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Forensic Anthropology Population Data

Sex estimation from the talus in a Thai population Pasuk Mahakkanukrauh a, Sithee Praneatpolgrang a, Sitthiporn Ruengdit a, Phruksachat Singsuwan a, Phuwadon Duangto b, D. Troy Case c,* a

Department of Anatomy, Faculty of Medicine, Chiang Mai University, 50120, Thailand Department of Anatomy, Faculty of Medical Science, Payao University, Payao 56000, Thailand c Department of Sociology & Anthropology, North Carolina State University, Campus Box 8107, Raleigh, NC 27695-8107, USA b

A R T I C L E I N F O

A B S T R A C T

Article history: Received 24 January 2013 Received in revised form 10 January 2014 Accepted 1 April 2014 Available online xxx

Previous research on sex estimation from the tarsals has shown that the talus is the most sexually dimorphic tarsal bone in most populations. In order to assess the sexing potential of the talus in a Thai population, 252 skeletons (126 male, 126 female) from the Chiang Mai University Skeletal Collection were measured. The sample represents Thai people who come from the local Chiang Mai area and who died within the past ten years. Ten measurements were taken on the left and right tali from each skeleton. Seven of these measurements are similar, or identical, to measurements used by other researchers. Three experimental measurements were also taken. Logistic regression equations were calculated for each measurement, and for pairs of measurements. The individual measurements were also examined using ROC analysis. Averaging the results from both sides, the individual measurements with the highest correct allocation accuracies based on logistic regression analysis were trochlear length (88.2%), trochlear breadth (87.3%), talar length (85.5%), and inferior articular surface length (84.5%). The ROC results followed a similar pattern, with Area Under the Curve values as follows: trochlear length (0.952), inferior articular surface length (0.937), trochlear breadth (0.935), and talar length (0.914). When pairs of measurements were considered by means of logistic regression, four equations produced predicted allocation accuracies greater than 90% – three from the right talus, and one from the left. The highest accuracy on both sides resulted from a combination of the two most sexually dimorphic individual measurements of trochlear length and trochlear breadth. Together, they produced predicted allocation accuracies of 91.3% on the right side, and 91.4% on the left side. Unlike many past studies that have found talar length to be the most sexually dimorphic measurement of the talus, our study found trochlear length and breadth to be the most accurate measurements for distinguishing the sexes. Researchers developing sexing equations for use with other populations should consider including trochlear length and breadth in their analyses. ß 2014 Elsevier Ireland Ltd. All rights reserved.

Keywords: Sex determination Foot Tarsals Thailand

1. Introduction Studies concerned with sexing from the tarsal bones have become increasingly common over the last two decades. The tarsals are good candidates for sex estimation because they often preserve well in forensic contexts, due to their generally dense structure and thick cortices, and because of the protection from scavengers and taphonomic forces often afforded by footwear [1– 3]. Tarsals are also good candidates because they are weightbearing bones, and sexual dimorphism in human weight is considerably higher than dimorphism in height [4]. The talus

* Corresponding author. Tel.: +1 919 515 9024. E-mail address: [email protected] (D.T. Case).

clearly exhibits the greatest size dimorphism in the tarsus [2,4–7]. Among all five past sex estimation studies that have included at least the calcaneus and talus, the talus has produced the highest allocation accuracies (88–94%), and the single most dimorphic measurement has generally been talar length. In a study by Harris and Case [2] that included all seven tarsals with no missing measurements, the only single measurement to achieve 90% allocation accuracy was talar length on the right side. Talar length and height together produced 90.9% allocation accuracy on the right side, and breadth and height together produced 92.4% allocation accuracy on the left side. The cuboid exhibited a slightly higher allocation accuracy on the right side (91.8%) than the talus, but a considerably lower accuracy on the left (84.7%). Therefore, the weight of evidence from past studies, including modern American, 19th Century Italian, and prehistoric Native American

http://dx.doi.org/10.1016/j.forsciint.2014.04.001 0379-0738/ß 2014 Elsevier Ireland Ltd. All rights reserved.

Please cite this article in press as: P. Mahakkanukrauh, et al., Sex estimation from the talus in a Thai population, Forensic Sci. Int. (2014), http://dx.doi.org/10.1016/j.forsciint.2014.04.001

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samples suggests that the talus is likely to be the most sexually dimorphic tarsal bone in most populations. The purpose of this study is to examine sexual dimorphism of the talus among skeletons from a modern Thai population, and to generate equations for sex estimation in a modern forensic context. To date, no studies of sex estimation have been published for the lower limbs of Thai individuals except for the femur [8]. This study will add a new tool for the analysis of forensic cases in Thailand. 2. Materials and methods The sample for this study consists of 252 skeletons (126 male, 126 female) from the Chiang Mai University Skeletal Collection housed in the Faculty of Medicine’s Forensic Osteology Research Center. The Chiang Mai collection is a documented sample of recently deceased individuals from the local area around Chiang Mai, Thailand. Initially, a reference sample of 200 skeletons (100 female, 100 male) was measured to generate equations for sexing. Age at death in the sample ranged from 22 to 91 years of age for males, 26 to 93 years of age for females. The mean age was 66 years for both sexes. Later, an additional 52 skeletons (26 male, 26 female) were measured to test the sex estimation equations. The skeletons in the collection represent people from various socioeconomic backgrounds, including many professionals from the middle class. Ten measurements of the talus were taken to the nearest 0.01 mm using either sliding calipers, or a mini-osteometric board (MOB) from Paleotech Concepts. Descriptions of all ten measurements are presented in Table 1 and drawings of each are provided in Fig. 1. All measurements on the reference sample were taken by authors SP, PS, and PD. SP took the MaxLg measurement, PS took the MaxBr and MaxHt measurements, and PD took the MaxTrLg, MaxTrBr, MaxIASLg, and MaxIASBr measurements. The three experimental measurements, MinIID, MaxLMSHt, and MinIDNk were also taken by PD. Each measurement was taken three times non-consecutively, and the mean of these three measurements

was recorded for each individual. Left and right tali were treated separately. Measurements were not taken if the bone exhibited significant osteophytosis or damage that would affect a specific dimension. Thus, some dimensions have a lower sample size than others. The talar length dimensions in particular were often affected by osteophytes around the trigonal process, and occasionally by abnormally large trigonal processes. Measurements 1–3 were taken with a mini-osteometric board following procedures described in Harris and Case [2]. The rest of the measurements were taken using calipers. Two of these measurements (4 and 5) follow procedures described in Murphy [9], which were borrowed from Steele [10] and originally derive from Martin [11]. Two additional measurements of articular dimensions (6 and 7) were based on figures in Bidmos and Dayal [12], which were in turn adapted from Martin and Knubmann [13]. Three experimental measurements were also taken. These are Measurements 8, 9, and 10 in Table 1. Intra- and Inter-observer error was calculated for the six measurements found to be most useful for sex estimation. Intraobserver error was calculated from the first two rounds of measurement taken on the reference sample of 200 skeletons. Interobserver error was calculated from a random sample of 10 males and 10 females with no missing measurements from the test sample. For the interobserver error analysis, the second observer was not given any instruction on how to take the measurements beyond the written descriptions from Table 1 (excluding the italicized text) and Fig. 1. The median absolute difference, median percent difference, and technical error of the measurement (TEM) were calculated. The TEM provides an estimate of the standard deviation of repeated measurements and is often used by anthropologists to assess intra- and inter-observer precision [14]. The median percent error was determined by calculating the difference between repeated measurements for each skeleton and then dividing the median of these values by the average of the male and female mean size for each dimension. Binary logistic regression analysis was performed on each individual measurement for both the right and left sides, and regression equations for sexing of modern Thai individuals were

Table 1 Description of measurements and instrument used. Measurement

Description

(1) MaxLg

Maximum talar length (identical to Harris and Case [2]): The distance from the most anterior point on the head of the talus to the most posterior point on the trigonal process using a mini-osteometric board. Maximum talar breadth (identical to Harris and Case [2]): The distance from the most lateral point on the articular facet for the lateral malleolus of the fibula to the medial surface of the talus using a mini-osteometric board. Maximum talar height (identical to Harris and Case [2]): The distance from the most superior point on the medial trochlear articular surface to the inferior surface of the talus using a mini-osteometric board. Maximum trochlear length (after Steele [10]; Murphy [9]): The maximum distance between the anterior edge of the trochlear articular surface and the posterior edge of the same surface. The measurement is taken parallel to the long axis of the trochlea using a caliper. Begin with the caliper at the posterior edge and the talar head directed away from the researcher. Maximum trochlear breadth (after Murphy [9]): The maximum distance between the medial edge of the trochlear articular surface and the lateral edge of the same surface. Because the superomedial edge of the trochlear surface is beveled, the caliper jaws are placed slightly below the highest point of the trochlear edge. The measurement is taken perpendicular to the long axis of the trochlea. Placement of the fingers along the medial and lateral sides of the trochlea help to hold the tips of the calipers in place. This measurement should be taken with the long axis of the trochlea directed mediolaterally. Maximum length of the inferior articular surface (modified from Bidmos and Dayal [12]): The longest distance between the medial edge of the inferior articular surface (subtalar joint surface) and the lateral edge of the same surface. The measurement is taken parallel to the long axis of the surface using a caliper. Begin with the caliper at the posterior edge and the talar head directed away from the researcher. Maximum breadth of the inferior articular surface (modified from Bidmos and Dayal [12]): The maximum distance between the anterior edge of the inferior articular surface (subtalar joint surface) and the posterior edge of the same surface. The measurement is taken perpendicular to the long axis of the surface using a caliper. This measurement is best taken by first placing the caliper jaws along the posterior edge of the surface. Minimum inferior interarticular distance: The minimum distance between the anterior edge of the subtalar joint surface and the posterior edge of the middle articular surface using a caliper. Maximum lateral malleolar surface height: The maximum height of only the articular portion of the lateral malleolar surface using a caliper. Minimum interarticular distance across the neck: The minimal distance between the edge of the medial malleolar surface and the edge of the articular surface of the head of the talus using a caliper.

(2) MaxBr (3) MaxHt (4) MaxTrLg

(5) MaxTrBr

(6) MaxIASLg

(7) MaxIASBr

(8) MinIID (9) MaxLMSHt (10) MinIDNk

Note: Comments in italics were added after the test and error samples were measured.

Please cite this article in press as: P. Mahakkanukrauh, et al., Sex estimation from the talus in a Thai population, Forensic Sci. Int. (2014), http://dx.doi.org/10.1016/j.forsciint.2014.04.001

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Fig. 1. Drawings indicating the dimensions measured for this study: (1) maximum talar length (MaxLg), (2) maximum talar breadth (MaxBr), (3) maximum talar height (MaxHt), (4) maximum trochlear length (MaxTrLg), (5) maximum trochlear breadth (MaxTrBr), (6) maximum length of the inferior articular surface (MaxIASLg), (7) maximum breadth of the inferior articular surface (MaxIASBr), (8) Minimum inferior interarticular distance (MinIID), (9) maximum lateral malleolar surface height (MaxLMSHt), (10) minimum interarticular distance across the neck (MinIDNk). Written descriptions of these measurements can be found in Table 1.

ROC analysis was also conducted on each of the measurements in order to explore some alternative threshold values that might be used to improve reporting of determined sexes when the measurement obtained lies some distance from the midpoint of the distribution. ROC analysis is commonly used by clinicians to evaluate the quality of diagnostic decisions or the efficacy of clinical tests [17,18]. The method allows evaluation of a particular diagnostic measure, such as a bone measurement, over the entire range of data points in the sample rather than just a single sectioning point at the midpoint of the distribution [19,20]. The

generated. These analyses were performed using SPSS Version 19. After each variable had been analyzed individually, pairs of measurements were considered using a forward conditional approach which selects the most dimorphic measurement first, then assesses the others for a significant additional contribution to the model. Binary logistic regression is an appropriate approach to sexing for this study because it is less sensitive to high correlations among predictor variables, which would be the case with multiple measurements from a single bone, and more tolerant of outliers than discriminant analysis [15,16].

Table 2 Descriptive statistics for talar measurements by sex (mm). Females Measure R-MaxLg L-MaxLg R-MaxBr L-MaxBr R-MaxHt L-MaxHt R-MaxTrLg L-MaxTrLg R-MaxTrBr L-MaxTrBr R-MaxIASLg L-MaxIASLg R-MaxIASBr L-MaxIASBr R-MinIASBr L-MinIASBr R-MaxLMSHt L-MaxLMSHt R-MinIDNk L-MinIDNk

N 74 83 98 94 98 96 92 88 96 93 94 94 98 96 98 97 83 75 74 82

Males Min 43.35–58.40 41.34–56.57 30.94–41.90 31.39–42.93 25.51–32.38 24.24–32.62 25.85–35.67 25.44–34.29 21.20–29.59 20.22–30.16 23.23–31.50 23.05–31.37 16.01–21.22 16.29–21.77 3.03–7.83 3.08–8.40 18.07–26.57 18.86–27.63 2.33–11.65 2.89–12.31

Mean 50.72 50.25 37.24 37.16 28.60 28.48 30.05 29.92 25.87 25.75 27.86 27.93 19.26 19.08 5.22 5.16 22.13 22.27 6.84 6.82

SD 2.669 2.699 1.904 1.934 1.544 1.765 1.769 1.681 1.497 1.658 1.611 1.609 1.002 1.069 1.057 1.016 1.824 1.716 1.425 1.715

N 95 86 97 97 100 100 93 88 98 99 99 94 100 100 100 99 84 90 87 74

Min 46.14–66.73 45.86–67.01 36.42–45.26 35.75–45.87 27.26–35.82 27.64–36.45 29.93–41.25 30.06–41.35 25.28–34.49 24.55–33.35 27.91–36.53 27.21–36.49 17.45–25.27 17.61–25.51 3.07–8.67 3.56–8.39 17.26–27.55 16.71–27.62 3.83–11.82 3.82–15.25

Mean 56.68 56.55 41.18 41.25 31.85 31.91 34.65 34.70 29.53 29.42 31.48 31.36 21.40 21.26 5.88 5.90 22.88 22.70 8.32 8.61

SD 3.532 3.621 2.129 2.282 1.793 1.827 2.425 2.330 1.762 1.823 1.769 1.797 1.419 1.500 1.010 1.034 2.289 2.498 1.584 1.752

Please cite this article in press as: P. Mahakkanukrauh, et al., Sex estimation from the talus in a Thai population, Forensic Sci. Int. (2014), http://dx.doi.org/10.1016/j.forsciint.2014.04.001

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Table 3 Results of intraobserver and interobserver error analyses. Interobserver

Intraobserver Measure

Median error (mm)

Median % error

TEM (mm)

Median error (mm)

Median % error

TEM (mm)

R-MaxLg L-MaxLg R-MaxBr L-MaxBr R-MaxHt L-MaxHt R-MaxTrLg L-MaxTrLg R-MaxTrBr L-MaxTrBr R-MaxIASLg L-MaxIASLg

0.01 0.01 0.03 0.04 0.03 0.02 0.16 0.18 0.18 0.16 0.16 0.16

0.02% 0.02% 0.08% 0.10% 0.10% 0.07% 0.49% 0.56% 0.65% 0.58% 0.54% 0.54%

0.01 0.01 0.10 0.08 0.08 0.05 0.18 0.20 0.18 0.19 0.18 0.20

0.05 0.04 0.04 0.05 0.04 0.04 0.46 0.38 0.64 0.90 0.29 0.42

0.08% 0.07% 0.10% 0.14% 0.12% 0.13% 1.41% 1.18% 2.29% 3.24% 0.98% 1.43%

0.04 0.04 0.03 0.05 0.03 0.04 0.44 0.51 0.63 0.73 0.39 0.44

overall efficacy of the diagnostic measure can be assessed by comparing the Area Under the Curve (AUC), which can range from 0.5 to 1.0. A higher value indicates better overall diagnostic ability. One valuable feature of ROC analysis is that it provides information about the probability of error at measurement points throughout the distribution, so that a specific measurement can be compared to these values, and the likelihood of error at a point nearer that actual measurement can be determined. For a more in depth discussion of ROC analysis and its application to metric sexing, see Khanpetch et al. [21]. Finally, a test of the logistic regression equations was conducted to determine whether the allocation accuracies predicted by the equations are robust. The test sample was selected such that the number of males and females was kept equal, at least 25 individuals of each sex were measured, and at least 20 measurements were recorded for each dimension in each sex. The final test sample included 52 skeletons. Based on this sample size, a single misclassified individual will affect the accuracy rate by approximately 4–5% within one of the sexes, and the overall classification rate by 2–2.5%. Thus, an equivalent result between the predicted and tested accuracies will be defined as one in which the tested accuracy is less than 5% below the predicted correct classification accuracy from the regression equations. Author SP tested the first three measurements, which are taken with a mini-osteometric board, and PD tested four measurements using calipers. Neither researcher had taken these measurements previously, nor were they given instruction on how to take the measurements beyond the written descriptions and Fig. 1. The goal was to test the equations from the perspective of a forensic

anthropologist or other professional using the equations for the first time. 3. Results Descriptive statistics for the ten measurements of the talus are provided in Table 2. Intra- and inter-observer error results are reported in Table 3. These results indicate a much lower error for MaxLg, MaxBr, and MaxHt, all of which were taken with a miniosteometric board, than for MaxTrLg, MaxTrBr, and MaxIASLg that were taken with sliding calipers. Intraobserver measurement differences were below 0.2 mm for all dimensions, whether assessed by the median difference or TEM, and the median percent difference was well below 1%. Interobserver errors were uniformly higher than intraobserver errors. However, the interobserver error results for measurements taken with the miniosteometric board were still quite low, with a median percent difference not exceeding 0.14%. For the caliper measurements, median percent differences were all below 1.5%, except for left and right MaxTrBr. The value for RMaxTrBr exceeded 2%, and that for LMaxTrBr slightly exceeded 3%. Some additional instructions were added to the measurement descriptions in Table 1 after the accuracy and error tests to help reduce interobserver error. These additional instructions are italicized. Logistic regression equations based on individual measurements are reported in Table 4. The measurements with the highest overall predicted accuracies were LMaxTrLg and RMaxTrBr, both yielding better than 89% correct allocation accuracy. The next highest was RMaxTrLg at 86.5%. The three experimental measurements did not

Table 4 Logistic regression equations. Measure

R-MaxLg L-MaxLg R-MaxBr L-MaxBr R-MaxHt L-MaxHt R-MaxTrLg L-MaxTrLg R-MaxTrBr L-MaxTrBr R-MaxIASLg L-MaxIASLg R-MaxIASBr L-MaxIASBr

N

169 169 195 191 198 196 185 176 194 192 193 188 198 196

Logit equation

0.5959*RMaxLg 31.627 0.6390*LMaxLg 33.937 0.9047*RMaxBr 35.415 0.8467*LMaxBr 33.089 1.0985*RMaxHt 33.119 1.0359*LMaxHt 31.219 1.1280*RMaxTrLg 36.190 1.3760*LMaxTrLg 44.070 1.3470*RMaxTrBr 37.138 1.1242*LMaxTrBr 30.868 1.4937*RMaxIASLg 44.120 1.2631*LMaxIASLg 37.356 1.7066*RMaxIASBr 34.487 1.4015*LMaxIASBr 28.085

Logistic regression results

Test sample results (N = 53)

Female %

Male %

Overall %

Female %

Male %

Overall %

86.5 88.0 81.6 81.9 80.6 82.3 84.8 89.8 90.6 86.0 86.2 85.1 83.7 80.2

84.2 83.7 82.5 82.5 85.0 81.0 88.2 89.8 87.8 84.8 84.8 81.9 79.0 78.0

85.2 85.8 82.1 82.2 82.8 81.6 86.5 89.8 89.2 85.4 85.5 83.5 81.3 79.1

87.5 87.5 88.5 88.5 88.5 88.5 85.0 90.5 80.8* 80.8* 92.0 84.0 84.6 84.6

83.3 84.0 96.2 87.5 88.5 76.9 80.0* 80.0* 92.3 92.3 79.2* 75.0* 80.8 84.6

85.4 85.7 92.3 88.0 88.5 82.7 82.2 84.8* 86.5* 86.5 85.7 79.6 82.7 84.6

Note: Enter variable measures in millimeters. * Indicates a value that is 5%+ lower than estimated.

Please cite this article in press as: P. Mahakkanukrauh, et al., Sex estimation from the talus in a Thai population, Forensic Sci. Int. (2014), http://dx.doi.org/10.1016/j.forsciint.2014.04.001

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Table 5 Multiple regression equations. Equation

Side

N

Logit equation

1 2 3 4 5 6 7 8 9 10

R R R R R L L L L L

183 194 181 185 193 174 184 188 192 165

0.7549*RMaxTrLg + 0.9200*RMaxTrBd 49.636 1.0199*RMaxTrBd + 0.5051*RMaxHt 43.320 0.7923*RMaxTrLg + 1.0945*RMaxIASLg 57.720 0.8402*RMaxTrLg + 0.5282*RMaxHt 42.922 1.2115*RMaxIASLg + 0.6606*RMaxHt 55.664 0.9371*LMaxTrLg + 0.7433*LMaxTrBd 50.584 0.6913*LMaxTrBd + 0.8944*LMaxIASLg 45.398 0.9220*LMaxIASLg + 0.5826*LMaxHt 44.831 0.8138*LMaxTrBd + 0.5480*LMaxHt 38.838 0.9062*LMaxTrBd + 0.3282*LMaxLg 42.177

Multiple regression results

Test sample results

Female %

Male %

Overall %

Female %

Male %

Overall %

91.2 90.6 91.0 89.1 89.4 90.7 89.0 90.4 90.3 91.1

91.3 91.8 90.2 88.2 88.9 92.0 90.3 87.2 85.9 88.4

91.3 91.2 90.6 88.6 89.1 91.4 89.7 88.8 88.0 89.7

90.0 84.6* 100.0 90.0 92.0 95.2 96.0 92.0 88.5 95.8

92.0 96.2 87.0 84.0 87.5 92.0 83.3* 87.5 96.2 96.0

91.1 90.4 92.9 86.7 89.8 93.5 89.8 89.8 92.3 95.9

Note: Enter variable measures in millimeters * Indicates a value that is 5%+ lower than estimated.

perform well. The highest allocation accuracy among them was for RMinIDNk at 70.2%. Therefore, they are not discussed further. If we consider the mean accuracy for both the left and right side equations, the results were: MaxTrLg (88.2%), MaxTrBr (87.3%), MaxLg (85.5%), MaxIASLg (84.5%), MaxHt (82.2%), MaxBr (81.7%), and MaxIASBr (80.2%). Among these seven dimensions, the only measurements that did not produce at least an 80% correct allocation accuracy for both sexes were MaxIASBr on both sides. Ten pairs of measurements were found to produce higher allocation accuracies by at least 2% when combined in a multiple regression than when considered separately (Table 5). Five of these pairs were from the right side, and five from the left. Four of these equations (three on the right, one on the left) had allocation accuracies of greater than 90%. MaxTrLg and MaxTrBr together produced an allocation accuracy of 91.3% on the right side, with nearly identical results for males and females. These two were also the best combination on the left side with 91.4% allocation accuracy. All ten equations produced correct allocation accuracies for the combined sexes of at least 88.0%. Results of the ROC analyses are reported in Tables 6a and 6b. See also Fig. 2 for an example of the ROC curves for left and right MaxTrLg. Table 6a shows three different sectioning points for individuals identified as male based on the regression equations. The sectioning points are labeled ‘‘Threshold’’ in the table. For each threshold, there is an estimate of the probability that a female would have a measurement of that size or higher, which we call the ‘‘Error’’. ‘‘Sensitivity’’ is the proportion of the male sample expected to have a measured size that is equal to or greater than the listed threshold. Among the many threshold values that were possible, the three

selected for each measurement were those that were closest to a 1%, a 5%, and a 10% probability of misclassification as female. At the 5% threshold value, an estimated 5% or less of females in a Thai sample would be expected to have a measurement of that size or larger. Table 6b shows the same data for individuals identified as female. In this case, any skeleton with a measurement equal to or below the threshold value would have the corresponding probability (or less) of being a male, and the sensitivity indicates the percentage of females who would be expected to have the stated bone size or below. Based on the AUC values, the ROC results suggest a similar ordering to the measurements with the highest correct allocation accuracies that were identified via the logistic regression analysis. If anything, the analogous bones on the left and right sides seem to cluster together a little better in the ROC results at the top end, and there seems to be a slight tendency for the right side to outperform the left. The measurements with the highest AUC values are left maximum trochlear length, followed by right inferior articular surface length, right maximum trochlear length, and then right maximum trochlear breadth. Left maximum trochlear breadth provides the fifth highest result. The maximum length, breadth, and height measures perform similarly to one another, bracketed by left maximum length at the higher end of the group, and left maximum breadth and height at the lower end. Inferior articular surface breadth is the poorest performer on both sides. Results from the test sample showed that some equations produced overall allocation accuracies more than 5% greater than predicted by the regression equations. Right and left maximum breadth, right maximum height, and left maximum inferior

Table 6a ROC results for individuals identified as male. Measure

AUC

Level 1 Errora

Level 1 Thresholdb

Level 1 Sensitivityc

Level 2 Errora

Level 2 Thresholdb

Level 2 Sensitivityc

Level 3 Errora

Level 3 Thresholdb

Level 3 Sensitivityc

L-MaxLg R-MaxLg L-MaxBr R-MaxBr L-MaxHt R-MaxHt L-MaxTrLg R-MaxTrLg L-MaxTrBr R-MaxTrBr L-IASLg R-IASLg L-IASBr R-IASBr

0.918 0.910 0.909 0.910 0.909 0.912 0.960 0.944 0.928 0.942 0.927 0.946 0.885 0.901

1.2% 1.4% 1.1% 1.0% 1.0% 1.0% 1.1% 1.1% 1.1% 1.0% 1.1% 1.1% 1.0% 1.0%

55.19 56.05 41.02 40.89 32.25 32.28 33.65 34.14 29.81 29.56 31.11 31.48 21.10 20.94

66.3% 61.1% 60.8% 56.7% 43.0% 44.0% 62.5% 54.8% 41.4% 48.0% 55.3% 52.5% 56.0% 58.0%

4.8% 5.4% 5.3% 5.1% 5.2% 5.1% 4.5% 5.4% 5.4% 5.2% 5.3% 5.3% 5.2% 5.1%

54.29 54.59 40.27 40.48 31.23 30.84 33.14 32.84 28.56 28.20 30.52 30.30 20.78 20.71

70.9% 74.7% 72.2% 66.0% 66.0% 73.0% 70.5% 74.2% 74.7% 81.6% 67.0% 71.7% 61.0% 67.0%

9.6% 9.5% 9.6% 10.2% 10.4% 10.2% 10.2% 9.8% 9.7% 10.4% 9.6% 9.6% 10.4% 10.2%

53.85 53.92 39.67 39.90 30.85 30.73 31.98 32.42 27.69 27.39 29.95 29.81 20.44 20.40

76.7% 78.9% 78.4% 71.1% 72.0% 74.0% 90.9% 83.9% 84.8% 88.8% 78.7% 81.8% 69.0% 76.0%

a b c

Indicates the estimated percentage of females expected to have a measurement equal to or higher than the listed dimension. Indicates the measured size (in mm) at which the listed error rate and the listed sensitivity apply. Indicates the estimated percentage of the male population expected to have dimensions equal to or greater than the listed value.

Please cite this article in press as: P. Mahakkanukrauh, et al., Sex estimation from the talus in a Thai population, Forensic Sci. Int. (2014), http://dx.doi.org/10.1016/j.forsciint.2014.04.001

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Table 6b ROC results for individuals identified as female. Measure

AUC

Level 1 Errora

Level 1 Thresholdb

Level 1 Sensitivityc

Level 2 Errora

Level 2 Thresholdb

Level 2 Sensitivityc

Level 3 Errora

Level 3 Thresholdb

Level 3 Sensitivityc

L-MaxLg R-MaxLg L-MaxBr R-MaxBr L-MaxHt R-MaxHt L-MaxTrLg R-MaxTrLg L-MaxTrBr R-MaxTrBr L-IASLg R-IASLg L-IASBr R-IASBr

0.918 0.910 0.909 0.910 0.909 0.912 0.960 0.944 0.928 0.942 0.927 0.946 0.885 0.901

1.2% 1.1% 1.0% 1.0% 1.0% 1.0% 1.1% 1.1% 1.0% 1.0% 1.1% 1.0% 1.0% 1.0%

47.240 48.470 35.980 36.420 27.670 27.590 30.580 30.040 25.120 25.380 27.370 28.490 18.360 18.200

15.7% 14.9% 27.7% 33.7% 32.3% 31.6% 68.2% 56.5% 34.4% 34.4% 34.0% 63.8% 24.0% 15.3%

4.7% 5.3% 5.2% 5.2% 4.0% 5.0% 4.5% 5.4% 4.0% 5.1% 5.3% 5.1% 5.0% 5.0%

50.820 50.830 37.070 37.610 28.750 28.940 31.390 31.560 26.220 26.500 28.720 28.840 19.000 19.270

59.0% 55.4% 48.9% 61.2% 57.3% 61.2% 83.0% 81.5% 65.6% 68.8% 71.3% 74.5% 47.9% 44.9%

10.5% 10.5% 10.3% 10.3% 10.0% 9.0% 10.2% 9.7% 10.1% 10.2% 9.6% 10.1% 10.0% 9.0%

52.170 52.400 38.120 38.180 29.540 29.340 32.110 31.790 26.660 27.310 29.160 29.330 19.440 19.660

74.7% 71.6% 71.3% 73.5% 76.0% 69.4% 90.9% 83.7% 77.4% 87.5% 77.7% 84.0% 63.5% 63.3%

a b c

Indicates the estimated percentage of males expected to have a measurement equal to or lower than the threshold value. Indicates the measured size (in mm) at which the listed error rate and the listed sensitivity apply. Indicates the estimated percentage of the female population expected to have dimensions equal to or lower than the listed value.

articular surface breadth outperformed their predicted allocation accuracies by the greatest margin. Four measurements followed the predicted results quite closely. These were RMaxLg, LMaxLg, RMaxTrLg, and RMaxIASBr. Only one measurement underperformed the predicted allocation accuracy for the combined sexes by 5% or more, but this was the measurement with the highest predicted allocation accuracy from the regression analysis (LMaxTrLg). Six measurements, including the one just mentioned, showed a difference between male and female allocation accuracies of 9% or greater. The largest predicted gap between the sexes based on the logistic regression equations was only 4.4%. In general, the measurements taken with the mini-osteometric board tended toward similar or higher accuracies in the test sample compared to

those predicted by the logistic regression equations, while those taken with calipers tended toward somewhat lower accuracy. This difference may relate to the low interobserver error associated with the mini-osteometric board measurements. The multiple regression equations based on two measurements generally performed better than predicted by the logistic regression analysis. Seven of ten equations exhibited higher correct allocation accuracies for the combined sexes, and one equation performed almost identically to the predicted results. Only Eq. (2) had a correct allocation accuracy for the combined sexes that was more than 5% lower than the predicted results. However, the gap between male and female allocation accuracies was often somewhat wider in the test sample. In particular, Eqs. (2) and

Fig. 2. Male ROC curves for RMaxTrLg (AUC = 0.960) and LMaxTrLg (AUC = 0.944). Note that RMaxTrLg diverges from the X-axis at a higher point than does LMaxTrLg. The sensitivity is a measure of the male classification accuracy, or the true positive proportion. The 1-specificity value is equal to one minus the proportion of females correctly classified. It is also referred to as the false positive proportion. Therefore, the higher up the x-axis the line diverges, the less the most masculine female encroaches on the male size distribution. In addition, the greater the size of the Area Under the Curve (AUC), the better the measurement at estimating sex.

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(7) exhibited gaps of greater than 10% between the allocation accuracy for males and females, with the accuracy for one of the two sexes falling below 85%. Both of these equations include MaxTrBr, with its relatively high interobserver error, as a variable.

4. Discussion Only a few previous studies have reported results for individual measurements of the talus on modern skeletal samples. Steele [10] found that, among five measurements of the talus, only talar length produced better than 80% accuracy in his mixed sample of Africanand European-Americans. In a study of modern Korean skeletons, Lee et al. [22] found that only inferior articular surface length exceeded 80% correct allocation accuracy, classifying 82.9% of the sample. The other six individual measurements, including talar length, talar width, talar height, trochlear length and breadth, and inferior articular surface breadth, all produced correct allocation accuracies of between 70.0% and 78.6%. Bidmos and Dayal [12] reported similarly poor results for their sample of white South Africans, with only one measurement – talar length – exceeding 80% correct allocation accuracy. Talar length produced an allocation accuracy of 81.7%, while another measurement – inferior articular surface breadth – achieved exactly 80% allocation accuracy. However, the same authors reported much better results among the black South African individuals from the same skeletal collection, with six measurements exceeding 80% correct allocation accuracy [23]. The two measurements with the highest allocation accuracies were trochlear length and trochlear breadth at 85% each. Finally, Harris and Case [2] reported three individual measurements among their sample of recent European-Americans that produced allocation accuracies ranging from 84.4% to 85.3% on the left side, and 83.6% to 90.0% on the right side. For both sides, the measurement with the greatest allocation accuracy was talar length. Thus, it would appear that populations can vary rather considerably in sexual dimorphism of the talus. The results of the current study are more in line with those of Bidmos and Dayal [23] on black South Africans, and of Harris and Case [2] on European-Americans. Six measurements produced predicted allocation accuracies on both sides that exceeded 81%. However, in contrast to many previous studies that have found talar length to be the most sexually dimorphic measurement [2], in our study talar length performed less well in the reference sample than maximum trochlear length and breadth, both of which produced predicted allocation accuracies of more than 89% on at least one side. One explanation for this result may be a difference in the talar length measurement used in this study versus some of the others. Measurements of talar length taken on a mini-osteometric board include the trigonal process of the talus, while measurements made with calipers avoid this structure. It varies somewhat in size among different individuals, and may fail to fuse to the talus in some individuals, existing instead as an accessory bone called the os trigonum [24]. A skeletal sample with high variability in the size of the trigonal process, or in the presence/absence of an os trigonum, would show more variability in measurements of talar length, perhaps leading to a few additional misclassifications. Despite use of a mini-osteometric board, Harris and Case [2] still found talar length to be among the most accurate estimators of sex among a European-American sample, but that sample may have exhibited less variability in the size of the trigonal process or in the frequency of os trigonum. It should also be noted that trochlear length and breadth are not always measured in studies of sex estimation from the tarsals, but given the relatively strong performance of these measurements in the current study and in that by Bidmos and Dayal [23], as well as a strong showing for trochlear length in the study of Korean skeletons by Lee et al. [22],

7

trochlear measurements should probably be included in future studies of sexual dimorphism of the talus. Combining the results from the reference and test samples, a slightly different picture emerges. If the lowest percent accuracy for either sex in the reference or test samples is used as a measure of the allocation accuracy for the measurement, then LMaxLg (83.7%) and RMaxLg (83.3%) would be the most accurate individual measurements. The next highest would be right and left MaxBr at 81.6% and 81.9%. These results are more in line with previous studies that have found talar length to be the single most sexually dimorphic talar measurement [2,10,12]. Thus, as individual measurements, trochlear length and trochlear breadth should not be the preferred measurements to use alone for sex estimation. Although the pooled allocation accuracies were above 82% for these measurements on both sides, there were relatively large gaps between the male and female accuracies. As individual measurements, left and right maximum length and maximum breadth should be preferred, when circumstances permit their use. Five previous studies have used multiple measurements of the talus to classify individuals by sex [2,7,10,12,23]. Comparisons will be made for the left side, as three of the studies only measured bones from that side [10,12,23]. Among these past studies, the most accurate sexing equations produced overall allocation accuracies ranging from 86.7% to 92.4%. Three of the five most accurate equations included talar length, three included talar height, and two included talar breadth. Only three of these previous studies included measures of trochlear length and breadth, and neither of these measurements appeared in any of the most accurate equations. By contrast, in the present study, trochlear length and breadth combine to produce the highest predicted allocation accuracy on both the left and right tali, at 91.4% and 91.3% respectively, and either trochlear length or trochlear breadth is present in four of the five most accurate equations for the left talus, and four of five equations for the right talus (Table 5). Thus, it would appear that trochlear length and breadth are relatively more sexually dimorphic among modern Thai people than in some other populations. The test results seem to confirm this finding. When MaxTrLg and MaxTrBr were combined, they produced test results that are similar to, or more accurate than, the results predicted by the multiple regression equations from the reference sample. They also produced results that were similar for both sexes (see Eqs. (1) and (6), Table 5). One explanation for this complementarity might be a high degree of independence between these two measurements. Indeed, when we calculated Pearson’s correlation coefficients between each measurement and all others on the right side, we found that RMaxTrBr had the lowest mean correlation with the other six dimensions at 0.755. The correlation with RMaxTrLg was 0.751. The other dimensions had mean correlations with the others that ranged between 0.772 (RMaxIASLg) and 0.831 (RMaxLg). Although the results of this study suggest that the talus can be used to sex Thai skeletons with allocation accuracies as high as 91.3% for two measurements from the right side, and 91.4% for the same two measurements on the left, they still underperform results from Thai humeri and femora, based on stepwise analysis of multiple variables from 70 males and 34 females [25,26]. The most accurate equation for the femur, based on maximum head diameter and bicondylar breadth was 94.2% for Thais, and the most accurate equation for the humerus was 97.1% based on vertical head diameter, minimum midshaft diameter, and epicondylar breadth. Such high levels of allocation accuracy using the talus are possible for some individuals by applying the ROC thresholds reported in Tables 6a and 6b, but not for the entire sample.

Please cite this article in press as: P. Mahakkanukrauh, et al., Sex estimation from the talus in a Thai population, Forensic Sci. Int. (2014), http://dx.doi.org/10.1016/j.forsciint.2014.04.001

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Comparing the results for the talus with recent studies of sexual dimorphism among the hands of Thai individuals from this same skeletal collection, it would appear that the talus exhibits similar sexual dimorphism to the proximal phalanges of the hands, and slightly more dimorphism than the metacarpals [21,27]. The proximal phalanges produced an equation for the first proximal phalanx with an allocation accuracy of 92.3% based on measurements of head width and midshaft diameter, and an equation for three measurements of the second proximal phalanx with 91.4% allocation accuracy. The metacarpals produced equations that were slightly less accurate, the highest being found for three measurements of the second metacarpal with an 89.8% predicted accuracy.

5. Conclusions The talus was found to be a useful bone for identification of sex among modern Thai individuals from the Chiang Mai area should the larger limb bones be damaged or unavailable. Accuracy rates as high as 89.8% were predicted with a single measurement from the left talus (LMaxTrLg) and four equations with accuracy rates over 90.0% were derived using two measurements. Using the ROC results from individual measurements, even higher levels of accuracy are possible for individuals whose talar dimensions fall relatively far from the mean for the population. Testing of the individual measurements on a sample of 52 skeletons found that a majority performed as well or better than predicted by the logistic regression equations. Those that underperformed by more than 5% in at least one of the sexes were MaxTrLg, MaxTrBr, and Max IASLg on both sides. Thus, as individual measurements, the lower accuracy rates from the test sample should probably be used for these measurements when estimating sex. When combined, however, most of these same measurements perform similarly to expectations based on multiple regression equations derived from the larger reference sample. The equation with both the highest pooled allocation accuracies, and the highest accuracy for each of the sexes independently, was found to be a combination of maximum trochlear length and maximum trochlear breadth on either the left or right side. Using these two measurements, allocation accuracy rates of 91.4% were estimated for the left talus, and 91.3% for the right talus. Test results yielded 91.1% accuracy on the left and 93.5% on the right. Maximum inferior articular length also obtained test results similar to predictions when combined with other measurements in three out of four equations. When using the equations from this study in a forensic context in Thailand, we recommend preferential use of MaxLg and MaxBr measurements when utilizing single dimensions, and Eqs. (1) and (6) from Table 5 when using pairs of dimensions. However, any of the ten equations from Table 5 should be acceptable for sex estimation in a forensic context, so long as the lowest accuracy for either sex, whether that be from the reference sample or the test sample, is treated as the accuracy level for the equation.

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Please cite this article in press as: P. Mahakkanukrauh, et al., Sex estimation from the talus in a Thai population, Forensic Sci. Int. (2014), http://dx.doi.org/10.1016/j.forsciint.2014.04.001