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Morphometricity:MeasuringtheNeuroanatomicalSignatureofaTrait

MertR.Sabuncua,b,TianGea,c,d,AvramJ.Holmesa,e,f,JordanW.Smollerc,d,RandyL.Bucknera,g,and

BruceFischla,b;fortheAlzheimer’sDiseaseNeuroimagingInitiative(ADNI)*

aAthinoulaA.MartinosCenterforBiomedicalImaging,DepartmentofRadiology,Massachusetts

GeneralHospital,Charlestown,MA02129,USA;bComputerScienceandArtificialIntelligence

Laboratory,MassachusettsInstituteofTechnology,Cambridge,MA02138,USA;cPsychiatricand

NeurodevelopmentalGeneticsUnit,CenterforHumanGeneticResearch,MassachusettsGeneral

Hospital,Boston,MA02114,USA;dStanleyCenterforPsychiatricResearch,BroadInstituteofMIT

andHarvard,Cambridge,MA02138,USA;eDepartmentofPsychology,YaleUniversity,NewHaven,

CT,06520,USA;fDepartmentofPsychiatry,MassachusettsGeneralHospital,HarvardMedicalSchool,

Boston,MA02114,USA;gDepartmentofPsychologyandCenterforBrainScience,HarvardUniversity,

Cambridge,MA02128,USA.

*DatausedinpreparationofthisarticlewereobtainedfromtheAlzheimer’sDiseaseNeuroimaging

Initiative(ADNI)database(adni.loni.usc.edu).Assuch,theinvestigatorswithintheADNIcontributed

tothedesignandimplementationofADNIand/orprovideddatabutdidnotparticipateinanalysisor

writingofthisreport.AcompletelistingofADNIinvestigatorscanbefoundat:

http://adni.loni.usc.edu/wp-content/uploads/how_to_apply/ADNI_Acknowledgement_List.pdf

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Abstract

Complexphysiologicalandbehavioraltraits,includingneurologicalandpsychiatricdisorders,often

associatewithdistributedanatomicalvariation.Thispaperintroducesaglobalmetric,called

morphometricity,asameasureoftheanatomicalsignatureofdifferenttraits.Morphometricityis

definedastheproportionofphenotypicvariationthatcanbeexplainedbymacroscopicbrain

morphology.Weestimatemorphometricityviaalinearmixedeffectsmodelthatutilizesan

anatomicalsimilaritymatrixcomputedbasedonmeasurementsderivedfromstructuralbrain

MagneticResonanceImaging(MRI)scans.Weexaminedover3,800uniqueMRIscansfrom9large-

scalestudiestoestimatethemorphometricityofarangeofphenotypes,includingclinicaldiagnoses

suchasAlzheimer’sdisease;andnonclinicaltraitssuchasmeasuresofcognition.Ourresults

demonstratethatmorphometricitycanprovidenovelinsightsabouttheneuroanatomicalcorrelates

ofadiversesetoftraits,revealingassociationsthatmightnotbedetectablethroughtraditional

statisticaltechniques.

Significance

Neuroimaginghaslargelyfocusedontwogoals:mappingassociationsbetweenneuroanatomical

featuresandphenotypes,andbuildingindividual-levelpredictionmodels.Thispaperpresentsa

complementaryanalyticstrategycalledmorphometricitythataimstomeasuretheneuroanatomical

signaturesofdifferentphenotypes.Inspiredbypriorworkonheritability,wedefinemorphometricity

astheproportionofphenotypicvariationthatcanbeexplainedbybrainmorphology,e.g.,as

capturedbystructuralbrainMagneticResonanceImaging(MRI).Inthedawningeraoflarge-scale

datasetscomprisingtraitsacrossabroadphenotypicspectrum,morphometricitywillbecriticalin

prioritizingandcharacterizingbehavioral,cognitive,andclinicalphenotypesbasedontheir

neuroanatomicalsignatures.Furthermore,theproposedframeworkwillbesignificantindissecting

thefunctional,morphological,andmolecularunderpinningsofdifferenttraits.

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Introduction

Thestructural,functional,andmolecularpropertiesofthebrainsupportnumeroustraitsspanning

thebehavioral,cognitiveandclinicalspectra.Neuroanatomicalfeaturesareinturninfluencedby

factorssuchasage,sex,training,andgenetics[1-4].Neuroimagingallowsustocharacterizethese

bidirectionalassociationsbyrevealingvariationinbrainstructureandfunctionacrossindividuals.

Conventionalmethodsthatweusetoprobetheseassociationsaimtoanatomicallymapeffects,build

predictionmodels,ortesthypotheses.Yet,wedonothaveastandardtechniquetomeasureand

comparetheoftenspatiallydistributedandcomplexpatternsofneuroanatomicalcorrelatesof

differentphenotypes.Herewepresentanovelmetriccalledmorphometricitythatoffersthis

capability.

Todate,structuralneuroimagingstudieshaveprimarilyreliedonthreeclassesofanalyticapproaches.

Thefirststrategyishypothesis-drivenandutilizesaregressionmodeltoexamineassociations

betweenbehavioraltraitsorclinicalconditionsandasmallnumberofaprioriimage-derived

measurements,suchasthoserestrictedtoananatomicalregionofinterest(ROI)[5].TheROI-based

approachprovidesusefulinsightsabouttheunderlyingbiologyandcanbeefficientinlimitedsample

sizescenarios,butisrestrictedtothetestedhypothesis.Thesecondapproachisexploratoryandaims

tocomputemapsofassociationsbyconductingbrain-widetests[6],asexemplifiedinvoxel-based

morphometry(VBM)[7],orvertex-wisecorticalthicknessanalysis[seee.g.,8].Suchmassive

univariateanalysescanofferacomprehensivepictureoftheunderlyinganatomicalassociations,yet

theycanalsobeinefficientinrevealingsubtle,multivariatepatternsofassociation,becauseeach

anatomicallocationistypicallyexaminedinisolationandtheburdenofmultipletestingcorrection

canconstrainstatisticalpower.ThethirdclassincludesmultivariatetechniquessuchasCanonical

CorrelationAnalysis(CCA)[9],PartialLeastSquares(PLS)[10],Bayesianinferencealgorithms[11],or

othermachinelearningmethods[12,13].Thesestudiesarefocusedoneitherdiscoveringthe

multivariatepatternsofassociationordemonstratingindividual-levelpredictioncapabilities,butthe

biologicalinterpretationoftrainedmultivariatemodelscanbechallenging[14].Furthermore,these

methodsoftensufferfromhighcomputationaldemand,andcanbesensitivetoimplementation

details,suchasthechoiceoflearningrule,optimizationalgorithm,andlocaloptimaintraining.

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Wepresentmorphometricityanalysisasanovelapproachtoexaminetheglobalstatistical

associationbetweenbrainmorphologyandobservabletraits.Inspiredbypriorworkontrait

heritabilityinpopulationandstatisticalgenetics[15,16],wedefinemorphometricityasthe

proportionofphenotypicvariationthatcanbeexplainedbybrainmorphology,e.g.,ascapturedby

measurementsderivedfromstructuralbrainMagneticResonanceImaging(MRI)scans.UnlikeROI-

basedormassiveunivariateassociationtests,morphometricityanalysisisnotconcernedwithspecific

anatomicalstructuresorthepreciseanatomiclocalizationofeffects.Incontrasttotheapplicationof

machinelearningtopopulationdata,theprimaryaimofmorphometricityanalysisisnottomaximize

individual-levelpredictionaccuracy,butexamineandquantifystatisticalassociations.Theproposed

strategythusaffordsauniqueperspectiveonthebiologicalunderpinningsofdifferentphenotypes,

andallowsustocompareandcontrastimagingmodalities,typesofanatomicalmeasurements,and

processingstreams.

Morphometricityisgroundedinlinearmixedeffects(LME)modeling,aclassicalstatisticalframework

thatwasrecentlyemployedinpopulationgeneticstoquantifytheheritabilityofatraitusinggenome-

widegeneticvariants[17-19].Themodelrelatesthevariationinbrainmorphologycomputedfrom

brain-wide,MRI-derivedmeasurementstothevariationinobservabletraits,andcanbefittedusing

well-established,robustcomputationaltools.Inourimplementation,weuseFreeSurfer[20],afreely

available,widelyused,andextensivelyvalidatedbrainMRIanalysissoftwarepackage,to

automaticallyprocessstructuralMRIscansandobtainavectorofvolumetricmeasurementsacross

subcorticalstructuresandcorticalthicknessmeasurementsacrosstheentirecorticalmantle,which

constituteacomprehensivedescriptionofthestructuralneuroanatomy.

Weappliedthemorphometricityanalysistoover3,800uniquebrainMRIscansfrom9large-scale

studiesandcomputedthemorphometricityofclinicalconditionsincludingAlzheimer’sdisease,

attention-deficithyperactivitydisorder(ADHD),schizophrenia,autismspectrumdisorder,and

Parkinson’sdisease;andnonclinicaltraitsincludingsex,age,intelligence,educationlevel,andan

arrayofcognitivemeasures.Ourresultsdemonstratethatmorphometricityanalysispromisestooffer

auniqueperspectiveontherelationshipbetweenbrainanatomy,andbehavioral,cognitiveand

physiologicaltraits.

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Results

OverviewoftheModel.Theproposedmorphometricityanalysisisbasedonthefollowinglinear

mixedeffects(LME)model:

𝒚 = 𝑿𝜷 + 𝒂 + 𝝐, (1)

where𝒚isan𝑁-dimensionalcolumnvectorofaquantitativephenotypewith𝑁beingthesamplesize

(i.e.,numberofsubjects),𝑿isthe(design)matrixofconfoundingvariables(sometimescalled

covariatesornuisancevariables)suchasageandsex,𝜷isthe(fixedeffect)coefficientvector,𝒂 ∼

N(𝟎, 𝜎/0𝑲/)isan𝑁-dimensionalrandomeffectvectordrawnfromazero-meanmultivariateGaussian

distributionwithacovariancematrixthatisequaltothescaledanatomicsimilaritymatrix(ASM)𝑲/,

andtheelementsofthenoisevector𝝐areassumedtobedrawnfromindependentandzero-mean

Gaussiandistributionswithhomogeneousvariance𝜎30.TheASMencodesglobalmorphological

resemblancebetweenpairsofindividualsinthesample,andinprinciplecanbeanynon-negative

definitematrixwithitsdiagonalelementsconstrainedtobeequalto1onaverage,and𝜎/0canthus

beinterpretedasthetotalvariancecapturedbytheASM.Inthispaper,weconsideredtwotypesof

intuitiveandwidelyusedmetricsthatquantifythesimilarityofvolumetricandcorticalthickness

measurementsextractedfromstructuralbrainMRIscansbetweenpairsofindividuals:(1)alinear

similaritymetric(i.e.,innerproductbetweennormalizedimagingmeasurements);and(2)anonlinear

Gaussian-typesimilaritymetric(seeMethods).Usingamodelselectionapproach,wefoundthatthe

Gaussiansimilaritymetricprovidedconsistentlybetterdescriptionofthedataacrossthetraitswe

studied(seeMethodsandSupplementaryTableS1).Therefore,allreportedmorphometricity

estimateswerebasedontheGaussianmetric.

Formally,wedefinemorphometricitybasedontheLMEmodelofEquation(1)as:

𝑚0 ≐𝜎/0

𝜎/0 + 𝜎30=𝜎/0

𝜎60,(2)

where𝜎60isthephenotypicvariance.Morphometricityisthustheproportionofphenotypicvariation

thatcanbeexplainedbybrainmorphology,thevariationofwhichiscapturedbytheASM.Estimates

ofmorphometricitycanbecomputedbypluggingtherestrictedmaximumlikelihood(ReML)

estimates[21,22]ofthevariancecomponents,𝜎/0and𝜎30,intoEquation(2).

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Weextendthisdefinitiontothecase-controldesign,i.e.,binarydiseasetraits(affectedvs.

unaffected),usingtheclassicalliability-thresholdmodel,whichiswidelyemployedinpopulationand

statisticalgeneticstudies[23,24].Themodelassumesthattheunderlyingdiseaseliability(whichisa

quantitativevariable)followsaGaussiandistributionandindividualsarecases(affected)iftheir

liabilityexceedsathreshold.Themorphometricityestimate𝑚0foradiseasetraitontheobserved

scale,obtainedbyfittingthemodelofEquation(1)tothebinaryphenotypedata,canbeeasily

transformedtotheliabilityscale[24,25]:

𝑚90 = 𝑚0 𝐾(1 − 𝐾)

𝜑(𝑡)0𝐾(1 − 𝐾)𝑃(1 − 𝑃) ,(3)

where𝑚90isthemorphometricityontheliabilityscale,𝐾istheprevalenceofthediseaseinthe

generalpopulation(i.e.,theproportionofthepopulationhavingthedisease),𝑃istheprevalenceof

thediseaseinthestudysample,𝑡 = ΦBC(1 − 𝐾)istheliabilitythreshold,ΦisthestandardGaussian

cumulativedistributionfunction,and𝜑isthestandardGaussiandensityfunction.Inrealdisease

studies,casesareoftenconsiderablyoversampledrelativetotheirpopulationprevalence(knownas

non-randomascertainment),inwhichcase𝑃islargerthan𝐾.Transformingmorphometricity

estimatesfromtheobservedscaletotheliabilityscalemakesthemindependentofpopulationand

sampleprevalence,andthuscomparableacrossdifferentdiseases.

OverviewoftheData.WeanalyzedbrainMRIscansandtraitdatafromover3,800uniqueindividuals

spanning9large-scalestudies:theHarvard/MassachusettsGeneralHospitalBrainGenomic

SuperstructProject(GSP)[26],theHumanConnectomeProject(HCP)[27],theAlzheimer’sDisease

NeuroimagingInitiative(ADNI)[28],theAttention-DeficitHyperactivityDisorder(ADHD200)sample

[29],theOpenAccessSeriesofImagingStudies(OASIS)cross-sectionalsample[30],theCenterfor

BiomedicalResearchExcellence(COBRE)schizophreniasample[31],theMINDClinicalImaging

Consortium(MCIC)schizophreniasample[32],theAutismBrainImagingDataExchange(ABIDE)[33],

andtheParkinsonProgressionMarkerInitiative(PPMI)[34].SeetheMethodssectionforfurther

detailsonthedatasets.Thetraitsofinterestweregroupedintothreecategories:clinicaldiagnoses,

generalnonclinicaltraitsandmeasuresofcognition.

MorphometricityofClinicalDiagnoses.TheclinicaltraitsweexaminedincludedAlzheimer’sdisease,

attention-deficithyperactivitydisorder(ADHD),schizophrenia,autismspectrumdisorder,and

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Parkinson’sdisease.Table1liststhecharacteristicsofthecorrespondingsamples,alongwith

morphometricityestimates(ontheliabilityscale)andassumedpopulationprevalencevalues[35-41].

Figure1showstheestimatedmorphometricityvaluesontheliabilityscale.Ouranalysesrevealed

thatAlzheimer’sdiseaseissubstantiallymorphometric(witha95%confidenceintervalof[0.94-1.00]),

suggestingthatthisclinicalconditionisassociatedwithasubstantialanatomicalsignature.Onthe

otherhand,ADHD,schizophreniaandautismshowedmoderatemorphometricityvalues,allgreater

than0.35.Finally,wefoundthatParkinson’sdiseasewasmodestlymorphometric,withanestimated

liability-scalevalueof0.20.Allexaminedclinicalconditionswerestatisticallysignificantlyassociated

withwhole-brainmacroscopicmorphology,i.e.,theestimatedmorphometricityvalueswere

significantlylargerthanzero(allp-values<0.005).SupplementaryTableS2listspointestimatesof

morphometricityandtheirstandarderrorscomputedviajackkniferesampling[42].Theseresultsare

instrongagreementwiththeparametricestimatesinTable1.

Wehadaccesstotwoindependentsamplesthatallowedustoreplicateourmorphometricity

estimatesofAlzheimer’sdisease(OASIS)andschizophrenia(COBRE).Weobservedthattherewas

strongagreementbetweentheestimatesfromindependentsamples(Figure1).SupplementaryTable

S3providesfurtherdataaboutthesereplicationanalyses.

MorphometricityofGeneral,NonclinicalTraits.Thenonclinicaltraitsweexaminedwereage,general

intelligence(IQ),sex,andeducationlevel.Table2liststhecharacteristicsofthesamplesusedinthe

primaryanalyses,alongwiththeestimatesofmorphometricity.Theseresultsrevealedthatallthe

examinedgeneraltraitsaresignificantlyandsubstantiallymorphometric(Figure2);all

morphometricitypointestimatesweregreaterthan0.8,andallp-values<1e-8.SupplementaryTable

S2listsmorphometricityestimatesandtheirstandarderrorscomputedviajackkniferesampling.

TheseresultsandtheparametricestimatesinTable1arevirtuallyidentical.

Wehadaccesstoindependentreplicationsamplesforallthegeneralnonclinicaltraitsweexamined.

ItcanbeseeninFigure2thatthereplicationanalysesrevealedremarkablyconsistent

morphometricityestimates.SupplementaryTableS4providesfurtherdataaboutthesereplication

analyses.

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ContrastingwithROI-basedAssociationAnalyses.Themostcommonanalyticstrategyintoday’s

neuroimagingstudiesinvolvesexaminingassociationsbetweentraitsandmeasurementsfrom

regionsofinterest(ROIs).Ourgoalinthisanalysiswastocontrasttheproposedwhole-brain

morphometricityanalysiswithsuchROI-basedtechniques.Werestrictedouranalysistothesix

phenotypes(age,IQ,sex,education,Alzheimer’sdisease,andschizophrenia),forwhichwehadtwo

independentdatasets.Wethenusedoneofthesamples(thereplicationsampleintheanalyses

above)forthediscoveryofthemostsignificantlyassociatedROIwiththetrait,andtheothersample

(theprimarysampleintheanalysesabove)toquantifythestrengthandmagnitudeofassociation.

SupplementaryTableS5liststhestructuresthatexhibitedthestrongestassociationwiththetraitsin

thediscoveryanalysis.

Figure3visualizesthemagnitudeofassociationbetweentheROI-basedmeasurementsand

phenotypicvariation,assessedusingthesameLMEmodelingframeworkofwhole-brain

morphometricity.Here,wereplacedtheglobalASMwithonecomputedbasedonROImeasurements

(seeMethodsforfurtherdetails).ItcanbeseenthattheproportionofvarianceexplainedbyROI-

basedmeasurementswasconsistentlylowerthanwhole-brainmorphometricityestimates(with

generalintelligenceexhibitingthesmallestdiscrepancy).Mostnotably,foreducationand

schizophrenia,ROI-basedassociationsweremuchweaker(bothinmagnitudeandstatistical

significance)thanwhole-brainassociations(Figure3andSupplementaryTableS5).Infact,education

andschizophreniadidnotexhibitastatisticallysignificantcorrelationwithindividualROI-based

measurements,whilewhole-brainmorphometricityanalysesrevealedsignificantassociations.

MorphometricityAnalysisofCognitiveMeasures.WeusedthemostrecentreleaseoftheHuman

ConnectomeProject(HCP)data(downloadedonDecember15,2015)tocomputemorphometricity

estimatesforanarrayofcognitivemeasures.Ourprimaryanalysisreliedon190non-twinsubjectsof

non-HispanicEuropeanancestry(28.9+/-3.8years,47.3%female),drawnfromseparatefamilies(i.e.,

therewerenosiblingsinthissample).Figure4showsthemorphometricityestimatescomputedfor

variablesthatmeasuresustainedattention,non-verbalandverbalepisodicmemory,working

memory,executivefunction,delaydiscounting,language(vocabularycomprehensionandreading

decoding),spatialorientation,processingspeed,fluidintelligence,andself-regulation(impulsivity).

Weconductedasecondary(replication)analysison208non-Hispanicwhitetwins(29.4+/-3.2years,

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61.4%female),withonetwindrawnfromeachfamily,andthustherewerenosiblingsinthis

replicationsample.Figure4showstheresultsobtainedfromthissecondaryanalysisaswell.

Ourresultsdemonstratedthatallexaminedvariables,exceptforthemeasureofself-regulation,are

statisticallysignificantlymorphometric.Wenotefurtherthattherewasanimportantamountof

variabilityinthedegreeofmorphometricityacrosscognitivemeasures.Thisvariationwasremarkably

consistentbetweentheprimaryandsecondaryanalyses.Measuresofattention,cognitiveflexibility,

workingmemory,verbalepisodicmemory,andinhibitionweresubstantiallymorphometric(with

estimatesgreaterthan0.80inbothprimaryandsecondaryanalyses).Measuresoflanguage,non-

verbalepisodicmemory,spatialorientation,processingspeed,andfluidintelligenceweremoderately

morphometric(withpointestimatesgreaterthan0.50).

Discussion

Morphometricity:ANovelMetrictoQuantifyWhole-brainAssociationswithaTrait.Inthispaper,

weintroducedanoveltechniqueforanalyzingtheneuroanatomicalunderpinningsofvariousclinical,

physiological,andbehavioraltraitsusinglarge-scaleneuroimagingdata.Incontrastwithassociation

testingtechniqueswidelyusedintoday’sneuroimagingstudies,ourapproachdoesnotfocusona

prioriROIsorconductindependent(massiveunivariate)interrogationsateachcandidateregionor

voxel.Instead,morphometricityisaglobalquantificationofthewhole-brainanatomicalsignatureof

atrait.

Whiletheproposedapproachisintimatelyrelatedtoimage-basedmultivariateprediction

performance,therearetwocharacteristicsofmorphometricitythatmakeitdifferentfromthe

applicationofmachinelearning.Firstly,themetricdoesnotrequirecross-validation,whichisoften

thetechniqueutilizedinmachinelearningtogaugepredictionaccuracy.Cross-validationisusually

computationallydemanding,andreliesontheunbiasedsettingofmodelparameters(whichmightbe

achievedviaanestedcrossvalidationstrategy),andrepeatedandbalancedpartitioningofdatainto

trainandtestsets.Incontrast,theproposedLME-basedapproachexploitstheentiredatasettofit

themodelandestimatetheunknownvariancecomponentparameters,andinturnmorphometricity,

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inanunbiasedfashion.Secondly,morphometricityisaclassicalstatisticalmeasureofexplained

varianceandisthereforefamiliartointerpret.

Morphometricityhasmanyparallelstoheritabilityingenetics[15,16].Bothconcepts,statisticalin

nature,areaboutphenotypicvariationandtheproportionofvarianceexplained.Thus,the

interpretationhastobecarriedoutwithinaprobabilisticframework,islimitedbythestudied

population,dependsonthetechniqueusedtoquantifythetrait,andcanbeconfoundedby

unmeasuredvariablesactingthroughunknownmechanisms.Thebiasesduetoconfoundssuchas

(cryptic)relatednessbetweensubjectsorpopulationadmixturearewell-studiedinheritability

analysis.Asweelaboratebelow,morphometricityalonecannotbeusedtoinfercausalrelationships,

buthastobefollowedupwithfurtherstudiesthatwillhomeinonpotentialmechanisms.Thecore

differencebetweenmorphometricityandheritabilityisthedirectionofassociation.Inheritability,

thisdirectionisknownandfixed,becausethereisnoknownbiologicalmechanismthatwouldallow

thephenotypetoalterthegenotype.Inmorphometricity,however,thedirectionalitycangoeither

wayandhastobedissectedwithfurtherbiologicalstudies.

TraitsCanBeMorphometrictoDifferentDegrees.Virtuallyalltraitsweexaminedinthisstudywere

significantlymorphometric.However,ouranalysesalsorevealedinterestingvariationinthewhole-

brainanatomicalsignatureofdifferenttraits.Certainphenotypes,suchasAlzheimer’sdisease,age,

and(maybesurprisingly)generalintelligence(IQ)weresubstantiallymorphometric(withestimates

exceeding0.90),whileothermeasures,suchasnon-verbalepisodicmemory,spatialorientation,

processingspeed,andfluidintelligenceexhibitedmoderatemorphometricity.Furthermore,the

psychiatricdisordersweexamined(schizophrenia,ADHDandautism)wereallmoderately

morphometric,unequivocallypointingtoaneuroanatomicalsubstratefortheseclinicalconditions.

Theproposedmorphometricityanalysisisthefirstcoherentframeworkthatenablesustodirectly

quantifyandcomparethemorphologicalsignaturesofsuchdiversesetsoftraits.

Thetraitswepresentedinthisstudyhavebeenexaminedextensivelyinpriorstructural

neuroimagingstudiestorevealmorphologicalcorrelates.Whilemanyofthesestudiesreliedon

regionalorvoxel-levelassociationteststhatareconductedateachlocationindependently,thereis

growingevidencethatmultiplebrainregionsareimplicatedincomplex,multivariaterelationships

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withmanycommonphenotypes.Forexample,patternsofatrophyinneurodegenerativeconditions

suchasAlzheimer’sdiseasehavebeenshowntospreadthroughlarge-scale,distributedbrain

networksthatcanbecircumscribedbasedonresting-stateactivity[43].Furthermore,developmental

mechanismssuchasneuronalmigration,synapseformation,myelination,andsynapticpruningfollow

predictableandrobustspatiotemporalpatterns,whicharelikelyassociatedwithbehavioraltraits

suchasintelligenceanddisruptedinpsychiatricdisorderssuchasschizophrenia[44,45].Ourdata

fromROI-basedanalysessupportthepremiseofanalyzingbrain-widepatterns,ratherthanisolated

regions,forassociationsbetweenneuroanatomicalfeaturesandbehavioralorclinicalphenotypes.

MorphometricityEstimatesAreConsistentAcrossIndependentSamples.Formostofthetraitswe

examinedinthisstudy,wereplicatedouranalysesonindependentdata.Allpointestimatesfell

within95%confidenceintervalsoftheestimatescomputedonthecorrespondingindependentdata.

Theseresultssuggestedthatthepresentedmorphometricityestimatesareconsistentacrossdifferent

samples.Wepresenttheseresultswithacautionarynotehowever.Asweemphasizedabove,

morphometricityisastatisticalmetricthatdependsonthestudiedpopulationandthemeasurement

ofthetrait.Thus,variationsinthepatientcompositionforexampleorchangesindiagnosticcriteria

willinevitablyleadtodifferentestimatesofmorphometricity.Inourreplicationanalyses,these

factorsseemedtoplayonlyaminorrole.

Whole-brainMorphometricityAnalysesCanBeMorePowerfulthanROI-basedAnalyses.We

presentmorphometricityanalysisasanalternativetotheclassicalregion-basedinterrogation

conductedinneuroimaging,whichisoftenfocusedondiscoveringorcharacterizingbiomarkersand

mappingbiologicaleffects.Thecentralchallengeinregion-basedapproachesisthatweneedto

eitherconfineouranalysestoaprioriROIs,orexhauststatisticalpowerbyprobingalargenumberof

candidateregions.Inourexperiments,weconductedadirectcomparisonbetweenwhole-brain

morphometricityanalysisandanROI-basedapproach.Toidentifytrait-specificROIs,adiscovery

analysiswasrunonindependentsamplesofeachtrait.TheassociationsbetweentheidentifiedROIs

andtraitswerethentestedinnon-overlappingsamples.IdentifyingthemostassociatedROIand

estimatingthemagnitudeofassociationinindependentsamplesavoidedtheissueofcircularanalysis

[46,47],andproducedunbiasedmorphometricityestimatesforindividualROIs.Ourresults

demonstratedthatwhole-brainmorphologyconsistentlyexplainedmoreofthephenotypicvariation

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thansingleROIs.Furthermore,morphometricityanalysiscouldrevealassociationsthatwerenot

detectablewhenfocusedonisolatedregions.Forexample,educationandschizophreniawerefound

tobenotsignificantlyassociatedwithvolumetric/thicknessmeasurementsofanyoftheindividual

ROIs;yet,bothtraitsweremoderatelyandsignificantlymorphometricinwhole-brainanalyses,which

indicatesthattheymayhavespatiallydistributedneuroanatomicalsignaturesthatcannotbe

capturedbyindividualROIs.Inaddition,whole-brainmorphometricityanalysisoffersthecapabilityof

capturinginteractionsbetweenbrainregionsandthuscanbemorepowerfulthananalyzingeachROI

independently.

PotentialLimitationsandDrawbacksofMorphometricity.Morphometricityisastatisticalmetricand

assumesaparticular,linearmodeloftherelationshipbetweenvariables.Onecriticalcomponentof

themodelistheAnatomicalSimilarityMatrix(ASM),whichcapturesthecovariancestructureofthe

randomeffectthataccountsforthemorphologicalvariationinthesample.Inthiswork,we

consideredalinearmetricandanonlinearGaussian-typemetrictoquantifythesimilarityof

volumetric/thicknessmeasurementsbetweenpairsofsubjects,andemployedamodelselection

techniquetofindthemetricthatbetterdescribesthedata.OuranalysessuggestthattheGaussian

metricisconsistentlybetterthanthelinearmetricacrossthetraitswestudied,andcapturesa

significantportionofrelevantinter-subjectvariationunderdifferentconditions.However,wehave

notattemptedtoexhaustivelyexploreothertypesofsimilaritymetrics,whichmayemphasize

differentaspectsofthedataandproducedifferentresults.Alternatively,theASMcanbebuiltusinga

bottom-upapproachandexpressedasacombinationofelementarymatrices,andtheparametersof

thiscombinationcanbetreatedasunknownvariables.Byincreasingtheunknownsinthemodel,

however,thisapproachwilllikelyreducestatisticalpower.

AnotherimportantpointtoconsideristhatASMshouldreflectbrain-wideglobalmorphologyand

cannotbeoptimizedforaspecifictrait.Thislatterobservationiscriticaltobeabletoobjectively

comparemorphometricityestimatesacrossdifferenttraits.OurglobaldefinitionofASMand

morphometricity,however,constrainstheinterpretationoftheresults.Certaintraitswithvery

dramaticyetfocaleffects,mightnotyieldlargemorphometricityestimates,sincetheproposed

modelisinsensitivetolocalizedeffects.

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Finally,asinanyassociationtestingframework,theinterpretationofmorphometricityanalysis

resultsshouldbedoneverycarefullyandconsiderconfoundingmechanisms.Thisiswellunderstood

inthecontextofheritability,wherenon-genetic(e.g.,dietary,cultural,socioeconomic)influences

thatvaryacrossracialgroupsorfamiliescanconfoundgeneticanalyses.Similardrawbacksapplyto

morphometricity.Forexample,siblingsmighthavesimilarbrainmorphologiesandphenotypic

expressions,yettheremightnotbeanycausallinkbetweenbrainmorphologyandthephenotype.

Therefore,werecommendrunningmorphometricityanalysesonasetofunrelatedsubjects.

Furthermore,weadviseconstrainingtheanalysis(ifpossible)toahomogeneoussampleofuniform

ancestry,andexplicitlycontrollingforotherpotentialconfoundingfactors,suchasage,sex,andscan

site.

PotentialUsesandExtensionsofMorphometricity.Morphometricityanalysiscanbeusedto

prioritizeimagingmodalities,acquisitionparameters,andprocessingpipelines.Forexample,there

areagrowingnumberofsoftwarepackagesthatallowustoautomaticallyextractnumerous

structuralmeasurementsfrombrainimages.Differentconstructionsoffeaturevectorsanddifferent

metricsthatquantifythesimilarityofimagingfeaturesbetweenindividualswillresultindistinct

ASM’s,whichcanbecomparedwiththemodelselectionframeworkemployedinthisstudy.

Therefore,morphometricityanalysisoffersawaytoquantitativelyandobjectivelyidentifythe

imagingfeaturesandinter-subjectsimilaritymetricthatbestdescribethetrait-relevantaspectsof

whole-brainmorphology.

Alternatively,onecanimagineestimatingthefunctional,structural,connectomic,andmolecular

signaturesofatraitwithinasinglestatisticalmodel,whereeachofthesecomponentsisrepresented

witharandomeffectandthecorrespondingsimilaritymatrixcomputedfromarelevantmodality.

Similarly,onecanpartitionthephenotypicvariationintocontributionsfrom,forinstance,corticaland

subcorticalfeatures,ordifferentlarge-scalebrainnetworks.Thisstrategymightoffernovelinsights

abouttheneuralcorrelatesofcertainphenotypesbyintegratingmultiplemodalitiesand/ormodeling

spatialheterogeneityinaunifiedanalyticframework.Thisnovelperspectivemightalsoallowusto

quantifythecomplementaryinformationcontainedindifferentimagingmodalitiesandspatial

locations.

14

Aslongitudinalimagingstudiescontinuetogrow,itwillbeinterestingtoextendmorphometricityto

examinetherelationshipsbetweentemporaldynamicsinbrainmorphology(e.g.,globalatrophy

rates)andclinicalorbehavioraltraits.Weenvisionemployingthelinearmixedeffectsstrategyto

modellongitudinaldata[48,49],andwewilldefinethemorphometricityoflongitudinalchangesin

phenotypeswithinthisframework.

Finally,theproposedframeworkcanalsoofferanovelperspectiveonexaminingrelationships

betweendifferentphenotypes.Weplantoextendmorphometricity,whichisessentiallythedegree

ofassociationbetweenglobalbrainmorphologyandaphenotype,toquantifythe“morphological

correlation”betweenphenotypes.Thiswillbeanalogoustogeneticcorrelationanalysis[50],which

quantifiesthegeneticoverlapbetweentraits.Webelievethatmorphologicalcorrelationwillbean

invaluabletooltoexaminethecomplexbiologicalrelationshipsbetweenthevariousdimensionsof

humanbehaviorandwillinformbasicandtranslationalresearchintoexploringandredefiningthe

landscapeofbraindiseases.

15

Methods

TheImagingMeasurements.Inthisstudy,weusedtheextensivelystudiedFreeSurfer-derived

measurementstodescribethewhole-brainmorphology.Theimagingmeasurementsincluded

volumesofnon-corticalstructures[51](leftandrightcerebralwhitematter,lateralventricle,inferior

lateralventricle,cerebellumwhitematter,cerebellumcortex,thalamusproper,caudate,putamen,

pallidum,hippocampus,amygdala,andthe3rdand4thventricles)andthicknessmeasurementsof

corticalregions[52](leftandrightsuperiorfrontal,rostralmiddlefrontal,caudalmiddlefrontal,pars

opercularis,parstriangularis,parsorbitalis,lateralorbitofrontal,medialorbitofrontal,precentral,

paracentral,frontalpole,superiorparietal,inferiorparietal,supramarginal,postcentral,precuneus,

superiortemporal,middletemporal,inferiortemporal,banksofthesuperiortemporalsulcus,

fusiform,transversetemporal,entorhinal,temporalpole,parahippocampal,lateraloccipital,lingual,

cuneus,pericalcarine,rostralanteriorfrontal,caudalanteriorfrontal,posteriorparietal,isthmus

parietal,andinsula).

TheAnatomicalSimilarityMatrix.Theanatomicalsimilaritymatrix(ASM)playsacentralroleinthe

proposedmorphometricityanalysis.TheASMisan𝑁×𝑁symmetricmatrix,where𝑁isthenumberof

subjectsintheanalyzedsample.EntriesintheASMquantifythepairwiseglobalsimilaritybetween

thebrainmorphologiesoftwoindividuals.Inprinciple,theASMcanbeanynon-negativedefinite

matrixwithitsdiagonalelementsconstrainedtobeequalto1onaverage.Inthisstudy,we

consideredtwowidelyusedsimilaritymetrics(linearandGaussian)toconstructtheASM.

Assumethat𝑣FGdenotesthe𝑘-thimagingmeasurementsfromsubject𝑖,𝑀isthetotalnumberof

measurements,and𝑠Gisthesamplestandarddeviationofthe𝑘-thmeasurement.ThefirstASMwe

consideredusesalinearkernel.Thus,thesimilarityismeasuredasthelinearcorrelationbetween

pairsofimagingvectorsandthe(𝑖, 𝑗)-thentryiscomputedas:

1𝑀

𝑣FG𝑣MG𝑠G0G

.(4)

Thisisequivalenttomodelingtherandomeffect𝒂inEquation(1)asalinearcombinationofthe

imagingfeatures:𝒂 = 𝒁𝒖,where𝒁isan𝑁×𝑀matrixcomprisingthestandardizedimaging

measurements(i.e.,the(𝑖, 𝑘)-thentryof𝒁is𝑣FG/𝑠G),and𝒖isan𝑀×1randomvectordistributedas

𝒖 ∼ N 𝟎, STU

V𝑰 ,i.e.,eachimagingmeasurementisassociatedwithanindependentandnormally

16

distributedeffectsize.Thecovarianceof𝒂canthenbecomputedas𝜎/0 ∙ 𝒁𝒁Y/𝑀,i.e.,𝒁𝒁Y/𝑀isthe

ASMwithitsentriesexplicitlystatedinEquation(4).

ThesecondASMweconsideredwascomputedusingaGaussiankernelonstandardizedimaging

features,withthe(𝑖, 𝑗)-thentrydefinedas:

exp −(𝑣FG − 𝑣MG)0

𝑀𝑠G0G

.(5)

NotethateachASMdefinitioncorrespondstodifferentmodelsoftrait-relevantvariation.For

example,theGaussiankernelcancapturenonlinearandmultivariateassociationsbetweenbrain

morphologyandtraits.Onecanfurtherdecidetoweighdifferentfeaturesdifferently,basedonfor

example,someaprioriinformationabouttraitrelevance.EachoftheseASMchoiceswillcorrespond

toaparticularsemi-parametricregressionmodel,wherethemorphologicalassociationiscaptured

withafunctionthatbelongstoaspecificspaceoffunctionsinducedbytheutilizedkernel[53].Below,

wedescribeanempiricalstrategytochoosethemostappropriateASMmodelfromaselectionof

candidates.

Inthepresentedstudy,foragivensimilaritymetric,wecomputedanASMforthecorticalthickness

measurementsandanASMforthehead-size-normalizedvolumesofnon-corticalstructures(i.e.,

dividedbytotalintracranialvolumeestimates).TheglobalASMwasthencomputedastheaverageof

thecorticalandnon-corticalASM’s.

ModelSelection.ToselecttheASMthatcanbestdescribethedata,weusedamodelselection

techniquederivedforLMEmodelsandproposedin[53].Specifically,foragivenASM𝑲/,ifwe

denote𝑽 = 𝜎/0𝑲/ + 𝜎30𝑰astheReMLestimateofthecovarianceof𝒚,𝑷 = 𝑽B𝟏 −

𝑽B𝟏𝑿(𝑿𝑽B𝟏𝑿)B𝟏𝑿𝑽B𝟏,anddefine𝑺 = 𝑰 − 𝜎30𝑷,itcanbeshownthattr(𝑺),i.e.,thetraceofthe

matrix𝑺,isameasureofmodelcomplexity.Liuetal.[53]thusproposedthefollowingAkaike

InformationCriterion(AIC)andBayesianInformationCriterion(BIC)intheLMEmodelingframework:

AIC = 𝑁log 𝑅𝑆𝑆 + 2tr 𝑺 ,BIC = 𝑁log 𝑅𝑆𝑆 + log 𝑁 ∙ tr 𝑺 ,(6)

where𝑅𝑆𝑆 = (𝒚 − 𝒚)Y 𝒚 − 𝒚 =𝜎30(𝑁 − tr 𝑺 )istheresidualsumofsquares(RSS)oftheLME

model.BothAICandBICrewardthegoodness-of-fit(thefirstterm)ofthemodelandpenalize

17

complexmodels(thesecondterm)toavoidoverfitting.BIChasalargerpenaltytermthanAICfor

large𝑁andthusfavorssimplermodels.WeselectedtheASMthatgavesmallerAIC/BICvalues.

TheAnalysisPipeline.WefirstranFreeSurferonallstructuralbrainMRIscansavailableineachofthe

analyzedstudies,anddroppedthesubjectsthatFreeSurferfailedtocompletesuccessfully.Next,we

conductedautomaticqualitycontrolonthemeasurementscomputedbyFreeSurferbyidentifying

outliers–if>25%oftheutilizedmorphometricvariablesexhibitedvaluesthatweremorethan2

standarddeviationsawayfromthepopulationmean,wedeemedthatsubjectanoutlierand

discardedit.Fortheremainingsubjects,wecomputedpairwisesimilaritymeasuresbasedonthe

linearorGaussiankerneldescribedabove.Ifthereweretwosubjectsthatexhibitedacorticaland

non-corticalsimilaritymeasuregreaterthan0.95,wedroppedoneofthosesubjects,accountingfor

thepossibilitythatthiswasaduplicatecaseoracloselyrelatedindividual.Finally,weincludedsex

andageascovariatesinallouranalyses(unlesssexoragewasthetraitofinterest,inwhichcasethat

variablewasnotincluded).WefurtherintroduceddummyvariablesthatindicatedsiteIDswhen

analyzingmulti-sitedata(exceptforADNI,wheretherewerealargenumberofsites,yettheimaging

parameterswerecarefullycalibratedacrosssites[28]).

Givenindividual-leveldataandtheASM,wefitthemodelofEquation(1)toestimatethevariance

componentparametersviatheRestrictedMaximumLikelihood(ReML)algorithm[21,22].InMatlab,

weimplementedanefficientFisherscoringmethodtoiterativelymaximizetherestrictedlikelihood

ofthemodel.Thestandarderrorofthevariancecomponentestimatescanbederivedusingthe

inverseoftheFisherinformationmatrixwhenthealgorithmconverges.Empiricallyweconfirmedthe

parametricestimatesusingjackkniferesampling(seeSupplementaryTableS2).Significanceofthe

morphometricityestimatewasobtainedviaalikelihoodratiotest,comparingLMEmodelswithand

withouttherandomeffects.Becausethenullhypothesis(𝜎/0 = 0)liesontheboundaryofthe

parameterspace,thelikelihoodratioteststatisticfollowsahalf-halfmixtureof𝜒p0(achi-square

distributionwithallprobabilitymassatzero)and𝜒C0(achi-squaredistributionwithonedegreeof

freedom)[54].Implementationsofthedevelopedmorphometricitytoolsareavailableat:

http://people.csail.mit.edu/msabuncu/morphometricity.

18

ROI-basedMorphometricityAnalysis.Inordertocomparetheproposedwhole-brain

morphometricityanalysistomoreconventionalROI-basedanalyses,weimplementedanROI-based

adaptationofEquation(1).Here,insteadofcomputingtheASMusinganarrayofvariablesthatspan

thebrain,wecomputedROI-basedASMsonlyusingasingleROIbiomarker–thevariablethathad

thestrongestassociationwiththetraitofinterest.ToidentifytheROIbiomarkerofeachtrait,we

conductedanindependentdiscoveryanalysisonanon-overlappingsample,examiningthe

associationbetweeneachofthecandidateimagingvariablesandthetraitinaregressionanalysis,

whileappropriatelycontrollingforage,sex,andsite.Theimagingvariablethatexhibitedthesmallest

p-valuewasthenidentifiedastheROIbiomarkerforthetraitofinterestandusedinthe

morphometricityanalysis.WenotethatfortheROI-discoveryanalysesweutilizedthereplication

(secondary)samplesofthewhole-brainmorphometricityanalyses.Thisway,wecomputedtheROI-

basedmorphometricityresultsusingtheprimarysamples.

TheData.WeemployedbaselinebrainMRIscans(T1-weightedacquiredon1.5Tmachines),clinical

diagnosis,anddemographicvariablesfromphase1oftheADNI[28].IntheADHD200sample[29],

casesweredefinedasthosewithevidenceofnon-typicaldevelopmentandanADHD-Combined

diagnosis,asperthepublishedphenotypickey

[http://fcon_1000.projects.nitrc.org/indi/adhd200/general/ADHD200_PhenotypicKey.pdf].Inthe

cross-sectionalOASISsample[30],subjects(of60yearsorolder)withaclinicaldementiarating(CDR)

greaterthan0wereclassifiedashavingdementia.Elderlysubjectswitha0CDRwereclassifiedas

healthycontrols.Forthe20controlsubjectswithrepeatscans,weonlyusedthedatafromthefirst

imagingsession.IntheCOBREsample[31],schizophreniasubjectswereidentifiedaccordingtothe

phenotypefile[http://fcon_1000.projects.nitrc.org/indi/retro/cobre.html].TheMCICdatawas

compiledfromasharedrepositoryofmulti-sitebrainimagingdatacollectedfortheclinical

investigationofschizophrenia[32].TheABIDEanalyses[33]wereconductedonsubjectswhowere

olderthan10years,andcasesweredefinedasthosehavinganon-zerodiagnosticgroupentryinthe

phenotypetable[http://fcon_1000.projects.nitrc.org/indi/abide/].InthePPMIanalyses[34],cases

weredeterminedtobethosediagnosedwithParkinson’sDiseaseatbaselineandcontrolswerethose

whowereclinicallyhealthyandnotprodromal,againatbaseline[http://www.ppmi-info.org/access-

data-specimens/download-data/].

19

Allgeneraltraitanalyseswereconductedonhealthycontrolsamples(seecriteriaofrelevantstudy).

BoththeOASISandGSPsamplescoverasubstantialportionoftheadultlifespanandthuswereused

toestimatethemorphometricityofage.AllGSPanalyseswereconstrainedtounrelated,healthy

controlsofnon-HispanicEuropeanancestry,withhigh-qualitystructuralbrainMRIscansacquiredon

a12-channelcoil[26].Inthegeneralintelligence(IQ)analyses,weutilizedtheWechslerAbbreviated

ScaleofIntelligenceasthephenotype(bothintheADHD200andABIDEsamples).Forthe

morphometricityanalysisofsex,wecreatedsubsamplesthatweregender-balanced(50%female)

andage-matchedbetweensexes.InthePPMIdata,educationwasmeasuredinyears(minimum9

andmaximum24),whereasintheOASISsample,educationlevelswereencodedas;1:lessthanhigh

schoolgraduate,2:highschoolgraduate,3:somecollege,4:collegegraduate,and5:beyondcollege.

Inthecognitivemeasureanalyses,weemployedthedemographicandbehavioralmeasuresreported

inthe‘openaccess’and‘restricted’subjectinformationspreadsheetsavailablefromtheHCP

databasewebsite[http://www.humanconnectome.org/data].TheHCPcollectedarangeofwell-

validatedandreliablebehavioralmeasures,includingthosefromtheNIHToolboxAssessmentof

NeurologicalandBehavioralFunction,andseveraladditionalmeasurestoassessdomainsnot

coveredbytheNIHToolbox.Formoreinformationontherationalebehindthedevelopmentofthe

behavioralbatteriesusedinHCP,see[55].

AllMRIscansfromADNI,OASIS,ADHD200,MCIC,COBRE,PPMI,andHCPwereprocessedwith

FreeSurferversion5.3.TheGSPMRIscanswereprocessedwithFreeSurferversion4.5.

20

Acknowledgements

SupportforthisresearchwasprovidedinpartbytheNationalInstituteforBiomedicalImagingand

Bioengineering(P41EB015896,R01EB006758,R21EB018907,R01EB019956),theNationalInstituteon

Aging(5R01AG008122,R01AG016495),theNationalInstituteforNeurologicalDisordersandStroke

(R01NS0525851,R21NS072652,R01NS070963,R01NS083534,5U01NS086625),andwasmade

possiblebytheresourcesprovidedbySharedInstrumentationGrants1S10RR023401,1S10RR019307,

and1S10RR023043.AdditionalsupportwasprovidedbytheNIHBlueprintforNeuroscienceResearch

(5U01-MH093765),partofthemulti-institutionalHumanConnectomeProject.

DatawereprovidedinpartbytheBrainGenomicsSuperstructProject(GSP)ofHarvardUniversity

andMGH,withsupportfromtheCenterforBrainScienceNeuroinformaticsResearchGroup,

AthinoulaA.MartinosCenterforBiomedicalImaging,CenterforHumanGeneticResearch,and

StanleyCenterforPsychiatricResearch.20individualinvestigatorsatHarvardandMGHgenerously

contributeddatatotheoverallproject.

ThisresearchwasalsofundedinpartbyNIHgrantsR01NS083534,R01NS070963,and

1K25EB013649-01and1R21AG050122-01A1(toMRS);K01MH099232(toAJH);K24MH094614and

R01MH101486(toJWS);anMGHECORTostesonPostdoctoralFellowshipAward(toTG).JWSisa

TepperFamilyMGHResearchScholar.BFhasafinancialinterestinCorticoMetrics,acompanywhose

medicalpursuitsfocusonbrainimagingandmeasurementtechnologies.BF'sinterestswerereviewed

andaremanagedbyMassachusettsGeneralHospitalandPartnersHealthCareinaccordancewith

theirconflictofinterestpolicies.

21

TablesandFigures

Figure1:Morphometricityestimatesofvariousdiseases(ontheliabilityscale)computedusingthe

Gaussiananatomicalsimilaritymatrix(ASM)ofEquation(5).Eachbarisannotatedwithstudy

namesusedtocomputetheseestimates.ForAlzheimer’sdiseaseandschizophrenia,wehad

independentsamplesusedtocomputereplicationestimates(purplebars).Errorbarsindicate

standarderroroftheestimates.

22

Figure2:MorphometricityestimatesofgeneralnonclinicaltraitscomputedusingtheGaussian

anatomicalsimilaritymatrix(ASM)ofEquation(5).IQdenotesgeneralintelligence.Eachbaris

annotatedwithstudynamesusedtocomputetheseestimates.Bluebarscorrespondtoresultsfrom

theprimaryanalyses,whereaspurplebarscorrespondtoindependentreplicationanalyses.Errorbars

indicatestandarderroroftheestimates.

23

Figure3:ROI-basedmorphometricityestimatesofgeneralnonclinicaltraits(age,intelligence,sex,

andeducation),Alzheimer’sdisease(AD),andschizophrenia(SCZ).ForADandSCZ,morphometricity

estimateshavebeentransformedtotheliabilityscale.Redcirclesdenotewhole-brain

morphometricityestimatesforeachtrait.Errorbarsindicatestandarderroroftheestimates.

24

Figure4:Morphometricityestimatesofvariousmeasuresofcognitioncomputedondatafromthe

HumanConnectomeProject(HCP)andusingtheGaussiananatomicalsimilaritymatrix(ASM).Blue

andpurplebarscorrespondtoprimaryandsecondaryanalyses,respectively.Errorbarsindicate

standarderroroftheestimates.

25

Table1:Samplecharacteristicsandmorphometricityestimatesforanalyzeddiseasetraits.

*P<5e-3,**P<5e-4,***P<5e-5

Disease Case N Case Age (mean±std)

Case Fem% Control N

Control Age (mean±std)

Control Fem %

Study Name

Alzheimer's 154 74.6±7.6 46.8 219 75.9±5 48.4 ADNIADHD 122 11.6±3.2 75.4 384 11.8±2.9 62.2 ADHDSchizophrenia 92 33±11.2 75.0 85 32.8±11.7 67.1 MCICAutism 209 17.6±7.9 14.4 305 17.3±7.2 18.4 ABIDEParkinson's 376 61.4±9.7 35.1 152 60.4±11.4 47.8 PPMI

Assumed Prevalance

Morphometricity (liability scale)

Standard Error

13% 1.00*** 0.031% 0.55** 0.161% 0.50*** 0.031% 0.38*** 0.060.2% 0.20* 0.06

Table2:Samplecharacteristicsandmorphometricityestimatesfortheanalyzedgeneralnonclinicaltraits.

Trait Name Sample

Size Age (mean±std)

[min-max] Female

% Study Name

Age 1073 22±5.8 [18-81] 56 GSPIQ 155 11.3±2.8 [7.2-17.7] 60 ADHDSex 1074 25.3±13.7 [18-84] 50 GSPEducation 152 60.4±11.4 [30-82] 34.8 PPMI

Morhopmetricity Estimate

Standard Error

1.00 0.010.95 0.050.93 0.020.81 0.08

26

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SupportingInformationfor“Morphometricity:MeasuringtheNeuroanatomical

SignatureofaTrait”

MertR.Sabuncu,TianGe,AvramJ.Holmes,JordanW.Smoller,RandyL.Buckner,andBruceFischl;

fortheAlzheimer’sDiseaseNeuroimagingInitiative(ADNI)*

SupplementaryTableS1:AkaikeInformationCriterion(AIC)andBayesianInformationCriterion(BIC)

values(Equation6)fortheprimarymorphometricityanalysesconductedwiththeLinear(Equation4)

andGaussian(Equation5)kernels.

AIC(x104) BIC(x104)

Disease/Trait Gaussian Linear Gaussian LinearAlzheimer's(ADNI) -1.508 -0.309 -1.362 -0.163ADHD -2.040 -0.655 -1.826 -0.441Schizophrenia (MCIC) -0.772 -0.216 -0.716 -0.160Autism (ABIDE) -2.022 -0.637 -1.804 -0.419Parkinson's -0.522 -0.194 -0.491 -0.163Age (GSP) -2.967 -0.276 -2.433 0.258IQ (ADHD 200) -0.521 -0.107 -0.474 -0.059Sex (GSP) -3.559 -0.992 -3.024 -0.457Education (PPMI) -0.512 -0.188 -0.477 -0.153

SupplementaryTableS2:Parametricandjackknifeestimatesofmorphometricityandstandarderrors.Morphometricityestimatesfordiseasetraitsareontheliabilityscale.

Morphometricity StandardError

Disease/Trait Parametric Jackknife Parametric JackknifeAlzheimer's(ADNI) 1.00 1.00 0.03 0.03 ADHD (ADHD 200) 0.55 0.55 0.16 0.17 Schizophrenia (MCIC) 0.50 0.50 0.03 0.03 Autism (ABIDE) 0.38 0.38 0.06 0.06

Parkinson's 0.20 0.20 0.06 0.06

Age (GSP) 1.00 1.00 0.01 0.01 IQ (ADHD 200) 0.95 0.95 0.05 0.06 Sex (GSP) 0.93 0.93 0.02 0.02

Education (PPMI) 0.81 0.81 0.08 0.07

SupplementaryTableS3:Independentreplicationonnon-overlappingdata:samplecharacteristics

andmorphometricityestimatesforanalyzeddiseasetraits.

Disease Case N Case Age (mean±std)

Case Fem% Control N

Control Age (mean±std)

Control Fem %

Study Name

Assumed Prevalance

Morphometricity (liability scale)

Standard Error

Alzheimer's 100 76.8±7.1 59.0 98 75.9±9.0 73.4 OASIS 13% 1.00 0.06Schizophrenia 56 35.8±12.4 16.1 73 35.7±11.6 31.5 COBRE 1% 0.45 0.08

SupplementaryTableS4:Independentreplicationonnon-overlappingdata:samplecharacteristics

andmorphometricityestimatesforanalyzedgeneralnonclinicaltraits.

Trait Name Sample

Size Age (mean±std)

[min-max] Female % Study Name

Trait (mean±std) [min-max]

Morhopmetricity Estimate

Standard Error

Age 124 68.0±13.7 [33-94] 72.6 OASIS N/A 1.00 0.03IQ 108 17.5±8.0 [10.5-56.2] 14.8 ABIDE 109.33±11.0[84-133] 0.95 0.06Sex 298 11.3±2.9 [7.17-21.74] 50 ADHD N/A 0.90 0.05Education 124 68.0±13.7 [33-94] 72.6 OASIS 3.5±1.2 [1-5] 0.79 0.13

SupplementaryTableS5:ROI-basedmorphometricityestimatesforthetraitswithtwoindependent

samples.MostassociatedROIswereidentifiedonindependentsample.*Fordiseasetraitswelist

morphometricityestimatesontheliabilityscale.

Trait Name ROI-basedMorphometricity StandardError P-value MostassociatedROIAge 0.82 0.03 <1e-15 3rdVentricleIQ 0.87 0.05 <1e-15 RightLateralVentricleSex 0.44 0.07 1.9e-9 RightThalamusEducation 0.00 0.06 1.00 RightHippocampusAlzheimer's* 0.66 0.16 2.6e-5 RightHippocampusSchizophrenia* 0.06 0.05 0.22 RightInferiorLateralVentricle