Table Of ContentFrontiers 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
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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 clini-
cal 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
