HeterogeneityHeterogeneity Questions IHeterogeneity Questions IIGroupsHeterogeneity Model I same sex pairsHomogeneity Model I same sex pairsScalar Model I same sex pairsModels for Concordant PairsHomogeneity Model II opposite sex pairsHeterogeneity Model II opposite sex pairsHomogeneity Model IIIHeterogeneity Model IIIScalar Model II opposite sex pairsScalar Model IIIModels for Concordant and Discordant PairsGeneral Model I same sex pairsGeneral Model II opposite sex pairsGeneral Model IIIMale-female genetic correlation (rg)General Model IVSummary of ModelsSlide 22Slide 23Slide 24! Estimate genetic and environmental components - ACED model ! OZ BMI data - younger females & males + opposite sex twins I! Estimate genetic and environmental components - ACED model ! OZ BMI data - younger females & males + opposite sex twins II! Estimate genetic and environmental components - ACED model ! OZ BMI data - younger females & males + opposite sex twins III! Estimate genetic and environmental components - ACED model ! OZ BMI data - younger females & males + opposite sex twins IVHeterogeneityHGEN619 class 2006Heterogeneity Questions IUnivariate 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 IIAre 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?GroupsComparison Concordant for group membershipDiscordant for group membershipgender MZ & DZ: MM & FF pairsDZ: opposite sex pairsage MZ & DZ: young & old pairsnationality MZ & DZ: OZ & US pairsenvironment MZ & DZ: urban & rural pairsMZ & DZ: urban/ rural pairsHeterogeneity Model Isame sex pairsEA11C1.5 1PMEAemam11Ccm1PMamcmemMale Maleam2 + cm2 + em2.5ama'm +cmc'mMaleMale.5ama'm +cmc'mam2 + cm2 + em2PFEAefaf11Ccf1.5 1EA11C1PFafcfefFemale Femaleaf2 + cf2 + ef2.5afa'f + cfc'fFemaleFemale.5afa'f + cfc'faf2 + cf2 + ef2Homogeneity Model I same sex pairsEAea11Cc1.5 1PMEAea11Cc1PMMale Malea2 + c2 + e2a2 + c2 + e2.5a2 + c2MaleMalePFEAea11Cc1.5 1EAea11Cc1PFFemale Femalea2 + c2 + e2a2 + c2 + e2.5a2 + c2FemaleFemaleScalar Model Isame sex pairsPFEAea11Cc1.5 1PMEAea11Cc1PFEAea11Cc1.5 1PFEAea11Cc1PFVkPFVkMale Malea2 + c2 + e2.5a2 +c2MaleMalea2 + c2 + e2.5a2 +c2Female FemaleFemaleFemalek(a2 + c2 + e2)k(a2 + c2 + e2)Vk(.5a2 + c2)Vk(.5a2 + c2)Models for Concordant PairsOS G1 G2 EPHeterogeneity 12 a1 c1 e1a2 c2 e26Homogeneity 12 a1 c1 e1a1 c1 e13Scalar 12 a1 c1 e1a1 c1 e1 k 4Homogeneity Model IIopposite sex pairsPFEAea11Cc1.5 1PMEAea11Cc1Male Femalea2 + c2 + e2a2 + c2 + e2.5a2 + c2MaleFemaleHeterogeneity Model IIopposite sex pairsPFEAefaf11Ccf1.5 1PMEAemam11Ccm1Male Femaleam2 + cm2 + em2af2 + cf2 + ef2.5afa'm + cfc'mMaleFemale.5ama'f + cmc'fHomogeneity Model IIIPFEA.3.811C.51.5 1PMEA.3.811C.51MZm MZf DZm DZf DZmfVariance .98 .98 .98 .98 .98Covariance .89 .89 .57 .57 .57Correlation .91 .91 .58 .58 .58Heterogeneity Model IIIPFEA.3.811C.51.5 1PMEA.3.511C.51MZm MZf DZm DZf DZmfVariance .59 .98 .59 .98 .59/.98Covariance .50 .89 .38 .57 .45Correlation .85 .91 .64 .58 .59Scalar Model IIopposite sex pairsPFEAea11Cc1.5 1PMEAea11Cc1PFVkMale Femalea2 + c2 + e2k(a2 + c2 + e2)Vk(.5a2 + c2)MaleFemalePFEA.3.811C.51.5 1PMEA.3.811C.51PF1.5MZm MZf DZm DZf DZmfVariance .98 2.20 .98 2.20 .98/2.2Covariance .89 2.00 .57 1.28 .85Correlation .91 .91 .58 .58 .58Scalar Model IIIModels for Concordant and Discordant PairsOS G1 G2 EPHeterogeneity 15 a1 c1 e1a2 c2 e26Homogeneity 15 a1 c1 e1a1 c1 e13Scalar 15 a1 c1 e1a1 c1 e1 k 4General 15 a1 c1 e1a2 c2 e2 rg7General Model Isame sex pairsMale Maleam2+cm2+em2+h2MaleMale.5am2 +cm2+.5h2am2+cm2+em2+h2.5am2 +cm2+.5h2PFEAefaf11Ccf1.5 1EA11C1PFafcfefFemale Femaleaf2 + cf2 + ef2.5afa'f + cfc'fFemaleFemale.5afa'f + cfc'faf2 + cf2 + ef2EA11C1.5 1PMEAemam11Ccm1Amh1PMamcmemAmh1.5PFEAefaf11Ccf1.5 1PMEAemam11Ccm1Amh1Male Femaleam2+cm2+em2+h2af2 + cf2 + ef2MaleFemale .5afa'm + cfc'm.5ama'f + cmc'fGeneral Model IIopposite sex pairsPFEA.3.811C.51.5 1PMEA.3011C.51Am.81MZm MZf DZm DZf DZmfVariance .98 .98 .98 .98 .98Covariance .89 .89 .57 .57 .25Correlation .91 .91 .58 .58 .26General Model IIIMale-female genetic correlation (rg) amaf rg= Vaf2 (am2+h2)If am2~=0 and af2~=0 and h2=0 then rg=1If am2=0 and h2~=0 then rg=0If am2~=0 and h2~=0 then 0<rg<1PFEAefaf11Ccf1.5rg 1PMEAemam11Ccm1Male Femaleam2 + cm2 + em2af2 + cf2 + ef2.5rgafa'm +cfc'mMaleFemale.5rgama'f +cmc'fGeneral Model IVSummary of ModelsHomogeneity Model:no quantitative, no qualitative differencesHeterogeneity Model:quantitative but no qualitative differencesScalar Model:special case of heterogeneity model with proportional quantitative differencesGeneral Model:quantitative and qualitative differencesHeterogeneitydifferences in variance componentsNOT mean differencesgroup membershipcontinuous heterogeneity#NGroups 8 ! Heterogeneity ModelTitle G1: Model Parameters Calculation Begin Matrices; X Lower nvar nvar Free Y Lower nvar nvar Z Lower nvar nvar Free W Lower nvar nvar Free H Full 1 1 Q Full 1 1 End Matrices; Matrix H .5 Matrix Q .25 Begin Algebra; A= X*X'; C= Y*Y'; E= Z*Z'; D= W*W'; End Algebra;Title G2: MZ data #include ozbmi.datSelect if zyg =1Begin Matrices = Group 1;Covariance A+C+E+D | A+C+D _ A+C+D | A+C+E+D; Title G3: DZ data #include ozbmi.datSelect if zyg =3Begin Matrices = Group 1;Covariance A+C+E+D | H@A+C+Q@D _ H@A+C+Q@D | A+C+E+D;Title G4: Standardization Begin Matrices = Group 1; Begin Algebra; V=A+C+E+D; P=A|C|E|D; S=P@V~; End Algebra; Interval S 1 1 - S 1 4Title G5: Model Parameters Calculation Begin Matrices; X Lower nvar nvar Free Y Lower nvar nvar Z Lower nvar nvar Free W Lower nvar nvar Free H Full 1 1 Q Full 1 1 End Matrices; Matrix H .5 Matrix Q .25 Begin Algebra; A= X*X'; C= Y*Y'; E= Z*Z';
View Full Document
Unlocking...