Sex estimation from sacrum and coccyx with discriminant analyses and neural networks in an equally distributed population by age and sex

Sex

estimation

from

sacrum

and

coccyx

with

discriminant

analyses

and

neural

networks

in

an

equally

distributed

population

by

age

and

sex

$

Yasin

Etli

,

Mahmut

Asirdizer

*

,

Yavuz

Hekimoglu

,

Siddik

Keskin

,

Alpaslan

Yavuz

a_{DepartmentofForensicMedicine,HospitalofFacultyofMedicine,SelcukUniversity,Konya,Turkey} b

DepartmentofForensicMedicine,FacultyofMedicine,VanYuzuncuYilUniversity,Van,Turkey

c

DepartmentofForensicMedicine,FacultyofMedicine,NamikKemalUniversity,Tekirdag,Turkey

d

DepartmentofBiostatistics,FacultyofMedicine,VanYuzuncuYilUniversity,Van,Turkey

e

DepartmentofRadiology,AntalyaTrainingandResearchHospital,HealthSciencesUniversity,Antalya,Turkey

ARTICLE INFO

Articlehistory: Received7March2019

Receivedinrevisedform21August2019 Accepted30August2019

Availableonline12September2019 Keywords:

Sacrum Coccyx Sexestimation

Discriminantfunctionanalysis Neural

Networks

ABSTRACT

Sexestimationisanessentialstepintheprocessoftheidentificationoftheskeletalremainsinforensic

anthropologysinceitreducesthenumberofpossiblematchesbyhalf.Inthisstudy,sexestimationwith

21sacralandcoccygealmetricparametersobtainedfromComputerizedTomographyimagesofaTurkish

populationwhich consistsof480patientsthatare equalizedaccordingtotheirsexesand ages, is

performed.Univariatediscriminantanalysis,lineardiscriminantfunctionanalysis,stepwisediscriminant

functionanalysis,andmultilayerperceptronneuralnetworksareusedinthisstudy.Amaximumof67.1%

accuracyforunivariatediscriminantanalysis,82.5%forlineardiscriminantfunctionanalysis,78.8%for

stepwisediscriminantfunctionanalysis,and86.3%formultilayerperceptronneuralnetworks,were

achieved.Althoughitdoesnotreachanacceptableaccuracyrateof95%ormoreforsacrumandcoccyx,

sexestimationwithneuralnetworksisapromisingfieldofresearchincorpseswhereidentificationis

otherwisenotpossible,andfurtherstudieswithotherbonesandwithnewtechniquesmightgiveuseful

information.

©2019ElsevierB.V.Allrightsreserved.

1.Introduction

Sex estimation is an essential step in the process of the

identificationoftheskeletalremainsinforensicanthropologyas

it reduces thenumber of possible matchesby half [1]. Metric

methodsandmorphologicmethodscanbeusedforthispurpose.

Althoughitprovidesvaluableinformation,morphological

meth-odsrequireexperienceinthefieldofForensicAnthropologyto

answerquestionsaboutfeaturesofbonessuchas:“Whichoneis

large?”,“Whichoneissmall?”or“Whichoneiscurved?”etc.[2].

Inrecentyears,metricmethodshavegainedpopularitytoverify

and quantify the observed shape differences in bones [2,3].

However,metricmethodsalsohavecertaindisadvantages.Firstly,

the results are highly population-specific, and the developed

methodcanonlybeappliedtocasesofthatancestralpopulation

fromwhichthetechniquewasdeveloped.Secondly,thelackof

well-preserved anatomical landmarks for measurements may

resultinaninabilitytoperformmeasurementsand,asaresult,

failureinsexestimation[4].

Caliper measurements and radiologic measurements can be

performed for metric evaluation [5]. After completing the

measurements, the results should be evaluatedstatistically for

final sex estimation result by Discriminant Function Analysis,

whichallowssexestimationusingmultiplevariablesatthesame

time [6]. Alternatively, there is a growing interest in Neural

Networks, an efficient sex estimation method in the field of

ForensicAnthropology[7–9].

Ofallbonesstudied,pelvicboneshavebeenshowntohavethe

most sexually dimorphic characteristics. It is stated that this

differenceinsexualdimorphismdevelopsduetotheadaptation

ofthesebonestoallowpassageofthefetusinfemales[10–19].

Sincesacrumisafunctionalpartofthepelvis,itisthoughttohave

sexuallydimorphiccharacteristics[1].Therearesomestudiesfor

metricsexestimationfromsacrumandcoccyx,andaccuracyrate

rangesbetween59.4%and95%inthesestudies.Thiswiderangeof

$ _{Thisarticlewasproduced from dataofthe expertisethesisentitled“Sex}

Determination from the Sacral and Coccygeal AnthropometricMeasurements Obtainedfrom Abdomino- PelvicComputerized TomographicImagesin Van (Turkey)”preparedbyDr.YasinEtliunderthesupervisionofProfessorDrMahmut Asirdizer.

* Corresponding author at: Department of Forensic Medicine, Faculty of Medicine,VanYuzuncuYilUniversity,65080,Van,Turkey.

E-mailaddresses:drysntl@gmail.com(Y.Etli),mahmutasirdizer@yyu.edu.tr, masirdizer@yahoo.com(M.Asirdizer),yhekimoglu@nku.edu.tr(Y.Hekimoglu), skeskin@yyu.edu.tr(S.Keskin),alp_yavuz@hotmail.com(A.Yavuz).

http://dx.doi.org/10.1016/j.forsciint.2019.109955 0379-0738/©2019ElsevierB.V.Allrightsreserved.

ContentslistsavailableatScienceDirect

Forensic

Science

International

resultscanbepartlyattributedtotheancestraldifferencesandto

the fact that metric methods are highly population-specific.

[4,5,11,20–24].Anotherfactorthatmayleadtothesedifferences

maybe the use of different combinations of measurement by

different authors. While some studies focused on the

measurementsof only the sacral base [5,20,23], other studies

also included the measurements from different parts of the

sacrum[11,21,22,24].Sinceage-relatedchangesinsacrumhave

beenshown[25,26],itisthoughtthatagedistributioninstudy

populationsmayalsoleadtodifferentresults.Forsuchreasons,

thereisaneedforstudiesondiverseancestralpopulations,with

as many measurements as possible, on equally distributed

populationsbyageandsex.

In this study, sacral measurements are performed on

Abdomino-Pelvic Computerized Tomography (CT) images of a

Turkishpopulationwhichconsistsof480patients(240males,240

females)thatareequallydistributedbyageandsex.Thestudyaims

to find out the accuracy of sex estimation using sacral and

coccygealmeasurementswith discriminantanalysisand neural

networks in the study population. According to the literature

reviewconductedbyus,thisstudyisthelargestscalestudyonsex

estimationfromthesacrum.

2.Materialsandmethods

The studywasperformedonAbdomino-PelvicCT imagesof

480livingindividualsofknownsexandage,whichappliedtothe

Radiology Department between 01.01.2016 and 01.01.2017.

Computed tomography (CT) examinations of the sacral bones

were performed by 16 Cross-Sectional Multislice Computed

Tomography (CT) machine (Somatom Sensation 16; Siemens

Medical Solutions, Erlangen, Germany) in the Department of

RadiologyofMedicineFacultyofVanYuzuncuYilUniversity.CT

devicewasadjustedasfollows:KV/EffectivemAs/Rotationtime

(sec) values 120/120 / 0.75; gantry rotation period 420ms;

physical detector collimation, 160.6mm; section thickness,

0.75mm;finalsectioncollimation320.63mm;feed/rotation,

6mm; Kernel, U90u; increment 0.5mm; resolution 512512

pixel. The obtained axial images were transferred to the

workstation (Leonardo, Siemens Medical Solutions, Erlangen,

Germany)forprocessinginDICOMformat.Subsequently,

multi-planar images and 3-dimensional (3D) reconstructions were

obtained using the “Volume Rendering Plus InSpace MPR” in

“SyngoVia” CT software on the Workstation. Anatomical

morphometric distance, angle and area measurements were

performed on sagittal and axial images by using electronic

calipersandfreehandROIselectionmethods,respectively.

2.1.Caseselectionandequalization

Intheselectionof 480cases,carewas takentoequalizethe

population according to age groups and sex (Table 1). Among

individualsaged21to70years,4casesfromeachageforbothsex

groupswerefoundandevaluated.Sincesuchanequalizationwas

notpossibleforindividualsaged71andover,anequalnumberof

females and males were found in this agegroup. Besides, the

subjectswereselectedsimilarlyintermsoftheaverageageofboth

sexesinthe71andoveragegroup.Thus,240femaleand240male

patientswithsimilaraveragesofageandsimilardistributionby

ageswereevaluated.

Forourstudy,duringthescreeningofpatientswhohadundergone

Abdomino-PelvicCTandestablishingalistofcandidatecasesforthe

study, patients with a record of a diagnosis of malignancy and

endocrine pathologies were excluded from the list. This procedure was

performedonthehospitalinformationmanagementsystemofour

hospital(ENLIL1HBYS)bytheITdepartmentofourhospitalwiththe

approvaloftheethicscommittee.Thus,thesecaseswerenotincluded

inthestudy.Additionally,1caseofcongenitaldysgenesisofanS2

vertebra,27casesoflumbarvertebralfractureorfixation,and19cases

ofpelvicorsacralfractureareexcludedfromthestudy.

2.2.Measurements

Eightlengthmeasurements,fouranglemeasurements,andan

areameasurement,alldefinedintheliterature,wereperformed

(Figs.1and2)[5,19,24,27].APD,MTD,PERIMETER,AREA,andMBA

measurementswereimplementedontheaxialplaneandASL,PSL,

ASCL,PSCL,LSBA,SBA,LSAandASAmeasurementswerecarried

outonthesagittalplane.Inordertoachieveaccurate

measure-mentsofthesacralbase,amultiplanarexaminationwasmadedue

tothevariableorientationofsacrum[28].

Also,fiveanglemeasurements,whichcouldnotbefoundin

theliterature,wereproposedaspredictorsofsexfromsacrum

andcoccyx.Thesemeasurementswereconductedinthestudy

population,andtheirutilitiesinsexestimationwereanalyzed.

(Fig.2).Onthesagittal plane,SCAwasobtainedbymeasuring

theanglebetweenthesuperiorlineofthefirstsacralvertebra

corpusandtheinferiorlineofthe lastsacralvertebracorpus.

Afterfindingthetwolinescuttingeachotherwiththewidest

angleamongsacralvertebracorpuslines,MSCAmeasurement

wasconducted.ForSCCA,theanglebetweenthesuperiorlineof

the firstsacral vertebracorpus andthe line of the last

inter-coccygeal joint was measured. After finding the two lines

cuttingeachotherwiththewidestangleamongsacralvertebrae

corpus lines and coccygeal vertebrae segments lines, MSCCA

Table1

Distributionofcasesbyagegroupsandsex.

SEX AGEGROUPS 21-30 31-40 41-50 51-60 61-70 71-71< TOTAL

FEMALE NUMBEROFCASES 40 40 40 40 40 40 240

MINIMUMAGE 21 31 41 51 61 71 21

MAXIMUMAGE 30 40 50 60 70 112 112

MEANAGE 25.5 35.5 45.5 55.5 65.5 80.5 51.3

STANDARDDEVIATION 2.9 2.9 2.9 2.9 2.9 7.7 18.8

MEDIANAGE 25.5 35.5 45.5 55.5 65.5 78 50.5

MALE NUMBEROFCASES 40 40 40 40 40 40 240

MINIMUMAGE 21 31 41 51 61 71 21 MAXIMUMAGE 30 40 50 60 70 95 95 MEANAGE 25.5 35.5 45.5 55.5 65.5 80.5 51.3 STANDARDDEVIATION 2.9 2.9 2.9 2.9 2.9 6.6 18.8 MEDIANAGE 25.5 35.5 45.5 55.5 65.5 80 50.5 PVALUE 1.000 1.000 1.000 1.000 1.000 .988 .998

measurement was carried out. These measurements were

proposed to evaluate the sacral and sacrococcygeal curve

objectively(Fig.2).

To objectively evaluate the lumbosacral curve, MLSCA, the

widestangleamongtheanglesofintersectingsacralandlumbar

vertebraecorpuslines,wasproposed(Fig.2).

2.3.Indexes

After completing the measurements, three indexes were calculated

accordingtotheliterature[29–31].SacralIndex(SI),Corporo-Basal

Index(CBI)andS1VertebraCorpusIndex(S1VCI)werecalculatedas

100XMBA/ASL,100XMTD/MBA,and100XAPD/MTD,respectively.

Fig.1.MeasurementsofAnteriorSacralLength(ASL),PosteriorSacralLength(PSL),AnteriorSacro-CoccygealLength(ASCL),PosteriorSacro-CoccygealLength(PSCL), MaximumBreadthofAlaeSacralis(MBA),MaximumAntero-PosteriorDiameterofS1VertebraCorpus(APD),MaximumTransverseDiameterofS1VertebraCorpus(MTD), AreaofS1VertebraCorpus(AREA)andPerimeterofS1VertebraCorpus(PERIMETER).

Fig.2.MeasurementsofSacralCurveAngle(SCA),MaximumSacralCurveAngle(MSCA),Sacro-CoccygealCurveAngle(SCCA),MaximumSacro-CoccygealCurveAngle(MSCCA), MaximumLumbo-SacralCurveAngle(MLSCA),SacralBaseAngle(SBA),Lumbo-SacralBaseAngle(LSBA),AnteriorSacralAngle(ASA),andLumbo-SacralAngle(LSA).

2.4.Statisticalanalysis

ThestatisticalanalysiswasperformedwithSPSS22.0,Minitab

17.1,andMicrosoftExcel2013.Thestatisticalsignificancelevelin

thecalculationswasat5%.Descriptivestatisticswerecalculated,

andsexwas determinedwithUnivariateDiscriminant Analysis,

Linear Discriminant Function Analysis, Stepwise Discriminant

Function Analysis, and Neural Networks using Multilayer

Perceptron.

Discriminant Function Analysis is a statistical method that

enablestheestimationofsexbyevaluatingtwoormorevariables

atthesametimeandhasbeenwidelyusedinrecentsexestimation

studies.During theprocessofDiscriminant FunctionAnalysis,a

valuecalledcentroidiscalculatedforeachsexgroup.Thecentroid

is defined asthe average valueof all variables involvedin the

analysis for a sex group in a multidimensional space. In this

multidimensionalspace,thecloserthepositionofthevaluesofan

individualwithinthepopulationtothelocationof thecentroid

valueofasexgroup,thegreatertheprobabilitythattheindividual

belongstothatsexgroup.Asaresultofthecalculations,aformula

calledDiscriminantFunctionisobtained.Whenthevaluesofan

individual are placed in this function, sex can be estimated

according to whether the result is larger or smaller than the

sectioningpoint[6].

Neuralnetworksaredevelopedtosimulatethefunctionalityof

thehumanbrainandmakeintelligentdecisionsbyusingit.Neural

networksconsistof4basiccomponents;aninputlayer,ahidden

layer,anoutputlayer,andsynapticconnectionsbetweenthelayers

mentioned above seen in Fig. 3. In utilized supervised neural

network method, two-thirds of the study population were

randomlyselectedforthetrainingphase.Inthisbackpropagation

learning process, the synaptic weights, the number of hidden

layers, and the bias factor were determined to obtain desired

results as accurately as possible. After training, the remaining

sample,one-thirdofthepopulationunderwentatestingphaseto

findouthowaccurateandreliabletheneuralnetworkcon

figura-tionthatwasestablishedinthelearningprocessis[7,8,32].

2.5.Inter-observerandintraobservererroranalysis

Measurements were performed by two observers (Y.E.; a

forensicmedicineexpertandM.A.;aforensicmedicineprofessor)

who are researchers in this study, without having information

aboutthesexofthepatients.All18measurementson480cases

wereperformedbothbyObserver1andObserver2.Inter-observer

reliabilityassessmentwasmadeontheresultsofthese

measure-ments.Additionally,toevaluate intra-observer reliability,all18

measurementswererepeatedon40randomlyselectedcasesfor

eachobserverafteratleasttendaysaftertheinitialmeasurement.

RelativeTechnicalErrorMeasurementsandIntraclassCorrelation

Coefficients were calculated. The acceptable Relative Technical

ErrorMeasurementsrateforinter-observererrorwasconsidered

tobelessthan2%.Forintra-observererror,itwasconsideredtobe

less than 1.5%. Whenthe IntraclassCorrelation Coefficient was

Fig.3.GraphicRepresentationofMultilayerNeuralNetworkandSynapticWeightswhichwereEstablishedandUsedforSexDeterminationAccordingtotheResultsof Observer1.

greaterthan0.75,itwasconsideredtobeaccurate.Also,thePaired

Sample t-test was applied to determine whether there was a

statisticallysignificant differencebetweenthemeasurementsof

tworesearchers.

3.Results

RelativeTechnicalErrorMeasurementsforintra-observererror

werelessthan1.5%(between0.253and1.410).Forinter-observer

error,thesewerelessthan2%(between0.375and1.643).Intraclass

Correlation Coefficients were above 0.75 (between 0.966 and

0.996). Differences were not statistically signi_ficant (p_>0.05)

betweentheresultsofObserver1andObserver2exceptforMTD,

AREA,CORPORO-BASALINDEX,andS1VERTEBRACORPUSINDEX

parametersinmalecases,andSCA,MSCA,SCCA,AREA,PERIMETER

andCORPORO-BASALINDEXparametersinfemalecases.

Descriptive statistics, discriminant analyses, and neural

network resultsof Observer2 areshown under separate titles

asSupplement1–6.

DescriptivestatisticsofObserver1aresummarizedinTable2.

Therewerestatisticallysignificantdifferencesbetweenbothsexes

inASL,PSL,ASCL,PSCL,APD,MTD,PERIMETER,AREA,LSA,ASA,

MLSCA,SacralIndex,Corporo-BasalIndexandS1VertebraCorpus

Index,whiletherewasnotasignificantdifferenceinMBA,LSBA,

SCA,MSCA,SCCA,andMSCCA.

Thesignificant increasesbyageinparametersof APD,MTD,

PERIMETER, AREA, SBA, SCA, MSCA, MLSCA, SI, and CBI were

determined by both observers. These increases affect sexual

dimorphismnegatively,especiallyinAPD,MTD,PERIMETER,AREA,

andCBI.

UtilizingUnivariate Discriminant Analysisdemonstrates that

APD was the most sexually dimorphic parameter with 67.1%

accuracy.APDwasfollowedbyAREA(66.3%),PSL(65.8%)andPSCL

(64.6%).

Linear Discriminant Function Analysis achieves 82.9% sex

estimationaccuracyinthemalegroup,82.1%forthefemalegroup

and82.5%intotalaccordingtotheresultsofObserver1.Discriminant

functionsfor eachsexgroup, thesummaryof classificationand

LinearDiscriminantFunctionAnalysissexestimationaccuracyrates

forseparateagegroupsareshowninTable3.

Stepwise Discriminant Function Analysis of Observer 1

concluded that ASL, PSL, SCA, MSCA, MSCCA, MLSCA, LSA,

APD,AREA,andPERIMETERmeasurementswereselectedforthe

discriminant function. In sex estimation, accuracy rates for

males, females, and the total is 79.6%, 77.9%, and 78.8%

respectively. Discriminant functions for each sex groups, the

summaryofclassificationandStepwiseDiscriminantFunction

Analysissexestimationaccuracyratesforseparateagegroups

areshowninTable4.

In the sexestimation by the Multilayer Perceptron Neural

Networks,341outof480caseswereinitiallychosenrandomlyfor

training viathebackpropagationphase bythesoftware.Having

finishedthetrainingprocess,itachieves87.2%accuracyformales,

85.8%forfemales,and86.5%forthetotaltrainingsampleofthe

population.Thetestprocesswasperformedontheremaining139

outof480casesandaccuraciesof83.6%,87.2%and85.6%formales,

for females and total population respectively, were achieved.

Whentheentirepopulationisconsidered,sexestimationaccuracy

rateswere86.3%forbothmales,females,andtotalpopulation.The

resultsareshowninTable5,Table6,andFig.3.

4.Discussion

Since the age and sex of a case can affect the results of

anthropological measurements [6,21], it is advantageous and

sometimesindispensabletoperformstudiesonequally

distrib-uted populations by age and sex. According to the literature

reviewdonehere,thereisnosuchstudyonsexingsacrumand

coccyxonequallydistributedpopulationsbyageandsex.When

sex estimation was performed with linear and stepwise

discriminantfunction analysison separateage groups,itwas

observedthattheaccuracyratesforsomeagegroupsaugment

to 98.8% (Tables 3 and 4). These results emphasize the

importance of including cases that belong to all of the age

groupsequallyandsufficientlytothestudies,anditcanbesaid

thathighaccuracyratesobtainedfromsmallpopulationswith

asymmetric distributions according to age groups are not

applicabletothegeneralpopulation.Furthermore,inrarecases

whereageisknownbutsexisunknown,theguidanceofthese

findingsmaybehelpful.

Additionally,ancestryaffectsresultsandstudiesfromdifferent

ancestralpopulationsshouldbeimplementedtoprovidedatafor

forensic anthropologydatabases [24]. Therefore,this studywas

carriedout,on480casesthatareequalizedaccordingtoageand

Table2

Descriptivestatisticsofallparameters.

ASL PSL ASCL PSCL APD** _MTD**

MALE FEMALE MALE FEMALE MALE FEMALE MALE FEMALE MALE FEMALE MALE FEMALE MEAN 111.7 104.6 115.2 106.5 126.9 118.7 138.0 128.1 35.6 32.8 55.5 52.5

SD 12.5 10.9 10.7 9.0 15.1 13.8 13.3 11.7 3.2 2.9 5.1 5.2

P <0.05* _<0.05* _<0.05* _<0.05* _<0.05* _<0.05*

PERIMETER** _AREA** _{MBA LSBA SBA}** _LSA

MALE FEMALE MALE FEMALE MALE FEMALE MALE FEMALE MALE FEMALE MALE FEMALE MEAN 127.1 119.2 1569.1 1493.7 118.2 117.3 15.3 16.4 41.8 42.9 55.7 60.8

SD 10.4 11.7 231.1 221.1 6.4 6.8 5.4 7.0 9.4 9.9 9.9 11.3

P <0.05* _<0.05* _{>0.05 >0.05 >0.05 <0.05}*

ASA SCA**

MSCA**

SCCA MSCCA MLSCA**

MALE FEMALE MALE FEMALE MALE FEMALE MALE FEMALE MALE FEMALE MALE FEMALE MEAN 60.6 57.3 42.4 40.8 60.5 57.8 97.2 95.5 116.4 115.2 70.9 73.7 SD 7.7 7.7 15.9 18.1 15.7 17.1 24.9 25.9 24.3 25.9 11.9 12.4 P <0.05* _{>0.05 >0.05 >0.05 >0.05 <0.05}*

SACRALINDEX**

CORPORO-BASALINDEX**

S1VERTEBRACORPUSINDEX

MALE FEMALE MALE FEMALE MALE FEMALE

MEAN 106.9 113.2 47.1 44.9 64.4 62.7

SD 11.1 12.3 4.0 4.6 5.6 5.6

P <0.05*

<0.05*

<0.05*

* _{Showsastatisticallysignificantdifferencebetweenthetwosexesintherelevantparameter.} **

sex,and ona populationfromVan province,locatedin eastern

Turkey,toprovidemorereliabledata,and torevealtheforensic

anthropologicalprofileofeasternTurkey.

Among parameters proposedtoevaluate sacral,

sacrococcy-geal,andlumbosacralcurve,MLSCAistheonlymeasurementthat

differssignificantlybetweentwosexesandisthemostsexually

dimorphicparameter (Table2).Thisresultalsoshows thatthe

lumbosacralcurveismorecurvedinfemalesthanthatinmales.

Although this is usually-accepted textbook knowledge about

sacral morphology [33], according to our results, it cannot be

confidentlysaidthatthesacrumismorecurvedinmalesthanthat

infemales,especiallywhenMSCAisconsidered(Table2).Evenso,

SCA, MSCA, MSCCA, and MLSCA parameters were selected by

Stepwise Discriminant Function Analyses for discriminant

functions;which indicatesthatthese parametersare usefulfor

sexestimation(Table4).

Thereisveryalimitednumberofstudiesaboutageestimation

and changes that occurby agingon sacrumand coccyxin the

adulthoodperiod.Thesestudiesfocusonmorphologicalchangesin

auricularsurfaceandfirstsacralvertebra[25,26].Also,inastudy

madebyFlander,itisstatedthatAPDandMTDmeasurementsare

themostage-correlatedmeasurementsofthesacrum; however,

thechangesthatoccurinthesetwoparametersdonotaffectthe

accuracy of sex estimation [21]. On the contrary, increases,

especially in APD,MTD, PERIMETER,AREA, andCBI parameters

byage,whichaffectsexualdimorphismnegatively,arediscovered

inourstudy.Ontheotherside,itisthoughtthatage-correlated

changes determined in the adulthood period on APD, MTD,

PERIMETER, AREA, SBA, SCA, MSCA, MLSCA, SI, and CBI are

importantandtheycouldbeusedforfutureageestimationstudies.

However,theseage-correlatedchangesneedtobeconfirmedwith

follow-upstudies.

Table3

LinearDiscriminantFunctionAnalysisresults. CLASSIFICATIONFUNCTIONCOEFFICIENTS

MALE FEMALE MALE FEMALE

CONSTANT 34812 34893 LSA 1 1 ASL 25 25 ASA 1 1 PSL 8 8 SCA 0 0 ASCL 4 5 MSCA 1 1 PSCL 4 4 SCCA 2 2 APD 552 553 MSCCA 2 2 MTD 516 517 MLSCA 2 2 PERIMETER 6 7 LSBA 5 5 AREA 0 0 SI 33 33 MBA 368 369 CBI 1027 1028 SBA 6 6 S1VCI 301 301

SUMMARYOFCLASSIFICATION(LEAVE-ONE-OUTCROSS-VALIDATEDRESULTS)

ESTIMATEDSEX ACCURACY

REALSEX MALE FEMALE

MALE 199 41 MALE 82.9%

FEMALE 43 197 FEMALE 82.1%

TOTAL 82.5%

LINEARDISCRIMINANTFUNCTIONANALYSISRESULTSOFSEPARATEAGEGROUPS

AGEGROUPS 21-30 31-40 51-60 61-70 71<

ACCURACY 95% 96.3% 77.5% 65% 61.3%

Table4

StepwiseDiscriminantFunctionAnalysisresults. CLASSIFICATIONFUNCTIONCOEFFICIENTS

MALE FEMALE MALE FEMALE

CONSTANT 239,21 215,82 LSA 0,62 0,66 ASL 0,59 0,65 SCA 0,21 0,15 PSL 0,90 0,77 MSCA 0,66 0,58 APD 3,05 2,7 MSCCA 0,26 0,25 PERIMETER 1,57 1,46 MLSCA 0,38 0,40 AREA 0,08 0,07

SUMMARYOFCLASSIFICATION(LEAVE-ONE-OUTCROSS-VALIDATEDRESULTS)

ESTIMATEDSEX ACCURACY

REALSEX MALE FEMALE

MALE 191 49 MALE 79.6%

FEMALE 53 187 FEMALE 77.9%

TOTAL 78.8%

STEPWISEDISCRIMINANTFUNCTIONANALYSISRESULTSOFSEPARATEAGEGROUPS

AGEGROUPS 21-30 31-40 41-50 51-60 61-70 71<

Intheunivariateanalysesofthesacrumandcoccyx,whichhave

beenconductedbyotherauthors,themostdimorphicparameters

havebeen foundto bethe onesthat belong tothe _firstsacral

vertebracorpus[11,20–24].Accordingtoourstudy,inparallelwith

literature,APD,AREA,andPERIMETERthatbelongtothefirstsacral

vertebrawerefoundtobethemostdimorphicparameterswhen

the results of both observers were considered. Furthermore,

althoughPSLandPSCLwerealsosaidtobedimorphicparameters,

theywerenotstudiedwidely[24,34].Accordingtotheunivariate

discriminant analysis conducted, these parameters achieve an

accuracyof65.8%and64.6%respectively,andtheyarethethirdand

fourthmostdimorphicparametersamongallmeasurementsdone.

Thus,itcanbesaidthatthesetwomeasurementsarepromising

sexestimationparameters, and theyshould betested onother

populations.

In studies that linear and stepwise discriminant function

analysis was performed on sacral and coccygeal

measure-ments, accuracy percentage ranges between 59.4% and 95%

[5,11,20–24,29,30]. The results of this study are compatible

withthatofZechetal.[5],Flander[21]andthatofTorimitsu

etal.[24].Itisstatedthattheancestraldifferencesgiveriseto

awiderangeofresults[5].

Another possible factor affecting different accuracy rates of

differentpopulationscouldbeage.InthestudyofSteynetal.[11],

theagesofsomecasesarereportedtobeunknown,mostofthe

casesareolderindividuals,andtheaverageageisover70.When

weappliedlineardiscriminantfunctionanalysisto61–70and70

and overagegroups inourpopulationseparately, theaccuracy

rates decrease to 65% and 61% respectively (Table 3). These

decreasesarethoughttobeduetotheresultofosteoporoticand

degenerativechanges, andit mightbethereasonforthelower

accuracyrate (59.4%)foundbySteynetal.[10]. Aboutthe

age-related changes,anotherexampleis thestudymadebyHegazy

[18]; which includes 50 males with a mean age of 35 (range

between29and41)and50femaleswithanaverageof32(range

between26and38).Thesexestimationaccuracyrateshavebeen

foundas97.5%forfemales,92.5%formalesand95%fortotal.These

resultswerealsoconfirmedbyourstudyachievingsexestimation

accuracies95%forthe21–30agegroupand96.3%forthe31–40age

group(Table3).Thus,itisthoughtthattheagecorrelatedchanges

insacrumaffectstheresultsevidently,andtheymightcausethese

extremeresults.

It hasbeen thoughtthat thesize ofthepopulation could

also lead to different results. Although the sizes of the

populations in the previous studies change in between 64

Table5

MultilayerPerceptronNeuralNetworkparameterestimatesaccordingtoresults. PREDICTOR

INPUTLAYER HIDDENLAYER OUTPUTLAYER

H(1:1) H(1:2) H(1:3) H(1:4) H(1:5) H(1:6) H(1:7) H(1:8) H(1:9) Male Female Bias 0,331 0,081 0,005 0,283 0,198 0,375 0,371 0,038 0,130 ASL 0,343 0264 0,022 0,354 0,435 0,312 0,215 0,114 0,276 ASCL 0,497 0,156 0,126 0,344 0,351 0,490 0,061 0,210 0,119 PSL 0,513 0,521 0,213 0,072 0,238 0,443 0,193 0,425 0,424 PSCL 0,144 0,305 0,126 0,219 0,176 0,221 0,028 0,419 0,562 SCA 0,029 0,317 0,434 0,089 0,048 0,194 0,183 0,486 0,104 MSCA 0,356 0,372 0,609 0,028 0,532 0,622 0,516 0,302 0,403 SCCA 0,329 0,434 0,064 0,024 0,410 0,273 0,462 0,583 0,464 MSCCA 0,606 0,408 0,370 0,236 0,458 0,072 0,105 0,568 0,067 LSBA 0,418 0,352 0,093 0,393 0175 0,396 0,499 0,054 0,707 SBA 0,385 0,266 0,455 0,202 0,434 0,153 0,026 0,129 0,175 MLSCA 0,248 0,280 0,186 0,551 0,088 0,456 0,222 0,304 0,525 LSA 0,063 0,348 0,369 0,037 0,046 0,251 0,437 0,130 0,336 ASA 0,280 0,227 0,264 0,199 0,220 0,563 0,301 0,268 0,136 APD 0,547 0,114 0,123 0,767 0,091 0,019 0,332 0,214 0,659 MTD 0,567 0,414 0,403 0,032 0,414 0,571 0,245 0,143 0,127 MBA 0,325 0,110 0,141 0,318 0,105 0,869 0,699 0,390 0,919 AREA 0,393 0,207 0308 0,100 0,343 0,412 0,365 0,470 0,235 PERIMETER 0,282 0,426 0,059 0,213 0,314 0,350 0,170 0,334 0,367 SI 0,460 0,176 0,380 0308 0,250 0,386 0,091 0,029 0,662 CBI 0,065 0,033 1,026 0,441 0,885 0,308 0,273 0,139 0,623 S1VCI 0,068 0,702 0,903 0,269 0,244 0,292 0,526 0,373 0,340 HIDDENLAYER Bias 0,180 0,100 H(1:1) 0,534 0,051 H(1:2) 0,075 0,042 H(1:3) 0,328 0,969 H(1:4) 0,548 0,604 H(1:5) 0,299 0,291 H(1:6) 0,598 0,665 H(1:7) 0,106 0,560 H(1:8) 0,339 0,500 H(1:9) 0,833 0,930 Table6

MultilayerPerceptronNeuralNetworksexdeterminationresults. SUMMARYOFCLASSIFICATION

REALSEX ESTIMATEDSEX ACCURACY MALE FEMALE

TRAININGSAMPLE MALE 156 23 87.2% FEMALE 23 139 85.8% TOTAL 86.5% TESTINGSAMPLE MALE 51 10 83.6% FEMALE 10 68 87.2% TOTAL 85.6%

and230[5,11,20–24,29,30],thisstudy,with480cases,isthe

largest-scalesex estimation research on sacrum and coccyx

accordingtoourliteraturereview.Itisthoughtthatitcouldbe

possible to achieve more reliable and less extreme results

usinglargerpopulations.

Theartificialneuralnetworksisapromisingclassification

methodforForensicAnthropologyasitusuallyreacheshigher

accuraciesthanClassicMultivariatemethods[7–9].Itcanbe

seenfromthisstudythatitachievessexestimationaccuracies

upto863%(86.5%forthetrainingsample,85.6%forthetesting

sample and 863% for the total population) which are also

higher than Multivariate Discriminant Analyses. As future

studies, it could be possible to obtain a greater number of

measurementsonagreaternumberofcasesinashortperiodof

timetomakemeasurementsmoreobjectiveandachievemore

accuratesexestimationresultsbyaddingNeuralNetworksto

Image Processing and Recognition methods to the research

process.

5.Conclusion

Inourstudy,thesacrumshowsmoderatesexualdimorphism

withthemaximumpercentageof863%sexestimationaccuracy.

Age,ancestry,andthenumberofcasesarethoughttoaffectthe

resultssignificantly,andtheyshouldbetakenintoconsideration

whileselecting thecasesandcreating a studypopulation. The

results also indicate that age estimation studies could be

performedonthesacrumandcoccyx.Sexestimationwithneural

networksisapromisingfieldofresearch,andfurtherstudieswith

other bones and with new techniques might give useful

information.

CRediTauthorshipcontributionstatement

YasinEtli:Conceptualization,Methodology,Software,

Valida-tion, Formal analysis, Investigation, Resources, Data curation,

Writing-originaldraft,Writing-review&editing,Visualization.

MahmutAsirdizer:Conceptualization,Methodology,Resources,

Datacuration,Visualization,Projectadministration.Yavuz

Heki-moglu: Investigation, Visualization. Siddik Keskin: Validation,

Formal analysis, Visualization. Alpaslan Yavuz: Investigation,

Resources,Visualization.

Acknowledgements

This study was approved by the Non-Interventional Clinical

ResearchEthicsCommitteeofYuzuncu YilUniversityFacultyof

Medicine,withthe20.06.2017date,07DecisionNumber.

AppendixA.Supplementarydata

Supplementarymaterialrelatedtothisarticlecanbefound,inthe

onlineversion,atdoi:https://doi.org/10.1016/j.forsciint.2019.109955.

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