amp Nathan Gillespie Types of Heterogeneity Terminology depends on research question Moderation confounding GxE Systematic differences Measured or Manifest moderatorconfounder Discrete traits ID: 647042
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Slide1
Heterogeneity
Sarah
Medland
& Nathan GillespieSlide2
Types of Heterogeneity
Terminology depends on research question
Moderation, confounding,
GxE
Systematic differences
Measured or Manifest moderator/confounder
Discrete traits
Ordinal & Continuous traits (Thursday)
Unmeasured or latent moderator/confounder
Moderation and
GxESlide3
Heterogeneity Questions
Univariate
Analysis:
What
are the contributions of additive genetic, dominance/shared environmental and unique environmental factors to the variance?
Heterogeneity:
Are
the contributions of genetic and environmental factors equal for different groups,
sex
, race, ethnicity, SES, environmental exposure, etc.?Slide4
The language of heterogeneity
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
source/nature of
the effects (qualitative)?
e.g. Are there different genetic/environmental factors influencing the trait in males and females?Slide5
The language of heterogeneity
Sex differences = Sex limitation
1948
1861
1840Slide6
The language of heterogeneity
Quantitative
-
differences in the magnitude of the effects
Qualitative
-
differences in the source/nature of the effects
Models
Scalar
Non-scalar
with OS twins
Models
Non-scalar without
OS twins
General Non-scalarSlide7
The language of heterogeneity
Scalar limitation (Quantitative)
% of variance due to A,C,E are the same between groups
The total variance is not
ie
:
var
Female
= k*
var
Male
A
Female
= k*AMaleCFemale = k*CMaleE
Female = k*EMalek
here is the scalar Slide8
Twin 1
E
C
A
1
1
1
Twin 2
A
C
E
1
1
1
1
1/.5
e
a
c
a
e
c
No HeterogeneitySlide9
Twin 1
E
C
A
1
1
1
Twin 2
A
C
E
1
1
1
1
1/.5
e
a
c
a
e
c
a
2
+c
2
+e
2
.5a
2
+c
2
.5a
2
+c
2
a
2
+c
2
+e
2
a
2
+c
2
+e
2
a
2
+c
2
a
2
+c
2
a
2
+c
2
+e
2
MZ DZSlide10
Male
Twin
E
C
A
1
1
1
Female
Twin
A
C
E
1
1
1
1
1/.5
e
a
c
k
*
a
k*
e
k*
c
Scalar Sex-limitation
aka scalar sex-limitation of the varianceSlide11
The language of heterogeneity
Non-Scalar limitation
Without opposite sex twin pairs (Qualitative)
var
Female
≠
var
Male
A
Female
≠
A
Male
CFemale ≠ CMaleEFemale
≠ EMaleSlide12
The language of heterogeneity
Non-Scalar limitation
Without opposite sex twin pairs (Qualitative)
Male Parameters
means
M
A
M
C
M
and E
M
Female Parameters
mean
F
A
F
C
F
and E
F
Parameters are estimated separatelySlide13
Twin 1
E
M
C
M
A
M
1
1
1
Twin 2
A
M
C
M
E
M
1
1
1
1
1/.5
e
M
a
M
c
M
a
M
e
M
c
M
Twin 1
E
F
C
F
A
F
1
1
1
Twin 2
A
F
C
F
E
F
1
1
1
1
1/.5
e
F
a
F
c
F
a
F
e
F
c
F
Male ACE model
Female ACE modelSlide14
The language of heterogeneity
Non-Scalar limitation
With
opposite sex twin pairs (
Quantitative)
Male Parameters
means
M
A
M
C
M
and E
M
Female Parameters
mean
F
A
F
C
F
and E
F
Parameters are estimated jointly – linked via the opposite sex correlations
r(
A
Female
,
A
male
) = .5
r(
C
Female
≠
C
Male
) =
1
r(
E
Female
≠ EMale ) = 0Slide15
Male
Twin
E
M
C
M
A
M
1
1
1
Female
Twin
A
F
C
F
E
F
1
1
1
1
.5/1
e
M
a
M
c
M
a
F
e
F
c
F
Non-scalar Sex-limitation
aka common-effects sex limitationSlide16
The language of heterogeneity
General
Non-Scalar limitation
With
opposite sex twin pairs
(semi-Qualitative)
Male Parameters
means
M
A
M
C
M
E
M
and
A
Specific
Extra genetic/ environmental effects
Female Parameters
mean
F
A
F
C
F
and E
F
Parameters are estimated jointly – linked via the opposite sex correlationsSlide17
Male
Twin
E
M
C
M
A
M
1
1
1
Female
Twin
A
F
C
F
E
F
1
1
1
1
.5/1
e
M
a
M
c
M
a
F
e
F
c
F
A
S
a
s
1
General Non-scalar Sex-limitation
aka general sex limitationSlide18
The language of heterogeneity
General
Non-Scalar limitation via
r
G
With
opposite sex twin pairs
(semi-Qualitative)
Male Parameters
means
M
A
M
C
M
E
M
Female Parameters
mean
F
A
F
C
F
and E
F
Parameters are estimated jointly – linked via the opposite sex correlations
r(
A
Female
,
A
male
) = ?
(estimated)
r(
C
Female
≠
C
Male
) =
1
r(
EFemale ≠
EMale ) = 0Slide19
Male
Twin
E
M
C
M
A
M
1
1
1
Female
Twin
A
F
C
F
E
F
1
1
1
1
?
e
M
a
M
c
M
a
F
e
F
c
F
General Non-scalar Sex-limitation
aka general sex limitationSlide20
How important is sex-limitation?
Let have a look
H
eight data example using older twins
Zygosity
coding
6 & 8 are MZF & DZF
7 & 9
are
MZM
&
DZM
10 is DZ
FM
Scripts
ACEf.R
ACEm.R ACE.RLeft side of the room ACEm.RRight side of the room ACE.RRecord the answers from the estACE* functionSlide21
How important is sex-limitation?
Female parameters
Male
parameters
Combined parameters
Conclusions?Slide22
Male
Twin
E
M
C
M
A
M
1
1
1
Female
Twin
A
F
C
F
E
F
1
1
1
1
?
e
M
a
M
c
M
a
F
e
F
c
F
General Non-scalar Sex-limitation
aka general sex limitation
Lets try this modelSlide23
twinHet5AceCon.R
Use data from all
zygosity
groupsSlide24
Male
Twin
E
M
C
M
A
M
1
1
1
Female
Twin
A
F
C
F
E
F
1
1
1
1
?
e
M
a
M
c
M
a
F
e
F
c
FSlide25
Male
Twin
E
M
C
M
A
M
1
1
1
Female
Twin
A
F
C
F
E
F
1
1
1
1
?
e
M
a
M
c
M
a
F
e
F
c
FSlide26
Means
Have a think about this as we go through
is this the best way to set this up?Slide27
CovariancesSlide28Slide29
Run it
What would we conclude?
Do we believe it?
Checking the alternate parameterisation…Slide30
Male
Twin
E
M
C
M
A
M
1
1
1
Female
Twin
A
F
C
F
E
F
1
1
1
1
?
e
M
a
M
c
M
a
F
e
F
c
F
General Non-scalar Sex-limitation
aka general sex limitation
Lets try this modelSlide31
af
= -.06
a
m = -.06
rg
= -.9
Dzr
= -.06*(.5*-.9) .06
=.45Slide32
Means
Add a correction using a regression model
expectedMean
=
maleMean
+
β
*sex
β
is the female deviation from the male mean
Sex is coded 0/1