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VCU HGEN 619 - Twin Analysis 103

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Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Slide 27Slide 28Slide 29Slide 30Slide 31Slide 32Slide 33Slide 34Slide 35Slide 36Slide 37Slide 38Slide 39Slide 40Slide 411Twin Analysis 103October 20102Specifications ContinuousmxMatrix mxAlgebraCholMZ T1 T2 expCovMZ T1 T2T1 #1 0 T1 var1 covT2 #2 #3 T2 cov var2T1 T2expMeanMZ#4 #5mzData selVarsfam bmi1 bmi21457 20 NA1782 25 24mxObjectivecovariance=expCovMZmeans=expMeanMZdimnames=selVarsmxDataobserved=mzDatatype=raw3MZ & DZ Twins Reared Together MZ twins DZ twins4 parameters4-2LL df Chi2*df p AIC Chi2#df pSat4055.91767ADE4063.417737.52 6 0.28517.4AE4067.6177311.73 7 0.11519.61ACE4067.6177311.73 6 0.07521.6CE4220.31774164.377 0672.3152.6 1 0E4591.71775535.868 01041.7524.1 2 0Goodness-of-FitChi2*: likelihood ratio test compared to saturated modelChi2#: likelihood ratio test compared to ADE or ACE model5a c e d a2c2e2d2SatADE 0.57 0.41 0.54 0.32 0.17 0.29AE 0.79 0.42 0.62 0.17ACE 0.79 0 0.42 0.62 0 0.17CE 0.68 0.56 0.46 0.32E 0.88 0.78Parameter Estimatesa2 , c2 etc. should be unstandardized variance components6Specifications BinarymxMatrix mxAlgebraexpCorMZ T1 T2T1 1 0T2 #2 1T1 T2expMeanMZ0 0expThreMZ#4 #5mzDataBinselVarsfam ob1 ob21457 0 NA1782 1 1mxObjectivecovariance=expCorMZmeans=expMeanMZdimnames=selVarsthresholds=expThreMZmxDataobserved=mzDataBintype=raw7Changes to OpenMx CodemzDataBin[,1:2] <- mxFactor(mzDataBin[,1:2], levels = c(0:1))# Constraint on variance of ordinal variablesmxConstraint( V== I, name="Var1"),# Matrix & Algebra for expected means vectormxMatrix( "Zero", 1, ntv, name="expMeanMZ" ),# Matrix & Algebra for expected thresholds# BinarymxMatrix( "Full", 1, nv, free=TRUE, values=.8, label="thre", name="Thre" ),mxAlgebra( cbind(Th,Th), dimnames=list('th1',selVars), name="expThre" ),# Ordinal mxMatrix( "Full", nth, ntv, free=T, values=thValues, lbound=thLBound, name="Thre"), mxMatrix( "Lower", nth, nth, free=FALSE, values=1, name="Inc" ), mxAlgebra( expression= Inc %*% Thre, name="ThreInc"), mxAlgebra( cbind(ThreInc,ThreInc),dimnames=list(thRows,selVars),name="expThreMZ" ),# Objective mxFIMLObjective( "ACE.expCovMZ", "ACE.expMean", selVars, thresholds="ACE.expThre" )8-2LL df Chi2*df p AIC Chi2#df pSatADE 3AE 4 1ACE 3CE 4 1E 5 2Goodness-of-FitChi2*: likelihood ratio test compared to saturated modelChi2#: likelihood ratio test compared to ADE or ACE model9a c e d a2c2e2d2SatADEAEACECEEParameter Estimatesa2 , c2 etc. should be unstandardized variance components10Specifications OrdinalmxMatrix mxAlgebraexpCorMZ T1 T2expThreMZth1t1 th1t2T1 1 0 th2t1 th2t2T2 #2 1 th3t1 th3t2T1 T2 Inc 1 0 0expMeanMZ0 0 1 1 0Thre #4 #5 1 1 1#6 #7#8 #9mzDataOrdselVarsfam ob1 ob21457 0 NA1782 1 1mxObjectivecovariance=expCorMZmeans=expMeanMZdimnames=selVarsthresholds=expThreMZmxDataobserved=mzDataOrdtype=raw11Heterogeneity12•Univariate Analysis: What are the contributions of additive genetic, dominance/shared environmental and unique environmental factors to the variance?•Are the contributions of genetic and environmental factors equal for different groups, such as sex, race, ethnicity, SES, environmental exposure, etc.?Heterogeneity Questions I13•Are these differences due to differences in the magnitude of the effects (quantitative)?•e.g. Is the contribution of genetic/environmental factors greater/smaller in males than in females?•Are the differences due to differences in the nature of the effects (qualitative)?•e.g. Are there different genetic/environmental factors influencing the trait in males and females?Heterogeneity Questions II14ComparisonConcordant for group membershipDiscordant for group membershipgenderMZ & DZ: MM & FF pairsDZ: opposite sex pairsageMZ & DZ: young & old pairsnationalityMZ & DZ: OZ & US pairsenvironmentMZ & DZ: urban & rural pairsMZ & DZ: urban/ rural pairsGroups15Heterogeneity Modelsame sex pairs16Homogeneity Modelsame sex pairs17OS G1 G2 EPHeterogeneity 12a1 c1 e1a2 c2 e26Homogeneity 12a1 c1 e1a1 c1 e13Models for Concordant Pairs18Heterogeneity Twin AnalysisHetTwinQnMaRawCon.R # Prepare Data and Print Summary Statistics# -----------------------------------------------------------------------data(twinData)summary(twinData)Vars <- 'bmi'nv <- 1selVars <- paste(Vars,c(rep(1,nv),rep(2,nv)),sep="") ntv <- nv*2mzfData <- subset(twinData, zyg==1, selVars)dzfData <- subset(twinData, zyg==3, selVars)mzmData <- subset(twinData, zyg==2, selVars)dzmData <- subset(twinData, zyg==4, selVars)colMeans(mzfData,na.rm=TRUE)....cov(mzfData,use="complete")....19ACE males/ femalesHetTwinQnMaRawCon.R# Fit Heterogeneity ACE Model with RawData and Matrices Input# -----------------------------------------------------------------------univHetACEModel <- mxModel("univHetACE",mxModel("ACE",# Matrices a, c, and e to store a, c, and e path coefficientsmxMatrix( "Full", nv, nv, free=TRUE, values=.6, label="am11", name="am" ),mxMatrix( "Full", nv, nv, free=TRUE, values=.6, label="cm11", name="cm" ),mxMatrix( "Full", nv, nv, free=TRUE, values=.6, label="em11", name="em" ),mxMatrix( "Full", nv, nv, free=TRUE, values=.6, label="af11", name="af" ),mxMatrix( "Full", nv, nv, free=TRUE, values=.6, label="cf11", name="cf" ),mxMatrix( "Full", nv, nv, free=TRUE, values=.6, label="ef11", name="ef" ),# Matrices A, C, and E compute variance componentsmxAlgebra( am %*% t(am), name="Am" ),mxAlgebra( cm %*% t(cm), name="Cm" ),mxAlgebra( em %*% t(em), name="Em" ),mxAlgebra( am %*% t(am), name="Af" ),mxAlgebra( cm %*% t(cm), name="Cf" ),mxAlgebra( em %*% t(em), name="Ef" ),20inverse Standard DeviationsHetTwinQnMaRawCon.R# Algebra to compute total variances and standard deviations (diagonal only)mxAlgebra( Am+Cm+Em, name="Vm" ),mxAlgebra( Af+Cf+Ef, name="Vf" ),mxMatrix( "Iden", nv, nv, name="I"),mxAlgebra( solve(sqrt(I*Vm)), name="isdm"),mxAlgebra( solve(sqrt(I*Vf)), name="isdf"),215 expected Cov MatricesHetTwinQnMaRawCon.R# Matrix & Algebra for expected means vectormxMatrix( "Full", 1, nv, free=TRUE, values= 20, label="mean", name="M" ),mxAlgebra( cbind(M,M), name="expMean"),# Algebra for expected variance/covariance matrix in MZmxAlgebra( rbind ( cbind(Am+Cm+Em , Am+Cm),cbind(Am+Cm , Am+Cm+Em)), name="expCovMZm" ), mxAlgebra( rbind ( cbind(Af+Cf+Ef , Af+Cf),cbind(Af+Cf , Af+Cf+Ef)), name="expCovMZf" ),# Algebra for expected variance/covariance matrix in DZ; 0.5, converted to 1*1


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VCU HGEN 619 - Twin Analysis 103

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