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September 26 2017
Speaker: Viswanath Devanarayan, PhD, FAAPS, Charles River Laboratories
Dr. Devanarayan is currently the Executive Director and Head of Global Statistics at Charles River Laboratories. He has over 21 years of combined pharmaceutical research experience from Eli Lilly, Merck, and AbbVie. His statistical & data-analytic contributions span a wide range of applications across drug discovery and development, such as target identification, high-throughput-screening, genomics, proteomics, bioanalytical methods, precision medicine, and exploratory clinical research. He has filed 10 patent applications, given over 100 invited talks at scientific meetings, and co-authored over 55 publications that includes several white-papers with regulatory, academic and industry scientists. He is an elected Fellow of the American Association of Pharmaceutical Scientists (AAPS), and is also serving as an Adjunct Professor at the University of Illinois in Chicago. He is currently volunteering as the AAPS Task Theme Chair on Predictive Modeling.
Title: Subgroup identification algorithms for precision medicine
Abstract: Causal mechanism of relationship between the clinical outcome (efficacy or safety endpoints) and putative biomarkers, clinical baseline, and related predictors is usually unknown and must be deduced empirically from experimental data. Such relationships enable the development of tailored therapeutics and implementation of a precision medicine strategy in clinical trials to help stratify patients in terms of disease progression, clinical response, treatment differentiation, and so on. These relationships often require complex modeling to develop the prognostic and predictive signatures. For the purpose of easier interpretation and implementation in clinical practice, defining a multivariate biomarker signature in terms of thresholds (cutoffs/cut points) on individual biomarkers is preferable. In this talk, we will propose some methods for developing such signatures in the context of continuous, binary and time-to-event endpoints. Results from simulations and case study illustration are also provided.
Biomarker-basedsubgroupidentificationforprecisionmedicine
V.Devanarayan,Ph.D.,FAAPSCharlesRiverLaboratories
JointworkwithDrs.XinHuang&YanSun,AbbVieInc.
PresentedforOntarioInstituteforCancerResearch,Toronto,Canada,September26,2017
SubgroupIdentificationforPrecisionMedicine|PresentationforOICR,September26,2017|V.Devanarayan
1. ImportanceofPrecisionMedicine
2. DifferencebetweenPredictivevs.PrognosticSignatures
3. “Threshold-basedmultivariatesignatures”:whyandhow
4. Predictingtheperformanceinafutureclinicaltrial(significance:p-value,effectsize,etc.)
5. Exampleofthisapplicationduringdrugdevelopment
Outline(“learningtopics”)
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Discovery Pre-clinical Phase 1,2 Phase 3 Phase 4
Drug Development
Discovery
Demonstration
Characterization
Qualification
SurrogacyPredictive use of efficacy &
safety biomarkers
Candidates attrition & refinement
Dose selection, PK/PD modeling
Efficacy & safety “valid” & putative markers
PoM, protocol design
Patient stratificationOther indications
Market differentiationPost approval surveillance
TranslationalMedicine
Biomarkerdevelopment&Drugdevelopmentareintertwined
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SubgroupIdentificationforPrecisionMedicine|PresentationforOICR,September26,2017|V.Devanarayan
WhyPrecisionMedicine?
EdwardAbrahamsandMikeSilver.TheCaseforPersonalizedMedicine.(2009)JournalofDiabetesScienceandTechnologyV3Issue4
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GenomicBiomarkersforPrecisionMedicinesinOncology
SikorskiRandYaoB.2010.VisualizingtheLandscapeofSelectionBiomarkersinCurrentPhase3OncologyClinicalTrials.ScienceTranslationalMedicine,2,34,34ps27
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SubgroupIdentificationforPrecisionMedicine|PresentationforOICR,September26,2017|V.Devanarayan
Biomarkersignaturesforsubgroupidentification
PredictiveSignatures - predicttheclinicalresponsetoaspecifictreatment(drugA)comparedtoothertreatments.
ØIdentifiespatientsthatrespondonlytodrugA,andnottootherdrugs.
PrognosticSignatures - predicttheclinicalresponseirrespectiveofthetreatment.Ø IdentifiespatientsthatrespondtodrugA,butmaynotbe
specifictothisdrug(i.e.,thesepatientsmayrespondtocompetitordrugsaswell).
Weproposesomedata-drivenstatisticalmethodsbasedondecision-tree®ression-basedmodelsfordevelopingunivariate&multivariatethreshold-basedbiomarkersignatures.
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• Foreaseofimplementationinclinicalpractice,needcut-pointsonbiomarkers forpredictingresponders/non-responders.
• i.e.,threshold-basedbiomarkersignatures
• E.g.,PatientswithGeneX1>…,GeneX2<…,arelikelyresponders.
• Thisshouldbe“Multivariate”.
• Derivedfromhigh-dimensional–omicsdata,and/orfocusedonatargetedpanel(specifictopathway,literature,etc.).
• Afterapromisingthreshold-basedsignatureisidentified,needtopredictit’sperformanceinafuturedataset,intermsofType-Ierror.
• i.e.,predicttreatmenteffectinthe“responder”subgroup,orpredictthesignatureeffectamongpatientsreceivingtreatment.
• Notmanyalgorithmsintheliterature.
Somestatisticalchallenges
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• Weevaluatedsomeofthepublishedalgorithmsforidentifyingoptimalpatientsubgroupsinclinicaltrials(e.g.,SIDES,GUIDE,etc.).Ø Didn’tyieldpositive/goodresultsinsomeofourclinicalprograms.
• Thismotivatedastrongneedtodevelopnewalgorithms.• Wedevelopedthefollowingalgorithms:
Ø1.PRIM,2.Sequential-BATTing,3.MC-AIM,4.MC-AIM-RULE,5.optAUC,6.SQUANT,etc.
Ø1-4havebeenpublished;Chenetal(2015),Huangetal(2017).
• Ourtestinghasshownthatnosinglemethodisalwaysthebest.Ø Fore.g.,regression-basedmethodsarebettersuitedforlinear
relationships,whiletree-basedmethodsaremorepowerfulfornonlinearrelationshipswheninteractionsarepresent.
Ourresearchonsubgroupidentificationmethods
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SubgroupIdentificationforPrecisionMedicine|PresentationforOICR,September26,2017|V.Devanarayan
vConsiderasupervisedlearningproblemwithdata 𝒙𝒊, 𝑦% , 𝑖 =1, 2, … , 𝑛, where𝒙𝒊 isap-vectorofpredictorand𝑦% isanoutcomevariable
vConsiderthreemajorapplications:• Linearregressionforcontinuousresponse
• Logisticregressionforbinaryresponse,where𝑦% ∈ 0, 1• Coxregressionforsurvivalresponse:𝑦% = (𝑇%, 𝛿%),where𝑇% isaright
censoredsurvivaltimeand𝛿% isthecensoringindicator
vDenotethelog-likelihoodorpartiallog-likelihoodbyℓ(𝜂; 𝑿, 𝒚),where𝜂 istheusuallinearcombinationofpredictors.Forexample:• linearpredictorinsimplelinearregression
• logoddsinlogisticregression
• loghazardinproportionalhazardsregression.
Prognostic&predictivesignaturesMathematicalframework
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SubgroupIdentificationforPrecisionMedicine|PresentationforOICR,September26,2017|V.Devanarayan
v Considerthefollowingmodelforprognosticsignatures (predictthediseaseoutcome,irrespectiveofthetreatment),
𝜂 = 𝛼 + 𝛽 ; 𝜔(𝑿),(1)
where𝜔 𝑿 = {0, 1} isthesignaturerule returninggroupingindicatorsforeachsubject.
v Considerfollowingmodelforpredictivesignatures(predicttheresponsetoaspecifictreatmentcomparedtotheothertreatment),
𝜂 = 𝛼 + 𝛽 ; 𝜔 𝑿 ×𝑟 + 𝛾 ; 𝑟,(2)
wherer isthetreatmentindicator.
v Ouralgorithmsderivesignaturerules,𝜔 𝑿 ,withtheobjective ofsearchingforabestgroupingtooptimizethesignificanceof𝛽 in(1)and(2)
Prognostic&predictivesignaturesMathematicalframework(contd.)
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Original Data
Tree 1>= C1< C1
Tree 2>= C2< C2 ……...
Tree B>= CB< CB
Aggregate Thresholds (C1, C2, …., CB)
BATTing Threshold (Median)
Bootstrapping (sampling with replacement)
Data 1 Data 2 Data B… … ...
Threshold is robust to small
perturbations in data, outliers, etc.
Bootstrapping&AggregatingofThresholdsfromTrees (BATTing)
(Devanarayan,1999)13 EVERY STEP OF THE WAY
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BATTing,contd.
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SequentialBATTing
Model Growing within the potential Sig+ group• Get the BATTing threshold for each unusedmarker• The best marker is selected to split the current sig+ group• This procedure continues in the new Sig+ group
Stopping Rule:• The new added predictor goes through the likelihood ratio test for
significance.
WholePopulation (Sig+)
Sig-
(Sig+) (Sig+) Sig+
Sig- Sig- Sig-
Marker7 Marker3 Marker9
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AdaptiveIndexModel
AIM(Tian&Tibshirani,2010)canbeusedforselectingmarkers&thresholds.• Output:AIMScore
• Anindexpredictor:#ofsatisfiedrules𝒔𝒄𝒐𝒓𝒆 = ∑ 𝑰(𝑋J ≤ 𝑐J)𝑲
𝒌O𝟏• ModeltogettheAIMscore
Prognostic:𝜂∗ = 𝜃S + 𝜽×𝒔𝒄𝒐𝒓𝒆,Predictive:𝜂∗ = 𝜃S + 𝛾 ; 𝑇 + 𝜽×𝑻×𝒔𝒄𝒐𝒓𝒆.
• Aninformationmatrixbasedfastalgorithmisusedtodoscoretesttoselectthresholdforeachmarker
• Markersareselectedoneatatime(forwardselection)• Optimal#ofmarkersisdeterminedviacrossvalidation
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AIM-BATTing
1. ObtaintheAIMScore
2. UseBATTing toderiveanoptimalAIMScorethresholdbasedonModel(1)&(2).Thethresholdisthenusedtostratifythepopulation.
Patient1
Patient2
Patientn
AIMI(X1≥c1)
+I(X2≤c2)
…..+
I(Xk≥ck)
Score1
Step1
Score2
Scoren
Step2
BATTingI( Score ≥ j )
Sig+Grp.
Sig- Grp.
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SubgroupIdentificationforPrecisionMedicine|PresentationforOICR,September26,2017|V.Devanarayan
SomeRefinementstotheAIM-BATTing algorithm
• MC-AIM-BATTing:– MonteCarloproceduretogetamorestableestimateofthe“optimal#of
markers”.
– i.e.,usethemedianofestimated“optimal#ofmarkers”acrossmultiplecrossvalidationrunswithdifferentrandomseeds
• MC-AIM-RULE-BATTing:– UseBATTing directlyontherules(Xi>c),insteadofscores,andgeta
cutoffontherulelist.
– Patientsmeetingalltheruleswithinthecutoffareassignedtothesig+group
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SubgroupIdentificationforPrecisionMedicine|PresentationforOICR,September26,2017|V.Devanarayan
Commonmistake:
• Theentiredatasetisusedtodevelopthesignature.
• Importantvariablesareselectedbyassociatingmarkerswithoutcomes(e.g.,stepwiseregression)
• Testandrelyonlackoffitassessmentoftheresultingmodel
• Assumingtheresultingmodeliscorrect,inferenceontheperformanceofthebiomarkersignatureismadeusingthissameentiredataset.
Performanceevaluation
Needtoapplythesignaturederivationalgorithm&assessperformanceusingindependenthold-outdatasetsviacross-validationorsimilarframework.Thishelps“predict”thesignificanceinafuturestudy,alongwiththeeffectsizeanddifferentperformancemeasures.
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SubgroupIdentificationforPrecisionMedicine|PresentationforOICR,September26,2017|V.Devanarayan
• PredictiveSignificanceofcut-point(rules-based)signaturescanbeevaluatedvia5-foldcross-validation(CV).– Stratificationforpatientsineachfoldarepredictedbyapplyingthealgorithmdevelopedfromtheotherfolds.
– “Cross-validated”effectsize,p-value,etc.,areestimatedafteraggregatingthepredictedstratificationsofalltheleft-outfolds.
• Amorestableestimateofthecross-validatedp-valuesisobtainedbyiteratingtheaboveprocedure50-100times.
• Followingperformancemetricsaretypicallyreported:– Medianp-value,andupper95%empiricallimit– EffectSize:thisismostimportantasithelpswithdesigning&validatinginfuturestudies.
– Othersummarymetricssuchassensitivity,specificity,PPV,NPV,hazardratio,oddsratiocanbereported.
“PredictiveSignificance”viacross-validationChenetal,StatisticsinMedicine,2015
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SubgroupIdentificationforPrecisionMedicine|PresentationforOICR,September26,2017|V.Devanarayan
“PredictiveSignificance”viacross-validationChenetal,StatisticsinMedicine,2015
Aggregated cross-validated p values from M iterations (p1, p2, …., pM)
predictive significance (median of this p-value distribution)
RepeatMultipleTimes
Note:otherperformancestatistics,e.g.,sensitivity,specificity,PPV,NPV,hazardratio,oddsratiocanbecalculatedsimilarly
Train
Test
Sig.
Train
Test
Sig.
Train
Test
Sig.
GroupLabel
GroupLabel
GroupLabel
GroupLabel
GroupLabel
Evaluatep-value(pi)
Signaturepositiveornegative?
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SubgroupIdentificationforPrecisionMedicine|PresentationforOICR,September26,2017|V.Devanarayan
• SimilarsimulationmodelasinLipkovich etal.,2011,2014(SIDES)witheachpredictorascontinuousinsteadofdichotomizedvalued
• Smalltrialstolargetrials(n=100,300,500)
• Numberofcandidatepredictorsisk=10and18withdifferentcorrelationstructures
• Effectsizeis0.2(low),0.5(medium),0.8(high)
SimulationDesign
Effect size = E(Y|Trt, sig+) - E(Y|ctrl, sig+) = 0.5
0.5
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SimulationResults
• Foreffectsize>=0.5andsamplesize>=300,ourproposedmethodshavemostofthetestingp-values<0.05andaccuracy~90%.SIDESmethodunder-performsinallscenarios.
• Foreffectsizeof0.2,ourproposedmethodsoutperformSIDESintermsoftheselectionaccuracy:theaccuracyofSIDESisaround50%whilethatofourproposedalgorithmsisfrom60%to70%forlargesamplesize.
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Case-Study
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SubgroupIdentificationforPrecisionMedicine|PresentationforOICR,September26,2017|V.Devanarayan
• Linifanib:Orallyactiveinhibitorofthevascularendothelialgrowthfactorreceptor(VEGFR)andplatelet-derivedgrowthfactorreceptor(PDGFR)familiesofreceptortyrosinekinases.
• AlthoughclinicalactiveinadvancedNSCLCinunselectedpatientpopulations,identificationofpredictivebiomarkerswasconsideredpotentiallyvaluableforfurtherdevelopment.
• Candidatemarkersconsidered:• CA125,CA15.3,CEA,CYFRA21-1,NSE,PlGF,ProGRP,andSCC
• Trainingdataset:• 241baselineplasmaspecimensfromfourNSCLCtrials,including
Linifanib(n=116),andthreeothertreatments(totaln=125).
• Validation/Testdataset:• 138patientswithstageIIIB/IVnon-squamousNSCLCfroma
phase-IIfirst-linestudywithLinifanib7.5mg/day,12.5mgdailyorplacebo,addedtoastandard3-weekregimenofcarboplatinandpaclitaxel.
Background/data
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SubgroupIdentificationforPrecisionMedicine|PresentationforOICR,September26,2017|V.Devanarayan
• SignaturederivedfromtheTrainingset:• CEA>3.0ng/mLandCYFRA21.1<7.0ng/mL,wasidentifiedas
providingthelowestHazardRatio(HR)estimateforsurvivalofNSCLCpatientsreceivingLinifanibversusthosereceivingothertreatments.
• Algorithmused:SequentialBATTing
• Thisbiomarkersignaturewasappliedtothepatientsfromthevalidation(test)datasettogrouptheminto“signaturepositive”and“signaturenegative”groups.ThedifferencebetweenthesegroupswithrespecttoPFSandOSwasassessedvialog-ranktest.Thetreatmentgroupswerecomparedforthesignaturepositiveandnegativegroupsseparately.
• OnlyLinifanib-treatedsignature-positivepatientshadsignificantimprovementinPFS.• MedianPFSwithplacebowas5.2monthsversus10.2months
(HR=0.49,p=0.049)forthosereceivinglinifanib 7.5mg,and8.3months(HR=0.38,p=0.029)forlinifanib 12.5mg.
Analysis&Results
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SubgroupIdentificationforPrecisionMedicine|PresentationforOICR,September26,2017|V.Devanarayan
Biomarker signature Median OS, months (95% CI); n
Linifanib Other treatments
Signature positive (49%) 13.1 (9.1-17.6), n=50 8.2 (5.8-9.6), n=67
Signature negative (51%) 7.4 (4.9-8.9), n=66 5.8 (3.3-8.8), n=58
p value (log-rank) 0.0017 0.7163
Moredetails:Trainingsetresults
Signatureassociatedwithimprovedsurvivalonlinifanib,butnotothertreatmentsinsecond- andthird-lineNSCLC
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SubgroupIdentificationforPrecisionMedicine|PresentationforOICR,September26,2017|V.Devanarayan
Moredetails:Trainingsetresults
--- Signature positive, N=50, median OS = 398 days --- Signature positive, N= 67, median OS = 248 days --- Signature negative, N=66, median OS = 225.5days --- Signature negative, N=58, median OS = 176 days
HR = 0.524 (p=0.002) HR = 0.925(p=0.716)
Kaplan-Meierestimateofoverallsurvivalforsignature-positiveandsignature-negativepatientsinsecond- andthird-linestudieswithlinifanib (left)orothertherapies(right)inadvancedNSCLC
Linifanib Other Treatments
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SubgroupIdentificationforPrecisionMedicine|PresentationforOICR,September26,2017|V.Devanarayan
Moredetails:Validation/Testsetresults
PFSandOSwithlinifanib orplaceboaddedtofirst-linecarboplatinandpaclitaxelchemotherapyinpatientswithadvancedNSCLC:unselectedpatients
NMedian
(months)p vs
placeboa
HR vs placebob
PFSCarboplatin/paclitaxel + placebo 47 5.4Carboplatin/paclitaxel + linifanib 7.5 mg 44 8.3 0.022 0.51Carboplatin/paclitaxel + linifanib 12.5 mg 47 7.3 0.118 0.64
OSCarboplatin/paclitaxel + placebo 47 11.3Carboplatin/paclitaxel + linifanib 7.5 mg 44 11.4 0.779 1.08Carboplatin/paclitaxel + linifanib 12.5 mg 47 13.0 0.650 0.89
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Moredetails:Validation/Testsetresults,contd.
PFSandOSwithlinifanib orplaceboaddedtofirst-linecarboplatinandpaclitaxelchemotherapyinpatientswithadvancedNSCLC:biomarkersignature-selectedpatients
NMedian
(Months)p vs
Placeboa
HR vs Placebob
PFS – Signature negativeCarboplatin/paclitaxel + placebo 26 5.4
Carboplatin/paclitaxel + linifanib 7.5 mg 18 8.3 0.480 0.48Carboplatin/paclitaxel + linifanib 12.5 mg 19 5.3 0.617 0.62
PFS – Signature positiveCarboplatin/paclitaxel + placebo 19 5.4Carboplatin/paclitaxel + linifanib 7.5 mg 24 10.2 0.049 0.49
Carboplatin/paclitaxel + linifanib 12.5 mg 26 8.3 0.029 0.38OS – Signature negative
Carboplatin/paclitaxel + placebo 26 13.3Carboplatin/paclitaxel + linifanib 7.5 mg 18 9.7 0.348 1.39Carboplatin/paclitaxel + linifanib 12.5 mg 19 8.2 0.382 1.36
OS – Signature positiveCarboplatin/paclitaxel + placebo 19 11.3Carboplatin/paclitaxel + linifanib 7.5 mg 24 12.5 0.858 1.02
Carboplatin/paclitaxel + linifanib 12.5 mg 26 17.4 0.137 0.54
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• PrecisionMedicinehasbeenaparadigmshiftindrugdevelopment.– NotjustinOncology,butalsoAlzherimer’s,Depression,Auto-Immunedisorders(RA,OA,GI,…),CHD,etc.
• Itrequires:– Fit-for-purposeBMx plan/strategy(Wholeand/ortargetedGx/Px,etc.)– Strongcollaborationbetweendifferentfunctionalareas&SMEs.– Useofavarietyofdataanalytic&subgroupidentificationmethods– Enrichmentdesignandsimulations– CDx andclinicaldevelopmentstrategy
• Algorithmsreviewedhereprovidethreshold-basedmultivariatesignatures viavariationsoftree®ression-basedmodels.
• Notjustfor“precisionmedicine”,butalsoforotherneeds,e.g.,disease/phenotypespecificity,reducingplaceboresponse,etc.
Summary
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1. HastieT,TibshiraniR,FriedmanJ(2011)TheElementsofStatisticalLearning:DataMining,Inference,andPrediction,SecondEdition,2nded.2009.Corr.7thprinting2013edition.Springer
2. Breiman L,FriedmanJ,StoneCJ,Olshen RA(1984)ClassificationandRegressionTrees,1edition.ChapmanandHall/CRC
3. ChenG,ZhongH,Belousov A,DevanarayanV(2015)APRIMapproachtopredictive-signaturedevelopmentforpatientstratification.StatMed34:317–342.doi:10.1002/sim.6343
4. SuX,TsaiC-L,WangH,etal.(2009)SubgroupAnalysisviaRecursivePartitioning.JMachLearnRes10:141–158.
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6. BergerJO,WangX,ShenL(2014)ABayesianapproachtosubgroupidentification.JBiopharm Stat24:110–129.doi:10.1080/10543406.2013.856026
7. DevanarayanV,CumminsD,Tanzer L,MooreR.(1999)ApplicationofGAMandtreemodelsforassessingtheroleofdrugresistanceproteinsinleukemiachemotherapy,JointStatisticalMeetings,8/1/1999.
8. TianL,TibshiraniR(2011)Adaptiveindexmodelsformarker-basedriskstratification.Biostatistics12:68–86.doi:10.1093/biostatistics/kxq047
9. TianL,Alizadeh A,GentlesA,TibshiraniR(2012)ASimpleMethodforDetectingInteractionsbetweenaTreatmentandaLargeNumberofCovariates.arXiv
10. TibshiraniR,Efron B(2002)Pre-validationandinferenceinmicroarrays.StatAppl GenetMol Biol.doi:10.2202/1544-6115.1000
11. FosterJC,TaylorJM,RubergSJ(2011)Subgroupidentificationfromrandomizedclinicaltrialdata.StatMed.30(24)2867-80
12. HuangX,SunY,TrowP,Chakravartty A,TianL,DevanarayanV(2017),Biomarkersignaturesforpatientsubgroupselectioninclinicaldrugdevelopment,StatisticsinMedicine.
13. McKeeganEM,AnsellPJ,DavisG,ChanS,Chandran RK,Gawell SH,DowellBL,BhathenaA,Chakravarty A,McKeeM,RickerJ,CarlsonD,Ramalingam SS,DevanarayanV(2015)Plasmabiomarkersignatureassociatedwithimprovedsurvivalinadvancednon-smallcelllungcancerpatientsonlinifanib ,LungCancer90(2015)296-301.
References
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