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Frontiers in Probability and the Statistical Sciences Riten Mitra Peter Müller Editors Nonparametric Bayesian Inference in Biostatistics Frontiers in Probability and the Statistical Sciences Editor-inChief: SomnathDatta DepartmentofBioinformatics&Biostatistics UniversityofLouisville Louisville,Kentucky,USA SeriesEditors: FrederiG.Viens DepartmentofMathematics&DepartmentofStatistics PurdueUniversity WestLafayette,Indiana,USA DimitrisN.Politis DepartmentofMathematics UniversityofCalifornia,SanDiego LaJolla,California,USA HannuOja DepartmentofMathematicsandStatistics UniversityofTurku Turku,Finland MichaelDaniels SectionofIntegrativeBiology DivisionofStatistics&ScientificComputation UniversityofTexas Austin,Texas,USA Moreinformationaboutthisseriesathttp://www.springer.com/series/11957 Riten Mitra • Peter Mu¨ller Editors Nonparametric Bayesian Inference in Biostatistics 123 Editors RitenMitra PeterMu¨ller DepartmentofBioinformatics DepartmentofMathematics andBiostatistics UniversityofTexas UniversityofLouisville Austin,TX,USA Louisville,KY,USA FrontiersinProbabilityandtheStatisticalSciences ISBN978-3-319-19517-9 ISBN978-3-319-19518-6 (eBook) DOI10.1007/978-3-319-19518-6 LibraryofCongressControlNumber:2015945621 SpringerChamHeidelbergNewYorkDordrechtLondon ©SpringerInternationalPublishingSwitzerland2015 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade. Printedonacid-freepaper SpringerInternational PublishingAGSwitzerlandispartofSpringerScience+Business Media(www. springer.com) Preface Nonparametric Bayesian (BNP) approaches are becoming increasingly more common in biostatistical inference. Many problemsinvolve an abundance of data thatallowstheuseofmoreflexibleandcomplexprobabilitymodelsbeyondtradi- tionalparametricfamilies.OneofthemosttraditionalapplicationareasforBNPis in survival analysis, including in particular survival regression. The nature of the recordedoutcomesmakes it natural to target inference on an entire unknowndis- tribution,ratherthanfocusonjustameanfunction.Manymorerecentapplications ofBNPinbiostatisticsandbioinformaticsinvolveinferenceonunknownpartitions. For example, this could be an arrangement of patients into clinically meaningful subpopulations.This volume coversthese and some more applicationsof BNP in biomedicalinferenceproblems.Theintentionofthisbookistoprovideagoodre- viewofandintroductiontorelatedapplicationareas. Part I starts with two introductory chapters. Chapter 1 provides a brief review of the most commonly used basic BNP models, including the Dirichlet process, Dirichletprocessmixtures,thedependentDirichletprocess,PolyatreesandGaus- sian processes.Thesemodelsandrelatedvariationsactasthe workhorsesofBNP methods in biostatistics applications. Chapter 2 discusses some related examples, spanningawiderangeofapplications. Part II includesseveralchaptersthat considerBNP methodsfor inferencewith genomicdata,includinggeneexpression,mutations,copynumberaberrationsand more.Manychaptersin this partinvolvea notionof clusteringbiomolecularenti- ties, e.g.genes, cells, genomiclocationsor proteins.The inferredclustersprovide insightsintounderlyingbiologicalstructureandfunctionalityoftheseentities.An- othermajorfeatureformostchaptersinthispartisthatthedataareobtainedfrom state-of-the-art experimental platforms, e.g. next generation sequencing counts in Chapter4. Although the exact form of raw data vary across chapters, all chapters areperfectillustrationsoftheubiquitousapplicabilityofthecommonBNPpriorsin bioinformatics.Forexample,Chapter3discussescurveclusteringmethods,focus- ing on Chinese restaurantprocesspriorsto cluster proteinsbased on their shapes. v vi Preface Theinferenceiscenteredaroundaninnerproductmatrixthatisbuiltusingaspecial metricontheshapespace.Inthisway,itefficientlyreducesthecomputationalscale of the problem from infinite-dimensional curves to clustering patterns in a finite matrix.Chapter4usesavariationoftheIndianbuffetprocesspriortoaddressthe challengingissue of estimating tumor heterogeneity.Inferringsubclonesof tumor cellsbasedongenomicprofilehasimportantimplicationsingenomicsandcancer research.Chapters9and6dealwithclusteringnotasgoalsinthemselves,butinter- estingly,asefficienttoolsfordimensionreduction.Chapter9clustersalargenum- ber of genes based on their expression and eventually uses these clusters to build regressionmodelsforpredictingseverityofmultiplemyeloma.Chapter6addresses theclassicalproblemofSNPdiseaseassociationthroughanormalizedgeneralized gamma (NGG) process. This is one of the first applications of this prior to large scale biostatistical inference.A thoroughreview of Bayesian network modelscan befoundin Chapter8. Inaddition,thechapterintroducesnovelandflexiblesemi- parametricextensionsofcurrentapproachestoinferenceforhighdimensionalgene networks.Chapter7reviewstherecentforayofBNPpriorsintotheclassicalfield of populationgenetics.The chapterdiscusses the problemof detectingpopulation clustersbasedonallelefrequenciesusinghierarchicalDPpriors.Populationadmix- turemodelsarenotonlyrelevantforunderstandingthepatternofhumanmigration and evolution,butare also criticalto accountfor confoundingin gene association studies. Finally, we would want the readers to take note that all clustering priors discussedinthispartarerelatedtoexchangeabledistributions.Thatis,theyassume that there is no natural orderingof the variables, which restrains their straightfor- ward application to segmentation problems where time or say, genomic locations canbeofgreatimportance.Chapter5discussesanelegantwaytocircumventthis issuebygeneralizinganexchangeablepriorthroughlatentvariables.Themethodis appliedtodetectregionsofcopynumbervariationsinthegenomeandiscompared withstandardsegmentationmethodslikehiddenMarkovmodels. Chapters in Part III discuss applicationsof BNP to survivalanalysis. Inference forsurvivaldataweresomeofthefirstproblemsthatmotivatedtheearlyBNPlit- erature.Thisisthecasebecauseforeventtimedataitisnaturaltofocusontheen- tire distribution,includingalldetailedfeatures,ratherthanjustlocationandscale. Chapter10motivatesMarkovprocessesasaflexibleclassofpriorsonhazardrates. Itdiscusseshowsuchpriorscanbeeasilyadaptedtocureratemodelsandcomplex multivariatesettings,likecompetingrisksandrecurrentevents.Chapter11linksthe relevantpriorsforbaselinehazardrateswiththestandardparametricmodelstopro- videacomprehensivereviewofsomecommonsemi-parametricapproachesinthe literature.Thechapterconcludeswitha discussiononspatially correlatedsurvival data.Chapter12introducesa fullynonparametricpriorto addressthechallenging andcomplexissuesofintervalcensoringandmisclassification. Part IV groups together chapters that include a notion of modeling some ran- domfunction(orresponsesurface).Chapter13usesGaussianprocess(GP)priors tomodelthetemporalevolutionofthefiringpatternsofagroupofneurons.Thetwo mainthemesofthischaptersareadaptingGPpriorstosignalingdataandmultivari- ate extensionsto capturecomplexspatio-temporaleffects. Next, in Chapter14 we Preface vii find an extensive review of general curve registration techniquesthat can account forphasevariabilityinfunctionaldata.Theseapproachesarecriticaltomanypublic health applications, as illustrated in their application to growth data and pharma- cokinetics. Chapter 15 delivers yet another flavor of BNP priors in the contextof new age adaptive clinical trials. The chapter focuses on a flexible modeling ap- proachforaclinicaloutcomeoveralargecovariatespace,wherethecovariatesare biomarkers.Thecomplexityoftherelatedresponsesurfaceisparticularlyrelevant forclinicaltrialsettingswherediseasestatusandprogressionarerelatedtohigher orderinteractionsbetween biomarkers.Part IV finally concludeswith a review of non-parametricmodelingofROCcurvesinChapter16.ROCcurvesareubiquitous in classification problems,especially in medical diagnostic tests. While providing anotherillustrationoftheutilityoftheDPMprior,thischapteralsoprovidesalucid descriptionofBayesianbootstrapmethods. Inferencefor spatio-temporaldata gives rise to a specific set of challengesand modeling needs. Part V discusses such models in considerable detail. Chapter 17 starts by providingan in-depth theoreticalintroductionto Gaussian processes and other BNP priors for spatial data. This review starts from semi-parametric mod- elsandgraduallybuildsuptofullynon-parametricmethods.Chapter18discusses twospecificpriorsforspatialdata.Oneofthehighlightsofthischapterisaclever methodofadaptingconventionalproductpartitionpriorstothespatialcontext.The finalchapterinthispart,Chapter19,dealswiththespecializedproblemofdetecting boundariesinspatialdata.ThechapterdiscussessomespecificBNPpriorsforthis problem.Inaddition,itformulatesthisproblemintheframeworkofBayesianmul- tiple hypothesis testing advocating ways to extract multiplicity-adjusted posterior probabilities. Increasingly stricter ethical standards, increasing cost and complexity of clinical studiesmake it ever moredifficultto carryoutrandomizedstudies. This leads toanincreaseduseofnon-randomizeddata.Derivingmeaningfulconclusionfrom suchdatarequiresadjustmentforthelackofrandomizationbytechniquesknownas “causalinference.”Manyofthesemethodsdealwithmissingdataaswell.Chapters inPartVIdiscussthisclassofmethods,includingaBNPpriorforrandomdiscon- tinuationdesignsin Chapter20and BNP priorsforinferencewith missing data in Chapter21. Finally,besidespopularizingtheuseofBNPmethodsinbiostatisticsandbioin- formaticsthis volume supportsBNP research by donatingany royalties to the In- ternational Society for Bayesian Analysis (ISBA) in support of travel awards for youngresearchersforupcomingmeetingsofthebiennialworkshopinnonparamet- ricBayesianinference. Louisville,KY,USA RitenMitra Austin,TX,USA PeterMu¨ller Contents PartI Introduction 1 BayesianNonparametricModels .............................. 3 PeterMu¨llerandRitenMitra 2 BayesianNonparametricBiostatistics .......................... 15 WesleyO.JohnsonandMigueldeCarvalho PartII GenomicsandProteomics 3 BayesianShapeClustering.................................... 57 ZhengwuZhang,DebdeepPati,andAnujSrivastava 4 Estimating LatentCellSubpopulationswithBayesianFeature AllocationModels ........................................... 77 YuanJi,SubhajitSengupta,JuheeLee,PeterMu¨ller, andKamalakarGulukota 5 SpeciesSamplingPriorsforModelingDependence:AnApplication totheDetectionofChromosomalAberrations ................... 97 FedericoBassetti,FabrizioLeisen,EdoardoAiroldi, andMicheleGuindani 6 ModelingtheAssociationBetweenClustersofSNPsandDisease Responses ................................................. 115 Raffaele Argiento,Alessandra Guglielmi, Chuhsing Kate Hsiao, FabrizioRuggeri,andCharlotteWang 7 BayesianInferenceonPopulationStructure:FromParametric toNonparametricModeling................................... 135 MariaDeIorio,StefanoFavaro,andYeeWhyeTeh ix