese. In the present study, fifteen measurements for every skull were taken from CT image of 382 Chinese. The sample was composed of 200 males and 182 females with an average age of 47 and 46 years, respectively. Discriminant function was used in sex determination and regression analysis was used in stature estimation from skull measurements. The stepwise analysis of all measurements yielded a sex classification accuracy rate of 89.3%. The classification accuracy rates of the univariate discriminant function analyses were from 50.5% to 84.8%. For stature estimation, the standard error of estimate (SEE) ranged from 5.072 to 6.355 cm for male, from 5.090 to 5.829 cm for female, respectively. This study is the first to provide a metric and statistical characterization of the skull in contemporary Chinese, and indicates that it is feasible to sex estimation by skull measurement. Furthermore, the equations presented for stature estimation in this study may be used as alternatives in forensic cases, particularly in cases where better predictors such as the long bones are not available.

Sex estimation from the calcaneus and talus using discriminant function analysis and its possible application in fossil remains

Foot bones have been shown to be sexually dimorphic and they are frequently used for sex estimation. In this study, we estimated the sex based on the calcaneus and the talus of a modern North American population obtained from the Hamann-Todd Osteological Collection, housed at the Cleveland Museum of Natural History (Ohio, USA). A total of 164 calcanei (84 males and 80 females) and 162 tali (83 males and 79 females) were studied. Several univariate discriminant functions were obtained, with accuracy ranging from 70.2 to 90.2%. The best variable for sex estimation in this sample is the talar length. Multivariate discriminant functions were also obtained. The accuracy (83.3 to 96.4%) was generally higher than that obtained with the univariate discriminant functions. The best multivariate equation is the one that uses all the variables measured in the talus. Discriminant functions previously reported in other studies were tested on the Hamann-Todd collection to verify their validity outside the population for which they were made. In addition, together with the equations reported here, they were applied on data from fossil remains belonging to three different groups (Homo neanderthalensis, hominins from the Sima de los Huesos, and anatomically modern Homo sapiens) in order to find some discriminant functions that allow for a valid determination of sex in this type of fossil populations. Several equations yielded good correct allocation percentages in fossil populations thus facilitating the estimation of sex for 16 fossil specimens of previously unknown sex.

Sexing the Cranium from the Foramen Magnum Using Discriminant Analysis in a Brazilian Sample.

In the identification process, the foramen magnum has shown controversial results in sex estimation. The present study aimed to analyze the morphometric variables of the foramen magnum in Brazilian adult cranium for sex estimation. The sample was composed of 100 craniums (53 males and 47 females) from the documented collection of the Institute of Teaching and Research in Forensic Sciences. The protocol measurement was constituted of two linear measurements: maximum length of the foramen magnum and maximum breadth of the foramen magnum and two formulas to calculate the area, method one (M1) and method two (M2). Descriptive statistics showed statistically significant differences between sex (p<0.05) for all variables. The univariate discriminant functions showed an accuracy between 56.0-62.0%, and the multivariate analysis showed a percentage of accuracy between 60.0-65.0%, the greatest accuracy was found combining the two linear measurements with M1(71.7%), even after cross-validation (66%). Receiver Operating Characteristic (ROC) curve analysis showed that M2 is the best parameter for estimating sex (AUC=0.693). A reference table for Brazilians using the foramen magnum parameters was developed based on the results of the ROC curve analysis. In conclusion, the foramen magnum should be used with caution to estimate sex in forensic cases of fragmentary craniums, due to the limited accuracy.

Sexual Dimorphism in Anthropometric Measurements of Adult Uttarkashi (India) Individuals: A Forensic Anthropological Study

Biological profiling of unknown human remains is the foremost task required in forensic/medico-legal death investigations and sex determination of such remains is an important element of biological identity of an individual. In present study, 12 anthropometric measurements were recorded on 298 Uttarkashi individuals (150 males and 148 females) between age group of 18-25 years. Majority of measurements were found to have a significant degree of sexual dimorphism among them; being highest for cubit and thumb lengths and lowest for left palm and right foot lengths (p &gt;0.001). From Univariate discriminant function analysis, cubit length and left foot length were selected as the best variables to discriminate sex of about 80% (84% males and 76% females) 79% (84.7% males and 73.6% females) individuals, respectively. Similarly, 86% subjects could be classified to their correct sex category from all the lineal measurements (88.5% males and 87.2% females) or the hand measurements only (83.1% males and 84.6% females) from the multivariate discriminant function analysis. The results of present study can be considered an addendum to the existing population data for forensic anthropological literature.