twin analysis 104
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Twin Analysis 104. October 2010. Bivariate Questions I. Univariate Analysis: What are the contributions of additive genetic, dominance/shared environmental and unique environmental factors to the variance? - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/1.jpg)
Twin Analysis 104October 2010
![Page 2: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/2.jpg)
• Univariate Analysis: What are the contributions of additive genetic, dominance/shared environmental and unique environmental factors to the variance?
• Bivariate Analysis: What are the contributions of genetic and environmental factors to the covariance between two traits?
Bivariate Questions I
![Page 3: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/3.jpg)
Two Traits
![Page 4: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/4.jpg)
• Two or more traits can be correlated because they share common genes or common environmental influences
• e.g. Are the same genetic/environmental factors influencing the traits?
• With twin data on multiple traits it is possible to partition the covariation into its genetic and environmental components
• Goal: to understand what factors make sets of variables correlate or co-vary
Bivariate Questions II
![Page 5: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/5.jpg)
individual twin
within between
trait
withinwithin-twin within-trait co(variance)
(cross-twin within-trait) covariance
between
(within-twin cross-trait) covariance
cross-twin cross-trait covariance
Bivariate Twin Data
![Page 6: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/6.jpg)
Bivariate Twin Covariance Matrix
X1 Y1 X2 Y2
X1 VX1 CX1Y1 CX1X2 CX1Y2
Y1 CY1X1 VY1 CY1X2 CY1Y2
X2 CX2X1 CX2Y1 VX2 CX2Y2
Y2 CY2X1 CY2Y1 CY2X2 VY2
![Page 7: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/7.jpg)
Genetic Correlation
![Page 8: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/8.jpg)
Alternative Representations
![Page 9: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/9.jpg)
Cholesky Decomposition
![Page 10: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/10.jpg)
Bivariate AE Model
![Page 11: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/11.jpg)
X1 Y1 X2 Y2
X1
Y1
X2
Y2
a112
+e112
a222+a21
2+e22
2+e212
a21*a11+e21*e11
a222+a21
2
a112
a21*a11
MZ Twin Covariance Matrix
![Page 12: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/12.jpg)
X1 Y1 X2 Y2
X1
Y1
X2
Y2
a112
+e112
a222+a21
2+e22
2+e212
a21*a11+e21*e11
.5a222+
.5a212
.5a112
.5a21*a11
DZ Twin Covariance Matrix
![Page 13: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/13.jpg)
Within-Twin Covariances [Mx]
![Page 14: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/14.jpg)
Within-Twin Covariances
![Page 15: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/15.jpg)
Cross-Twin Covariances
![Page 16: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/16.jpg)
• Within-twin cross-trait covariances imply common etiological influences
• Cross-twin cross-trait covariances imply familial common etiological influences
• MZ/DZ ratio of cross-twin cross-trait covariances reflects whether common etiological influences are genetic or environmental
Cross-Trait Covariances
![Page 17: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/17.jpg)
• Dataset: MCV-CVT Study
• 1983-1993
• BMI, skinfolds (bic,tri,calf,sil,ssc)
• Longitudinal: 11 years
• N MZF: 107, DZF: 60
Practical Example I
![Page 18: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/18.jpg)
Bivariate
• Saturated Model
• equality of means/variances
• Genetic Models (ACE)
• bivariate -> Cholesky Decomposition
![Page 19: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/19.jpg)
> parameterSpecifications(bivACEFit)model:ACE, matrix:a [,1] [,2] [1,] [a11] 0 [2,] [a21] [a22]model:ACE, matrix:c [,1] [,2] [1,] [c11] 0 [2,] [c21] [c22]model:ACE, matrix:e [,1] [,2] [1,] [e11] 0 [2,] [e21] [e22]model:ACE, matrix:Mean [,1] [,2][1,] [NA] [NA]
![Page 20: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/20.jpg)
Multivariate
• Saturated Model
• equality of means/variances
• Genetic Models (ACE)
• multivariate -> Cholesky Decomposition
• Independent Pathway
• Common Pathway
![Page 21: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/21.jpg)
Scientific Questions
• Are these measures influenced by the same genes (single common factor)?
• Is there more than one factor (overall fat- fat distribution)?
• What is the structure of C and E?
• Contribution of A, C, E factors to covariance between traits
![Page 22: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/22.jpg)
Cholesky
TextText
F1 F2 F3 F4
P1 f11
P2 f21
P3 f31
P4 f41
![Page 23: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/23.jpg)
F1 F2 F3 F4
P1 f11 0P2 f21 f22
P3 f31 f32
P4 f41 f42
![Page 24: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/24.jpg)
F1 F2 F3 F4
P1 f11 0 0P2 f21 f22 0P3 f31 f32 f33
P4 f41 f42 f43
![Page 25: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/25.jpg)
F1 F2 F3 F4
P1 f11 0 0
0P2 f21 f22 0
0P3 f31 f32 f33
0P4 f41 f42 f43
f44
![Page 26: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/26.jpg)
Phenotypic
![Page 27: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/27.jpg)
Cholesky Decomposition
F1 F2 F3 F4
P1 f11 0 0
0P2 f21 f22 0
0P3 f31 f32 f33
0P4 f41 f42 f43
f44
F1 F2 F3 F4
P1 f11 f21 f31 f41
P2 0 f22 f32
f42
P3 0 0 f33
f43
P4 0 0 0
f44
%*%
F %*% t(F)
Estimate covariance matrix, fully saturated
![Page 28: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/28.jpg)
Genetic
![Page 29: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/29.jpg)
& Environmental
![Page 30: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/30.jpg)
model:ACE, matrix:a [,1] [,2] [,3] [,4] [,5] [1,] [a11] 0 0 0 0 [2,] [a21] [a22] 0 0 0 [3,] [a31] [a32] [a33] 0 0 [4,] [a41] [a42] [a43] [a44] 0 [5,] [a51] [a52] [a53] [a54] [a55]model:ACE, matrix:c [,1] [,2] [,3] [,4] [,5] [1,] [c11] 0 0 0 0 [2,] [c21] [c22] 0 0 0 [3,] [c31] [c32] [c33] 0 0 [4,] [c41] [c42] [c43] [c44] 0 [5,] [c51] [c52] [c53] [c54] [c55]model:ACE, matrix:e [,1] [,2] [,3] [,4] [,5] [1,] [e11] 0 0 0 0 [2,] [e21] [e22] 0 0 0 [3,] [e31] [e32] [e33] 0 0 [4,] [e41] [e42] [e43] [e44] 0 [5,] [e51] [e52] [e53] [e54] [e55]model:ACE, matrix:Mean [,1] [,2] [,3] [,4] [,5][1,] [NA] [NA] [NA] [NA] [NA]
![Page 31: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/31.jpg)
• IP
![Page 32: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/32.jpg)
Common Factor
![Page 33: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/33.jpg)
F1 P1 f11
P2 f21
P3 f31
P4 f41
F1 F2 F3 F4
P1 f11 f21 f31 f41
%*%
F %*% t(F)
![Page 34: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/34.jpg)
Residuals
![Page 35: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/35.jpg)
E1 E2 E3 E4
P1 f11 0 0
0P2 0 f22 0 0P3 0 0 f33
0P4 0 0 0
f44
%*%
E %*% t(E)
E1 E2 E3 E4
P1 f11 0 0
0P2 0 f22 0 0P3 0 0 f33
0P4 0 0 0
f44
![Page 36: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/36.jpg)
F %*% t(F) + E %*% t(E)
![Page 37: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/37.jpg)
with Twin Data
![Page 38: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/38.jpg)
twin 1
![Page 39: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/39.jpg)
GeneticCommon Factor
![Page 40: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/40.jpg)
Shared environmentalCommon Factor
![Page 41: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/41.jpg)
Unique environmental Common Factor
![Page 42: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/42.jpg)
Genetic Residuals& C & E Residuals
![Page 43: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/43.jpg)
A1 P1 a11
P2 a21
P3 a31
P4 a41
P1 P2 P3 P4
A1 a11 a21 a31 a41
%*%
ac %*% t(ac)
![Page 44: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/44.jpg)
A1 A2 A3 A4
P1 a11 0 0
0P2 0 a22 0 0P3 0 0 a33
0P4 0 0 0
a44
%*%
as %*% t(as)
P1 P2 P3 P4
A1 a11 0 0
0A2 0 a22 0
0A3 0 0 a33
0A4 0 0 0
a44
![Page 45: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/45.jpg)
model:ACE, matrix:ac [,1] [1,] [ac11][2,] [ac21][3,] [ac31][4,] [ac41][5,] [ac51]model:ACE, matrix:cc [,1] [1,] [cc11][2,] [cc21][3,] [cc31][4,] [cc41][5,] [cc51]model:ACE, matrix:ec [,1] [1,] [ec11][2,] [ec21][3,] [ec31][4,] [ec41][5,] [ec51]model:ACE, matrix:as [,1] [,2] [,3] [,4] [,5] [1,] [as11] 0 0 0 0 [2,] 0 [as21] 0 0 0 [3,] 0 0 [as31] 0 0 [4,] 0 0 0 [as41] 0 [5,] 0 0 0 0 [as51]model:ACE, matrix:cs [,1] [,2] [,3] [,4] [,5] [1,] [cs11] 0 0 0 0 [2,] 0 [cs21] 0 0 0 [3,] 0 0 [cs31] 0 0 [4,] 0 0 0 [cs41] 0 [5,] 0 0 0 0 [cs51]model:ACE, matrix:es [,1] [,2] [,3] [,4] [,5] [1,] [es11] 0 0 0 0 [2,] 0 [es21] 0 0 0 [3,] 0 0 [es31] 0 0 [4,] 0 0 0 [es41] 0 [5,] 0 0 0 0 [es51]model:ACE, matrix:M [,1] [,2] [,3] [,4] [,5][1,] [NA] [NA] [NA] [NA] [NA]
![Page 46: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/46.jpg)
Independent Pathway
• Biometric model
• Different covariance structure for A, C and E
![Page 47: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/47.jpg)
IP Model
![Page 48: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/48.jpg)
Variance Componen
ta2 c2 e2
Common Factors
acnv x 1
ccnv x 1
ecnv x 1
Residual Factors
asnv x nv
csnv x nv
esnv x nv
![Page 49: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/49.jpg)
• CP
![Page 50: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/50.jpg)
Latent Phenotype
![Page 51: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/51.jpg)
F1 P1 f11
P2 f21
P3 f31
P4 f41
F1 F2 F3 F4
P1 f11 f21 f31 f41
%*%
F %*% t(F)
![Page 52: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/52.jpg)
ACE Model
![Page 53: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/53.jpg)
F1 P1 f11
P2 f21
P3 f31
P4 f41
F1 F2 F3 F4
P1 f11 f21 f31 f41
%*% al11 %*% t(al11) %*%
fl %*% al %*% t(al) %*% t(fl)
fl %x% al %*% t(al)
![Page 54: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/54.jpg)
Same Residuals
![Page 55: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/55.jpg)
model:ACE, matrix:al [,1][1,] [NA]model:ACE, matrix:cl [,1][1,] [NA]model:ACE, matrix:el [,1][1,] [NA]model:ACE, matrix:fl [,1] [1,] [fl11][2,] [fl21][3,] [fl31][4,] [fl41][5,] [fl51]
model:ACE, matrix:as [,1] [,2] [,3] [,4] [,5] [1,] [as11] 0 0 0 0 [2,] 0 [as21] 0 0 0 [3,] 0 0 [as31] 0 0 [4,] 0 0 0 [as41] 0 [5,] 0 0 0 0 [as51]model:ACE, matrix:cs [,1] [,2] [,3] [,4] [,5] [1,] [cs11] 0 0 0 0 [2,] 0 [cs21] 0 0 0 [3,] 0 0 [cs31] 0 0 [4,] 0 0 0 [cs41] 0 [5,] 0 0 0 0 [cs51]model:ACE, matrix:es [,1] [,2] [,3] [,4] [,5] [1,] [es11] 0 0 0 0 [2,] 0 [es21] 0 0 0 [3,] 0 0 [es31] 0 0 [4,] 0 0 0 [es41] 0 [5,] 0 0 0 0 [es51]model:ACE, matrix:M [,1] [,2] [,3] [,4] [,5][1,] [NA] [NA] [NA] [NA] [NA]
![Page 56: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/56.jpg)
Common Pathway
• Psychometric model
• Same covariance structure for A, C and E
![Page 57: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/57.jpg)
CP Model
![Page 58: Twin Analysis 104](https://reader035.vdocuments.us/reader035/viewer/2022062408/5681328d550346895d99247a/html5/thumbnails/58.jpg)
Variance Compon
enta2 c2 e2
Common
Factors
al1 x 1
cl1 x 1
el1 x 1
flnv x 1
Residual Factors
asnv x nv
csnv x nv
esnv x nv