Craniofacial identification standards: A review of reliability, reproducibility, and implementation.

There are numerous anatomical and anthropometrical standards that can be utilised for craniofacial analysis and identification. These standards originate from a wide variety of sources, such as orthodontic, maxillofacial, surgical, anatomical, anthropological and forensic literature, and numerous media have been employed to collect data from living and deceased subjects. With the development of clinical imaging and the enhanced technology associated with this field, multiple methods of data collection have become accessible, including Computed Tomography, Cone-Beam Computed Tomography, Magnetic Resonance Imaging, Radiographs, Three-dimensional Scanning, Photogrammetry and Ultrasound, alongside the more traditional in vivo methods, such as palpation and direct measurement, and cadaveric human dissection. Practitioners often struggle to identify the most appropriate standards and research results are frequently inconsistent adding to the confusion. This paper aims to clarify how practitioners can choose optimal standards, which standards are the most reliable and when to apply these standards for craniofacial identification. This paper describes the advantages and disadvantages of each mode of data collection and collates published research to review standards across different populations for each facial feature. This paper does not aim to be a practical instruction paper; since this field encompasses a wide range of 2D and 3D approaches (e.g., clay sculpture, sketch, automated, computer-modelling), the implementation of these standards is left to the individual practitioner.

The Doppelgänger effect? A comparative study of forensic facial depiction methods.

This study attempted to assess the reproducibility of 2D and 3D forensic methods for facial depiction from skeletal remains (2D sketch, 3D manual, 3D automated, 3D computer-assisted). In a blind study, thirteen practitioners produced fourteen facial depictions, using the same skull model derived from CT data of a living donor, a biological profile and relevant soft tissue data. The facial depictions were compared to the donor subject using three different evaluation methods: 3D geometric, 2D face recognition ranking and familiar resemblance ratings. Five of the 3D facial depictions (all 3D methods) demonstrated a deviation error within ± 2 mm for ≥ 50% of the total face surface. Overall, no single 3D method (manual, computer assisted, automated) produced consistently high results across all three evaluations. 2D comparisons with a facial photograph of the donor were carried out for all the 2D and 3D facial depictions using four freely available face recognition algorithms (Toolpie; Photomyne; Face ++; Amazon). The 2D sketch method produced the highest ranked matches to the donor photograph, with overall ranking in the top six. Only one 3D facial depiction was ranked highly in both the 3D geometric and 2D face recognition comparisons. The majority (67%) of the facial depictions were rated as limited or moderate resemblance by the familiar examiner. Only one 2D facial depiction was rated as strong resemblance, whilst two 2D sketches and two 3D facial depictions were rated as good resemblances by the familiar examiner. The four most geometrically accurate 3D facial depictions were only rated as limited or moderate resemblance to the donor by the familiar examiner. The results suggest that where a consistent facial depiction method is utilised, we can expect relatively consistent metric reliability between practitioners. However, presentation standards for practitioners would greatly enhance the possibility of recognition in forensic scenarios.

Confronting historical legacies of biological anthropology in South Africa-Restitution, redress and community-centered science: The Sutherland Nine.

We describe a process of restitution of nine unethically acquired human skeletons to their families, together with attempts at redress. Between 1925-1927 C.E., the skeletonised remains of nine San or Khoekhoe people, eight of them known-in-life, were removed from their graves on the farm Kruisrivier, near Sutherland in the Northern Cape Province of South Africa. They were donated to the Anatomy Department at the University of Cape Town. This was done without the knowledge or permission of their families. The donor was a medical student who removed the remains from the labourers' cemetery on his family farm. Nearly 100 years later, the remains are being returned to their community, accompanied by a range of community-driven interdisciplinary historical, archaeological and analytical (osteobiographic, craniofacial, ancient DNA, stable isotope) studies to document, as far as possible, their lives and deaths. The restitution process began by contacting families living in the same area with the same surnames as the deceased. The restitution and redress process prioritises the descendant families' memories, wishes and desire to understand the situation, and learn more about their ancestors. The descendant families have described the process as helping them to reconnect with their ancestors. A richer appreciation of their ancestors' lives, gained in part from scientific analyses, culminating with reburial, is hoped to aid the descendant families and wider community in [re-]connecting with their heritage and culture, and contribute to restorative justice, reconciliation and healing while confronting a traumatic historical moment. While these nine individuals were exhumed as specimens, they will be reburied as people.

Anemia design effects in cluster surveys of women and young children in refugee settings.

BACKGROUND: Nutrition surveys in many refugee settings routinely estimate anemia prevalence in high-risk population groups. Given the lack of information on anemia design effects (DEFF) observed in surveys in these settings, the goal of this paper is to better understand the magnitude and distribution of DEFFs and intracluster correlation coefficients (ICCs) in order to inform future survey design. METHODS: Two-stage cluster surveys conducted during 2013-2016 were included if they measured hemoglobin in refugee children aged 6-59 months and/or non-pregnant women aged 15-49 years. Prevalence of anemia, anemia DEFFs and ICCs, mean cluster size, number of clusters, and total sample size were calculated per-survey for non-pregnant women and children. Non-parametric tests were used to assess differences and correlations of ICC and DEFF between women and children and inter-regional differences. RESULTS: Eighty-seven unique cluster surveys from nine countries were included in this analysis. More than 90% of all surveys had ICC values for anemia below 0.10. Median ICC for children was 0.032 (IQR: 0.015-0.048), not significantly different from that observed for non-pregnant women for whom the median was 0.024 (IQR: -0.002-0.055). DEFFs were significantly higher for children [1.54 (IQR: 1.21-1.82)] versus women [1.20 (IQR: 0.99-1.46)]. Regional differences in DEFFs and ICCs were observed. CONCLUSIONS: Both ICCs and DEFF were relatively small for both non-pregnant women and preschool children and fall in a narrow range. Differences in ICCs between women and children were non-significant, suggesting similar inter-cluster distributions of anemia; significant differences in DEFF were likely attributable to differing cluster sizes. Given regional differences in both ICCs and DEFFs, location-specific values are preferred. However, in the absence of other context-specific information, we suggest using DEFFs of 1.4-1.8 if mean cluster size is around 20, and DEFFs of 1.2-1.4 if mean cluster size is around 10.

Effects on child growth of a reduction in the general food distribution ration and provision of small-quantity lipid-based nutrient supplements in refugee camps in eastern Chad.

BACKGROUND: We used the United Nations High Commissioner for Refugees Standardised Expanded Nutrition Survey data to evaluate the effect of a change in food ration on child growth in refugee camps in eastern Chad. METHODS: We compared trends of wasting and stunting prevalence over time and the association between the coexistence of being both stunted and wasted using Pearson's χ2 test. We analysed the effect of an approximate 50% reduction in the general food distribution, with the introduction of a 20 g daily ration of small quantity lipid-based nutrient supplements given to all children aged 6-23 months, on child growth. This was done using interrupted time-series analysis to observe differences in levels and trends in mean height-for-age z-score (HAZ) and weight-for-height z-score (WHZ) over time and by age group (6-24 months and 24-59 months). RESULTS: Overall the prevalence of stunting and wasting decreased significantly over time. The odds of being both stunted and wasted was 1.38 higher than having one or the other condition separately (p<0.001, 95% CI=1.29 to 1.47). Trends in mean HAZ and WHZ before and after a ration change in 2014 indicate that growth had either slowed down or worsened. In the period following the ration change, children 24-59 months saw a significant decrease in mean HAZ of 0.04 per year (p=0.02, 95% CI=-0.07 to -0.01) and for the younger age group, there was a significant decrease in mean WHZ of 0.06 per year (p=0.03, 95% CI=-0.12 to -0.01). CONCLUSIONS: The dual burden of stunting and wasting is a considerable challenge in refugee camp settings. Changes to the food distribution had adverse effects on child growth for both age groups. Broadening the scope of interventions aimed at children in camps is essential when tackling malnutrition with increased efforts essential during periods of wider food assistance shortages.

Pet Food-Associated Dietary Exogenous Thyrotoxicosis: Retrospective Study (2016-2018) and Clinical Considerations.

Dietary exogenous thyrotoxicosis is infrequently observed in pet food. A retrospective evaluation of pet food investigations (PFI) was conducted for 17 dogs, including review of medical records, dietary and environmental exposure interviews, food testing, and regulatory action. Five PFIs occurring between 2016 and 2018 involved 7 food products including 2 food types, jerky treats or canned food, made from beef or bison. The dogs' serum thyroid hormone concentrations were evaluated before and after diet change. The foods were tested for active thyroid hormones and hormone precursors using high performance liquid chromatography with inductively coupled plasma mass spectrometry detection. The foods were also examined microscopically. Serum thyroid hormone concentrations of thyroxine (T4) varied depending on the food type consumed. Dogs that consumed dried jerky containing greater T4 concentrations often had increased serum T4 concentrations, whereas dogs that consumed canned products containing greater and 3,4,5- and 3,5,3'-triiodothyronine (T3) concentrations often had decreased serum T4 concentrations. After the diets were changed, serum T4 and T3 concentrations normalized at 1 month. Seven foods containing beef or bison had iodine concentrations greater than 11 mg/kg, and iodine speciation identified variable concentrations of iodide, T4, T3, monoiodotyrosine (MIT), and di-iodotyrosine (DIT). Thyroid gland was found in microscopic sections from one finished food and one ingredient, gullet. FDA performed Health Hazard Evaluations to categorize the exposure risk, and 5 foods were recalled for which the product packaging had not been discarded. Dietary exogenous thyrotoxicosis should be considered in dogs exhibiting clinical signs compatible with hyperthyroidism, especially if consuming beef-based food. A thyroid panel that includes serum iodine, coupled with a thorough feeding history can aid in diagnosis. Thyrotoxicosis is typically reversible after removing the contaminated food from the diet.

Malnutrition trends in Rohingya children aged 6-59 months residing in informal settlements in Cox's Bazar District, Bangladesh: An analysis of cross-sectional, population-representative surveys.

BACKGROUND: More than 700,000 ethnic Rohingya have crossed the border from Rakhine State, Myanmar to Cox's Bazar District, Bangladesh, following escalated violence by Myanmar security forces. The majority of these displaced Rohingya settled in informal sites on previously forested land, in areas without basic infrastructure or access to services. METHODS AND FINDINGS: Three cross-sectional population-representative cluster surveys were conducted, including all informal settlements of Rohingya refugees in the Ukhia and Teknaf Upazilas of Cox's Bazar District. The first survey was conducted during the acute phase of the humanitarian response (October-November 2017), and the second and third surveys were conducted 6 (April-May 2018) and 12 (October-November 2018) months later. Anthropometric indices (weight, height, mid-upper arm circumference [MUAC], oedema) and haemoglobin (Hb) were measured in children aged 6-59 months following standard procedures. Final samples for survey rounds 1, 2, and 3 (R1, R2, and R3) included 1,113, 628, and 683 children, respectively, of which approximately half were male (50.7%-53.5% per round) and a third were 6-23 months of age (32.4%-33.3% per round). Prevalence of global acute malnutrition (GAM) as assessed by weight for height in R2 (12.1%, 95% CI: 9.6-15.1) and R3 (11.0%, 95% CI: 8.4-14.2) represent a significant decline from the observed prevalence in R1 (19.4%, 95% CI: 16.8-22.3) (p < 0.001 for both comparisons). Overall, the prevalence of anaemia significantly declined (p < 0.001) between the first 2 rounds (47.9%, 95% CI: 44.1-51.7 and 32.3%, 95% CI: 27.8-37.1, respectively); prevalence increased significantly (p = 0.04) to 39.8% (95% CI, 34.1-45.4) during R3 but remained below R1 levels. Reported receipt of both fortified blended foods (12.8%) and micronutrient powders (10.3%) were low during R1 but increased significantly (p < 0.001 for both) within the first 6 months to 49.8% and 29.9%, respectively. Although findings demonstrate improvement in anthropometric indicators during a period in which nutrition programme coverage increased, causation cannot be determined from the cross-sectional design. CONCLUSIONS: These data document significant improvements in both acute and micronutrient malnutrition among Rohingya children in makeshift settlements. These declines coincide with a scaleup of services aimed at prevention and treatment of malnutrition. Ongoing activities to improve access to nutritional services may facilitate further reductions in malnutrition levels to sustained below-crisis levels.

A guided manual method for juvenile age progression using digital images.

Predicting the possible age-related changes to a child's face, age progression methods modify the shape, colour and texture of a facial image while retaining the identity of the individual. However, the techniques vary between different practitioners. This study combines different age progression techniques for juvenile subjects, various researches based on longitudinal radiographic data; physical anthropometric measurements of the head and face; and digital image measurements in pixels. Utilising 12 anthropometric measurements of the face, this study documents a new workflow for digital manual age progression. An inter-observer error study (n = 5) included the comparison of two age progressions of the same individual at different ages. The proposed age progression method recorded satisfactory levels of repeatability based on the 12 anthropometric measurements. Seven measurements achieved an error below 8.60%. Facial anthropometric measurements involving the nasion (n) and trichion (tr) showed the most inconsistency (14-34% difference between the practitioners). Overall, the horizontal measurements were more accurate than the vertical measurements. The age progression images were compared using a manual morphological method and machine-based face recognition. The confidence scores generated by the three different facial recognition APIs suggested the performance of any age progression not only varies between practitioners, but also between the Facial recognition systems. The suggested new workflow was able to guide the positioning of the facial features, but the process of age progression remains dependant on artistic interpretation.

Craniofacial reconstruction of the Indus Valley Civilization individuals found at 4500-year-old Rakhigarhi cemetery.

Despite academic efforts to study the Indus Valley Civilization (IVC), there have as yet been no successful attempts to unveil the IVC people's craniofacial appearance. We investigated the IVC cemetery area of Rakhigarhi site, which was estimated to be of 2273 ± 38 and 2616 ± 73 years BCE. By craniofacial reconstruction (CFR) procedure using computed tomography (CT) data of two Rakhigarhi skulls (A1 BR02 and A2 BR36), we successfully reconstructed the faces of the IVC individuals who were buried about 4500 years ago. This is the first attempt to unveil scientifically accurate representations of IVC people's actual facial morphology.

The burden of anaemia among displaced women and children in refugee settings worldwide, 2013-2016.

INTRODUCTION: Displaced persons have a unique risk for developing anaemia due to often limited diets, overcrowding, new infections and inadequate sanitation and hygiene. The lack of anaemia prevalence estimates among the displaced inhibit global planning for anaemia reduction. METHODS: We analysed population representative, cross-sectional nutrition surveys from 2013 to 2016 conducted by the United Nations High Commissioner for Refugees and partner agencies. Included surveys measured haemoglobin concentration among children 6-59 months, non-pregnant women 15-49 years, or both groups. For each survey, we calculated mean haemoglobin and prevalence of total anaemia (<110 g/L in children, <120 g/L in women), and classified public health severity following WHO guidelines. Pearson correlations between indicators from women and children surveys were calculated where both subpopulations were measured. RESULTS: Analysis included 196 surveys among children and 184 surveys among women from 121 unique refugee settings in 24 countries. The median prevalence of total anaemia in children and women was 44% and 28%, respectively. Sixty-one per cent of child surveys indicated a problem of severe public health importance compared with 25% of surveys in women. The prevalence of total anaemia in children and women was strongly correlated (ρ=0.80). Median prevalence of total anaemia was approximately 55% greater and mean haemoglobin was 6 g/L lower among children age 6-23 months compared with children 24-59 months. West and Central Africa region had the highest median prevalence of anaemia both in women and children. CONCLUSION: While the burden of anaemia is high among the displaced, it mirrors that of the general population. Haemoglobin should continue to be measured in nutrition surveys in refugee settings. Sustained, multisectoral efforts to reduce anaemia are needed, with specific focus on children under 2 years of age and refugee settings in the West and Central Africa region.

The Affordances of 3D and 4D Digital Technologies for Computerized Facial Depiction.

3D digital technologies have advanced rapidly over recent decades and they can now afford new ways of interacting with anatomical and cultural artefacts. Such technologies allow for interactive investigation of visible or non-observable surfaces, haptic generation of content and tactile experiences with digital and physical representations. These interactions and technical advances often facilitate the generation of new knowledge through interdisciplinary and sympathetic approaches.Scientific and public understanding of anatomy are often enhanced by clinical imaging technologies, 3D surface scanning techniques, 3D haptic modelling methods and 3D fabrication systems. These digital and haptic technologies are seen as non-invasive and allow scientists, artists and the public to become active investigators in the visualisation of, and interaction with, human anatomy, remains and histories.Face Lab is a Liverpool John Moores University research group that focuses on creative digital face research; specifically the further development of a 3D computerized craniofacial depiction system, utilizing 3D digital technologies in facial analysis and identification of human remains for forensic investigation, or historical figures for archaeological interpretation.This chapter explores the affordances of such interactions for the non-destructive production of craniofacial depiction, through a case-study based exploration of Face Lab workflow.

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.

Sexing the cranium from the foramen magnum using discriminant analysis in a brazilian sample

Abstract 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.

Resumo No processo de identificação humana, a análise do forame magno apresenta resultados controversos para estimativa do sexo. O presente estudo teve como objetivo analisar as variáveis morfométricas do forame magno em crânios adultos brasileiros para estimação sexual. A amostra foi composta por 100 crânios (53 sexos masculino e 47 sexo feminino) pertencentes a coleção osteológica documentada do Instituto de Ensino e Pesquisa em Ciências Forenses. A medida do protocolo foi constituída por duas medidas lineares: comprimento máximo do forame magno e largura máxima do forame magno e duas fórmulas para calcular a área, método um (M1) e método dois (M2). As estatísticas descritivas evidenciaram diferenças estatisticamente significativas (p<0,05) para todas as variáveis. As funções discriminantes univariadas apresentaram uma porcentagem de acerto entre 56,0-62,0% e a análise multivariada mostrou uma porcentagem de acerto entre 60,0-65,0%. A análise da curva ROC apontou que M2 é o melhor parâmetro para estimar o sexo (AUC=0,693). Uma tabela de referência para brasileiros que utilizam os parâmetros do forame magnum foi desenvolvida com base nos resultados da análise da curva ROC. Em conclusão, o foram e magnum deve ser usado com precaução para estimar o sexo em casos forenses de cranio fragmentado, devido à precisão limitada.

Assessment of accuracy and recognition of three-dimensional computerized forensic craniofacial reconstruction.

Facial reconstruction is a technique that aims to reproduce the individual facial characteristics based on interpretation of the skull, with the objective of recognition leading to identification. The aim of this paper was to evaluate the accuracy and recognition level of three-dimensional (3D) computerized forensic craniofacial reconstruction (CCFR) performed in a blind test on open-source software using computed tomography (CT) data from live subjects. Four CCFRs were produced by one of the researchers, who was provided with information concerning the age, sex, and ethnic group of each subject. The CCFRs were produced using Blender® with 3D models obtained from the CT data and templates from the MakeHuman® program. The evaluation of accuracy was carried out in CloudCompare, by geometric comparison of the CCFR to the subject 3D face model (obtained from the CT data). A recognition level was performed using the Picasa® recognition tool with a frontal standardized photography, images of the subject CT face model and the CCFR. Soft-tissue depth and nose, ears and mouth were based on published data, observing Brazilian facial parameters. The results were presented from all the points that form the CCFR model, with an average for each comparison between 63% and 74% with a distance -2.5 ≤ x ≤ 2.5 mm from the skin surface. The average distances were 1.66 to 0.33 mm and greater distances were observed around the eyes, cheeks, mental and zygomatic regions. Two of the four CCFRs were correctly matched by the Picasa® tool. Free software programs are capable of producing 3D CCFRs with plausible levels of accuracy and recognition and therefore indicate their value for use in forensic applications.

Facial preservation following extreme mummification: Shrunken heads.

Shrunken heads are a mummification phenomenon unique to South America. Ceremonial tsantsa are ritually reduced heads from enemy victims of the Shuar, Achuar, Awajún (Aguaruna), Wampís (Huambisa), and Candoshi-Shapra cultures. Commercial shrunken heads are comparatively modern and fraudulently produced for the curio-market, often using stolen bodies from hospital mortuaries and graves. To achieve shrinkage and desiccation, heads undergo skinning, simmering (in water) and drying. Considering the intensive treatments applied, this research aims to identify how the facial structure can alter and impact identification using post-mortem depiction. Sixty-five human shrunken heads were assessed: 6 ceremonial, 36 commercial, and 23 ambiguous. Investigations included manual inspection, multi-detector computerised tomography, infrared reflectography, ultraviolet fluorescence and microscopic hair analysis. The mummification process disfigures the outer face, cheeks, nasal root and bridge form, including brow ridge, eyes, ears, mouth, and nose projection. Melanin depletion, epidermal degeneration, and any applied staining changes the natural skin complexion. Papillary and reticular dermis separation is possible. Normal hair structure (cuticle, cortex, medulla) is retained. Hair appears longer (unless cut) and more profuse following shrinkage. Significant features retained include skin defects, facial creases, hairlines and earlobe form. Hair conditions that only affect living scalps are preserved (e.g. nits, hair casts). Ear and nose cartilage helps to retain some morphological information. Commercial heads appear less distorted than ceremonial tsantsa, often presenting a definable eyebrow shape, vermillion lip shape, lip thickness (if mouth is open), philtrum form, and palpebral slit angle. Facial identification capabilities are considered limited, and only perceived possible for commercial heads.

Discriminant analysis of mandibular measurements for the estimation of sex in a modern Brazilian sample.

The present study aimed to evaluate the accuracy of mandibular measurements for sex determination in a Brazilian population. The sample was composed of 100 mandibles, of which 53 were female and 47 were male, and the average age was 57.03 years. The mandible measurement protocol was composed of 15 measurements, of which six were bilateral and nine were unique. Mandibles were directly measured using a digital caliper and a protractor. The descriptive analysis of the present study revealed higher mean values for male mandibles compared to those for female mandibles with the exception of the left mandibular angle. Among the 21 measures analyzed in this group, 15 were statistically significant (p < 0.05). Univariate discriminant analyses produced a mean percentage of correct predictions that varied between 49 and 79%. The association of variables increased the percentage of correct prediction of sex to vary from 76 to 86%. The receiver operator characteristic (ROC) curve analysis indicated that the best variable for estimating sex was bigonial breadth (BGB; area under the ROC curve (AUC) = 0.764) followed by the right maximum ramus height (MRHr; AUC = 0.763). A reference table for estimating sex in a Brazilian population using mandible measurements was developed based on the ROC curve analysis. Mandibular measures provide a simple and reliable method for sex discrimination in Brazilian adults due to the sexual dimorphism revealed by analysis of the metric variables and the satisfactory results demonstrated by discriminant formulas, ROC curve analysis, and the reference table.