Analyzing the effect of APOE on Alzheimer's disease progression using an event-based
model for stratified populations
Alzheimer's Disease Neuroimaging Initiative
DOI
10.1016/j.neuroimage.2020.117646
Publication date
2020
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NeuroImage
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Alzheimer's Disease Neuroimaging Initiative (2020). Analyzing the effect of APOE on Alzheimer's disease
progression using an event-based model for stratified populations. NeuroImage, 227, [117646].
https://doi.org/10.1016/j.neuroimage.2020.117646
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ContentslistsavailableatScienceDirect
NeuroImage
journalhomepage:www.elsevier.com/locate/neuroimage
Analyzing
the
effect
of
APOE
on
Alzheimer’s
disease
progression
using
an
event-based
model
for
stratified
populations
Vikram
Venkatraghavan
a,∗,
Stefan
Klein
a,
Lana
Fani
c,
Leontine
S.
Ham
a,
Henri
Vrooman
a,
M.
Kamran
Ikram
c,d,
Wiro
J.
Niessen
a,b,
Esther
E.
Bron
a,
for
the
Alzheimer’s
Disease
Neuroimaging
Initiative
1a Biomedical Imaging Group Rotterdam, Department of Radiology & Nuclear Medicine, Erasmus MC, University Medical Center Rotterdam, the Netherlands b Quantitative Imaging Group, Dept. of Imaging Physics, Faculty of Applied Sciences, Delft University of Technology, Delft, the Netherlands
c Department of Epidemiology, Erasmus MC, University Medical Center Rotterdam, the Netherlands d Department of Neurology, Erasmus MC, University Medical Center Rotterdam, the Netherlands
a
r
t
i
c
l
e
i
n
f
o
Keywords:
Disease Progression Modeling Event-Based Model Alzheimer’s Disease
APOE
a
b
s
t
r
a
c
t
Alzheimer’sdisease(AD)isthemostcommonformofdementiaandisphenotypicallyheterogeneous.APOEisa
triallelicgenewhichcorrelateswithphenotypicheterogeneityinAD.Inthiswork,wedeterminedtheeffectof
APOEallelesonthediseaseprogressiontimelineofADusingadiscriminativeevent-basedmodel(DEBM).Since
DEBMisadata-drivenmodel,stratificationintosmallerdiseasesubgroupswouldleadtomoreinaccuratemodels
ascomparedtofittingthemodelontheentiredataset.Henceoursecondaryaimistoproposeandevaluatenovel
approachesinwhichwesplitthedifferentstepsofDEBMintogroup-aspecificandgroup-specificparts,where
theentiredatasetisusedtotrainthegroup-aspecificpartsandonlythedatafromaspecificgroupisusedto
trainthegroup-specificpartsoftheDEBM.Weperformedsimulationexperimentstobenchmarktheaccuracyof
theproposedapproachesandtoselecttheoptimalapproach.Subsequently,thechosenapproachwasappliedto
thebaselinedataof417cognitivelynormal,235mildcognitivelyimpairedwhoconverttoADwithin3years,
and342ADpatientsfromtheAlzheimersDiseaseNeuroimagingInitiative(ADNI)datasettogainnewinsights
intotheeffectofAPOEcarriershiponthediseaseprogressiontimelineofAD.Inthe𝜀4carriergroup,themodel
predictedwithhighconfidencethatCSFAmyloid𝛽42andthecognitivescoreofAlzheimer’sDiseaseAssessment
Scale(ADAS)areearlybiomarkers.Hippocampuswastheearliestvolumetricbiomarkertobecomeabnormal,
closelyfollowedbytheCSFPhosphorylatedTau181(PTAU)biomarker.Inthehomozygous𝜀3carriergroup,the
modelpredictedasimilarorderingamongCSFbiomarkers.However,thevolumeofthefusiformgyruswas
identifiedasoneoftheearliestvolumetricbiomarker.Whilethefindingsinthe𝜀4carrierandthehomozygous
𝜀3carriergroupsfitthecurrentunderstandingofprogressionofAD,thefindinginthe𝜀2carriergroupdidnot.
Themodelpredicted,withrelativelylowconfidence,CSFNeurograninasoneoftheearliestbiomarkersalong
withcognitivescoreofMini-MentalStateExamination(MMSE).Amyloid𝛽42wasfoundtobecomeabnormal
afterPTAU.Thepresentedmodelscouldaidunderstandingofthedisease,andinselectinghomogeneousgroup
ofpresymptomaticsubjectsat-riskofdevelopingsymptomsforclinicaltrials.
1. Introduction
Dementiaaffectsroughly 5%of theworld’selderlypopulationof whom60−70%areaffectedbyAlzheimer’sDisease(AD),whichisthe mostcommonformofdementia(Organization,2017).Thereareseveral neurobiologicalsubtypesofAD(Ferreiraetal.,2020)andeachsubtype potentiallyneedsadifferentstrategytopreventorslowtheprogression
∗Correspondingauthor.
E-mailaddress:v.venkatraghavan@erasmusmc.nl(V.Venkatraghavan).
1 DatausedinpreparationofthisarticlewereobtainedfromtheAlzheimer’sDiseaseNeuroimagingInitiative(ADNI)database(adni.loni.usc.edu).Assuch,the
investigatorswithintheADNIcontributedtothedesignandimplementationofADNIand/orprovideddatabutdidnotparticipateinanalysisorwritingofthis
report.AcompletelistingofADNIinvestigatorscanbefoundat:http://adni.loni.usc.edu/wp-content/uploads/how_to_apply/ADNI_Acknowledgement_List.pdf
of AD.Understandingthepathophysiologicalprocesses inADis thus crucialforselectingnovelpreventiveortherapeutictargetsforclinical trialsofdiseasemodifyingtreatments,identifyingtargetgroupsforsuch trialsandtrackingthediseaseprogressioninpatients.
While several studies have looked into the pathophysiology of AD (Bloom,2014; JackJr. etal., 2013; Weigandetal., 2019),itis stillnotcompletelyunderstood.AlthoughithasbeenobservedthatAD
https://doi.org/10.1016/j.neuroimage.2020.117646
Received15September2020;Receivedinrevisedform12November2020;Accepted10December2020
Availableonline16December2020
Fig.1. OverviewofthestepsinvolvedinDEBM.InputfortheDEBMmodelisacross-sectionaldataset𝑋 with𝑀 subjectsandvariousbiomarkers(𝐴,𝐵,𝐶 and𝐷)
representingdifferentaspectsofneuro-degeneration.UsingGaussianmixturemodeling(GMM),mixingparameters(𝜃𝑖)andprobabilitydensityfunctionsofnormal
(𝑝(𝑥⋅,𝑖|¬𝐸𝑖))andabnormal(𝑝(𝑥⋅,𝑖|𝐸𝑖))levelsareestimatedforeachbiomarker.Thisisfollowedbytheestimationofsubject-specificorderings(𝑠𝑗),foreachsubjectin thedataset.Diseaseprogressiontimelineconsistingofcentralordering(𝑆)andevent-centers(𝜆)areestimatedbasedonthesesubject-specificorderings.Basedon theconstructeddiseaseprogressiontimeline,patientstages(Υ𝑗)ofsubjectsinanindependenttest-setcanbeestimated.
isphenotypicallyheterogeneous(Auetal.,2015;Murrayetal.,2011; Patterson,2018)withpotentiallydifferentpathwaysfordisease progres-sion,thesepathwaysremainunclear.Thereishenceaneedto under-standthephenotypicheterogeneityinADwhileleveraging neuroimag-ing,fluidandcognitivebiomarkers.
APOEisatriallelicgeneinwhichthe𝜀2allelereducestheriskof AD(vanderLeeetal.,2018),the𝜀3alleleactsasareferencealleleand the𝜀4alleleisamajorgeneticriskfactorofAD(Geninetal.,2011;Kim etal.,2009;Saundersetal.,1993).APOEhasbeenshowntocorrelate withphenotypicheterogeneityinAD(Weintraubetal.,2019).Hencewe hypothesizethatthepathophysiologyofADcanbebetterunderstood whenconsideringtheeffectofAPOEcarriershiponbiomarkerchanges. Inthecontextofdata-drivenmethodsforunderstandingAD patho-physiology,diseaseprogressionmodelshavebeenusedtostudythe tra-jectoriesofindividualbiomarkers(Jedynaketal.,2012;Lorenzietal., 2019;Schirattietal.,2015)aswellastheirprogressionwithrespectto eachother(Fonteijnetal.,2012;HuangandAlexander,2012; Venka-traghavan etal., 2017; Young etal., 2014). Unliketypical machine learningapproaches,thesemodelsareinterpretablebydesignand pro-videinsightforunderstandingthemechanismsofdiseaseprogression. Event-basedmodels(EBMs)areaclassofsuchinterpretabledisease pro-gressionmodelsthatestimatethetimelineofneuropathologicchange duringADprogressionusingcross-sectionaldata(Fonteijnetal.,2012; Venkatraghavanetal.,2019a).
Our primary aim is touse the discriminativeevent-based model (DEBM),whichwas showntobe moreaccuratethanpreviously pro-posedEBMs(Venkatraghavanetal.,2019a),tounderstandtheeffectof differentAPOEallelesonthediseasetimelineofAD.Toshedlighton differentaspectsofneurodegenerationandidentifytheearliestbrain regions affected, we included commonlystudied cerebrospinal fluid (CSF) biomarkers,cognitivescores, and volumetricbiomarkers from neuroimaging.
Thedefaultapproachforestimatingthediseaseprogressiontimeline wouldbetostratifythepopulationbasedontheirAPOE𝜀2−4carrier statusandindependentlytraintheDEBMmodelonthestratified pop-ulations(Youngetal., 2014).However,sinceDEBMisadata-driven model,stratification into smallergroupswouldlead tolessaccurate modelsthanthoseobtainedbytheoriginalmethodontheentiredataset. Henceoursecondaryaimistoproposeandevaluateanovelapproach inwhichwesplitthedifferentstepsofDEBMintogroup-aspecificand group-specificparts,wheretheentiredatasetisusedtotrainthe group-aspecificpartsandonlythedatafromaspecificgroupisusedtotrainthe group-specificpartsoftheDEBM.Wepresenttwodifferentvariations ofthisapproachandwehypothesizethattheoptimalsplitoftheDEBM stepsintothegroup-aspecificandgroup-specificpartswouldresultin betteraccuracyoftheestimateddiseaseprogressiontimeline.Sincethe ground-truthtimelinesareunknowninaclinicalsetting,weevaluate theaccuracyoftheproposedvariationsusingsimulationexperiments andweselecttheoptimalmethodfortheanalysisontheeffectofAPOE
ontheADprogressiontimelineonpatientdata.
Tosummarize,ourcontributionsinthispaperincludeproposingand evaluatinganovelapproachforusingDEBMinstratifiedpopulations andestimatingacomprehensivetimelineofADprogression,intermsof biomarkerchanges,inthepresenceofdifferentAPOEalleles.
2. Methods
AnintroductiontotheDEBMmodel(Venkatraghavanetal.,2019a) isprovidedinSection2.1.InSection2.2weproposeournovelapproach forusingDEBMinstratifiedpopulationswithitstwovariations.
2.1. Discriminativeevent-basedmodeling
In a cross-sectional dataset (𝑋) of 𝑀 subjects, including cogni-tivelynormalindividuals(CN),subjectswithmildcognitiveimpairment (MCI)andpatientswithAD,let𝑋𝑗 denoteameasurementof biomark-ersforsubject𝑗∈ [1,𝑀],consistingofscalarbiomarkervalues𝑥𝑗,𝑖for 𝑖∈ [1,𝑁].𝑥⋅,𝑖denotesthe𝑖thbiomarkerforanyunspecified𝑗.DEBM
estimatestheposteriorprobabilitiesofindividualbiomarkersbeing ab-normal.Theseposteriorprobabilitiesareusedtoestimatetheordering ofbiomarkerchangesforeachsubjectindependently.Thecentral order-inganddiseaseprogressiontimelinefortheentiredatasetareestimated basedonthesesubject-specificorderings.Theresultingdisease progres-siontimelineisusedforassessingtheseverityofdiseaseinanindividual basedonhis/herbiomarkervalues.Figure1showsthedifferentsteps involvedinDEBM.
Step 1-MixtureModeling:AsADischaracterizedbyacascade ofneuropathologicalchangesthatoccursoverseveralyears, presymp-tomaticCNsubjectscanhavesomeabnormalbiomarkervalues.Onthe otherhand,insomeclinicallydiagnosedADsubjects,aproportionof biomarkersmaystillhavenormalvalues,astheymightnothavean un-derlyingADpathologyorcouldhaveatypicalAD.Henceclinicallabels cannotdirectly be propagatedtoindividualbiomarkers tolabel nor-malandabnormalbiomarkervalues.Weshallrefertothisasbiomarker labelnoiseintherestofthepaper.Inordertoestimatetheposterior probabilitiesofindividualbiomarkersbeingabnormal,DEBM,similar topreviouslyproposedEBMs(Fonteijnetal.,2012;Huangand Alexan-der,2012;Youngetal.,2014),fitsaGaussianmixturemodel(GMM) toconstructthenormal/pre-eventprobabilitydensityfunction(PDF),
𝑝(𝑥⋅,𝑖|¬𝐸𝑖),andabnormal/post-eventPDF,𝑝(𝑥⋅,𝑖|𝐸𝑖).Event𝐸𝑖inthis
notationisusedtodenotethecorrespondingbiomarkerbecoming ab-normaland¬𝐸𝑖denotesthecorresponndingbiomarerbeingnormal.The aforementionedPDFscanbeexpressedas:
𝑝(𝑥⋅,𝑖|¬𝐸𝑖)=(𝜇𝑖,¬𝐸;𝜎𝑖,¬𝐸) (1)
𝑝(𝑥⋅,𝑖|𝐸𝑖)=(𝜇𝑖,𝐸;𝜎𝑖,𝐸) (2)
Where,(⨘ ,∫)isthenormaldistributionwithmean𝜇 andstandard deviation𝜎.
Fig.2. OverviewofGMMoptimizationinDEBM.
For estimating these parameters robustly in the presence of biomarkerlabelnoise,thenormalandabnormalPDFestimatesarefirst initializedusingthemeanandstandarddeviationsaftertruncatingthe overlappingtailsoftheobserveddistributionsinCNandADsubjects. ThiscanbeobservedinFig.2,wheretheinitializationisperformedonly basedonthenon-overlappingpartsofgreenandredcurves,whilethe overlappingpartisleftouttoaccountforbiomarkerlabelnoise.Atthis stageofGMMinitialization,MCIsubjectsareleftoutaswell,because itisunsureaprioriwhethertheirbiomarkersarenormalorabnormal. TheresultinginitializedPDFsaredenotedaŝ𝑝(𝑥⋅,𝑖|¬𝐸𝑖))and̂𝑝(𝑥⋅,𝑖|𝐸𝑖).
Thisis followedbyanalternatingGMMmaximumlikelihood op-timizationschemeuntilboththeGaussian parametersaswellasthe mixingparametersconverge.Allthesubjects,includingMCI,areused forGMMoptimization.Afterconvergence,theseGaussiansareusedto representthePDFs𝑝(𝑥⋅,𝑖|¬𝐸𝑖)and𝑝(𝑥⋅,𝑖|𝐸𝑖).Themixingparameters(𝜃𝑖) areusedaspriorprobabilitiestoconvertthesePDFstoposterior prob-abilities𝑝(¬𝐸𝑖|𝑥⋅,𝑖)and𝑝(𝐸𝑖|𝑥⋅,𝑖).Fig.2showsanoverviewofthis opti-mizationscheme.
Step2-Subject-specificOrderings:𝑝(𝐸𝑖|𝑥𝑗,𝑖)∀𝑖areusedtoestimate thesubject-specificorderings𝑠𝑗.𝑠𝑗isestablishedsuchthat:
𝑠𝑗∋𝑝 ( 𝐸𝑠𝑗(1)|||𝑥𝑗,𝑠𝑗(1) ) >...>𝑝(𝐸𝑠𝑗(𝑁)|||𝑥𝑗,𝑠𝑗(𝑁) ) (3)
Step3-CentralOrdering:DEBMcomputesthecentralevent order-ing𝑆 fromthesubject-specificestimates𝑠𝑗.Todescribethedistribution
of𝑠𝑗,ageneralizedMallowsmodelisused(FlignerandVerducci,1988). Thecentralorderingisdefinedastheorderingthatminimizesthesumof distancestoallsubject-specificorderings𝑠𝑗,withprobabilisticKendall’s
Taubeingthedistancemeasure(Venkatraghavanetal.,2019a).While𝑆
denotesthesequenceofbiomarkerevents,therelativepositionofthese events(event-centers)inanormalizedscaleof[0,1]isdenotedbythe vector𝜆.Thepair{𝑆,𝜆}togetherformsadiseaseprogressiontimeline.
Step4-PatientStaging:Oncethediseaseprogressiontimelineis created,subjectsinanindependenttestset(𝑇)canbe placedonthis timelinetoestimatediseaseseverity.Thisisachievedbyconvertingthe biomarkervaluesofthetestsubjectstoposteriorprobabilities𝑝(𝐸𝑖|𝑥𝑗,𝑖), ∀𝑗∈𝑇.Thesecanbeusedtoestimatediseaseseveritiesintestsubjects byfirstestimating theconditionaldistribution 𝑝(𝑖|𝑆,𝑋𝑗),which esti-matestheprobability thatthefirst𝑖eventsof𝑆 haveoccurredfora test-subjectandtherestareyettooccur.
𝑝(𝑖|𝑆,𝑋𝑗)∝∏𝑖𝑙=1𝑝 ( 𝐸𝑆(𝑙)|||𝑥𝑗,𝑆(𝑙) ) × ∏𝑁 𝑙=𝑖+1 𝑝(‶𝐸𝑆(𝑙)|||𝑥𝑗,𝑆(𝑙) ) (4)
Thepatientstageofatestsubject(Υ𝑗)isdefinedastheexpectation of𝜆(𝑖)withrespecttotheconditionaldistribution𝑝(𝑖|𝑆,𝑋𝑗).
Υ𝑗 = ∑𝑁 𝑖=1𝜆(𝑖)𝑝(𝑖|𝑆,𝑋𝑗) ∑𝑁 𝑖=1𝑝(𝑖|𝑆,𝑋𝑗) (5)
2.2. Group-specificandgroup-aspecificpartsofDEBM
WeproposeextensionsofDEBMforstratifiedpopulations,i.e.,when thedataset𝑋 canbe subdividedin groups𝑔∈ [1,𝐺],basedon,e.g., genotype orphenotypeof thesubjects.Since DEBMis adata-driven model,datastratificationintosmallergroupswouldleadtomore inac-curatemodels(Venkatraghavanetal.,2019a).ToobtainbetterDEBM accuraciesinsuchscenario,weproposetoco-trainDEBMforestimating diseasetimelines∀𝑔 bysplittingDEBMintogroup-aspecificand group-specificparts.Thegroup-aspecificpartsofDEBMareestimatedusing
Fig.3. OverviewofGMMoptimizationstrategiesinthedifferentapproaches
forDEBManalysisinstratifiedpopulations.(a)Thedefaultapproachinwhich
GMMineachgroupistrainedindependently.(b)GMMincoupledDEBM,where
thedifferentgroupssharetheGaussianparameters,butthemixingparameters
areestimatedindependently.(c)GMMinco-initDEBMinwhichthedifferent
groupsarejointlyinitializedbeforetheGMMoptimization,buttheoptimization
isdoneindependentlyforeachgroup.
theentiredatasetandgroup-specificpartsareestimatedforeachgroup independently.
We firstdiscussthedefaultway ofindependentlytrainingDEBM inthedifferentgroupsandthenproposetwodifferentapproachesfor splittingDEBMintogroup-aspecificandgroup-specificparts.
Approach1:IndependentDEBM
Inthisdefaultapproach,eachgroupisconsideredasanindependent datasetandthediseaseprogressiontimelineineachgroupisestimated independently.GMMinsuchascenarioisillustratedinFig.3a.
Approach2:CoupledDEBM
DEBM→ {
𝑝(𝑥⋅,𝑖|¬𝐸𝑖),𝑝(𝑥⋅,𝑖|𝐸𝑖) group-aspecific
Inthisapproach,weassumethatthedifferentgroupssharethenormal andabnormalPDFs,buttheorderinginwhichthesebiomarkersbecome abnormalaredifferent.Themixingparameters(𝜃𝑖,𝑔)areconsideredas
group-specificpartof theDEBMalgorithmbecausetheproportionof subjectswithnormalandabnormalbiomarkervaluesineachgroup𝑔
iscorrelatedwiththepositionofthebiomarkeralongtheordering𝑆𝑔,
whichweexpecttobedifferentineachgroup.
Hence, in our approach, we modify the alternating GMM opti-mizationschemetojointlyoptimizetheGMMparametersofmultiple groups.First,theGMMalgorithmisinitializedwithoutconsideringthe groups,asexplainedinSection2.1.Secondly,aswiththedefaultDEBM, Gaussianparametersandmixingparametersarealternatelyoptimized. IncontrastincoupledDEBM,theGaussianparametersareestimated jointlyforallgroups,whilemixingparametersareestimatedseparately foreachgroup.ThishasbeenillustratedinFigure3b.
OncetheGMMoptimizationhasbeenperformed,𝑆𝑔and𝜆𝑔are
es-timatedineachgroup.Patientstaging(Υ𝑗)ofthetest-subjectsingroup
𝑔 arecomputedbasedonthediseaseprogressiontimeline{𝑆𝑔,𝜆𝑔}.
Approach3:Co-initDEBM
DEBM→ ⎧ ⎪ ⎨ ⎪ ⎩ ̂𝑝(𝑥⋅,𝑖|¬𝐸𝑖),̂𝑝(𝑥⋅,𝑖|𝐸𝑖) group-aspecific 𝑝𝑔(𝑥⋅,𝑖|¬𝐸𝑖),𝑝𝑔(𝑥⋅,𝑖|𝐸𝑖) group-specific 𝜃𝑖,𝑔,{𝑆𝑔,𝜆𝑔} group-specific (7)
Inthisapproach,weassumethatthedifferentgroupsdonotshare thenormalandabnormalPDFs,butthattheyareclosetoeachother. Hence, in co-init DEBM, we relax the constraint on 𝑝(𝑥⋅,𝑖|¬𝐸𝑖) and
𝑝(𝑥⋅,𝑖|𝐸𝑖)andinsteadconsidertheinitializedvaluesofnormaland abnor-malPDFs(̂𝑝(𝑥⋅,𝑖|¬𝐸𝑖)and̂𝑝(𝑥⋅,𝑖|𝐸𝑖))tobegroup-aspecificpartofDEBM. Weestimate𝑝𝑔(𝑥⋅,𝑖|¬𝐸𝑖)and𝑝𝑔(𝑥⋅,𝑖|𝐸𝑖)independentlyforeachgroup. ThisisillustratedinFig.3c.
Aswiththepreviousapproach,𝑆𝑔,𝜆𝑔andthepatientstagingofthe
test-subjectsingroup𝑔 arecomputedindependentlyforeachgroup.
3. Experiments
Section 3.1 describes the experiments to evaluate the proposed DEBMapproachesonastratifiedpopulation.Sinceground-truth order-ingsareunknown inrealclinicaldata,weusesimulateddatasetsfor evaluatingthemethods.Afterevaluatingtheproposedapproaches,we selectthebestapproachforanalyzingtheeffectofAPOEonAD progres-sionusingsubjectsfromtheAlzheimer’sDiseaseNeuroimaging Initia-tive(ADNI)database.Section3.2descibesthedetailsofthese experi-ments.
3.1. Simulationexperiments
WeusedtheframeworkdevelopedbyYoungetal.(2015)for simu-latingcross-sectionaldataconsistingofscalarbiomarkervaluesforCN, MCIandADsubjectsintwogroups.Inthisframework,disease progres-sioninasubjectis modeledbyaseriesofbiomarkerchanges repre-sentingthetemporalcascadeofbiomarkerabnormalityasestimatedby anEBM.Individualbiomarkertrajectoriesarerepresentedbysigmoids varyingfromthebiomarker’snormalvaluetoitsabnormalvalue.To ac-countforinter-subjectvariability,thenormalandabnormalvaluesfor differentsubjectsaredrawnrandomlyfromGaussiandistributions.
The simulation dataset used in our experiments are based on a set of seven biomarkers as described in thesimulation experiments ofVenkatraghavanetal.(2019a).Thesimulateddatasetswere strati-fiedintotwogroups,witheachgrouphavingitsowndistinctdisease progressionpatterns.Therearetwowaysinwhichtheprogressionof diseaseinthegroupscandiffer:1.differenceinground-truthorderings
𝑆1 and𝑆2; 2.differencein theabnormalbiomarkerPDFsinthetwo
groupsi.e.𝑝1(𝑥⋅,𝑖|𝐸𝑖)and𝑝2(𝑥⋅,𝑖|𝐸𝑖).Eachofthesedifferencescould
af-fecttheaccuracyoftheproposedapproaches.Hence,weevaluatedthe proposedapproachesinthepresenceofeachofthesedifferences. Nor-malizedKendall’sTaudistancebetweentheestimatedordering(𝑆)and
theground-truthordering(𝑆𝑔𝑡)wasusedasanevaluationmeasurein theseexperiments: 𝜀𝑆=𝐾(𝑆,𝑆𝑔𝑡 ) (𝑁 2 ) (8)
where𝐾(𝐴,𝐵)is thenumberof swapsrequiredtoobtainorderingB fromorderingA.
Thenormalizationensuresthat𝜀𝑆fallsintherange[0,1],with0as
thedistancewhenthetwoorderingsarethesame,and1asthedistance whenthetwoorderingsarethereverseofeachother.
Experiment1:Thefirstsimulationexperimentstudiedtheeffectof thedifferenceinorderingbetweenthetwogroups.Theorderinginthe firstgroup(Group1)wasfixedandtheorderinginthesecondgroup (Group 2)wasselected randomlysuchthatthenormalizedKendall’s Taudistancebetweenthetwogroupswasafixednumber,say𝜀𝑂.𝜀𝑂
wasvariedfrom0to1instepsof0.2.ThenumberofsubjectsinGroup 2waskeptconstantat900.Thenumberofsubjectsin Group1was variedfrom100to900instepsof200,tostudyhowthedifferent ap-proachesperforminsmallaswellaslargegroups.Thenormaland ab-normalbiomarkerslevelsinthetwogroupsweresampledfromthesame Gaussiandistributionforthisexperiment.Wegenerated50random rep-etitionsofthesimulateddatasets,andreportedmeanandstandard de-viationof𝜀𝑆forindependentDEBM,coupledDEBM,andco-initDEBM ingroups1and2.
Experiment2:Thisexperimentstudiedtheperformanceofthe pro-posedapproacheswiththe𝜇𝑔,𝑖,𝐸parameterofthe𝑝𝑔(𝑥⋅,𝑖|𝐸𝑖)distribution beingdifferentinthetwogroups.𝜇1,𝑖,𝐸wasfixed,and𝜇2,𝑖,𝐸wasvaried
suchthatthedifference𝜇2,𝑖,𝐸−𝜇1,𝑖,𝐸(𝜀𝐺)wasoneof{−0.2𝑑,0,+0.2𝑑}
where𝑑=𝜇1,𝑖,𝐸−𝜇1,𝑖,¬𝐸.0isconsideredthereferencelevel,wherethe
abnormalGaussiansarethesameinthetwogroups.𝜇𝑔,𝑖,¬𝐸 werekept
thesame inthe twogroups.Hence, when𝜀𝐺=−0.2𝑑,theabnormal
biomarkerlevelsareclosertothenormalbiomarkerlevelsinGroup 2thaninGroup1.Thisresults inGroup2biomarkersbeingweaker thantheirGroup1counterpartswhen𝜀𝐺=−0.2𝑑 andstrongerwhen 𝜀𝐺=+0.2𝑑.ThenumberofsubjectsinGroup2waskeptaconstantat
900,whilethesubjectsinGroup1increasedfrom100to900.𝜀𝑂 be-tweenthetwogroupswasfixedat0.4.Weagaingenerated50random repetitionsofthesimulateddatasets,andreportedmeanandstandard deviationof𝜀𝑆forcoupledDEBM,co-initDEBMandDEBM.
Theseexperimentswereusedtoevaluatethedifferent approaches mentioned inSection2andselectthebestmethod foranalyzingthe effectofAPOEallelesinADprogression.
3.2. StudyingtheeffectofAPOE
Weconsideredthebaselinemeasurementsfrom417CN, 235MCI convertersand342ADsubjectsinADNI1,ADNIGOandADNI2studies.2
TheMCIconvertersaresubjectswhohadMCIatbaselinebutconverted toADwithin3yearsofbaselinemeasurement.Weexcludedsubjects withsignificantmemoryconcerns(withoutadiagnosisofADorMCI) andMCInon-convertersinourexperimentstoselectamore phenotyp-icallyhomogeneousgroupofsubjectswithprevalentorincidentAD.In eachoftheexperiments,thedatasetwasdividedintothreegroups(𝜀2 carriers,homozygous𝜀3carriers,and𝜀4carriers)basedonthesubject’s
APOEcarriership(vanderLeeetal.,2018).SubjectswithAPOE𝜀2,4 (n=34)werenot includedineithergroupbecauseof thepresenceof both𝜀2and𝜀4alleles
2TheADNIwaslaunchedin2003asapublic-privatepartnership,ledby
Prin-cipalInvestigatorMichaelW.Weiner,MD.TheprimarygoalofADNIhasbeen
totestwhetherserialmagneticresonanceimaging(MRI),positronemission
to-mography(PET),otherbiologicalmarkers,andclinicalandneuropsychological
assessmentcanbecombinedtomeasuretheprogressionofmildcognitive
im-pairment(MCI)andearlyAlzheimersdisease(AD).Forup-to-dateinformation,
Table1
Demographicsfortheusedpopulation.2⋆representsthesubjectswithAPOE
alleles𝜀2,2and𝜀2,3.33representsthesubjectswithreferenceAPOEallele𝜀3,3.
⋆4representsthesubjectswithAPOEalleles𝜀3,4and𝜀4,4.Subjectswithboth
𝜀2and𝜀4alleleswereexcludedfromthisstudy(n=34).Edu.isanabbreviation usedforEducation.
Demographics Diagnosis CN MCIc AD 𝑛 417 235 342 APOE 2 ⋆ /33/ ⋆ 4 57/244/110 6/66/156 12/101/219 Sex M/F 209∕208 145∕90 189∕153 Age [yrs.] ( 𝜇 ± 𝜎) 74 . 8 ± 5 . 7 73 . 7 ± 7 . 0 75 . 0 ± 7 . 8 Edu [yrs.] ( 𝜇 ± 𝜎) 16 . 3 ± 2 . 7 15 . 9 ± 2 . 7 15 . 2 ± 3 . 0 Table2
BiomarkeravailabilityinnumberofsubjectsintheAPOEbasedgroupsof𝜀2
carriers,homozygous𝜀3carriers,and𝜀4carriers.
Biomarker availability Biomarker 𝜀 2 carriers ( 𝑁 = 75) Homozygous 𝜀 3 carriers ( 𝑁 = 411) 𝜀 4 carriers ( 𝑁 = 485) Imaging 74 408 481 ABETA 57 301 357 PTAU 57 301 357 TAU 57 299 348 NG 21 113 131 NFL 23 118 137 MMSE 75 411 485 ADAS 74 410 477
SubjectdemographicsandtheirAPOEcarriershipsaresummarized inTable1.Themodalitiesconsideredwerestructuralimaging biomark-ers,biomarkers extractedfrom cerebrospinal fluid(CSF),and cogni-tivebiomarkers.Structuralimagingbiomarkerswereobtainedfrom T1-weightedMRI acquiredat1.5Tor3T. DetailsoftheMRIacquisition protocolsofADNIcanbefoundinJackJr.etal.,2008,2015.
Imagingbiomarkers wereestimated fromT1-weighted MRI scans analysedwithFreeSurfersoftwarev6.0cross-sectionalstreamand out-putswerevisuallychecked.Weassumedasymmetricpatternof atro-phyinADandaveragedimagingbiomarkersbetweentheleftandright hemisphere.
Experiment3:Forthisexperiment,theselectedimagingbiomarkers were:hippocampalvolume,volumeoftheentorhinalcortex,fusiform gyrusvolume,middle-temporalgyrusvolume,precuneusvolume, to-getherwithwholebrainvolumeandvolumeoftheventricles(Archetti et al., 2019; Frisoni et al., 2010; Vemuri and Jack, 2010). The se-lected CSF based biomarkers were: CSF concentrationsof
Amyloid-𝛽42(ABETA),totalTau(TAU)andphosphorylatedTau181(PTAU)
pro-teins (Blennow and Hampel, 2003; Blennow et al., 2010), Neuro-granin(Thorselletal.,2010)andNeurofilamentlightchain(Jinetal., 2019;deWolfetal.,2020).Minimentalstateexamination(MMSE)and Alzheimer’sDiseaseAssessmentScale-Cognitive(13items)(ADAS13) wereusedascognitivebiomarkers.Theavailabilityofthesemultimodal biomarkersintheADNIdatabaseissummarizedinTable2.
Wedownloaded theCSFmeasurements fromthe ADNIdatabase. Themeasurementsof ABETA,TAU andPTAUhadbeenmade using themicrobead-based multiplex immunoassay, theINNO-BIAAlzBio3 RUO(Olssonetal.,2005).ThemeasurementofNFLhadbeenmadewith enzyme-linkedimmunosorbentassayNF-lightELISAkit(Mattssonetal., 2017).NGhadbeenmeasuredbyelectrochemiluminescence technol-ogy(MesoScaleDiscovery) usingamonoclonalantibodyspecificfor NG(Ng7)forcoatingtogetherwithadetectorantibodypolyclonal neu-rograninanti-rabbit(ab23570,Upstate)(Porteliusetal.,2015).As de-scribedpreviouslyinVenkatraghavanetal.(2019a),theTAUandPTAU measurementsweretransformedtologarithmicscalestomakethe dis-tributionslessskewedandmoresuitableforDEBManalysis.
Thevolumesoftheselectedregionswereregressedwithage,sexand intra-cranialvolume(ICV)andtheeffectsofthesefactorswere subse-quentlycorrectedfor,beforebeingusedasbiomarkers.Theeffectsof ageandsexwereregressedoutofCSFfeatures,whereaseffectsofage, sexandeducationwereregressedoutofcognitivescores.
Forthe12selectedbiomarkers,weestimatedthediseasetimelinesin thethreeaforementionedgroupsusingthemethodselectedafter simu-lationexperiments.Westudiedthepositionalvarianceoftheestimated orderingsbycreating100bootstrappedsamplesofthedata.Inorder toevaluateiftheestimatedorderingsinthethreegroupswere signif-icantly differentfrom oneanother, weusedpermutation testing and estimatedthedistributionoftheKendall’sTaudistanceunderthenull hypothesis.Tocomputethisdistribution,wegenerated10,000random permutationsofthethreegroups.Wethencomputedtheone-sided𝑝 -valuesfortheactualKendall’sTaudistancesbetweentheorderingsof thethreegroups,calculatedastheproportionofsampledpermutations wherethedistancewasgreaterthanorequaltotheactualdistance,and usingBonferronicorrectiontoaccountformultipletesting.
Experiment 4:Inthisexperiment,wevalidatedthediseasestage (Υ𝑗)bycomputingitscorrelationwiththesubjects’MMSEandADAS13 values.Weuseda10-foldcrossvalidation,wherethetrainingsetwas usedtoestimatethediseasetimelineintheaforementionedgroupsand thetestsubjects’diseasestagewasevaluatedbyplacingthemonthis diseasetimeline.Weusedthevolume-basedandCSF-basedbiomarkers fromExperiment3,butexcludedMMSEandADAS13scoresfromthe model.
4. Results
4.1. Simulations
Experiment1:Fig.4(a)and(b)showtheorderingerrors(𝜀𝑆)in Group1ofthesimulationdatasetsforDEBM,coupledDEBMand co-init DEBMasa functionofnumberof subjectsinGroup1,when𝜀𝑂
betweenthetwogroupschangesfrom0to1.Fig.4(c)–(e)show𝜀𝑆in Group2ofthesimulationdatasetsfortheaforementionedmethods,asa functionofnumberofsubjectsinGroup1.Inourexperiments,Group1 datasetremainsthesamewhileGroup2datasetchangesas𝜀𝑂increase. HenceDEBMresultsdonotchangewithchangein𝜀𝑂inFig.4(a)and
(b),whereasinFig.4(c),DEBMresultsdonotchangewithincreasein numberofsubjectsinGroup1.
Itcanbeseenthatbothcoupled-trainingmethods(i.e.,co-initDEBM andcoupledDEBM) outperformthedefaultmethodof independently trainingDEBMmodels.Itcanalsobeobservedthatinbothco-initDEBM andcoupledDEBMtheordering errorsdecrease as𝜀𝑂 increasesand
thatco-initDEBMoutperformscoupledDEBMforlowervaluesof𝜀𝑂,
whereastheperformanceisonparwithcoupledDEBMforhighervalues of𝜀𝑂.
Experiment2:Fig.5(a)and(b)show𝜀𝑆inGroup1andFig.5(c)–
(e)showthesameinGroup2,whenvarying𝜀𝐺.Evenwith𝜀𝐺≠ 0,
cou-pledtraining(i.e.,co-initDEBMandcoupledDEBM)outperformedthe defaultmethodofindependentlytrainingDEBMmodels.Co-initDEBM showednegligiblechangeintheerrorswhen𝜀𝐺≠ 0.Theperformance
ofcoupledDEBMinGroup1worsenedfor𝜀𝐺=+0.2𝑑 (Fig.5(a))and inGroup2for𝜀𝐺=−0.2𝑑 (Fig.5(d)).
4.2. StudyingtheeffectofAPOE
Theresultsin Experiments1and2showthattheperformanceof co-initDEBMismoreaccurateandrobustthancoupledDEBMinmost scenarios.WehenceanalyzedExperiments3and4usingco-initDEBM.
Experiment3:Fig.6showsorderingsofCSF,globalcognitionand volumetricbiomarkersintheAPOEbasedgroupsof𝜀2carriers, homozy-gous𝜀3carriers,and𝜀4carriersalongwiththeiruncertaintyestimates. Itcan beseen thattheuncertaintyof theordering inthe𝜀2carriers groupwashigh.Despitethisuncertainty,somebiomarkers(i.e.MMSE,
Fig.4. Experiment1:Theeffectof𝜀𝑂(thedifferenceingroundtrutheventorderingsinthetwogroups)ontheperformanceoftheproposedmethods.Theshaded regionintheseplotsrepresentsstandarddeviationoftheerrorinestimationoftheproposedmethodsin50randomiterationsofsimulations.Theplotsin(a)and(b)
showtheorderingerrorsinGroup1usingCoupledDEBMandCo-initDEBMwithindependentDEBMshowninboth(a)and(b),asafunctionofnumberofsubjects
inGroup1.Theplotsin(c),(d)and(e)showtheorderingerrorsinGroup2usingindependentDEBM,CoupledDEBMandCo-initDEBMrespectivelyasafunction
ofnumberofsubjectsinGroup1.
NGandPTAU)seemtooccurearlierthantheotherbiomarkersinthis group.
Inthehomozygous𝜀3carriergroup,ABETAwasveryprominently the earliest biomarker, followed by cognitive scores of MMSE and ADAS13.AmongtheCSFbiomarkers,PTAUfollowedimmediately af-terABETA,whichwasinturnfollowedbyTAU.NFLandNGwerelate biomarkers.Amongthestructuralbiomarkers,volumesoffusiformand middle-temporalgyriwerethefirsttobecomeabnormal,followedby ventricularvolumeandwholebrainvolume.Hippocampus,precuneus andentorhinalvolumeswerelatebiomarkersinthisgroup.
Inthe𝜀4carriergroup,theCSFbiomarkersfollowedapatternthat wassimilartothatofthehomozygous𝜀3carriergroup.Thecognitive biomarkerswereearlybiomarkersinthisgroupaswell.Howeverthe orderinginstructuralbiomarkerswasverydifferent fromthatinthe homozygous 𝜀3carrier group. Hippocampus andentorhinalvolumes
wereearlybiomarkersinthisgroup,followedbymiddle-temporaland fusiformgyrivolumes.Wholebrain,ventricularandprecuneusvolumes werelatebiomarkers.
Theorderingofthe𝜀2carriergroupwassignificantlydifferentfrom thatofthehomozygous𝜀3carriergroup(𝑝=0.0156,afterBonferroni correctionformultipletesting).Similarly,theorderingsfortheother twogroupsweresignificantaswell:𝑝=0.0147forthedifference be-tween 𝜀2 carrier group and𝜀4 carrier group and𝑝=0.0003 for the difference between the homozygous 𝜀3carrier group and 𝜀4 carrier group.
Experiment4:ThevariationofMMSEandADAS13scoreswith re-specttotheestimateddiseasestageshasbeenplottedinFig.7,forall threegroups.Thepatientstagesshowedasignificantcorrelationwith bothMMSEandADAS13scores.Thecorrelationcoefficientswerealso comparableinthethreegroups.
Fig.5. Experiment2:Theeffectof𝜀𝐺(differenceinabnormalbiomarkerlevelsinthetwogroups),ontheperformanceoftheproposedmethods.Theshadedregion
representsstandarddeviationoftheerrorin50randomiterations.Theplotsin(a)and(b)showtheorderingerrorsinGroup1usingCoupledDEBMandCo-init
DEBMwithindependentDEBMshowninboth(a)and(b),asafunctionofnumberofsubjectsinGroup1.Theplotsin(c),(d)and(e)showtheorderingerrorsin
Group2usingindependentDEBM,CoupledDEBMandCo-initDEBMrespectivelyasafunctionofnumberofsubjectsinGroup1.
5. Discussion
DEBMmodelshavebeenshowntobeeffectiveindeterminingthe temporal cascadeof biomarkerabnormality as AD progresses, from cross-sectionaldata.Inthiswork,weintroducedanovelconceptof split-tingthedifferentstepsofDEBMintogroup-specificandgroup-aspecific partsforcoupledtraininginstratifiedpopulation.Weconsideredtwo novelvariationstosplitthestepsofDEBMinthismannerandthrough thoroughexperimentationinsimulationdatasetsweobservedthat co-initDEBMhelpsin obtainingmore accurateorderingsinastratified population.Usingthismethod,weestimatedthebiomarkercascadesin ADprogressionwith𝜀2alleles,homozygous𝜀3alleles,and𝜀4allelesof
APOE,basedoncross-sectionalADNIdata.Whilethefindingsinthe ho-mozygous𝜀3carrierand𝜀4carriergroupsfitthecurrentunderstanding ofprogressionofADwithhigh-confidence,thefindinginthe𝜀2carrier groupshowsevidenceforanalternativepathway(withrelativelylow confidence).Inthissection,wediscusstheinsightsprovidedbythe sim-ulationexperiments(Section5.1)usedformethodselectionaswellas theinsightsintotheADprogressionpathwaysprovidedbyour experi-mentsontheADNIdataset(Section5.2).
5.1. Choiceofthemethod
Coupled DEBM and co-init DEBM both split DEBM into group-specificandgroup-aspecific stepsfor coupledtrainingof anEBMin stratifiedpopulations.Experiment1and2showedthatcoupled
train-ingof thegroup-aspecific partsof DEBMandindependentlytraining thegroup-specificpartsofDEBMresultsinmoreaccurateorderingsin thegroupsbetterthanthedefaultapproachofindependentlytraininga DEBMmodelineachgroup.
WhilesplittingDEBMintogroup-specificandgroup-aspecificparts, westartedwiththeassumptionthatthelatenttruenormaland abnor-malbiomarkerdistributionsinthegroupsareeithersameorsimilar. Thedifferencebetweenco-initDEBMandcoupledDEBMisthat, co-initDEBMaccountsforslightdifferencesintheunderlyingbiomarker distributionsbetweenthegroupswhereascoupledDEBMdoesnot.
ThesimulationdatasetgeneratedinExperiment1hadthesametrue normalandabnormalbiomarkerdistributionsinthedifferentgroups, from whichthe simulatedsubjects wererandomlysampled,aligning wellwiththeassumptionofcoupledDEBM.However,thisdidnot re-sultinoverallbetteraccuraciesforcoupledDEBMthanthatofco-init DEBM.Co-initDEBMwasalsomorerobustthancoupledDEBMasits ac-curacywaslessdependenton𝜀𝑂,thedistancebetweentheground-truth
orderingsinthetwogroups.
Another observationin Experiment1, which wasrather counter-intuitive,wasthattheerrorsmadebytheco-initandcoupledDEBM modelsdecreasedasthedistancebetweentheground-truthorderings inthetwogroupsincreased.Whentheorderingsarefurtherapart,the combinedbiomarkerdistributionsinCNandADgroupshavealarger overlap.Thenon-overlappinginitialization(beforetheGMM optimiza-tion)thus resultsinthenormalandabnormaldistributionstobe fur-ther apart.Wehypothesizethatthis resultsin abetterestimationof
Fig. 6. Experiment 3: Orderings of CSF, global cognition and volumetric
biomarkersintheAPOEbasedgroupsof𝜀2carriers,homozygous𝜀3carriers,
and𝜀4carriersalongwiththeiruncertaintyestimates.Uncertaintyinthe
esti-mationoftheorderingwasmeasuredby100repetitionsofbootstrapping,in
thethreeAPOEbasedgroups.Thecolor-mapisbasedonthenumberoftimes
abiomarkerisatapositionin100repetitionsofbootstrapping.Thenumberof
subjectsinthethreegroupswere75,411and485respectively.Theorderings
wereobtainedusingCo-initDEBM.
themixingparametersduringGMMoptimizationandin-turnresulted inmoreaccurateorderings,asmixing-parametersaredependentonthe biomarker’spositionintheordering.
InExperiment2, wecheckedthe performanceofour approaches whentheassumption(truenormalandabnormalbiomarker distribu-tionsbeingsameacrossgroups)isviolatedinthedataset.This experi-mentshowedthattheorderingsobtainedusingco-initDEBMaremore robust todifferencesbetween theabnormal Gaussians across groups thanthoseobtainedwithcoupledDEBM.WithcoupledDEBM,theerror increasedinthegroupwithweakerbiomarkersi.e.,Group1inthecase of𝜀𝐺=+0.2𝑑 andGroup2inthecaseof𝜀𝐺=−0.2𝑑.Thisshowsthat coupledDEBMintroducesasystematicbiasintheestimationofordering thatisdetrimentaltothegroupwithweakerbiomarkers.Co-initDEBM alsoshowedasimilarbias,buttoamuchlesserextent.
Wehenceselectedco-initDEBMasthepreferredapproachfor split-tingandperformedouranalysisonADNIdatasetusingthisapproach. We expect that this idea of splitting DEBM into group-specific and group-aspecific parts can be easily extended tothe EBMintroduced byFonteijnetal.(2012).
5.2. CascadeofbiomarkerchangesintheAPOEbasedgroups
Dividing the total population into groups based on APOE car-riership enabled us to create more phenotypically homogeneous groups(Weintraubetal.,2019),eachwithpotentiallyspecificdisease progression timeline. Inthis section,we discussour results in these
APOEcarriershipbasedgroups.
Our findings show that the three APOE-carriership based groups have significantlydifferenttemporalcascadesof diseaseprogression. Thissuggeststhattheunderlyingpathwaysofprogressionaredifferent forthethreegenotypes.AmongtheCSFbiomarkersinthehomozygous
𝜀3carrierandthe𝜀4carriergroups,ABETAabnormalityistheearliest biomarkereventfollowedbyPTAU.Thisfitscurrentunderstandingof ADprogression(Bloom,2014).Italsoconfirmstheneedforpreventing theaccumulationofABETAinhigh-riskpatients.NFLandNGarelate biomarkersinthehomozygous𝜀3carrierand𝜀4carriergroups,which suggeststhataxonal(Ashtonetal.,2019)andsynaptic(Thorselletal., 2010)degenerationdonotoccuruntilverylateinthediseaseprocessin thesegroups.NGbeingabnormalafterPTAUandTAUinthe homozy-gous𝜀3carrierand𝜀4carriergroupsisalsoconsistentwiththeprevious findingsthatTaumediatessynapticdamageinAD(Jadhavetal.,2015). Inthe𝜀2carriergroup,wefoundthattheabnormalNGandPTAU aretheearliestCSFevents,evenbeforeABETAbecomesabnormal.This couldhintattheexistenceofanalternativepathwayfortheformation of tautanglesinthebrainbeforeABETAaccumulation,assuggested inWeigandetal.(2019),butneedsmoreextensivevalidation.
Amongthevolumetricbiomarkers,Entorhinalcortexisoneofthe earlybiomarkersinthe𝜀4carriergroupwhichissupportedbythe find-ingsinHuijbersetal.(2014),butisoneofthelastbiomarkersto be-comeabnormal inthehomozygous𝜀3carriergroup.Ventricular vol-umeisalatebiomarkerinthe𝜀4carriergroupbutitbecomes abnor-malquiteearlyinthehomozygous𝜀3carriergroupasalsoobserved byNestoretal.(2008).Hippocampusvolumeistheearliestbiomarker in the𝜀4carrier group,butisa relativelylatebiomarkerinthe ho-mozygous𝜀3carrierand𝜀2carriergroups.Thissuggeststhatincidence ofhippocampalsparingAD(Ferreiraetal.,2017)couldcorrelatewith
APOEcarriership.
Thefindings relatedtothese orderingsof biomarkereventswere validatedbycorrelatingthepatientstagesderivedfromtheseorderings withMMSEandADAS13scores.Patientstagesofsubjectsinallthree groups,whenusedastest-subjectsinacross-validatedmanner,showeda significantcorrelation(𝑝<0.001)withthesescores.Thesecorrelations validateourfindingsandsuggestthatthesegenotype-specificdisease progressiontimelinescouldbeusedforpatientmonitoring.
Fig. 7.Experiment 4: Correlation of
esti-mateddiseasestageswithMMSEandADAS
scoresintheAPOEbasedgroupsof𝜀2carriers, homozygous𝜀3carriers,and𝜀4carriers.The
plotontopofeachsubfigureshowsthe
prob-abilitydensityfunctionofthediseasestages,
andtheplotontherightof eachsubfigure
showstheprobabilitydensityfunctionofthe
cognitivescoreinthesubfigure.The2Dplot
ineachsubfigureshowsthejointdensity func-tionofthetwoaxes.Thelineineachsubfigure
showsthelinearregressionofMMSE/ADAS
scoreswiththeestimateddiseasestageandthe shadedareaaroundthelineshowsits95% con-fidenceinterval.Figures(a),(c)and(e)depict
correlationbetweenMMSEscoreandobtained
diseasestagesinthethreeAPOEbasedgroups. Figures(b),(d)and(f)depictcorrelation
be-tweenADAS13scoreandtheobtaineddisease
stagesinthethreeAPOEbasedgroups.
6. Conclusionandfuturework
Weconcludethatco-initDEBMprovidesthebestaccuracyand ro-bustness when estimating orderings in stratified populations. Future workonco-initDEBMcanfocusonextendingtheapproachfor high-dimensionalimagingbiomarkers(Venkatraghavanetal.,2019b).This
work also provides groundwork for extending the method towards hypothesis-free,data-drivenstratificationofphenotypes.
WegainednewinsightsintothediseaseprogressiontimelineofAD intheAPOEbasedgroupsof𝜀2carriers,homozygous𝜀3carriers,and
𝜀4carriers.Whileweobservedthattheestimateddiseaseprogression timelines in the𝜀4 carrierandthehomozygous𝜀3 carriergroupsfit
thecurrentunderstandingofADprogressionwithhighconfidence,the estimatedtimelinesinthe𝜀2carriergroupmaysuggestanalternative pathwayfortheformationoftautanglesinthebrainbeforeamyloid
𝛽 accumulation,albeitwithrelativelylow condence.Weexpect that
thesegenotype-specificdiseaseprogressiontimelineswillbenefitpatient monitoringinthefuture,andmayhelpoptimizeselectionofeligible subjectsforclinicaltrials.
Acknowledgement
ThisworkispartoftheEuroPONDinitiative,whichisfundedbythe EuropeanUnion’sHorizon2020researchandinnovationprogramme undergrantagreementNo. 666992. E.E.Bronacknowledgessupport fromtheDutchHeartFoundation(PPPAllowance,2018B011),Medical DeltaDiagnostics3.0:DementiaandStroke,andtheNetherlands Cardio-VascularResearchInitiative(Heart-Brain Connection:CVON2012-06, CVON2018-28).Datacollectionandsharingforthisprojectwasfunded bytheAlzheimer’sDiseaseNeuroimagingInitiative(ADNI)(National InstitutesofHealthGrantU01AG024904)andDODADNI(Department ofDefenseawardnumberW81XWH-12-2-0012).ADNIisfundedbythe NationalInstituteonAging,theNationalInstituteofBiomedical Imag-ingandBioengineering,andthroughgenerouscontributionsfromthe following: AbbVie,AlzheimersAssociation;Alzheimer’sDrug Discov-eryFoundation;AraclonBiotech;BioClinica,Inc.;Biogen;Bristol-Myers SquibbCompany;CereSpir,Inc.;Cogstate;EisaiInc.;Elan Pharmaceu-ticals,Inc.;EliLillyandCompany;EuroImmun;F.Hoffmann-LaRoche LtdanditsaffiliatedcompanyGenentech, Inc.;Fujirebio;GE Health-care;IXICOLtd.;JanssenAlzheimerImmunotherapyResearch& Devel-opment,LLC.;Johnson&JohnsonPharmaceuticalResearch& Develop-mentLLC.;Lumosity;Lundbeck;Merck&Co.,Inc.;MesoScale Diagnos-tics,LLC.;NeuroRxResearch;NeurotrackTechnologies;Novartis Phar-maceuticalsCorporation;PfizerInc.;PiramalImaging;Servier;Takeda PharmaceuticalCompany;andTransitionTherapeutics.TheCanadian InstitutesofHealthResearchisprovidingfundstosupportADNI clin-icalsitesinCanada.Privatesectorcontributionsarefacilitatedbythe FoundationfortheNationalInstitutesofHealth(www.fnih.org).The granteeorganizationistheNorthernCalifornia InstituteforResearch andEducation,andthestudyiscoordinatedbytheAlzheimer’s Thera-peuticResearchInstituteattheUniversityofSouthernCalifornia.ADNI dataaredisseminatedbytheLaboratoryforNeuroImagingatthe Uni-versityofSouthernCalifornia.
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