Academia.eduAcademia.edu

Mandibular sexual dimorphism analysis in CBCT scans

2016, Journal of Forensic and Legal Medicine

The aim of this study was to evaluate sexual dimorphism using anthropometric measurements on mandibular images obtained by cone beam computed tomography (CBCT). The sample consisted of 160 CT scans collected from a Brazilian population (74 males, 86 females) aged 18-60 years. The CBCT images were analyzed by five reviewers. Six measurements (ramus length, gonion-gnathion length, minimum ramus breadth, gonial angle, bicondylar breadth, and bigonial breadth) were collected for the sexual prediction analysis. For the statistical analysis, intraclass correlation was used to evaluate intra-and inter-reviewers, analysis of variance was used to compare the mean values of these measurements, binary logistic regression equations were created to predicts sex. Using these four variables, the rate of correct sex classification was 95.1%. After, the discriminant function was used to validate the formula built. Accuracy of 93.33% and 94.74% was found for estimating male and females, respectively. Thus, the formula developed in this study can be used for sex estimation in forensic settings.

Accepted Manuscript Mandibular sexual dimorphism analysis in CBCT scans Thiago de Oliveira Gamba, MsC, Marcelo Corrêa Alves, PhD, Francisco Haiter-Neto, PhD PII: S1752-928X(15)00239-5 DOI: 10.1016/j.jflm.2015.11.024 Reference: YJFLM 1284 To appear in: Journal of Forensic and Legal Medicine Received Date: 16 June 2015 Revised Date: 25 October 2015 Accepted Date: 29 November 2015 Please cite this article as: de Oliveira Gamba T, Alves MC, Haiter-Neto F, Mandibular sexual dimorphism analysis in CBCT scans, Journal of Forensic and Legal Medicine (2016), doi: 10.1016/ j.jflm.2015.11.024. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. ACCEPTED MANUSCRIPT MANDIBULAR SEXUAL DIMORPHISM ANALYSIS IN CBCT SCANS Thiago de Oliveira Gamba,1 MsC, Marcelo Corrêa Alves,2 PhD, Francisco Haiter-Neto,1 PhD 1 Division of Oral Radiology, Piracicaba Dental School, State University of Campinas, , Limeira Avenue, RI PT 901, PO Box 52, Piracicaba, SP, Brazil Department of Oral Diagnosis 2Superior School of Agriculture "Luiz de Queiroz" Technical Section of Information Technology, University of São Paulo, Pádua Dias Avenue, 11, PO Box 19, Piracicaba, SP, Brazil M AN US C Tel: (+55) 19 32106-5321 E-mail: thiagodeo.gamba@hotmail.com Tel: (+55) 19 34294540. E-mail: macalves@usp.br Tel: (+55) 19 32106-5321. E-mail: haiter@fop.unicamp.br Corresponding author Thiago de Oliveira Gamba Rua Limeira, 901, PO Box 52 AC C EP TE E-mail: thiagodeo.gamba@hotmail.com D Piracicaba, SP, Brazil 1 ACCEPTED MANUSCRIPT ABSTRACT The aim of this study was to evaluate sexual dimorphism using anthropometric measurements on mandibular images obtained by cone beam computed tomography (CBCT). The sample consisted of 160 CT scans collected from a Brazilian population RI PT (74 males, 86 females) aged 18–60 years. The CBCT images were analyzed by five reviewers. Six measurements (ramus length, gonion-gnathion length, minimum ramus breadth, gonial angle, bicondylar breadth, and bigonial breadth) were collected for the M AN US C sexual prediction analysis. For the statistical analysis, intraclass correlation was used to evaluate intra- and inter-reviewers, analysis of variance was used to compare the mean values of these measurements, binary logistic regression equations were created to predicts sex. Using these four variables, the rate of correct sex classification was 95.1%. After, the discriminant function was used to validate the formula built. Accuracy of 93.33% and 94.74% was found for estimating male and females, respectively. Thus, the D formula developed in this study can be used for sex estimation in forensic settings. TE Keywords: Forensic science, sex, forensic dentistry, mandible, cone-beam computed AC C EP tomography 2 ACCEPTED MANUSCRIPT 1. Introduction Identity can be described as a set of characteristics that individualize a person and differentiate one person from another; the term is widely used in forensic studies. The process of comparing details in missing individuals and searching for coincidences RI PT between previously recorded data is called identification.1 Sexual prediction is one of the parameters used for preliminary identification of missing people. Craniofacial structures have advantages because they consist of dense M AN US C long bones that are comparatively indestructible. A high diagnostic value can be assigned to well-preserved skeletal parts, such as the mandible.2,3,4,5 Distinct morphologic and morphometric manifestations of sexual dimorphism have been observed in different populations in most countries throughout the world, including the United States, China, Japan, and Europe. Such differences have been TE current skeletal features.6,7,8,9,10,11 D reported in many studies, therefore it is essential to target a specific population with Kharoshah et al.12 used mandibular osteometric measurements on computed EP tomography (CT) images to estimate the sex of a specific population. The measurements involved the longest ramus,13 gonial angle, mandibular base length, and AC C shorter length of the mandibular branch. Measurements were made in sagittal view reconstructed in three dimensions, and the distance between the gonia and between the condyles was measured in three-dimensional (3D) axial view.12,14,15 CT, a method of diagnostic imaging using X-radiation, reproduces sections of the human body in all planes of space.16,17,18 Two CT systems are available according to their operating principles: fan beam CT (FBCT) and cone beam CT (CBCT). CBCT was the first technique used to examine the maxillofacial complex.19,20 3 ACCEPTED MANUSCRIPT Biwasaka et al.21 and Angel et al.22 studied sexual prediction and age using CBCT images in different views of reconstruction. Angel et al.22 performed measurements on anatomic structures that frequently present anatomical variations, such as the mandibular canal and the mandibular and mental foramina, and found some sex- RI PT specific characteristics.23 The aim of this study was to create a formula with potential predictive variables using anthropometric mandibular measurements on CBCT images in Brazilians and M AN US C compare the values between the sexes. Variables were evaluated to check for their suitability for sex estimate. 2. Material and methods This retrospective study included 160 CBCT images of the mandible of adult patients (74 males and 86 females), aged between 18 and 60 years, selected from a D database of clinical examinations made at the Dental Radiology Clinic, Piracicaba TE Dental School, State University of Campinas. This study was approved by The Ethics (no. 109/2011) EP Committee in Research of the Piracicaba Dental School - State University of Campinas, AC C The images were selected visually by a dentomaxillofacial radiologist. CBCT images of individuals who had any type of pathologic condition or mandibular fractures in the jaw region were excluded. CBCT images were obtained using an i-CAT scanner (Imaging Sciences, Hatfield, PA, USA), and the following parameters: 80 kVp, 4.8 mA, acquisition time 40 s, reconstruction time 62 s, voxel size 0.3 mm, and an extended field of view (FOV) of 23 cm × 17 cm. The images were of patients with orthodontic indications. This FOV was selected to provide images with all the fundamental elements of the mandibular anthropometric points for the present study. 4 ACCEPTED MANUSCRIPT CBCT scans were obtained with the patients seated. The head position was kept in the midsagittal plane perpendicular to the horizontal plane and the Camper plane (an imaginary line that runs from the nose to the wing tragus), thus remaining parallel to the horizontal plane. During the examination, the patients remained immobile for maximum RI PT intercuspation. 2.1 Tomographic Measurements Tomographic measurements were made on multiplanar reconstruction images M AN US C generated by the software tools (OnDemand3D, Cybermed, Seoul, Korea) on a liquid crystal display computer monitor. Initially, the evaluators marked out the 3D locations of the three anthropometric landmarks: gonion, condylion, and gnathion. The gonion is the most inferior, posterior, and lateral point on the external angle of the mandible. The condylion is the most D superior and posterior point of the mandibular condyle. The gnathion is the most TE inferior and anterior point on the profile curvature of the chin. Then, six measurements were taken in the jaws on CBCT images according to Kharoshah12: gonial angle (GA), EP ramus length (RL), minimum ramus breadth (MRBr), gonion-gnathion length (GGL), bicondylar breadth (BicBr) and bigonial breadth. The first four measurements were AC C obtained from 3D sagittal views (Fig 1) and the latter two, from 3D axial views (Fig 2). The junction of the posterior and lower borders of the mandible forms the gonial angle. The distance between the anatomic landmarks condylion and gonion is the ramus length, the distance between the gonion and gnathion is the gonion-gnathion length and the shortest width of the mandibular branch is the minimum ramus breadth. The distance between the most lateral points on the two condyles is the bicondylar breadth. The distance between the right and left gonion is the bigonial breadth. 5 ACCEPTED MANUSCRIPT Five PhD students in Oral Radiology with experience in CBCT image diagnosis performed all measurements. After 15 days, the measurements were repeated for 25% of the sample. RI PT 2.2 Statistical Analysis Statistical analysis of the data was done using the SAS system (SAS Institute Inc., SAS system, release 9.2. SAS Institute Inc., Cary, NC, USA). The reliability of the measurements was assessed by the intraclass correlation coefficient (ICC) using the M AN US C Shrout-Fleiss test (ICC3,1) for the intra-reviewer analysis and ICC2,k for the interreviewer analysis.24 A one-way analysis of variance (ANOVA) model appropriate for experiments with a factor with repeated measures was used. The model was adjusted using logistic regression with stepwise selection of variables. A significance level of 5% was used for D all statistical tests. Discriminant function analysis was done to confirm the results TE obtained with the logistic regression, as well as to validate the formula. AC C 3.1 ICC EP 3. Results The Shrout-Fleiss intraclass correlation coefficient (ICC1,3) showed substantial intra-reviewer agreement (>0.70). Exceptions were the GA variable when measured by reviewers 1 and 3 and the GGL variable when measured by examiner 1, cases with ICC less than 0.3, an unsatisfactory agreement (Table 1). Significant inter-examiner differences (Shrout-Fleiss test, ICC2,k) were found when comparing the mean values of the measurements. The ICC values for RL and GA 6 ACCEPTED MANUSCRIPT were >0.8, in contrast with the ICC value for BicBr (<0.3) in the inter-reviewer analysis (Table 1).24 3.2 ANOVA RI PT ANOVA showed no significant difference between the sexes in mean MRBr (p = 0.3414) but provided strong evidence (p < 0.01) of differences in all other variables (Table 2). M AN US C 3.3 Logistic Regression: Univariate Model A model of logistic regression was used as a form of sex estimation using four mandibular measurements: RL, GA, BicBr, BigBr (Table 3). The equation for sexual estimate using the most predictive distances were calculated using the full sample (Table 4). Logistic regression (LR) analysis produces regression coefficients for each measurement included in a model, as well as a constant. D To use this information to assess the sex of an individual, a log-odd or logit must first TE be calculated using the following formula: EP Logit= 85.64 – 0.48 × RL – 0.13 × GA – 0.20 × BigBr – 0.24 × BicBr AC C A negative logit indicates a male mandible and a positive logit indicates a female mandible. The logit value can also be used to calculate the probability of female sex (Pf) using the function Pf = elogit(p)/(1+ elogit(p)) The probability of male sex is simply Pm = 1 − Pf. In practice, if Pf > 0.5, then the most likely sex is female, and if Pf < 0.5, the most likely sex is male. The closer the value of Pf is to 1, the greater the probability that the individual is female, and the closer 7 ACCEPTED MANUSCRIPT the value of Pf is to 0, the greater the probability that the individual is male. Combining the four variables considered in this study, a concordance index of 95.1% was found. 3.4 Discriminant Function RI PT To apply the discriminant analysis, the sample was randomly divided into two parts: the first part (126 images) was used to develop the model and the second part (34 images not used to develop the model) was used to validate the model in a re- M AN US C substitution process. Of the 160 images in the study, 34 were not used to develop the linear discriminant functions; they were reserved for testing the quality of the analysis. The success of estimating the sex of individuals was 92.96% for females and 85.45% for males, giving high accuracy for sexual estimate (Table 5). The separate values used to validate the formula had an accuracy of 93.33% for estimating the sex of males and 94.74% for females. These percentages are greater than 90%, confirming the reliability D of the formula, according with rate accuracy and error tested (Table 6 and 7). TE 4. Discussion EP Forensic dentistry has long used specific methods for assessing sexual dimorphism and identifying missing people through skeletal remains. Such estimations AC C can be made using anthropometric measurements in the jaw with the aid of calipers. The mandible is one of the strongest and most durable skull bones in humans with a high degree of sexual dimorphic characteristics. This study describes an osteometric approach using mandibular measurements to estimate sex in a Brazilian population; such a model could be used as an auxiliary tool for predict sex in forensic dentistry. Evaluating sexual dimorphism using CT images, Kharoshan et al.12 evaluated six mandibular measurements and found greater mean values for three variables (BicBr, 8 ACCEPTED MANUSCRIPT GA, and MRBr) in males. Similarly, in the present study, five measurements (RL, GGL, GA, BigBr, and BicBr) showed higher mean values for men. Most variables were similar in both studies, except that the variable MRBr was excluded in our study population. When the measurements selected by the logistic regression test in the two RI PT studies are compared, it can be seen that the variable MRBr was not selected in the Brazilian population, showing that the morphological characteristics of the mandible are different in different populations, which may be explained by different eating habits. M AN US C Indicators for sex prediction were examined using stepwise discriminant analysis in a population of 330 Egyptians and BicBr, GA, RL, and MRBr were found to be potential indicators with an accuracy of 83.9%.12 The present study in a Brazilian population used the stepwise method, derived from the RL test, and showed the most predictive measurements. The four variables (RL, GA, BigBr, and BicBr) assessed showed 95.1% accuracy in sex estimation, a rate with great reliability when compared with those found D in the literature. TE Saini et al.13 observed that the maximum and minimum lengths of the mandible EP were less frequently used for sex estimation within an Indian population. In a Brazilian study, the variable MRBr showed dimorphism between sexes; however, these AC C measurements and the measurement of the longest mandibular branch were lower in these populations. For this reason, in Brazilians and Egyptians, this variable might be inappropriate because it shows little confidence in the investigation of sexual dimorphism. The accuracy rate (95.1%) found in the present study was similar to those observed in previous studies involving populations from countries other than Brazil. Iscan et al.7 found an accuracy of 84.1% (for an association between the cranium and mandible) and 83.7% (skull) in a Japanese population. The rates were 82% to 86% for 9 ACCEPTED MANUSCRIPT jaws and skull, respectively, in white South Africans. In a study of black South Africans, Kieser and Groeneveld11 found a 91% accuracy rate for the maxilla and mandible combined and 78% for GGL. The lower jaw bone is frequently found among unidentified remains and can provide accuracy rates of 80% plus. RI PT Loth and Henneberg9 studied the jaws of black South Africans and found an accuracy rate of approximately 92% in the Dart collection, resulting in a standard osteometric tool for sexual prediction using skulls of white South Africans. Based on M AN US C the accuracy rates found in different countries, our results suggest that the methodology used in the present study to analyze sexual prediction in Brazilians might be reliable for use in forensic dentistry. Thus, this forensic application is carried out through of sexual prediction that acts as an auxiliary method in order to achieve to human identification. Several studies have used CT images involving other bony structures to analyze D sexual prediction. Uthmann et al.17, using measurements of the maxillary sinus on CT TE images, reported an accuracy rate of 73.9% and showed viable results for sex estimation. Uthmann et al.18 evaluated the accuracy and reproducibility of the foramen EP magnum and other cranial measurements in sexual classification and found an accuracy rate of 90.7% for the identification of males and 73.3% for females. The present study, AC C using different mandibular measurements made on 3D CBCT images, revealed a high accuracy rate (95.1%) for sexual prediction, suggesting that such images can be used for effective and accurate anthropometric measurements. An important issue to consider is that the presence of high-density materials in the FOV may degrade the image quality and compromise CBCT-based measurements, although this is not the case in this study. Gamba et al.25 demonstrated that image artifacts arising from metallic restorations have a negative influence on the reliability of orthodontic measurements. Current studies comparing osteometric and tomographic measurements confirm that CBCT images can 10 ACCEPTED MANUSCRIPT be used for sexual prediction in forensic dentistry, application aimed at achieving human identification of an unknown individual.15 Estimating the age at death of adult men on CT images of the pelvis, Ferrant et RI PT al.26 found ICC values higher than 0.05 in an inter-reviewer analysis test. Similarly, in the present study, the mean ICC value was >0.8, except for the variable GA, for which reviewers 1 and 3 recorded values <0.2. In the inter-reviewer analysis, variables GA and RL showed mean ICC values >0.8 (favorable), whereas the value for BicBr was <0.3 M AN US C (unfavorable). Thus, GA presented a low rate of intra-reviewer agreement, which shows that GA has the least reproducibility of all the measurements. The inter-reviewer analysis revealed differences between the reviewers, however, these results do not undermine the effectiveness of measures of sex prediction, because both were selected by different D analyses, providing a high rate of accuracy for estimating sex. TE The results of different statistical analyses with proven reliability confirm the high accuracy of logistic regression in this sample population and mostly validate the EP formula developed in this study, providing forensic professionals with an imaging AC C metric that can assist and expedite the work of the dental examiner. 5. Conclusion In conclusion, of the variables assessed, BigBr, RL, BicBr, and GA showed better reliability for sex estimation. The measurements for males were higher than those for females, except for MRBr, which showed no statistically significant difference between sexes. Thus, the formula developed in this study can be used for sexual prediction in forensic dentistry. 11 ACCEPTED MANUSCRIPT References 1. Iscan MY. Global forensic anthropology in the 21st century. Forensic Sci Int. 2001 Mar;117(1-2):1–6. 2. Holland TD. Use of the cranial base in the identification of fire victims. J 3. RI PT Forensic Sci. 1989 Mar;34(2):458–60. Saini V, Srivastava R, Rai RK, Shamal SN, Singh TB, Tripathi SK. Mandibular ramus: an indicator for sex in fragmentary mandible. J Forensic Sci. 2011 Jan; 56 Suppl 1:S13-6. Robinson MS, Bidmos MA. The skull and humerus in the determination of sex: M AN US C 4. reliability of discriminant function equations. Forensic Sci Int. 2009 Apr;186(13):86.e1-5. 5. Spradley MK, Jantz RL. Sex estimation in forensic anthropology: skull versus postcranial elements. J Forensic Sci. 2011 Mar;56(2):289–96. 6. Iscan MY. Forensic anthropology of sex and body size. Forensic Sci Int. 2005 Jan;147(2-3):107–12. Iscan MY, Steyn M. Craniometric determination of population affinity in South D 7. 8. TE Africans. Int J Legal Med. 1999 Dec;112(2):91–7. Iscan MY, Miller-Shaivitz P. Sexual dimorphism in the femur and tibia. In: EP Reichs KJ, editor. Forensic osteology: advances in the identification of human remains. Springfield, IL: Charles C Thomas, 1986;102–11. Loth SR, Henneberg M. Mandibular ramus flexure: a new morphologic indicator AC C 9. of sexual dimorphism in the human skeleton. Am J Phys Anthropol. 1996 Mar; 99(3):473–85. 10. Ayoub F, Rizk A, Yehya M, Cassia A, Chartouni S, Atiyeh F, et al. Sexual dimorphism of mandibular angle in a Lebanese sample. J Forensic Leg Med. 2009 Apr;16(3):121–4. 11. Kieser JA, Groeneveld HT. Multivariate sexing of the human viscerocranium. J Forensic Odontostomatol. 1986 Dec; 4(2):41–6. 12 ACCEPTED MANUSCRIPT 12. Kharoshah MA, Almadani O, Ghaleb SS, Zaki MK, Fattah YA. Sexual dimorphism of the mandible in a modern Egyptian population. J Forensic Leg Med. 2010 May;17(4):213–15. 13. Saini V, Srivastava R, Rai RK, Shamal SN, Singh TB, Tripathi SK. Mandibular 56(1):13–6. 14. Steyn M, Iscan MY. Sexual dimorphism in the crania and mandibles of South African whites. Forensic Sci Int. 1998 Nov;98(1-2):9–16. 15. RI PT ramus: an indicator for sex in fragmentary mandible. J Forensic Sci. 2011 Jan; Brough AL, Bennett J, Morgan B, Black S, Rutty GN. Anthropological M AN US C measurement of the juvenile clavicle using multi-detector computed tomography affirming reliability. J Forensic Sci. 2013 Jul;58(4):946–51. 16. Cevidanes LH, Bayley LJ, Tucker GR Jr, Styner MA, Mol A, Phillips CL, et al. Superimposition of 3D cone-beam CT models of orthognathic surgery patients. Dentomaxillofac Radiol. 2005 Nov;34(6):369–75. 17. Uthman AT, Al-Rawi NH, Al-Naaimi AS, Al-Timimi JF. Evaluation of maxillary sinus dimensions in gender determination using helical CT scanning. J Uthman AT, Al-Rawi NH, Al-Timimi JF. Evaluation of foramen magnum in TE 18. D Forensic Sci. 2011 Mar;56(2):403–8. gender determination using helical CT scanning. Dentomaxillofac Radiol. 2012 19. EP Mar;41(3):197–202. Mozzo P, Procacci C, Tacconi A, Martini PT, Andreis IA. A new volumetric CT machine for dental imaging based on the cone-beam technique: preliminary 20. AC C results. Eur Radiol 1998 Jun;8(9):1558–64. Marmulla R, Wörtche R, Mühling J, Hassfeld S. Geometric accuracy of the NewTom 9000 Cone Beam CT. Dentomaxillofac Radiol. 2005 Jan;34(1):28–31. 21. Biwasaka H, Aoki Y, Tanijiri T, Sato K, Fujita S, Yoshioka K, et al. Analyses of sexual dimorphism of contemporary Japanese using reconstructed threedimensional CT images--curvature of the best-fit circle of the greater sciatic notch. Leg Med. 2009 Apr;11(1):260–2. 13 ACCEPTED MANUSCRIPT 22. Angel JS, Mincer HH, Chaudhry J, Scarbecz M. Cone-beam computed tomography for analyzing variations in inferior alveolar canal location in adults in relation to age and sex. J Forensic Sci. 2011 Jan;56(1):216–9. 23. Neves FS, Nascimento MC, Oliveira ML, Almeida SM, Bóscolo FN. Comparative analysis of mandibular anatomical variations between panoramic Aug 24. [Epub ahead of print] 24. Shrout PE, Fleiss JL. Intraclass correlations: uses in assessing rater reliability. Psychol Bull. 1979 Mar;86(2):420–8. Gamba TO, Oliveira ML, Flores IL, Cruz AD, Almeida SM, Haiter-Neto F, M AN US C 25. RI PT radiography and cone beam computed tomography. Oral Maxillofac Surg. 2013 Lopes SL. Influence of cone-beam computed tomography image artifacts on the determination of dental arch measurements. Angle Orthod. 2014 Mar;84(2):2748. Ferrant O, Rougé-Maillart C, Guittet L, Papin F, Clin B, Fau G, et al. Age at death estimation of adult males using coxal bone and CT scan: a preliminary EP TE D study. Forensic Sci Int. 2009 Apr;186(1-3):14–21. AC C 26. ACCEPTED MANUSCRIPT Table 1—Intra- and inter-observer analyses for observers 1 to 5 using the Shrout-Fleiss test: ICC(3,1) and ICC(2,k). Intra-observer Inter-observer RI PT Variable Measured in Millimeters 2 3 4 5 1, 2, 3, 4 and 5 RL 0.88 0.89 0.87 0.87 0.87 0.87 GGL 0.57 0.90 0.85 0.87 0.93 0.64 GA 0.01 0.64 0.10 0.53 0.56 0.92 MRBr 0.96 0.97 0.97 0.96 0.98 0.70 BigBr 0.99 0.99 0.80 0.99 0.99 0.50 BicBr 0.97 0.94 0.84 0.98 0.98 0.21 AC C EP TE D M AN US C 1 ACCEPTED MANUSCRIPT Table 2—Mean values (MV), standard deviation (SD) and confidence interval (CI) for six mandibular measurements comparing differences between males and females. Variable Males Measured MV in Millimeters 95% CI SD MV 95% CI RL 54.36 (54–53) 4.73 49.41 (49–49) GGL 70.37 (70–69) 4.65 67.14 (67–66) (122–120) 8.21 119.83 (29–28) 3.44 (119–117) (95–94) MRBr 28.70 BigBr 118.48 BicBr 94.96 3.93 <0.01 6.68 0.0140 2.69 0.3414(NS) 5.99 110.03 (110–109) 4.65 <0.01 6.08 (87–86) 5.36 <0.01 D TE EP 3.84 <0.01 (28–29) P > 0.01: non-significant (NS). P < 0.01: significant. AC C (120–119) SD RI PT 121.28 p value M AN US C GA Females 28.91 87.47 ACCEPTED MANUSCRIPT Table 3—Logistic regression: optimal model with stepwise selection of variables. Effect Score (ChiSquare) Pr > Chi-Square BigBr 64.12 <0.0001 RL 20.68 <0.0001 BicBr 16.09 <0.0001 GA 8.09 0.0044 GGL 3.88 0.0488 0.0542 EP TE D GGL AC C RI PT Removed M AN US C Entered ACCEPTED MANUSCRIPT Table 4— Table adjustment: analysis of maximum likelihood. Estimate Standard Error Wald ChiSquare Pr>Chi-Square Intercept 85.6458 14.2826 35.9582 <0.0001 RL –0.4773 0.1056 20.4359 GA –0.1339 0.0494 7.3480 BigBr –0.1994 0.0634 9.8974 BicBr –0.2410 0.0653 13.6058 M AN US C D TE EP AC C RI PT Parameter <0.0001 0.0067 0.0017 0.0002 ACCEPTED MANUSCRIPT Table 5—Model table discriminant analysis: number of observations and percentage classified by sex. % Male Female 66 92.96 5 Male 8 14.55 Total 74 58.73 % Total % 7.04 71 100.00 47 85.45 55 52 41.27 126 RI PT Female AC C EP TE D M AN US C Sex 100.00 100.00 ACCEPTED MANUSCRIPT Table 6—Test table discriminant analysis: number of observations and percent classified into sex. % Male Female 14 93.33 1 Male 1 5.26 Total 15 44.12 % Total % 6.67 15 100.00 18 94.74 19 19 55.88 34 RI PT Female AC C EP TE D M AN US C Sexes 100.00 100.00 ACCEPTED MANUSCRIPT Table 7—Test table discriminant analysis: error count in sex classification. Error count in sex estimate Male Total Rate 0.0667 0.0526 0.0596 Priors 0.5000 0.5000 AC C EP TE D M AN US C RI PT Female 1 D M AN US C RI PT ACCEPTED MANUSCRIPT AC C EP TE Figure 1: (RL) ramus length; (MRBr) minimum ramus breadth; (GA) gonial angle; (GGL) gonion-gnathion length 2 M AN US C RI PT ACCEPTED MANUSCRIPT AC C EP TE D Figure 2: (BigBr) Bigonial breadth (distance between the two gonia); (BicBr) Bicondylar breadth (distance between the two condyles). ACCEPTED MANUSCRIPT The logistic regression was used to selection of measures: RL, GA, BicBr, BigBr. - Combining the four variables, a concordance index of 95.1% was found. - The success of estimating the sex was 92.96% for females and 85.45% for males. - Values used to test the formula had an accuracy of 93.33% (males) 94.74% RI PT - AC C EP TE D M AN US C (females).