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Heterogeneity. Sarah Medland & Nathan Gillespie. Types of Heterogeneity. Terminology depends on research question Moderation, confounding, GxE Systematic differences Measured or Manifest moderator/confounder Discrete traits Ordinal & Continuous traits (Thursday)

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heterogeneity

Heterogeneity

Sarah Medland

& Nathan Gillespie

types of heterogeneity
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 GxE
heterogeneity questions
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.?
the language of heterogeneity
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?
the language of heterogeneity1
The language of heterogeneity

1861

  • Sex differences = Sex limitation

1948

1840

the language of heterogeneity3
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:
      • varFemale= k*varMale
      • AFemale= k*AMale
      • CFemale= k*CMale
      • EFemale= k*EMale

k here is the scalar

slide8

1

1/.5

C

A

C

E

E

A

1

1

1

1

1

1

a

e

c

a

c

e

Twin 1

Twin 2

No Heterogeneity

slide9

1

1/.5

C

A

C

E

E

A

1

1

1

1

1

1

a

e

c

a

c

e

MZ DZ

Twin 1

Twin 2

slide10

1

1/.5

C

A

C

E

E

A

1

1

1

1

1

1

k*e

a

e

c

k*a

k*c

Male

Twin

Female

Twin

Scalar Sex-limitation

aka scalar sex-limitation of the variance

the language of heterogeneity4
The language of heterogeneity
  • Non-Scalar limitation
    • Without opposite sex twin pairs (Qualitative)
      • varFemale≠ varMale
      • AFemale≠ AMale
      • CFemale≠ CMale
      • EFemale≠ EMale
the language of heterogeneity5
The language of heterogeneity
  • 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

slide13

1

1

Male ACE model

1/.5

1/.5

EM

EF

CM

CF

AF

AM

AF

AM

CM

CF

EM

EF

1

1

1

1

1

1

1

1

1

1

1

1

aM

aF

eM

eF

cM

cF

aM

aF

cM

cF

eM

eF

Twin 1

Twin 1

Twin 2

Twin 2

Female ACE model

the language of heterogeneity6
The language of heterogeneity
  • 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
slide15

1

.5/1

CM

AM

CF

EF

EM

AF

1

1

1

1

1

1

eF

aM

eM

cM

aF

cF

Male

Twin

Female

Twin

Non-scalar Sex-limitation

aka common-effects sex limitation

the language of heterogeneity7
The language of heterogeneity
  • 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

slide17

1

.5/1

CM

AM

CF

EF

EM

AF

1

1

1

1

1

1

eF

aM

eM

cM

aF

cF

AS

as

1

Male

Twin

Female

Twin

General Non-scalar Sex-limitation

aka general sex limitation

the language of heterogeneity8
The language of heterogeneity
  • 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
slide19

1

?

CM

AM

CF

EF

EM

AF

1

1

1

1

1

1

eF

aM

eM

cM

aF

cF

Male

Twin

Female

Twin

General Non-scalar Sex-limitation

aka general sex limitation

how important is sex limitation
How important is sex-limitation?
  • Let have a look
    • Height data example using older twins
    • Zygosity coding
      • 6 & 8 are MZF & DZF
      • 7 & 9 are MZM & DZM
      • 10 is DZ FM
    • ScriptsACEf.RACEm.R ACE.R
    • Left side of the room ACEm.R
    • Right side of the room ACE.R
    • Record the answers from the estACE* function
how important is sex limitation1
How important is sex-limitation?
  • Female parameters
  • Male parameters
  • Combined parameters
  • Conclusions?
lets try this model
Lets try this model

1

?

CM

AM

CF

EF

EM

AF

1

1

1

1

1

1

eF

aM

eM

cM

aF

cF

Male

Twin

Female

Twin

General Non-scalar Sex-limitation

aka general sex limitation

twinhet5acecon r
twinHet5AceCon.R
  • Use data from all zygosity groups
slide24

1

?

CM

AM

CF

EF

EM

AF

1

1

1

1

1

1

eF

aM

eM

cM

aF

cF

Male

Twin

Female

Twin

slide25

1

?

CM

AM

CF

EF

EM

AF

1

1

1

1

1

1

eF

aM

eM

cM

aF

cF

Male

Twin

Female

Twin

means
Means
  • Have a think about this as we go through
    • is this the best way to set this up?
run it
Run it
  • What would we conclude?
  • Do we believe it?
  • Checking the alternate parameterisation…
lets try this model1
Lets try this model

1

?

CM

AM

CF

EF

EM

AF

1

1

1

1

1

1

eF

aM

eM

cM

aF

cF

Male

Twin

Female

Twin

General Non-scalar Sex-limitation

aka general sex limitation

slide31

af = -.06

  • am = -.06
  • rg = -.9

Dzr = -.06*(.5*-.9) .06

=.45

means1
Means
  • Add a correction using a regression model
  • expectedMean = maleMean + β*sex

Sex is coded 0/1

β is the female deviation from the male mean