Two-stage genome search design in affected-sib-pair method

132 Pages·1997·5.1 MB·English

by  Teng, Chi-Hse

TWO-STAGEGENOMESEARCHDESIGNINAFFECTED-SIB-PAIRMETHOD
By
CHI-HSETENG
ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL
OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT
OFTHEREQUIREMENTSFORTHEDEGREEOF
DOCTOROFPHILOSOPHY
UNIVERSITYOFFLORIDA
1997
:
©Copyright1997
by
CHI-HSETENG
ACKNOWLEDGMENTS
Iwouldliketothankthechairmanofmycommittee,ProfessorMarkC.K.Yang,
forintroducingmetothefieldofgeneticstatisticsandhiswiseguidancethroughout
mygraduatestudyatUF. IalsowanttothankProfessorRandyCarter, Professor
FrankMartin,ProfessorSueMcGorrary,andProfessorJinXiongShe. Theiradvice,
encouragement, and patiencewereessential. Last but not least, Iwant to thank
Ms. MargaretJoynerforhergraciouseditorialhelpandeffort. Finally,mydeepest
appreciationgoestomyparents,brother,sister,andparents-in-lawfortheirloveand
never-endingsupport andtomywifeHsiao-YunandourdaughterGillianfortheir
sweetcompany.
in
TABLEOFCONTENTS
ACKNOWLEDGMENTS
iii
LISTOFTABLES vi
ABSTRACT viii
CHAPTERS
1 INTRODUCTION 1
2 LITERATUREREVIEW 8
2.1 MapFunction 8
2.2 AnIntroductiontoHumanLinkageDataforGeneticDissection 11
2.3 IdenticalbyState,IdenticalbyDescent 16
2.4 DistributionsofIBD 17
2.5 RiskRatio 24
2.6 TestStatisticsBasedonIBDScore 25
2.7 LikelihoodRatioTest 30
2.8 HeterogeneityandHomogeneity 33
2.9 Polygenes 37
2.10 Two-stageGenomeSearch 38
3 TWO-STAGEGENOMESEARCHFORSIMPLEMENDELIANDIS-
EASE 40
3.1 Assumptions 41
3.2 Two-StageProcedure 42
3.3 ProbabilityofAllocatingtheCorrectMarker 43
3.4 TypeIErrorandPowerofClaimingLinkage 72
3.5 Discussion 76
4 TWO-STAGEGENOMESEARCHFORCOMPLEXDISEASE .... 78
4.1 GeneticModelandAssumptions 78
IV
4.2 Two-stageGenomeSearch 79
4.3 ProbabilityofAllocatingtheCorrect MarkerforaComplex
Disease 81
4.4 Discussion 110
5 CONCLUDINGREMARKS 112
REFERENCES 114
BIOGRAPHICALSKETCH 120
LISTOFTABLES
Table Page
1.1 ResultsofMendel'scrossesexperiments 2
1.2 TheresultsofBatesonandBunnet'sexperiment 5
2.1 Multilocus-feasibilityofseveralmapfunctions 12
2.2 Somesamplingissuesinlinkagestudies 16
2.3 ThevaluesofPr(IBDoftraitgene IBDofmarkerandrelationship). 20
|
2.4 TheprobabilityofIBDscorefordifferentrelatives 26
3.1 ThejointdistributionofIBDscoreofthelocus1andlocus2 57
3.2 ThejointdistributionofX,jandX,/j 58
3.3 Optimalresourceallocationintwo-stagegenomesearchforrarereces-
sivegene 64
3.4 Optimalresourceallocationintwo-stagegenomesearchforraredom-
inantgene 68
3.5 The95%percentileoftheuniquemaximumofRBinomial(n2,0.25). . 74
3.6 The95%percentileoftheuniquemaximummarkergroupofRBinomial(n2,
0.25) 75
4.1 TraitIBDdistributionconditionalonparentalgenotypeandEvector. 83
4.2 Exclusiveeventsforthecase"GiisfoundbutG2isnot." 84
4.3 Exclusiveeventsforthecase"G2isfoundbutG\isno." 85
4.4 ExclusiveeventsforthecaseUG\andG2arefound." 85
4.5 ConditionaldistributionofX\3andX%jgiven7\ 87
VI
4.6 P(bothaffected|Ei, E2)andpossibletraitIBDgivenExandE2 89
4.7 Optimalresourceallocationintwo-stagegenomesearchforrarereces-
sivegene,assumedtwogenes 95
vii
AbstractofDissertationPresentedtotheGraduateSchool
oftheUniversityofFloridainPartialFulfillment
oftheRequirementsfortheDegreeof
DoctorofPhilosophy
TWO-STAGEGENOMESEARCHDESIGNINAFFECTED-SIB-PAIRMETHOD
By
CHI-HSETENG
December,1997
Chairman: MarkC.-K.Yang
MajorDepartment: Statistics
Since Penrose proposed the sib-pair method in 1935 and the affected-sib-pair
(ASP) methodin 1950 and 1953, thesemethodshavebeenwidelyusedinlinkage
studies. CombinedwithcontemporaryDNA-levelgeneticmarkerstechnology,ASP
methodcannowbeusedforgenome-widesearchesfordiseasegenes.
Atwo-stagesearchinvolvesfirstascreeningsearchtoeliminatenonviablemarker
loci,thenanintensivesearchtoidentifygenelocationusingtheremainingmarkers.
Althoughthisapproachhasbeensuggestedintheliterature,itspropertieshavenot
beenthoroughlyinvestigated. Thespacingbetweenmarkers,thenumberofASPsto
beusedintheexperimentofeachstage,andthecriteriaformarkerstopassthefirst
stageneedtobedetermined.Themajordifficultiesofthetwo-stageapproachare(1)
thejointdistributionofthenonindependentstatisticsisdifficulttohandle; (2)the
"random" dependencestructureoftheteststatisticsinthesecondstage;and(3)in
mostpracticallyavailablesamplesizesthehighnumberoftiesintestscoresmake
asymptoticapproachesinappropriate. Thispaperintendstoprovideasolutionfor
designinganoptimaldesignforrareautosomalrecessiveanddominantdiseases.
vin
Powercomputationsusingthemultinomialdistributionsupportedbysimulation
showthatinmostcasesatwo-stagedesignisusuallybetterthanaonestagedesign,
butnotalways. Combiningdatafromtwostageswillgainasmallincreaseinaccuracy.
Theoptimaldesignsforresourceallocationineachofthetwostagesareobtainedand
presentedintables.
IX
CHAPTER
1
INTRODUCTION
Modern genetics began with the work ofGregor Mendel (1822-84) conducted
between1856and1863,formingthebasisforhis1866paper(KlugandCummings,
1997). GregorMendel,anAustrianmonk,performedaseriesofexperimentsonthe
gardenpeas. Basedontheresultsoftheseexperiments,heproposedaparticulate
inheritancetheorywhichhypothesizedthatheritablebiologicalcharacteristicswere
carriedand controlledbyindividual "units." Wecalltheseunitsgenestoday, but
Mendelcalledeachunita"Merkmal,"theGermanwordfor"Character"(Levineand
Miller,1991).
InMendel'sgardenpeaexperiments,hestudiedsevencharactersofgardenpeas.
Theyare: roundorwrinkledripeseeds,yelloworgreenseedinteriors,purpleorwhite
petals,inflatedorpinchedripepods,greenoryellowunripepods, axialorterminal
flowers,andlongorshortstems(Griffithsetal, 1993). Foreachoneoftheseseven
characters,Mendelobtainedpurelinesofplants. "APurelineisapopulationthat
alloffspringproducedbyselfingorcrossingwithinthepopulationshowthesameform
ofthecharacterbeingstudied" (Griffithsetal., 1993). Theparental generation,
denotedasF,inMendel'sexperimentaretheplantsofthesepurelines. Mendelfirst
studiedthesecharactersseparately;hecrossedtwopurelines,oneforeachphenotype,
ofeverycharacterstoobtain thefirst filial generation, denoted as Fi. Allthe
individualsofF! haveonlyonephenotypeofeachcharacters. Next, Mendelself-
fertilizedFiandobtainedsecondfilialgeneration,denotedasF2. Theresultsare
showedinTable1.1. Mendelestablishedtwoprinciplestoexplainthepatternofthe