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DRAWING INFERENCES FROM GROUP DATA: Construc)ng 2 nd level models, working with ROIs, and avoiding sta)s)cal circularity

DRAWING INFERENCES FROM GROUP DATA...Working with repeated measures data ¨ You have data from a group of subjects and you want to look for acJvity changes across condiJons ¨ The

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DRAWINGINFERENCESFROMGROUPDATA:Construc)ng2ndlevelmodels,workingwithROIs,

andavoidingsta)s)calcircularity

Soyouhavegroupdata…Whatnow?

¨  Whole-brainvoxelwiseanalysis¤ ConstrucJngappropriate2ndlevelmodels

n Characterizingwithin-subject(repeatedmeasures)effects

n Characterizingbetween-subject(group)effects

n Usingcovariatesatthe2ndlevel

¨  Region-of-interest(ROI)analysis¤ ChoosingyourROIs¤ Avoiding“voodoo”

n a.k.a.inferenJalcircularity;non-independenceerrors

Workingwithrepeatedmeasuresdata

¨  YouhavedatafromagroupofsubjectsandyouwanttolookforacJvitychangesacrosscondiJons

¨  Thesimplestapproachistocreatecontrastimagesforeachsubjectandthenconductaone-samplet-testacrosssubjects

¨  ContrastimagesaresimplyweightedlinearcombinaJonsofcondiJon-specificbetaimages

¤  e.g.,CondA-CondB:[1-1]

¤  ReferredtoasCOPEimagesinFSLand.conimagesinSPM

Workingwithrepeatedmeasuresdata

¨  ContrastswithmorethantwocondiJons:

¤  CondAandCondBvs.CondC:[11-2]

n NOTE:IfCondA&Bhavevastlydifferent#’softrials,itmaybebecertorunanewGLMthatcombinesthesecondiJons,oralternaJvelyyoucouldweighteachcondiJonbythe#oftrials

¤  (CondA–CondB)vs.(CondC–CondD):[1-1-11]

n  TheinteracJonterm!

¨  Nullhypothesis:

¤  acrosssubjectmeanofcontrastvariable=0

Workingwithrepeatedmeasuresdata

¨  Probingforparametriceffectswithlinearcontrastcoefficients

¤  3condiJons:[-101]

¤  4condiJons:[-3-113]

¤  5condiJons:[-2-1012]

¤  6condiJons:[-5-3-1135]

¨  Canalsoprobefor2ndorder(quadraJc)and3rdorder(cubic)effects

¨  Anysetofcontrastcoefficientscanwork,solongastheysumtozero

¤  WriteyourcontrastcoefficientsasposiJvenumbersandthensubtractthemeanfromeachnumber

¤  Butnotethatcustomcontrastsmightnotbeorthogonaltoeachother

Example:MappinglinearandquadraJccontrasts

Example:Mappingcustomcontrasts

Todd&Marois(2004)Nature

AlternaJveapproach:Separatepairwisetests

Chenetal.(2013)AJNRAmJNeuroradiol

AlternaJveapproach:Separatepairwisetests

Chenetal.(2013)AJNRAmJNeuroradiol

Workingwithrepeatedmeasuresdata

¨  Probingforparametriceffectswithlinearcontrastcoefficients

¤  3condiJons:[-101]

¤  4condiJons:[-3-113]

¤  5condiJons:[-2-1012]

¤  6condiJons:[-5-3-1135]

¨  Canalsoprobefor2ndorder(quadraJc)and3rdorder(cubic)effects

¨  Anysetofcontrastcoefficientscanwork,solongastheysumtozero

¤  WriteyourcontrastcoefficientsasposiJvenumbersandthensubtractthemeanfromeachnumber

¤  Butnotethatcustomcontrastsmightnotbeorthogonaltoeachother

Theone-samplet-test(inFSL)

TheimagesinpucedintoEV1canbe:Ø  thebetaesJmatesfromasinglecondiJonØ  thedifferencebetweentwocondiJonsØ  anylinearcontrastbetweencondiJons

Take-homepoint:Aone-samplet-testcanaccomplishalot!

AnalternaJve(slightlymoreinvolved)waytotestforadifferencebetween2condiJons

¨  FSLrepresentaJonof2ndlevelmodelforpairedt-test

8subjects2condiJons(A&B)

Whythetwoapproachesareequivalent

PLoSBiology(2015)

WhatifonesubjectismissingdatafromagivencondiJon?

¨  RelaJvelycommonsituaJontobefacedwith¤ E.g.,AnalysisofCorrectvs.Incorrecttrials

n  subjectmayhavenoincorrecttrials

¨  PotenJalsoluJons:¤ Analysiscanberunomipngthatsubject’sdata

¤ Or,analysiscanberunasanunpairedt-test(essenJallyconsideringthetwocondiJonsastwoseparategroupsofsubjects)n MoreconservaJve,butmaysomeJmesbeuseful,especiallyifmulJplesubjectsaremissingdata

Between-subjectmodels

¨  Wehavetwogroupsofsubjects(e.g.,9paJentsand7controls)withpotenJallydifferentcross-subjectvariance.¤ Two-SampleT-Test(equalvariancenotassumed)

¨  SpecifytwogroupmembershipssothatFSL’sFEATesJmateseachgroup'scross-subjectvarianceseparately.¤ SPM’sdefaultisalsotoassumeunequalvariance

¨  WewanttotestwhetherornotacJvitybetweenthetwogroupsisequivalentforagivencondiJon

Two-sampleunpairedt-test

Howabouttwogroupswithtwocondi)ons?

¨  E.g.,Comparingthemagnitudeofpre-vs.post-trainingacJvaJonchangesinpaJentsandcontrols¤ Within-subjectfactor:pre-vs.post-training¤  Across-subjectfactor:paJentsvs.controls

¨  Oneeasy-to-implementapproach:¤  FirstcomputeA-Bdifferenceimageforeachsubject¤  Thenperformsimpletwo-sample(unpaired)t-testtofindgroupdifferencesn  i.e.,groupxcondiJoninteracJon

¨  ThisbasicapproachcangeneralizetoanylinearcombinaAonofrepeatedmeasuresfactors

Howabouttwogroupswithtwocondi)ons?

¨  AnalternaJveapproach(slightlymoreinvolved):

SpecificaJonofmorecomplexgroup-levelmodelscangettrickyinFSL

¨  SeeFSLFEATuserguideforexamplesofmulJ-factorANOVAmodels

¨  hCp://fsl.fmrib.ox.ac.uk/fsl/fslwiki/FEAT/UserGuide

Introducingcovariatesintoyourmodels

¨  Singlegroupwithcovariate¤ Youhaveasinglegroupofsubjectsandyoualsohavemeasuredage.YouwouldliketoseeifthereisanageeffectonbrainacJvity.

n Whatwouldthemodellooklike?

n Whatcontrastswouldyouspecifyfortheageeffect?

Use age Use demeaned age

•  Both models will give exactly the same result for C2, but C1 will be different.

Singlegroupwithcovariate

SlidefromJeaneCeMumford

Simulateddata

Takehome:MeancenteringisonlynecessaryifyouwantyourPEofcolumnof1stobetheoverallmean

SlidefromJeaneCeMumford

TwogroupswithaconJnuouscovariate

¨  Wehavetwogroupsandaconfoundingcovariate(e.g.,depressionscore).

¨  OurprimaryinterestisinthedifferenceofmeanbrainacJvaJonbetweenthetwogroups.

¨  Wewanttomakesurethisdifferencewasn’tduetobetweengroupdifferencesindepression.

¨  Whatshouldthemodellooklike?

SlidefromJeaneCeMumford

¨  Okaytodemeantheconfoundingmeasureacrossallsubjects

¤  Butonlynecessaryifyouintendtolookateachgroupvs.baseline(e.g.,[100])

¨  ButdoNOTdemeantheconfoundingmeasurewithingroup

¤  Thiscouldremoveanyconfoundingeffectthemeasuremighthave

TwogroupswithaconJnuouscovariate

SlidefromJeaneCeMumford

Whyyoushouldn’tdemeanwithingroup

¨  Whatifthisiswhatyourdatalooklike?¤ ApparentdifferenceinmeansisclearlyduetorangeofXsampled,notthegroupmembership

SlidefromJeaneCeMumfordFormorediscussionofissuessurroundingmean-centering:hCp://mumford.fmripower.org/mean_centering/

FormoreinformaJononmean-centering

hCp://mumfordbrainstats.tumblr.com

TesJngtheinteracJon

¨  WhatifyouwanttotestwhethertherelaJonshipbetweenbrainacJvityanddepressionscorediffersbetweenyourgroups?¤ mean-centeringisnotnecessaryhere

010-1SlidefromJeaneCeMumford

2ndlevelanalysesinSPM

2ndlevelanalysesinSPM

2ndlevelanalysesinSPM

2ndlevelanalysesinSPM

2ndlevelanalysesinSPM

2ndlevelanalysesinSPM

AlternaJvestovoxelwiseanalysis

¨  ConvenJonalfMRIstaJsJcscomputeonestaJsJcalcomparisonpervoxel.¤  Advantage:candiscovereffectsanywhereinbrain.¤  Disadvantage:lowstaJsJcalpowerduetomulJplecomparisons.

¨  SmallVolumeCorrecAon:OnlyruntestsonasmallproporJonofvoxels(byreducingthesearchspace,allowsformorelenientvoxel-levelstats)

¨  Region-of-interest:PooldataacrossaregionforsinglestaJsJcaltest.

SVC ROI SPM

Example: how many comparisons on this slice?

• Voxelwise: 1600

• SVC: 57

• ROI: 1

SlidefromChrisRorden

WhyuseROIs?

¨  ConvenientwaytoalleviatethemulJplecomparisonsproblemsthatariseinwhole-brainanalyses¤  ShouldsAlladjuststatsfor#ofROIstested!

¨  Allowsformorehypothesis-drivenanalyses¤  ExploringtheenJredatasetcanbeunwieldyandsomeJmesleadstounfocusedandhighly-speculaJvepapers

¤  ROIresultsareeasiertopresentanddiscuss

¤ HemodynamicJmecourseplotscanbeinformaJve

¤  ROIsdon’trequiresubjectstoacJvatetheexactsamevoxeln  ButanROI-onlyanalysisisvulnerabletoTypeIIerrors!

Region-of-interestanalysis

¨  ChoosingtherightROI(s)¤ Anatomically-defined

n Atlas-based(e.g.,AALatlas)

Region-of-interestanalysis

¨  ChoosingtherightROI(s)¤ Anatomically-defined

n AutomatedsegmentaJon-based(e.g.,Freesurfer)

Region-of-interestanalysis

¨  ChoosingtherightROI(s)¤ Anatomically-defined

n AutomatedsegmentaJon-based(e.g.,Freesurfer)

Region-of-interestanalysis

¨  ChoosingtherightROI(s)¤ Anatomically-defined

n Hand-tracedusinganatomicallandmarks

Region-of-interestanalysis

¨  ChoosingtherightROI(s)¤ Anatomically-defined

n Coordinate-based(e.g.,basedonapreviousstudy)

Region-of-interestanalysis

¨  ChoosingtherightROI(s)¤ Anatomically-defined

n Coordinate-based(e.g.,basedonapreviousstudy)

Region-of-interestanalysis

¨  ChoosingtherightROI(s)¤ Anatomically-defined

n Coordinate-based(e.g.,basedonameta-analysis)

Region-of-interestanalysis

¨  ChoosingtherightROI(s)¤ Anatomically-defined

n Network-based

!

Region-of-interestanalysis

¨  ChoosingtherightROI(s)¤ Anatomically-defined

n Network-based

Poweretal.(2013)CurrOpinNeurobio

Region-of-interestanalysis

¨  ChoosingtherightROI(s)¤ Anatomically-defined

n Network-based

Gordonetal.(2014)CerebralCortex

Region-of-interestanalysis

¨  ChoosingtherightROI(s)¤ Anatomically-defined

n Network-based

Gordonetal.(2014)CerebralCortex

Region-of-interestanalysis

¨  ChoosingtherightROI(s)¤ FuncAonally-defined

n BasedonaparJcularacJvaJoneffectinyourdatan ROI-definingcontrastneedstobeorthogonaltostaJsJcaltestsconductedonextracteddata

n  Independent“localizer”taskscanbeusefulhere

n AVOIDDOUBLE-DIPPINGATALLCOSTS!

Isthisokay?

Ø  IdenAfyaclusterthatshowsabovesignificantacJvityforbothCatsandDogs(viaconjunc)onanalysis)

Ø  TestwhetherthisregionshowssignificantacJvityforDogs>Snakes

Ø  TestwhetherthisregionshowssignificantacJvityforHorses>Snakes

Ø  IdenAfyaclusterthatshowsCats>Dogseffect

Ø  TestwhetherthisregionshowssignificantacJvityforCats>Snakes

Ø  TestwhetherthisregionshowssignificantacJvityforSnakes>Dogs

Ø  TestwhetherthisregionshowssignificantacJvityforDogs>Snakes

Isthisokay?

Ø  IdenAfyaclusterthatshowssignificanteffectofsJmulustypeinone-wayANOVA(F-test)thatincludesalltaskcondiJons(Cats,Dogs,Snakes,Horses)

Ø  TestwhetherthisregionshowssignificantacJvityforCats>Dogs

Ø  TestwhetherthisregionshowssignificantacJvityfor(Cats&Dogs&Horses)>Snakes

Isthisokay?

StrongMemory

ModerateMemory

WeakMemory

***

StrongMemory

ModerateMemory

WeakMemory

*

*

IdenJfyROIsbasedon2contrasts:StrongMemory>WeakMemoryStrongMemory>ModerateMemory

Okaytolookatplotstomakesurethatnothingweirdisgoingon,buteffectsizeswillbeinflatedandsignificancebracketsarehighlymisleading

Isthisokay?

StrongMemory

ModerateMemory

WeakMemory

***

StrongMemory

ModerateMemory

WeakMemory

*

*

IdenJfyROIsbasedonanatomicalboundaries

NotappropriatetodrawanyconclusionsaboutthesetworegionsshowingdissociableprofilesofacJvityunlessyoudirectlytestforaregionxcondiJoninteracJon

The“implied”interacJon

Nieuwenhuisetal.(2011)NatureNeuroscience

The“implied”interacJon

Nieuwenhuisetal.(2011)NatureNeuroscience

The“implied”interacJon

Nieuwenhuisetal.(2011)NatureNeuroscience

¨  “…theerrorofcomparingsignificancelevelsisespeciallycommonintheneuroimagingliterature,inwhichresultsaretypicallypresentedincolor-codedstaJsJcalmapsindicaJngthesignificancelevelofaparJcularcontrastforeach(visible)voxel.

¨  Avisualcomparisonbetweenmapsfortwogroupsmighttempttheresearchertostate,forexample,that“thehippocampuswassignificantlyacJvatedinyoungeradults,butnotinolderadults”.

¨  However,theimpliedclaimisthatthehippocampusisacJvatedmorestronglyinyoungeradultsthaninolderadults,andsuchaclaimrequiresadirectstaJsJcalcomparisonoftheeffects.

¨  Similarly,claimsaboutdifferencesinacJvaJonacrossbrainregionsmustbesupportedbyasignificantinteracJonbetweenbrainregionandthefactorunderlyingthecontrastofinterest.”

ROIdefiniJonisaffectedbynoise

SlidefromNikoKriegeskorte

true region

overfitted ROI

RO

I-ave

rage

ac

tivat

ion

overestimated effect

independent ROI

Baker, Hutchison, & Kanwisher

(2007)

High selectivity from pure

noise. SlidefromEdVul

ROIdefiniJonisaffectedbynoise

VoodoocorrelaJons

EdVul

VoodoocorrelaJons

VoodooPuzzlinglyhighcorrelaJons

VoodoocorrelaJons

r = 0.82

Neuralcorrelatesofhumanvirtuejudgment

r = -0.83

VoodoocorrelaJons

Thisfigureistherealdata

VoodoocorrelaJons

“Tosumup,then,weareledtoconcludethatadisturbinglylarge,andquite

prominent,segmentoffMRIresearchonemoJon,personality,andsocialcogniJon

isusingseriouslydefecJveresearchmethodsandproducingaprofusionofnumbersthatshouldnotbebelieved.Althoughwehavefocusedhereon

studiesrelaJngtoemoJon,personality,andsocialcogniJon,wesuspectthatthequesJonableanalysismethodsdiscussedherearealsowidespreadinotherfields

thatusefMRItostudyindividualdifferences,suchascogniJve

neuroscience,clinicalneuroscience,andneurogeneJcs.”

Vuletal.(2009)

ToavoidselecJonbias,wecan...

...performanonselecAveanalysisOR...makesurethatselecJonandresultsstaJsJcsareindependentunderthenullhypothesis,becausetheyareeither:¨  inherentlyindependent¨  orcomputedonindependentdata

¤ e.g.,separatestudy;funcAonallocalizer;cross-validaAon

e.g.independentcontrasts

e.g.whole-brainmapping(noROIanalysis)

SlidefromNikoKriegeskorte

FormoreinformaJon…

¨  PuzzlinglyHighCorrelaAonsinfMRIStudiesofEmoAon,Personality,andSocialCogniAon.Vul,E.,HarrisC.,Winkielman,P.,&Pashler,H.(2009)PerspecJvesonPsychologicalScience,4,274-290.[FormerlyJtled:VoodooCorrelaJonsinSocialNeuroscience].

¨  Circularanalysisinsystemsneuroscience–thedangersofdoubledipping.KriegeskorteN,SimmonsWK,BellgowanPSF,BakerCI.(2009)NatureNeuroscience12(5):535-40.

¨  Everythingyouneverwantedtoknowaboutcircularanalysis,butwereafraidtoask.KriegeskorteN,LindquistMA,NicholsTE,PoldrackRA,VulE.(2010)JCerebBloodFlowMetab.30(9):1551-7.

¨  Voodooandcircularityerrors.Vul,E.andPashler,H.(2012).NeuroImage,62,945-948.