Multivariable analysis : a practical guide for clinicians

219 Pages·2006·4.05 MB·English

by  Mitchell H Katz

Multivariable Analysis
APracticalGuideforClinicians
Whydoyouneedthisbook?
Multivariableanalysisisconfusing!Whetheryouareperformingyourfirstresearchproject
orattemptingtointerprettheoutputfromamultivariablemodel,youhaveundoubtedly
foundthistobetrue.Basicbiostatisticsbooksareoflittletonohelptoyou,sincetheir
coverageoftenstopsshortofmultivariableanalysis.However,existingmultivariableanalysis
booksaretoodensewithmathematicalformulasandderivationsandarenotdesignedto
answeryourmostbasicquestions.Isthereabookthatstepsasidefromthemathandsimply
explainshowtounderstand,perform,andinterpretmultivariableanalyses?
Yes.MultivariableAnalysis:APracticalGuideforCliniciansispreciselythereferencethat
willleadyourway.Infact,Dr.MitchellKatzhasaskedandansweredallofyourquestionsfor
you!
WhyshouldIdomultivariableanalysis?
HowdoIchoosewhichtypeofmultivariabletouse?
HowmanysubjectsdoIneedtodomultivariableanalysis?
WhatifIhaverepeatedobservationsofthesamepersons?
Answersanddetailedexplanationstothesequestionsandmorearefoundinthisbook.Also,
itisloadedwithusefultips,summarycharts,figures,andreferences.
Ifyouareamedicalstudent,resident,orclinician,MultivariableAnalysis:APractical
GuideforClinicianswillproveanindispensableguidethroughtheconfusingterrainof
statisticalanalysis.
Thisneweditionhasbeenfullyrevisedtobuildontheenormoussuccessofits
predecessor.Newfeaturesincludeanextensivereviewofanalysisofclustereddata,including
theuseofgeneralizedestimatingequationsandmixed-effectsmodels,anewchapteron
propensityscores,andmoredetailonPoissonregressionandanalysisofvariance.
Praiseforfirstedition
“Thisisthefirstnonmathematicalbookonmultivariableanalysisaddressedtoclinicians.Its
range,organization,brevity,andclaritymakeitusefulasareference,atext,andaguidefor
self-study.Thisbookis‘apracticalguideforclinicians.’”
LeonardE.Braitman,Ph.D.,AnnalsofInternalMedicine
MitchellH.KatzisClinicalProfessorofMedicine,Epidemiology,andBiostatisticsatthe
UniversityofCalifornia,SanFrancisco;heisalsoDirectoroftheSanFranciscoDepartment
ofPublicHealth.

Multivariable Analysis
A Practical Guide for Clinicians
Second Edition
Mitchell H. Katz
DepartmentofMedicine,Epidemiology,and
Biostatistics,UniversityofCalifornia,USA
cambridge university press
Cambridge,NewYork,Melbourne,Madrid,CapeTown,Singapore,Sa˜oPaulo
CambridgeUniversityPress
TheEdinburghBuilding,CambridgeCB22RU,UK
PublishedintheUnitedStatesofAmericabyCambridgeUniversityPress,NewYork
www.cambridge.org
Informationonthistitle:www.cambridge.org/9780521840514
(cid:1)C M.H.Katz,1999,2006
Thisbookisincopyright.Subjecttostatutoryexception
andtotheprovisionsofrelevantcollectivelicensingagreements,
noreproductionofanypartmaytakeplacewithout
thewrittenpermissionofCambridgeUniversityPress.
Firstpublished1999
Secondeditionpublished2006
PrintedintheUnitedKingdomattheUniversityPress,Cambridge
AcatalogrecordforthisbookisavailablefromtheBritishLibrary
LibraryofCongressCataloginginPublicationdata
ISBN-13 978-0-521-84051-4hardback
ISBN-10 0-521-84051-1hardback
ISBN-13 978-0-521-54985-1paperback
ISBN-10 0-521-54985-Xpaperback
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websitesis,orwillremain,accurateorappropriate.
Everyefforthasbeenmadeinpreparingthisbooktoprovideaccurateandup-to-dateinformation
whichisinaccordwithacceptedstandardsandpracticeatthetimeofpublication.Althoughcase
historiesaredrawnfromactualcases,everyefforthasbeenmadetodisguisetheidentitiesofthe
individualsinvolved.Nevertheless,theauthors,editors,andpublisherscanmakenowarrantiesthatthe
informationcontainedhereinistotallyfreefromerror,notleastbecauseclinicalstandardsare
constantlychangingthroughresearchandregulation.Theauthors,editors,andpublisherstherefore
disclaimallliabilityfordirectorconsequentialdamagesresultingfromtheuseofmaterialcontainedin
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manufacturerofanydrugsorequipmentthattheyplantouse.
To my parents, for their unwavering support

Contents
Preface page xiii
1 Introduction 1
1.1 WhyshouldIdomultivariableanalysis? 1
1.2 Whatareconfoundersandhowdoesmultivariableanalysis
helpmetodealwiththem? 6
1.3 Whataresuppressersandhowdoesmultivariableanalysishelp
metodealwiththem? 9
1.4 Whatareinteractionsandhowdoesmultivariableanalysishelp
metodealwiththem? 11
2 Common uses of multivariable models 14
2.1 Whatarethemostcommonusesofmultivariablemodelsin
clinicalresearch? 14
2.2 HowdoIchoosewhattypeofmultivariableanalysistouse? 23
3 Outcome variables in multivariable analysis 24
3.1 Howdoesthenatureofmyoutcomevariableinfluencemy
choiceofwhichtypeofmultivariableanalysistodo? 24
3.2 WhattypeofmultivariableanalysisshouldIusewithan
intervaloutcome? 24
3.3 Whatarethedifferenttypesofanalysisofvarianceandwhen
aretheyused? 25
3.4 WhatshouldIdoifmyoutcomevariableisordinalornominal? 27
3.5 WhattypeofmultivariableanalysisshouldIusewitha
dichotomousoutcome? 28
vii
viii Contents
3.6 WhattypeofmultivariableanalysisshouldIusewitha
time-to-outcomevariable? 28
3.7 WhattypeofmultivariableanalysisshouldIusewitharare
outcomeoracount? 32
4 Type of independent variables in multivariable analysis 35
4.1 WhattypeofindependentvariablescanIusewith
multivariableanalysis? 35
4.2 WhatshouldIdowithmyordinalandnominalindependent
variables? 35
5 Assumptions of multiple linear regression, multiple
logistic regression, and proportional hazards analysis 38
5.1 Whataretheassumptionsofmultiplelinearregression,
multiplelogisticregression,andproportionalhazards
analysis? 38
5.2 Whatisbeingmodeledinmultiplelinearregression,multiple
logisticregression,andproportionalhazardsanalysis? 38
5.3 Whatistherelationshipofmultipleindependentvariablesto
outcomeinmultiplelinearregression,multiplelogistic
regression,andproportionalhazardsanalysis? 42
5.4 Whatistherelationshipofaninterval-independentvariableto
theoutcomeinmultiplelinearregression,multiplelogistic
regression,andproportionalhazardsanalysis? 43
5.5 Whatifmyinterval-independentvariabledoesnothavea
linearrelationshipwithmyoutcome? 46
5.6 Assumingthatmyinterval-independentvariablefitsalinear
assumption,isthereanyreasontogroupitintointerval
categoriesorcreatemultipledichotomousvariables? 51
5.7 Whataretheassumptionsaboutthedistributionofthe
outcomeandthevariance? 52
5.8 WhatshouldIdoifIfindsignificantviolationsofthe
assumptionsofnormaldistributionandequalvarianceinmy
multiplelinearregressionanalysis? 55
5.9 Whataretheassumptionsofcensoring? 56
5.10 Howlikelyisitthatthecensoringassumptionisvalid
inmystudy? 59
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5.11 HowcanItestthevalidityofthecensoringassumption
formydata? 64
6 Relationship of independent variables to one another 68
6.1 Doesitmatterifmyindependentvariablesarerelated
toeachother? 68
6.2 HowdoIassesswhethermyvariablesaremulticollinear? 69
6.3 WhatshouldIdowithmulticollinearvariables? 71
7 Setting up a multivariable analysis 73
7.1 WhatindependentvariablesshouldIincludeinmy
multivariablemodel? 73
7.2 HowdoIdecidewhatconfounderstoincludeinmymodel? 73
7.3 WhatindependentvariablesshouldIexcludefrommy
multivariablemodel? 74
7.4 HowmanysubjectsdoIneedtodomultivariableanalysis? 77
7.5 WhatifIhavetoomanyindependentvariablesgivenmy
samplesize? 81
7.6 WhatshouldIdoaboutmissingdataonmyindependent
variables? 87
7.7 WhatshouldIdoaboutmissingdataonmyoutcomevariable? 94
8 Performing the analysis 96
8.1 WhatnumbersshouldIassignfordichotomousorordinal
variablesinmyanalysis? 96
8.2 DoesitmatterwhatIchooseasmyreferencecategoryfor
multipledichotomous(“dummied”)variables? 97
8.3 HowdoIenterinteractiontermsintomyanalysis? 98
8.4 HowdoIentertimeintomyproportionalhazardsorother
survivalanalysis? 101
8.5 Whataboutsubjectswhoexperiencetheiroutcomeontheir
startdate? 106
8.6 Whataboutsubjectswhohaveasurvivaltimeshorterthan
physiologicallypossible? 107
8.7 Whatarevariableselectiontechniques? 109
8.8 WhatvalueshouldIspecifyfortoleranceinmylogistic
regressionorproportionalhazardsmodel? 114
x Contents
8.9 Howmanyiterations(attemptstosolve)shouldIspecifyfor
mylogisticregressionorproportionalhazardsmodel? 114
8.10 WhatvalueshouldIspecifyfortheconvergencecriteriafor
mylogisticregressionorproportionalhazardsmodel? 115
8.11 Mymodelwon’tconverge.WhatshouldIdo? 115
9 Interpreting the analysis 117
9.1 Whatinformationwilltheprintoutfrommyanalysisprovide? 117
9.2 HowdoIassesshowwellmymodelaccountsfortheoutcome? 117
9.3 Whatdothecoefficientstellmeabouttherelationship
betweeneachvariableandtheoutcome? 124
9.4 HowdoIgetoddsratiosandrelativehazardsfromthe
multivariableanalysis?Whatdotheymean? 126
9.5 HowdoIinterprettheoddsratioandrelativehazardwhenthe
independentvariableisinterval? 129
9.6 HowdoIcomputetheconfidenceintervalsfortheoddsratios
andrelativehazards? 130
9.7 WhatarestandardizedcoefficientsandshouldIusethem? 131
9.8 HowdoItestthestatisticalsignificanceofmycoefficients? 131
9.9 HowdoIinterprettheresultsofinteractionterms? 134
9.10 DoIhavetoadjustmymultivariableregressioncoefficients
formultiplecomparisons? 134
10 Checking the assumptions of the analysis 137
10.1 HowdoIknowifmydatafittheassumptionsofmy
multivariablemodel? 137
10.2 HowdoIassessthelinearity,normaldistribution,andequal
varianceassumptionsofmultiplelinearregression? 138
10.3 HowdoIassessthelinearityassumptionofmultiplelogistic
regressionandproportionalhazardsanalysis? 139
10.4 WhatareoutliersandhowdoIdetecttheminmymultiple
linearregressionmodel? 139
10.5 HowdoIdetectoutliersinmymultiplelogisticregression
model? 141
10.6 Whataboutanalysisofresidualswithproportionalhazards
analysis? 142
10.7 WhatshouldIdowhenIdetectoutliers? 142