Table Of ContentApplied Bioinformatics and Biostatistics
in Cancer Research
SeriesEditors
JeaneKowalski
JohnHopkinsUniversity,Baltimore,MD,USA
StevenPiantadosi
CedarsSinaiMedicalCenter,LosAngeles,CA,USA
Forothertitlespublishedinthisseries,goto
www.springer.com/series/7616
Xiaochun Li · Ronghui Xu
Editors
High-Dimensional Data
Analysis in Cancer Research
ABC
Editors
XiaochunLi RonghuiXu
HarvardMedicalSchool UniversityofCalifornia
Dana-FarberCancerInstitute SanDiego
Dept.Biostatistics DepartmentofFamily
375LongwoodSt. andPreventiveMedicine
BostonMA02115 andDepartmentofMathematics
USA 9500GilmanDr.
[email protected] LaJollaCA92093-0112
USA
[email protected]
ISBN:978-0-387-69763-5 e-ISBN:978-0-387-69765-9
DOI:10.1007/978-0-387-69765-9
LibraryofCongressControlNumber:2008940562
(cid:176)c SpringerScience+BusinessMedia,LLC2009
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Toourchildren,Anna,Sofia,andJames
Preface
In an era with a plethora of high-throughput biological technologies, biomedical
researchersareinvestigatingmorecomprehensiveaspectsofcancerwithever-finer
resolution.Notonlydoesthisresultinlargeamountofdatabutalsodatawithhun-
dredsifnotthousandsofdimensions.
Multivariateanalysisisamainstayofstatisticaltoolsintheanalysisofbiomed-
ical data. It concerns with associating data matrices of n rows by p columns, with
rows representing samples or patients and columns attributes, to certain response
or outcome variables. Classically, the sample size n is much larger than the num-
berofattributes p.Thetheoreticalpropertiesofstatisticalmodelshavemostlybeen
discussedundertheassumptionoffixedpandinfiniten.However,theadvanceofbi-
ologicalsciencesandtechnologieshasrevolutionizedtheprocessofinvestigations
in cancer. The biomedical data collection has become much more automatic and
muchmoreextensive.Weareintheeraof pasalargefractionofn,orevenmuch
largerthann,whichposeschallengestotheclassicalstatisticalparadigm.Takepro-
teomics as an example. Although proteomic techniques have been researched and
developed for many decades to identify proteins or peptides uniquely associated
with a given disease state, until recently this has mostly been a laborious process,
carriedoutoneproteinatatime.Theadventofhighthroughputproteome-widetech-
nologiessuchasliquidchromatography-tandemmassspectroscopymakeitpossible
togenerateproteomicsignaturesthatfacilitaterapiddevelopmentofnewstrategies
forproteomics-baseddetectionofdisease.Thisposesnewchallengesandcallsfor
scalablesolutionstotheanalysisofsuchhigh-dimensionaldata.
In this volume, we present current analytical approaches as well as systematic
strategiestotheanalysisofcorrelatedandhigh-dimensionaldata.
Thevolumeisintendedasareferencebookforresearchers,statisticians,bioin-
formaticians,graduatestudents,anddataanalystsworkinginthefieldofcancerre-
search.Ouraimistopresentmethodologicaltopicsofimportantrelevancetosuch
analyses, and in a single volume such as this we do not attempt to exhaust all the
analyticaltoolsthathavebeendevelopedsofar.
Thisvolumecontainssevenchapters.Theydonotnecessarilycoveralltopicsrel-
evanttohigh-dimensionaldataanalysisincancerresearch.Instead,wehaveaimed
vii
viii Preface
tochoosethosefieldsofresearchthatareeitherrelativelymature,butmaynothave
beenwellreadinappliedstatistics,suchasriskestimation,orthosefieldsthatare
fastdevelopingandalsohaveobtainedsubstantialnewerresultsthatarereasonably
wellunderstoodforpracticaluse,suchasvariableselection.Ontheotherhand,we
have omitted such an important topic as multiple comparisons, which is currently
undergoingmuchtheoreticaldevelopment(asreflectedintheAugust2007issueof
Annals of Statistics, for example), and we find it possibly difficult to provide an
accurate stationary yet updated picture for the moment. Such topic, however, can
befoundinseveralotherrecentlypublishedbooksthatcontainitsclassicalresults
readyforpracticaluse.Allthechaptersincludedinthisbookcontainpracticalex-
amplestoillustratetheanalysismethods.Inaddition,theyalsorevealthetypesof
researchthatareinvolvedindevelopingthesemethods.
Theopeningchapterprovidesanoverviewofthevarioushigh-dimensionaldata
sources,thechallengesinanalyzingsuchdata,andinparticular,strategiesinthede-
signphase,aswellaspossiblefuturedirections.Chapter2discussesmethodologies
andissuessurroundingvariableselectionandmodelbuilding,includingpostmodel
selectioninference.Thesehavealwaysbeenimportanttopicsinstatisticalresearch,
andevenmoresointheanalysisofhigh-dimensionaldata.Chapter3isdevotedto
thetopicofmultivariatenonparametricregression.Multivariateproblemsarecom-
mon in oncological research, and often the relationship between the outcome of
interest and its predictors is either nonlinear, or nonadditive, or both. This chapter
focusesonthemethodsofregressiontreesandsplinemodels.Chapter4discusses
themorefundamentalproblemofriskestimation.Thisisthebasisofmanyproce-
duresand,inparticular,modelselection.Itreviewsthetwomajorapproachestorisk
estimation,i.e.,covariancepenaltyandresampling,andsummarizesempiricaleval-
uationsoftheseapproaches.Chapter5focusesontree-basedmethods.Afterabrief
review of classification and regression trees (CART), the chapter presents in more
detailtree-basedensembles,includingboostingandrandomforests.Chapter6ison
supportvectormachines(SVMs),oneofthemethodologiesstemmingfromthema-
chinelearningfieldthathasgainedpopularityforclassificationofhighdimensional
data. The chapter discusses both two-class and multiclass classification problems,
andlinearandnonlinearSVM.Forhigh-dimensionaldata,aparticularlyimportant
aspectissparselearning,thatis,onlyarelativelysmallsubsetofthepredictorsare
truly involved with the classification boundary. Variable selection is then again a
criticalstep,andvariousapproachesassociatedwithSVMaredescribed.Thelast,
but by no means the least, chapter, presents Bayesian approaches to the analyses
of microarray gene expression data. The emphasis is on nonparametric Bayesian
methods,whichallowflexiblemodelingofthedatathatmightarisefromunderly-
ingheterogeneousmechanisms.Computationalalgorithmsarediscussed.
Ithasbeenanexcitingexperienceeditingthisvolume.Wethankalltheauthors
fortheirexcellentcontributions.
Boston,MA XiaochunLi
LaJolla,CA RonghuiXu
Contents
1 On the Role and Potential of High-Dimensional Biologic Data
inCancerResearch ......................................... 1
RossL.Prentice
1.1 Introduction.............................................. 1
1.2 PotentialofHigh-DimensionalDatainBiomedicalResearch..... 1
1.2.1 Background ...................................... 1
1.2.2 High-DimensionalStudyoftheGenome .............. 2
1.2.3 High-DimensionalStudiesoftheTranscriptome........ 3
1.2.4 High-DimensionalStudiesoftheProteome ............ 4
1.2.5 OtherSourcesofHigh-DimensionalBiologicData...... 5
1.3 StatisticalChallengesandOpportunitieswithHigh-Dimensional
Data .................................................... 6
1.3.1 ScopeofthisPresentation .......................... 6
1.3.2 Two-GroupComparisons ........................... 6
1.3.3 StudyDesignConsiderations........................ 7
1.3.4 More Complex High-Dimensional Data Analysis
Methods ......................................... 8
1.4 NeededFutureResearch ................................... 9
References..................................................... 10
2 VariableSelectioninRegression–Estimation,Prediction,Sparsity,
Inference .................................................. 13
JaroslawHarezlak,EricTchetgen,andXiaochunLi
2.1 OverviewofModelSelectionMethods ....................... 13
2.1.1 DataExample .................................... 15
2.1.2 UnivariateScreeningofVariables .................... 15
2.1.3 SubsetSelection .................................. 16
2.2 MultivariableModeling:Penalties/Shrinkage .................. 16
2.2.1 Penalization ...................................... 16
2.2.2 RidgeRegressionandNonnegativeGarrote............ 17
2.2.3 LASSO:Definition,PropertiesandSomeExtensions.... 18
2.2.4 SmoothlyClippedAbsoluteDeviation(SCAD) ........ 20
ix
x Contents
2.3 LeastAngleRegression .................................... 21
2.4 DantzigSelector .......................................... 22
2.5 PredictionandPersistence.................................. 25
2.6 DifficultieswithPost-ModelSelectionInference ............... 26
2.7 PenalizedLikelihoodforGeneralizedLinearModels ........... 28
2.8 SimulationStudy ......................................... 28
2.9 ApplicationoftheMethodstotheProstateCancerDataSet ...... 30
2.10 Conclusion............................................... 32
References..................................................... 32
3 MultivariateNonparametricRegression ........................ 35
CharlesKooperbergandMichaelLeBlanc
3.1 AnExample.............................................. 36
3.2 LinearandAdditiveModels ................................ 36
3.2.1 ExampleRevisited ................................ 37
3.3 Interactions .............................................. 37
3.4 BasisFunctionExpansions ................................. 39
3.5 RegressionTreeModels.................................... 40
3.5.1 Background ...................................... 40
3.5.2 ModelBuilding ................................... 41
3.5.3 BackwardsSelection(Pruning) ...................... 42
3.5.4 ExampleRevisited ................................ 43
3.5.5 IssuesandConnections............................. 44
3.6 SplineModels ............................................ 44
3.6.1 OneDimensional.................................. 44
3.6.2 Higher-DimensionalModels ........................ 46
3.6.3 ExampleRevisited ................................ 47
3.7 LogicRegression ......................................... 47
3.7.1 ExampleRevisited ................................ 49
3.8 High-DimensionalData .................................... 50
3.8.1 VariableSelectionandShrinkage .................... 51
3.8.2 LASSOandLARS ................................ 51
3.8.3 DedicatedMethods ................................ 52
3.8.4 ExampleRevisited ................................ 52
3.9 SurvivalData............................................. 53
3.9.1 ExampleRevisited ................................ 55
3.10 Discussion ............................................... 56
References..................................................... 56
4 RiskEstimation............................................. 59
RonghuiXuandAnthonyGamst
4.1 Risk .................................................... 59
4.2 CovariancePenalty........................................ 60
4.2.1 ContinuousOutcomes.............................. 60
4.2.2 BinaryOutcomes.................................. 61
4.2.3 AConnectionwithAIC ............................ 63
