Haplotype-analysis

[e-mail],BostonAaMaMmamThisindividualhasaaandMmgenotypesandamandaMhaplotypesHaplotypesAaMAMmAmThisindividualhasAAandMmgenotypesandAMandAmhaplotypesAaMAMmamThisindividualhasAaandMmgenotypeandAMandamhaplotypes…AaMAMmamThisindividualhasAaandMmgenotypeandAMandamhaplotypes…butgivenonlygenotypedata,consistentwithAm/aMaswellasAM/amHaplotypeanalysis1.Estimatehaplotypesfromgenotypes2.AssociatehaplotypeswithtraitHaplotypeFreq.OddsRatioAAGG40%1.00*AAGT30%2.21CGCG25%1.07AGCT5%0.92*baseline,fixedto1.00MeasuringhaplotypesExpectation–MaximisationalgorithmApplicableinsituationswheretherearemorecategoriesthancanbedistinguishedi.e.‘incompletedataproblems’Completedata=(Observeddata,Missingdata)Haplotypedata=(Genotypedata,Phasedata)MeasuringhaplotypesGenotypesHaplotypesA/AB/bC/cABC/AbcorPhasesABc/AbCE-Malgorithm1.Guesshaplotypefrequencies2.(E)Usethosefrequenciestoreplaceambiguousgenotypeswithfractionalhaplotypecounts3.(M)Estimatefrequencyofeachhaplotypebycounting4.Repeat(2)and(3)untilconvergenceDatasettobephased4individualsgenotypedfor2diallelicmarkersID1A/AB/BID2A/ab/bID3A/aB/bID4a/ab/bDatasettobephased4individualsgenotypedfor2diallelicmarkersID1A/AB/BAB/ABID2A/ab/bAb/abID3A/aB/bAB/ab?Ab/aBID4a/ab/bab/abE-stepReplaceambiguousA/aB/bgenotypewith:AB/ab:Ab/aB:E-stepPAB=0.25PaB=0.25PAb=0.25Pab=0.25ReplaceambiguousA/aB/bgenotypewith:AB/ab:2×PAB×PabAb/aB:2×PAb×PaBE-stepPAB=0.25PaB=0.25PAb=0.25Pab=0.25ReplaceambiguousA/aB/bgenotypewith:AB/ab:2×PAB×Pab=2×0.25×0.25=0.125Ab/aB:2×PAb×PaB=2×0.25×0.25=0.125=0.125/(0.125+0.125)=0.50=0.125/(0.125+0.125)=0.50E-stepIncompletedataCompletedataCountA/AB/BAB/AB1.00A/ab/bAb/ab1.00A/aB/bAB/ab0.50Ab/aB0.50a/ab/bab/ab1.00M-stepIncompletedataCompletedataCountA/AB/BAB/AB1.00A/ab/bAb/ab1.00A/aB/bAB/ab0.50Ab/aB0.50a/ab/bab/ab1.00CountingABhaplotype=2×1+1×0.5=2.5M-stepIncompletedataCompletedataCountA/AB/BAB/AB1.00A/ab/bAb/ab1.00A/aB/bAB/ab0.50Ab/aB0.50a/ab/bab/ab1.00CountingaBhaplotype=1×0.5=0.5M-stepIncompletedataCompletedataCountA/AB/BAB/AB1.00A/ab/bAb/ab1.00A/aB/bAB/ab0.50Ab/aB0.50a/ab/bab/ab1.00CountingAbhaplotype=1×1+1×0.5=1.5M-stepIncompletedataCompletedataCountA/AB/BAB/AB1.00A/ab/bAb/ab1.00A/aB/bAB/ab0.50Ab/aB0.50a/ab/bab/ab1.00Countingabhaplotype=1×1+1×0.5+2×1=3.5M-stepHaplotypecounts,frequenciesfromcompletedataCountFreqAB2.50.3125aB0.50.0625Ab1.50.1875ab3.50.4375Sum8.01.0000backtotheE-step….PAB=0.25PaB=0.25PAb=0.25Pab=0.25PAB=0.3125PaB=0.0625PAb=0.1875Pab=0.4375arenowreplacedwiththeupdatedestimatesbacktotheE-step….ReplaceambiguousA/aB/bgenotypewith:AB/ab:2×PAB×Pab=2×0.3125×0.4375=0.273Ab/aB:2×PAb×PaB=2×0.1875×0.0625=0.023=0.023/(0.273+0.023)=0.08=0.273/(0.273+0.023)=0.92PAB=0.25PaB=0.25PAb=0.25Pab=0.25PAB=0.3125PaB=0.0625PAb=0.1875Pab=0.4375arenowreplacedwiththeupdatedestimatesbacktotheM-step…IncompletedataCompletedataCountA/AB/BAB/AB1.00A/ab/bAb/ab1.00A/aB/bAB/ab0.92Ab/aB0.08a/ab/bab/ab1.00CountingABhaplotype=2×1+1×0.92=2.92backtotheM-step…Haplotypecounts,frequenciesfromcompletedataCountFreqAA2.920.365aB0.080.010Ab1.080.135ab3.920.490Sum8.01.0000andback,again,totheE-step…andback,again,totheM-step…andback,again,totheE-step…andback,again,totheM-step…andback,again,totheE-step…andback,again,totheM-step………HaplotypefrequencyestimatesABaBAbabi00.2500.2500.2500.250i10.3150.06250.18750.4375.i20.3650.0100.1350.490……………iN0.3750.0000.1250.500PosteriorprobabilitiesHHGPHGPHPHGPGHP)|()|()()|()|(BayesRulePosteriorProbabilitiesExample:GenotypeAaBbHaplotypefrequenciesABaBAbab0.37500.1250.510125.015.0375.015.0375.01)/()/|()/()/|()/()/|()|/(aBAbPaBAbAaBbPabABPabABAaBbPabABPabABAaBbPAaBbabABPPosteriorprobabilitiesGenotypePhaseP(H|G)A/AB/BAB/AB1.00A/ab/bAb/ab1.00A/aB/bAB/ab1.00Ab/aB0.00a/ab/bab/ab1.00MissinggenotypedataA/A0/0c/cconsistentwith3phasesPhaseP(H|G)ABc/ABc(PABc×PABc)/SABc/Abc(2×PABc×PAbc)/SAbc/Abc(PAbc×PAbc)/SwhereS=PABc×PABc+2×PABc×PAbc+PAbc×PAbcUsingparentalgenotypesCanoftenhelptoresolvephaseA/aB/bC/cUsingparentalgenotypesCanoftenhelptoresolvephaseA/AB/BC/ca/ab/bc/cA/aB/bC/cUsingparentalgenotypesCanoftenhelptoresolvephaseA/AB/BC/ca/ab/bc/cA/aB/bC/cABC/abcUsingparentalgenotypesCanoftenhelptoresolvephaseA/AB/BC/ca/ab/bc/cA/aB/bC/c…butnotalwaysA/aB/bC/cA/aB/bc/cA/aB/bC/cABC/abcA(slightly)lesstrivialexample11112122121112322111241212115121112611222271211228221111912122210222222??211/212??122/122112/212211/211?222/2220.0000.0500.1000.1500.2000.2500.3000.3501234567891011121314151617111112121122211212221222haplotypefrequenciesE-MiterationEstimatedhaplotypefrequencylog-likelihood-logLk2829303132333435361234567891011121314151617HaplotypefrequenciesHP(H)2110.2999961120.2353912220.1354021220.1146042120.1146021210.0999941110.0000102210.000000IDchrHapP(H|G)111110.0001234121220.0001234111120.9998766121210.9998766211110.0000411222120.0000411211120.9999589222110.9999589312111.0000000322121.0000000411110.0000000422210.0000000411211.0000000422111.0000000511110.0000411522120.0000411511120.9999589522110.9999589IDchrHapP(H|G)611221.0000000621221.0000000711121.00000