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Bivariate analysis. HGEN619 class 2006. Univariate ACE model. Expected Covariance Matrices. Bivariate Questions I. Univariate Analysis: What are the contributions of additive genetic, dominance/shared environmental and unique environmental factors to the variance?

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Bivariate analysis

Bivariate analysis

HGEN619 class 2006




Bivariate questions i
Bivariate Questions I

  • 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 ii
Bivariate Questions II

  • 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 twin data
Bivariate Twin Data

(cross-twin within-trait)

covariance

(within-twin within-trait

co)variance

(cross-twin within-trait)

covariance

cross-twin cross-trait

covariance


Bivariate twin covariance matrix
Bivariate Twin Covariance Matrix

VX1 CX1X2

CX2X1 VX2

CX1Y1

CX2Y2

CX1Y2

CX2Y1

CY1X1

CY2X2

CY1X2

CY2X1

VY1 CY1Y2

CY2Y1 VY2







Mz twin covariance matrix
MZ Twin Covariance Matrix

a112+e112

a112

a21*a11+

e21*e11

a222+a212+

e222+e212

a21*a11

a222+a212


Dz twin covariance matrix
DZ Twin Covariance Matrix

a112+e112

.5a112

a21*a11+

e21*e11

a222+a212+

e222+e212

.5a21*a11

.5a222+

.5a212





Cross trait covariances
Cross-Trait Covariances

  • 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





Practical example i
Practical Example I

  • Dataset: MCV-CVT Study

  • 1983-1993

  • BMI, skinfolds (bic,tri,calf,sil,ssc)

  • Longitudinal: 11 years

  • N MZF: 107, DZF: 60


Practical example ii
Practical Example II

  • Dataset: NL MRI Study

  • 1990’s

  • Working Memory, Gray & White Matter

  • N MZFY: 68, DZF: 21


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