Machine learning and discriminant function analysis in the formulation of generic models for sex prediction using patella measurements.

Sex prediction from bone measurements that display sexual dimorphism is one of the most important aspects of forensic anthropology. Some bones like the skull and pelvis display distinct morphological traits that are based on shape. These morphological traits which are sexually dimorphic across different population groups have been shown to provide an acceptably high degree of accuracy in the prediction of sex. A sample of 100 patella of Mixed Ancestry South Africans (MASA) was collected from the Dart collection. Six parameters: maximum height (maxh), maximum breadth (maxw), maximum thickness (maxt), the height of articular facet (haf), lateral articular facet breadth (lafb), and medial articular facet breath (mafb) were used in this study. Stepwise and direct discriminant function analyses were performed for measurements that exhibited significant differences between male and female mean measurements, and the "leave-one-out" approach was used for validation. Moreover, we have used eight classical machine learning techniques along with feature ranking techniques to identify the best feature combinations for sex prediction. A stacking machine learning technique was trained and validated to classify the sex of the subject. Here, we have used the top performing three ML classifiers as base learners and the predictions of these models were used as inputs to different machine learning classifiers as meta learners to make the final decision. The measurements of the patella of South Africans are sexually dimorphic and this observation is consistent with previous studies on the patella of different countries. The range of average accuracies obtained for pooled multivariate discriminant function equations is 81.9-84.2%, while the stacking ML technique provides 90.8% accuracy which compares well with those presented for previous studies in other parts of the world. In conclusion, the models proposed in this study from measurements of the patella of different population groups in South Africa are useful resent with reasonably high average accuracies.

Sex estimation from dimensions of the base of the skull in Black South Africans.

The pelvis and the skull are the two most utilised skeletal elements to estimate sex from skeletonised remains due to their sexually dimorphic traits. However, as increasingly more fragmented remains have been presented for analyses, other bones and their fragments have now been subjected to analyses for sex estimation. In the skull particularly, the base has shown to survive harsh conditions. In this study the foramen magnum region was explored in Black South Africans to estimate sex during forensic analyses. Seven measurements of the foramen magnum and surrounding areas were measured in 120 male and female crania and subjected to discriminant function analyses. The average accuracies for the stepwise discriminant functions ranged from 60-71% whilst the average accuracies for the direct discriminant functions ranged from 63-69%. The average accuracies obtained in this study are similar to other studies performed using the foramen magnum. However, these average accuracies are much lower than other skeletal elements that have been used for sex estimation in South Africans. Thus, the equations in this study should be used with caution and only in the absence of more accurate elements. The cranial base has always shown to have a low to moderate expression of sexual dimorphism. The cranial base of Black South Africans is no different.

Accuracies of discriminant function equations for sex estimation using long bones of upper extremities.

One of the scopes of practice of forensic anthropologists is the estimation of sex from skeletal remains. As a result, population-specific discriminant function equations have been developed from measurements of various bones of the human skeletons. Steyn, Patriquin (Forensic Sci Int 191 (1-3):113, 2009) noted that the lack of skeletal collections and data from most parts of the world has made this process impractical. Previous attempts to develop global discriminant function equations from measurements of the pelvis showed that population-specific equations are not necessary as equations derived from other populations yielded high sex estimation scores when applied to a different population. However, information on the suitability and applicability of generalised equations in sex estimation using long bones is still scarce. It is, therefore, the aim of this study to assess the accuracies of population-specific discriminant function equations derived from measurements of long bones of the upper limb of South African population groups. Data analysed in the current study were obtained from Mokoena, Billings, Bidmos, Mazengenya (Forensic Sci Int 278:404, 2017) and Mokoena, Billings, Gibbon, Bidmos, Mazengenya (Science & Justice 6(59):660-666, 2019) in which a total sample of 988 bones (humeri, radii, and ulnae) of South Africans of African descent (SAAD), South Africans of European descent (SAED) and Mixed Ancestry South Africans (MASA) were measured. Stepwise and direct discriminant function analyses were performed on the pooled data. Each function was used to estimate the sex of cases in each population group separately and average accuracies calculated. Thereafter, population-specific discriminant function equations were formulated for each population group and then applied to other population groups. The average accuracies of functions for pooled data ranged between 80.7 and 86.5%. The cross-validation average accuracies remained unchanged for most functions, confirming the validity of derived functions. A drop in average accuracies (0.8-5.3%) was observed when the functions were tested on a sample of SAAD while increased average accuracy was observed for the SAED and MASA (0.5-6.9%). When population-specific functions for a particular population group were applied to other groups, a wide range of a drop in average accuracies was observed (1.3 to 22.4%). This thereby confirms that population-specific equations should not be applied to other population groups. However, discriminant function equations from the pooled data of South Africans are accurate in the estimation of sex and efforts should be made towards the development and validation of such equations from as many bones of the human skeleton.

Forensic utility of cranial measurements in stature reconstruction in South Africans of European descent.

The height of an individual (stature) is one of the biological profiles that is estimated as part of human identification process from various components of the human skeleton. The anatomical method is often used for this purpose when a complete and intact skeleton is available for forensic analysis because it is accurate. Since complete skeletons are seldom present in most forensic cases, the mathematical method, which shows linear relationship between stature and bone measurements, becomes the method of choice. Population and sex-specific regression equations for stature estimation have been formulated using intact and fragmentary long bones amongst South African whites and blacks. Individual and combinations of measurements of other skeletal elements including bones of the feet have also been used in the formulation of regression equations. However, few studies have utilized measurements of the skull for stature reconstruction. Skeletal height, calculated from a suite of measurements, was regressed on six cranial measurements. Basibregmatic height and basion-nasion length presented with the highest correlation coefficient for an individual variable in males (0.50) and females (0.48), respectively. The range of correlation coefficient from multivariate analyses in males (0.58-0.63) is similar to that obtained in females (0.55-0.62). The standard error of estimates of the equations, a measure of the accuracy of the equations, for male sample (6.74-7.09) was slightly higher than that for females (5.47-5.89). Regression equations presented in this study should be used with caution in forensic cases when only the skull is available for human identification. Significance of main findings: 1. Skull measurements show low to moderate correlation with stature. 2. Use of skull dimensions is advised only in the absence of intact long bones and other skeletal elements in South Africa.

Development of discriminant functions to estimate sex in upper limb bones for mixed ancestry South Africans.

South Africa has one of the highest murder rates in the world, which is associated with an increasing number of unidentified individuals. Forensic anthropologists can assist in these cases to reduce the number of potential victims the remains may belong to. Sex estimation potentially decreases the number of possible victims by half. The mixed ancestry population in South Africa is the second largest group of people; however, there remains a paucity of data and population-specific methods for sex estimation in this group. The aim of this study was to assess the potential for metrices obtained around the nutrient foramen and the maximum length of upper limb long bones to estimate sex in mixed ancestry South Africans using discriminant function analysis. A total of 328 humeri, radii and ulnae from individuals of mixed ancestry were analysed. Sex was correctly classified with an average classification accuracy of 84.3% in the humeri, 88.3% for radii and 83.5% for the ulnae. Total length was the single best predictor of sex; the combination of total length with dimensions related to the nutrient foramen produced high classification accuracies in the current study. Overall, sexual dimorphism was observed in mixed ancestry South Africans upper limb long bones. The findings of this study further emphasise the need for population-specific standards of sexing in an attempt to improve current methods of forensic identification of descendants.

Dimensions around the nutrient foramina of the tibia and fibula in the estimation of sex.

Sex estimation from skeletal remains is one of the key components in establishing a biological profile and consequent identification of an individual in a forensic and medico-legal practice. The use of dimensions around the nutrient foramen in instances where long bones may be fragmented and damaged is of benefit due to the fact that the nutrient foramen is easily identifiable and may be preserved on the shaft of long bones. This study is an investigation of the usefulness of various measurements around the nutrient foramen of the tibia and fibula of South Africans in an attempt to develop osteometric standards for sex estimation. The sample included 206 tibiae and 204 fibulae of South African Africans (SAA) and South African whites (SAW) procured from the Raymond A. Dart Collection of Human Skeletons based at the University of the Witwatersrand. Sex was correctly classified for the tibia with an accuracy ranging between 79-82% in SAA and 84-88% in SAW, with the circumference at the level of the nutrient foramen as the single best predictor of sex in both populations. An accuracy ranging from 69 to 74% in SAA and 70-77% in SAW was observed for the combined measurements on the fibula. The current study confirms the usefulness of measurements around the nutrient foramen of the tibia in the assignment of sex. However functions of the fibula generally performed poorly and should be used with caution.

Measurements of the talus in the assessment of population affinity.

As part of their routine work, forensic anthropologists are expected to report population affinity as part of the biological profile of an individual. The skull is the most widely used bone for the estimation of population affinity but it is not always present in a forensic case. Thus, other bones that preserve well have been shown to give a good indication of either the sex or population affinity of an individual. In this study, the potential of measurements of the talus was investigated for the purpose of estimating population affinity in South Africans. Nine measurements from two hundred and twenty tali of South African Africans (SAA) and South African Whites (SAW) from the Raymond A. Dart Collection of Human Skeletons were used. Direct and step-wise discriminant function and logistic regression analyses were carried out using SPSS and SAS. Talar length was the best single variable for discriminating between these two groups for males while in females the head height was the best single predictor. Average accuracies for correct population affinity classification using logistic regression analysis were higher than those obtained from discriminant function analysis. This study was the first of its type to employ discriminant function analyses and logistic regression analyses to estimate the population affinity of an individual from the talus. Thus these equations can now be used by South African anthropologists when estimating the population affinity of dismembered or damaged or incomplete skeletal remains of SAA and SAW.

Assessing the use of the anatomical method for the estimation of sub-adult stature in Black South Africans.

Stature estimation is rarely attempted in sub-adults due to the general lack of available standards as a result of the dearth of sufficiently large sub-adult skeletal collections with known demographic information. To overcome this problem sub-adult research mainly relies on modern imaging modalities. In the current study Magnetic Resonance Imaging (MRI) scans were used to assess the use of the anatomical method for stature estimation in sub-adults. A total of 53 Black South African sub-adult males (n=24) and females (n=29) aged between 10 and 17 years participated in the study by voluntarily completing a full-body MRI scan. A stadiometer was used to measure living stature prior to all MRI scans. Skeletal elements that contribute directly to stature were measured from the MRI scans using OsiriX and summed to compute the total skeletal height. Total skeletal height was calculated using the diaphyseal, maximum and physiological long bone lengths and correlated to living stature using Pearson's correlations. Subsequently least squares regression equations were generated for the estimation of sub-adult stature. Results indicated strong, statistically significant positive correlations between living stature and total skeletal heights in sub-adult males, females and a combined sex sample. The regression equations were characterized by small standard error of estimates which are comparable to that reported for Black South African adults. Based on these results the anatomical method can be used to accurately describe living stature in Black South African sub-adults. This method is therefore encouraged as it will add valuable information when dealing with unknown sub-adult skeletal remains.

Sex estimation using dimensions around the nutrient foramen of the long bones of the arm and forearm in South Africans.

South Africa has had an increase in rates of crime, interpersonal violence and homicide since the introduction of democracy in 1994. Forensic osteological standards was lacking for South Africans of different population groups necessitating the generation of new standards for forensic identification of individuals from skeletal remains. For these reasons, there is a concerted demand for methods of identifying skeletal remains with sex being amongst the most important of the biological characteristics required. The nutrient foramen has been used to estimate sex in lower limb long bones with much accuracy but this has not been demonstrated in the upper limb long bones. The aim of this study was to develop osteometric standards for sex estimation from measurements around the nutrient foramen of the arm and forearm bones of South Africans of different population affinities. A total of 660 bones consisting of humeri, radii and ulnae of black South Africans and white South Africans were assessed for sex estimation using dimensions related to the nutrient foramen. Sex was correctly classified with a range of 84-85% for the humerus and 83-88% for the arm bones. The study showed that length measurements were more sexually dimorphic than width dimensions in South Africans, as length was consistently selected as the best predictor of sex in all bones. However, the average accuracy increased when length was used in combination with measurements related to the nutrient foramen. In conclusion, the dimensions of upper limb long bones that are directly related to the nutrient foramen are sexually dimorphic and are useful in the estimation of sex in South Africans, with the highest accuracy shown in the white South African population group.

The accuracy of the anatomical method for stature estimation in Black South African females.

The anatomical method is considered the most accurate stature estimation method, but investigation has shown that it continuously underestimates stature. This underestimation is believed to be related to the use of universal soft tissue correction factors. Therefore, the aim of this study was to assess the accuracy of the soft tissue correction factors in a living population of Black South African females and to subsequently calculate a new soft tissue correction factor, specific for stature estimation in this population group. Thirty Black South African adult females voluntarily participated in this study and underwent a full body Magnetic Resonance Imaging (MRI) scan. Living stature was measured with a stadiometer and total skeletal height (TSH) was calculated from the MRI measurements. Stature was estimated from the TSH of each participant using Fully's (1956) [17], Raxter et al.'s (2006) [38] and Bidmos and Manger's (2012) [5] methods. Results indicated strong, statistically significant positive correlations between living and estimated statures, however, paired t-tests revealed that living stature was significantly underestimated using Fully's and Raxter et al.'s methods, while the method by Bidmos and Manger significantly overestimated stature. A lack of statistically significant correlations between soft tissue correction factors and the total skeletal height was found. Likewise, an absence of statistically significant correlations between age and the estimation error, with and without age adjustments were also observed. A new soft tissue correction factor, specific for stature estimation in Black South African females was calculated. The newly proposed regression equation presented improved stature estimation accuracies for this population group.

Stature estimation from the femur and tibia in Black South African sub-adults.

Stature estimation can play a role in the positive identification of unknown individuals and as such it is routinely assessed during the examination of adult remains. Unfortunately, this is not a standard procedure when dealing with sub-adult remains due to the general lack of standard procedures for the estimation of sub-adult stature. The aim of this study was therefore to derive regression equations for the estimation of stature in black South African sub-adults. Fifty nine black South African sub-adult males and females, aged 10-17 years, voluntarily participated in the study by undergoing a full body Magnetic Resonance Imaging (MRI) scan. Living stature was measured with a stadiometer and the maximum and diaphyseal lengths of the femur and tibia were measured from the MRI scans using the image processing software OsiriX. Pearson's correlation coefficients and linear least square regression analyses were used to assess the correlations between living stature and the measurements and to generate sub-adult stature estimation equations for males, females and a combined sex sample. Measurements of the femur, tibia and the combined measures thereof showed strong statistically significant positive correlations with living stature, while the obtained regression equations were characterized by low standard error of estimates. The strong correlations and low standard error of estimates are comparable to stature estimation models reported for Black South African adults and therefore these variables can be considered good estimators of sub-adult stature which will contribute valuable information to the biological profile of unidentified sub-adult skeletal remains.

The history and composition of the Raymond A. Dart Collection of Human Skeletons at the University of the Witwatersrand, Johannesburg, South Africa.

The Raymond A. Dart Collection of Human Skeletons (Dart Collection) is housed in the School of Anatomical Sciences at the University of the Witwatersrand, Johannesburg, South Africa, and comprises one of the largest documented cadaver-derived human skeletal assemblages in the world. This collection originated in the early 1920s as a result of the efforts of Raymond Dart and continues to grow. The skeletons included represent varied indigenous and immigrant populations from southern Africa, Europe and Asia. This contribution documents the history of the collection and provides an updated inventory and demographic assessment of this valuable research collection. According to a recent inventory the Dart Collection currently comprises 2,605 skeletons representing individuals from regional SA African (76%), White (15%), Coloured (4%) and Indian (0.3%) populations. A large proportion of the skeletons (71%) represent males. The recorded ages at death range from the first year to over 100 years of age, but the majority of individuals died between the ages of 20 and 70. The Dart Collection has been affected by collection procedures based on availability. All of the cadavers collected before 1958, and large proportions subsequently, were derived from unclaimed bodies in regional South African hospitals. Some details of documentation (age at death, population group) are estimates and some aspects of the collection demographics (sex ratios) do not closely reflect any living South African population. Our inventory and analysis of the Dart Collection is aimed to assist researchers planning research on the materials from this collection.

Further evidence to show population specificity of discriminant function equations for sex determination using the talus of South African blacks.

Several studies have shown that osteometric differences exist between different population groups. Thus, discriminant function equations derived for the determination of sex from skeletal elements are population specific. In a previous study, the authors derived such equations from nine measurements of the talus of South African whites with high levels of average accuracies. The validity of some of the equations was tested on data collected from a South African black sample that consisted of 120 tali, equally distributed by sex, derived from the Raymond A. Dart Collection of Human Skeletons. The average accuracies dropped significantly. This necessitated the derivation of new equations for the South African black population and the average accuracies obtained ranged between 80% and 89%. The validity of the equations derived from the present study was tested using the leave-one-out classification and two independent samples (1 and 2). The applicability of the equations with very high classification rate from the present study was tested on Independent sample 1 of 10 white tali with poor results. The result of the validity of these equations on an Independent sample 2 of 10 black tali revealed acceptably high average accuracies in correct classification thereby supporting earlier observations on population specificity of discriminant function equations.

Discriminant function sexing of the calcaneus of the South African whites.

The skull and some postcranial elements, such as the humerus, femur, and tibia, have been used in their intact states for sex determination in forensic and archaeological cases. But, in practice, these bones are often recovered in fragmented states, which render them unsuitable for use in sex determination. The calcaneus is a compact bone that is able to withstand high tensile forces. Some of its parameters have been used for sex determination in American whites and blacks (1) and Italians (2). This bone has not been used for sex determination in the South African white population. Therefore, the aim of this study was to assess the degree of sexual dimorphism of the calcaneus of the South African white population sample, derive discriminant function score equations for use in sex determination, and determine the level of accuracy of its sex-determining ability. Nine parameters were measured on each pair of 53 male and 60 female calcanei of known South African white skeletons, obtained by a random sampling technique from the Raymond A. Dart Collection of Human Skeletons, School of Anatomical Sciences, University of the Witwatersrand, Johannesburg. Basic statistic and discriminant function analysis was performed on the acquired data. The basic statistics showed that all measured parameters were sexually dimorphic. Discriminant function score equations were generated for use in sex determination. The average accuracy of sex classification ranged from 73 to 86% for the univariate method, 81 to 91% for the stepwise method, and 82 to 92% for the direct method. It is concluded that the calcaneus is useful for sex determination in the South African white population.