INTRODUCTION

The principal characteristics of biological identity are sex, age, stature and ethnic origin (^{Scheuer, 2002}). Determining sex is important for forensic anthropology when an unknown individual needs to be identified. Determining sex may be more difficult in cases such as natural disasters, accidents or situations in which bodies are subjected to high temperatures, when individuals must be identified from their remains. The cranium (including the mandible) and the pelvis are considered to be the structures presenting the greatest sexual dimorphism (^{Sharma et al., 2016}), with accuracies of 92 % and 95 % respectively (^{Krogman & Iscan, 1986}). The mandible is a bone which forms the lower third of the face (^{Alves & Cândido, 2016}). It is a very important structure for determining sex as it is very strong and presents high sexual dimorphism (^{Ongkana & Sudwan, 2009}).

Some studies have analysed the morphological characteristics of the mandible, observing that the ramus flexure (^{Kemkes-Grottenthaler et al., 2002}; ^{Saini et al., 2011}), gonial eversion (Kemkes-Grottenthaler et al.) and shape of the chin (^{Deana & Alves, 2017}) present important sexual dimorphism. However, sexual dimorphism can be more accurately assessed by anthropometric methods, since classification by visual analysis may be more subjective, varying between researchers (^{Ogawa et al., 2013}). Morphological features may present variation between different populations; factors such as socio-economic status, environmental and climatic effects, genetic composition, nutritional state and diet may result in some features being more or less accentuated in a given population (^{Angel, 1976}; Krogman & Iscan; ^{Rogers, 2005}; ^{Oettlé et al., 2009}; ^{Evteev et al., 2014}). It is therefore, important to carry out anthropometric studies in every population in order to have up-to-date information available to aid anthropologists and forensic investigators in determining the sex of an individual. The objective of the present study was to determine sex by metrical analysis of macerated mandibles of Brazilian adults.

MATERIAL AND METHOD

Sample: In the present study we analysed 113 fully dentate macerated mandibles of Brazilian adults, 47 belonging to women and 66 to men. They belonged to the Department of Morphology and Genetics, UNIFESP (Brazil). Mandibles for which there was no information on sex or nationality, those which were partially or completely edentate, and those which were damaged or presented any kind of pathology were excluded from the study.

The researchers were calibrated prior to carrying out the measurements. The following measurements were taken with a digital calliper: bicondilar breadth, bigonial breadth, bimental foramina breadth, distance between mental foramen and mandibular base, mandibular ramus height, maximum mandibular ramus breadth, minimum mandibular ramus breadth and mandibular body length (Table I).

Statistical analysis: Descriptive analysis was by mean value with standard deviation. Measurements were compared using a t test for independent samples. We constructed a ROC curve to analyse the best diagnostic test. We carried out direct and stepwise discriminant analysis and a Fisher discrimination analysis. The discriminant function was obtained for the female and male sexes as follows: Sex = constant + (r1 × m1) + (r2 × m2) + (r3 × m3)..., where r is the discriminant coefficient and m is the discriminant variable (mandible measurements). In this model, the measurements can be substituted in the 2 functions and the results compared. The diagnosis was carried out as follows: female > male = male; female < male = female; and female = male, sex not defined. The SPSS v.22 software was used, with a significance threshold of 5 %.

Table I Description and abbreviations of the measurements analysed. 

RESULTS

We observed that all the measurements presented statistically significant differences between the sexes, with greater mean values for males than for females (Table II). No statistical differences were found between sides, therefore the measurements were analysed together using the ROC curve.

BG was the distance presenting the greatest area under curve (AUC) (Fig. 1) (Table III), with good accuracy and the best balance between sensitivity and specificity, followed by MRH and BC. All the other measurements presented AUC of less than 0.700. The BM distance presented the smallest AUC and lowest sensitivity (Fig. 1) (Table III). Table III shows the cut-off point (PC), representing the ideal point for sex determination for each measurement analysed in the mandible.

We observed through discriminant analysis that the measurement offering the best prediction of sex was BG (80.5 %), followed by MRH (76.1 %), BC (69.9 %) and MiRB (66.8 %). BM was the measurement which presented the poorest sex prediction (55.8 %) (Table IV). Direct discriminant analysis presented 85.0 % mean correct prediction; stepwise analysis presented 83.2 % mean correct prediction using the BG and MRH measurements (Table V). Table V shows the discriminant function generated for each sex.

Fig. 1 ROC curve for the measurements analysed. 

Table II Mean values (in millimetres), standard deviation (SD), Confidence interval (CI) and p-value of the measurements analysed, by sex and side. 

Table III Analysis of the ROC curve for the measurements taken in the mandible. 

^{AUC, Area under curve; CP, Cut-off point; A, Accuracy; SS, Sensitivity; SE, Specificity}.

Table IV Discriminant analysis of measurements analysed. 

Table V Sex prediction and equation using stepwise discriminant analysis. 

DISCUSSION

Biological identification of sex is one of the most important techniques established by forensic science; it is essential in the recognition of individuals officially declared dead in situations such as mass disasters, atrocities and criminal investigations (^{de Oliveira et al., 2015}; ^{Schmeling et al., 2016}).

The reliability and accuracy of sex prediction are directly dependent on the anatomical region of the remains (^{Mai et al., 2005}). The mandible is originally bipartite, with each half developing absolutely independently (^{Testut & Latarjet, 1968}). It presents marked sexual dimorphism due to the development of the muscular-skeletal system, especially the chewing muscles attached to the mandible (^{Hu et al., 2006}; ^{Franklin et al., 2007}). Different life styles and diets, as well as chewing habits and hormonal factors, affect the size and shape of the mandible (Hu et al.); this may result in differences in mandible morphology between different populations.

Various methods have been used to determine the accuracy of sexing by mandible analysis. Initially the simplest methods are applied, since before a more expensive or complex method is adopted, several variables must be considered, such as the conservation state of the skeleton, the clarity of the characteristics present and the precision required in each case (^{Krishan et al., 2016}). Sex determination by analysis of morphological characteristics is quicker and easier, but it is more difficult to obtain a decision because the nutrition, occupation, descent and geographical origin of the individual must be considered (^{Kranioti et al., 2008}). Nonetheless, in the hands of an expert observer non-metric assessment may offer great accuracy in determining sex (Krishan et al.). On the other hand, metric analysis is more accurate than visual analysis; however there are specific measurements for each population subject to trends in modern habits, so every population must be analysed separately (^{Dayal et al., 2008}).

Sexual dimorphism in the mandible can be observed in individuals aged over 16 years (de Oliveira et al.), therefore only adult individuals aged over 18 years were included in this study. Only completely dentate mandibles were selected due to the morphological alterations which may result from tooth loss (^{Alves, 2009}; Alves & Cândido).

In the present study BG presented the greatest AUC and the best balance between sensitivity and specificity, corroborating previous studies in Brazilian populations (^{Gamba et al., 2016}; ^{Lopez-Capp et al., 2018}). The mean values found for BG in the present study were similar to those found for individuals from Northern Thailand (Ongkana & Sudwan) and for Black South Africans (Dayal et al.) (Table VI). ^{Marinescu et al. (2013}), in individuals from Romania, and Lopez-Capp et al. in Brazilian individuals, found that BG was the measurement which presented the greatest sexual dimorphism, corroborating the findings of the present study.

In a study of individuals of European descent, the researchers observed that this measurement offers good sex prediction and can be used for sexing (^{Ilgüy et al., 2014}). In discriminant analysis, we observed that this measurement presented the greatest mean correct prediction, with 80.5 %, corroborating the findings of Lopez-Capp et al.

In an earlier study in a Brazilian population, the researchers observed that BC presented great sexual dimorphism (Gamba et al.; Lopez-Capp et al.); this was corroborated by the present study, where we found good sex determination (AUC: 0.778) and good accuracy (75.2 %). In discriminant analysis we observed that this measurement achieved 69.9 % mean correct prediction, higher than reported in another study also carried out on a Brazilian population (66 %) (Lopez-Capp et al.). The mean values found for BC in the present study were lower than those foundin Chinese (^{Dong et al., 2015}) and Japanese populations (Ongkana & Sudwan); similar to those reported for Brazilians (Lopez-Capp et al.) and Romanians (Marinescu et al.), and higher than reported in another study in a Brazilian population (Gamba et al.) (Table VI). In Chinese individuals, Dong et al. observed that this measurement presented great sexual dimorphism with an accuracy of 75 % for males and 83.2 % for females. For individuals of European descent on the other hand, it was observed that this measurement was of no assistance in determining sex (Ilgüy et al.).

de Oliveira et al. assessed sexual dimorphism and age from analysis of the MRH and reported that this measurement was reliable only for estimating the age of the individual, but presented no difference between sexes. However, other studies in Brazilian populations (Gamba et al.; Lopez-Capp et al.) observed that this measurement presented great sexual dimorphism; this corroborates the findings of the present study, where this measurement presented the second best AUC, good balance between sensitivity and specificity, and good accuracy. Discriminant analysis of this measurement in the present study showed a value of 76.1 % mean correct prediction, higher than reported by Lopez-Capp et al. also in a Brazilian population, with values of 70 % for the right side and 67 % for the left. Values reported for Black South Africans (Dayal et al.), Brazilians (Gamba et al.) and Chinese (Dong et al.) were lower than found in our study. Similar values to those found in the present work were reported for individuals of European descent (Ilgüy et al.) and in another study on a Brazilian population (Lopez-Capp et al.). In populations from Japan (Ogawa et al.), Northern Thailand (Ongkana & Sudwan) and Egypt (^{Kharoshah et al., 2010}), the MRH values were higher than those found for the population analysed in our study (Table VI). In a study of individuals of European descent, the researchers observed that this measurement offers good sex prediction, corroborating the results of the present study (Ilgüy et al.).

Table VI Mean values in millimetres reported in the literature. CBCT cone-beam computarized tomography, R right, L left. 

In the present study, the other measurements taken (BM, MF-MB, MaRB, MiRB and MBL) presented AUC less than 0.700, with accuracy varying between 76.6 % and 68.7 %. The cut-off point presented in Table III can be used as a reference for determining sex from the mandible of unknown individuals. In discriminant analysis, BM, MF-MB, MaRB, MiRB and MBL presented sexual dimorphism with correct prediction varying between 66.8 % and 55.8 %.

Direct discriminant analysis achieved 85 % sex prediction, whereas stepwise analysis achieved 83.2 % mean correct prediction using BG and MRH, with better sex prediction in men than women. The correct sex prediction found in the present study agrees with previous studies. Dong et al. also found greater accuracy in sex prediction using the direct method (84.2 %) than the stepwise method (83.3 %). Lopez-Capp et al. found between 76 % and 83 % in an analysis of Brazilian macerated mandibles. In Egyptians, Kharoshah et al. found 83.9 % correct prediction using MRH, BC, MiRB and the gonial angle. In individuals of European descent, Ilgüy et al. found 83.2 % predictive accuracy using MRH, MBL, BG and gonial angle. Similar values were also found for Romanians (Marinescu et al.), with 84 % accuracy obtained from three measurements: chin height, BG and BC. In Black South Africans (Dayal et al.), accuracy of 85 % was achieved using BG, MRH and total mandibular length. Slightly higher predictive accuracy than that found in our study was reported by ^{Zheng et al. (2018}) in individuals from north-eastern China, with mean correct prediction of 87.4 %. The accuracy was slightly higher for women (89 %) than men (85.7 %). They used 7 measurements in the final correct prediction: mandibular angle, area of mandibular foramen, BG, distance between left and right coronoid processes, minimum height, mandibular notch and palatal breadth. High accuracy of 95.1 % was reported in another study in a Brazilian population (Gamba et al.), using MRH, BC, BG and gonial angle. Values slightly lower than ours were reported by ^{Carvalho et al. (2013}), who found 78.13 % for females and 76.47 % for males in an analysis of Brazilian mandibles using BG and MRH.

In the present study, all the measurements analysed presented sexual dimorphism, with greater values for men than for women. BG, MRH and BC presented better sex prediction in both discriminant analysis and the ROC curve; this corroborated previous studies also carried out in Brazilian populations (de Oliveira et al.; Gamba et al.; Lopez-Capp et al.).

CONCLUSION

The mandibles studied presented great sexual dimorphism under metric analysis. Of the measurements taken, BG, MRH and BC presented great accuracy in predicting sex, while BM presented the lowest predictive power. The measurements analysed in this study can be used in determining the sex of Brazilian individuals.