1HeterogeneityHGEN619 class 2007Heterogeneity Questions I Univariate Analysis: What are the contributionsof additive genetic, dominance/sharedenvironmental and unique environmental factorsto the variance? Are the contributions of genetic andenvironmental factors equal for different groups,such as sex, race, ethnicity, SES, environmentalexposure, etc.?2Heterogeneity Questions II Are these differences due to differences in themagnitude of the effects (quantitative)? e.g. Is the contribution of genetic/environmentalfactors greater/smaller in males than in females? Are the differences due to differences in thenature of the effects (qualitative)? e.g. Are there different genetic/environmental factorsinfluencing the trait in males and females?GroupsMZ & DZ:urban/ rural pairsMZ & DZ:urban & rural pairsenvironmentMZ & DZ:OZ & US pairsnationalityMZ & DZ:young & old pairsageDZ:opposite sex pairsMZ & DZ:MM & FF pairsgenderDiscordant for groupmembershipConcordant for groupmembershipComparison3Heterogeneity 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 Isame sex pairsEAea11Cc1.5 1PMEAea11Cc1PMMale Malea2 + c2 + e2a2 + c2 + e2.5a2 + c2MaleMalePFEAea11Cc1.5 1EAea11Cc1PFFemale Femalea2 + c2 + e2a2 + c2 + e2.5a2 + c2FemaleFemale4Scalar Model Isame sex pairsPMEAea11Cc1.5 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 Pairs3a1 c1 e1a1 c1 e112Homogeneity4a1 c1 e1 ka1 c1 e112Scalar6a2 c2 e2a1 c1 e112HeterogeneityEPG2G1OS5Homogeneity 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'f6Homogeneity Model IIIPFEA.3.811C.51.5 1PMEA.3.811C.51.58.58.58.91.91Correlation.57.57.57.89.89Covariance.98.98.98.98.98VarianceDZmfDZfDZmMZfMZmHeterogeneity Model IIIPFEA.3.811C.51.5 1PMEA.3.511C.51.59.58.64.91.85Correlation.45.57.38.89.50Covariance.59/.98.98.59.98.59VarianceDZmfDZfDZmMZfMZm7Scalar Model IIopposite sex pairsPFEAea11Cc1.5 1PMEAea11Cc1PFVkMale Femalea2 + c2 + e2k(a2 + c2 + e2)Vk(.5a2 + c2)MaleFemalePFEA.3.811C.51.5 1PMEA.3.811C.51PF1.5.58.58.58.91.91Correlation.851.28.572.00.89Covariance.98/2.22.20.982.20.98VarianceDZmfDZfDZmMZfMZmScalar Model III8Models for Concordant andDiscordant Pairs77a2 c2 e2 rga2 c2 e2 rca1 c1 e1a1 c1 e11515General I II4a1 c1 e1 ka1 c1 e115Scalar3a1 c1 e1a1 c1 e115Homogeneity6a2 c2 e2a1 c1 e115HeterogeneityEPG2G1OSGeneral 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 1PMEAemam11Ccm1Amh1PMamcmemAmh1.59PFEAefaf11Ccf1.5 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.81.26.58.58.91.91Correlation.25.57.57.89.89Covariance.98.98.98.98.98VarianceDZmfDZfDZmMZfMZmGeneral Model III10Male-female genetic correlation (rg) amaf rg= Vaf2 (am2+h2) If am2~=0 and af2~=0and h2=0 then rg=1 If am2=0 and h2~=0then rg=0 If am2~=0 and h2~=0then 0<rg<1PFEAefaf11Ccf1.5rg 1PMEAemam11Ccm1Male Femaleam2 + cm2 + em2af2 + cf2 + ef2.5rgafa'm +cfc'mMaleFemale.5rgama'f +cmc'fGeneral Model IV11Summary of Models Homogeneity Model: no quantitative, no qualitative differences Heterogeneity Model: quantitative but no qualitative differences Scalar Model: special case of heterogeneity model with proportionalquantitative differences General Model: quantitative and qualitative differencesHeterogeneity differences in variance components NOT mean differences group membership continuous heterogeneity12 #NGroups 8 ! Heterogeneity Model Title 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.dat Select if zyg =1 Begin Matrices = Group 1; Covariance A+C+E+D | A+C+D _ A+C+D | A+C+E+D; Title G3: DZ data #include ozbmi.dat Select if zyg =3 Begin 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 4 Title 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'; D= W*W'; End Algebra; Title G6: MZ data #include ozbmi.dat Select if zyg =2 Begin Matrices = Group 5; Covariance A+C+E+D | A+C+D _ A+C+D | A+C+E+D; Title G7: DZ data #include ozbmi.dat Select if zyg =4 Begin Matrices = Group 5; Covariance A+C+E+D | H@A+C+Q@D _ H@A+C+Q@D | A+C+E+D; Title G8: Standardization Begin Matrices = Group 5; Begin Algebra; V=A+C+E+D; P=A|C|E|D; S=P@V~; End Algebra; Interval S 1 1 - S 1 4 Option Sat=5995.659,2667ozbmifmyace4.mx #NGroups 6 ! Homogeneity Model Title 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.dat Select if zyg =1 Begin Matrices = Group 1; Covariance A+C+E+D | A+C+D _ A+C+D |
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