Heterogeneity Testing

Report
Heterogeneity Testing
Elizabeth Prom-Wormley and Hermine Maes
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.?
Getting a Feel for the Data
• Gentlemen- Open ACEm.R
• Ladies- Open ACEf.R
• Zygosity Coding
–
–
–
–
–
MZF = 6
DZF = 8
MZM = 7
DZM = 9
Opp Sex = 10
• First Steps?
0.0
0.2
0.4
0.6
0.8
1.0
Getting a Feel for the Data
rMZM
rDZM
rMZF
rDZF
rOppSex
What’s the Question?
Qualitative Differences
• Are the differences due to differences in the
source/nature of the effects (qualitative)?
– Are there different genetic/environmental factors
influencing the trait in males and females?
Classic Univariate ACE Model
MZ = 1 / DZ = 0.5
1
A
a
C
E
c
T1
e
A
C
a
E
c
T2
e
Classic Univariate ACE Model +
Qualitative Sex Differences
MZ = 1 / DZ = 0.5
1
Am Cm
a
cm
Am
Em
em
Cm Em
am
cm em
m
T1
T2
MZ = 1 / DZ = 0.5
Male Model
1
Af
af
Cf
cf
Ef
ef
Af
Cf
af
T1
cf
T2
Female Model
Ef
ef
Testing Qualitative Differences
• Non-Scalar limitation
– Without opposite sex twin pairs (Qualitative)
• Male Parameters
– meansM
– AM CM and EM
• Female Parameters
– meanF
– AF CF and EF
Parameters are
estimated separately
varMale ≠ varFemale
AMale ≠ AFemale
CMale ≠ CFemale
EMale ≠ EFemale
Conclusions from Qualitative
Modeling?
Limitations of Qualitative
Modeling?
0.0
0.2
0.4
0.6
0.8
1.0
Getting a Feel for the Data
rMZM
rDZM
rMZF
rDZF
rOppSex
What’s the Question?
Quantitative Differences
• Are these differences due to differences in the
magnitude of the effects (quantitative)?
– Is the contribution of genetic/environmental factors
greater/smaller in males than in females?
• Test Models of Scalar and Non-Scalar
Influences
Classic Univariate ACE Model
No Heterogeneity
MZ = 1 / DZ = 0.5
1
A
a
C
E
c
T1
e
A
C
a
E
c
T2
e
Classic Univariate ACE Model +
Scalar Sex Limitation on the Variance
MZ = 1 / DZ = 0.5
1
C
A
a
c
T1F
A
E
e
k*a
C
k*c
T2M
E
k*e
Scalar limitation (Quantitative)
• Proportion of variance due to A,C,E are the same
between groups
• The total variance is not ie:
• varFemale = k*varMale
• AFemale = k*AMale
• CFemale = k*CMale
• EFemale = k*EMale
Quantitative Differences
Non-Scalar Limitation
• With opposite sex twin pairs (Quantitative)
• Male Parameters
– meansM
– AM CM and EM
• Female Parameters
– meanF
– AF CF and EF
Parameters are estimated jointly – linked
via the opposite sex correlations
r(AFemale ,Amale) = .5
r(CFemale ≠ CMale ) = 1
r(EFemale ≠ EMale ) = 0
Classic Univariate ACE Model +
Non-Scalar Sex Limitation
rODZ = 0.5
1
Am
am
Cm
cm
T1F
Em
em
Af
af
Cf
cf
T2M
Ef
ef
General Non-Scalar limitation via rG
– With opposite sex twin pairs (semi-Qualitative)
• Male Parameters
– meansM
– AM CM EM
• Female Parameters
– meanF
– AF CF and EF
Parameters are estimated jointly – linked
via the opposite sex correlations
r(AFemale ,Amale) = ? (estimated)
r(CFemale ≠ CMale ) = 1
r(EFemale ≠ EMale ) = 0
Classic Univariate ACE Model +
General Non-Scalar Limitation via rG
rODZ = ??
1
Am
am
Cm
cm
T1F
Em
em
Af
af
Cf
cf
T2M
Ef
ef
Open twinHet5AceCon.R
General Non-Scalar limitation
– With opposite sex twin pairs (semi-Qualitative)
• Male Parameters
– meansM
– AM CM EM and ASpecific
– Extra genetic/
environmental effects
• Female Parameters
– meanF
– AF CF and EF
Parameters are estimated jointly – linked
via the opposite sex correlations
Classic Univariate ACE Model +
General Non-Scalar Sex Limitation
rODZ = 0.5/1
1
Am
am
Cm
cm
Em
em
Af
af
Cf
cf
As
as
T1F
T2M
Ef
ef
Open alt_twinHet5AceCon.R
So How Important is SexLimitation Working?
Review- Heterogeneity Questions
• Quantitative- Are these differences due to
differences in the magnitude of the effects?
– Is the contribution of genetic/environmental factors
greater/smaller in males than in females?
• Qualitative- Are the differences due to
differences in the source/nature of the effects?
– Are there different genetic/environmental factors
influencing the trait in males and females?
Review- The language of
heterogeneity
Quantitative
- differences in the
magnitude of the
effects
Models
- Scalar
- Non-scalar with OS
twins
Qualitative
- differences in the
source/nature of the
effects
Models
- Non-scalar without OS
twins
- General Non-scalar
Heterogeneity Terminology
• Depends on research question
– Moderation, confounding, interaction (or GxE)
• Systematic differences
– Measured or manifest moderator/confounder
– Unmeasured (latent) moderator/confounder

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