Transcript Some Issues in GxE, Comorbidity & Factor Analysis

GxE and GxG
interactions
Michael C Neale
Boulder Workshop March 6 2009
Background I
• Various kinds of E and G
–Latent/Observed
• GxG interaction
–Observed x Observed
–Latent x Latent
–Latent x Observed
• Same for GxE
Background II
• Latent Genotype x Measured Environment Interaction
– Kendler, KS & Eaves, LJ 1986 Models for the joint effect of
genotype and environment on liability to psychiatric illness. Am
J Psychiat 143:279-89
– Heath, AC, Cates, R, Martin, NG, Meyer, JM, Hewitt, JK, Neale,
MC & Eaves, LJ (1993) Genetic contributions to smoking
initiation: Comparisons across cohorts and across cultures.
Journal of Substance Abuse 5: 221-246
– Neale, MC & Cardon, LR (1992) Methodology for Genetic
Studies of Twins & Families. Dordrecht, NL: Kluwer.
• Models based on multiple-group approach: binary/nominal
classifications “Heterogeneity”
Background III
• 1994: Definition variables in Mx
– Enables ‘continuous’ version of multiple group analysis
• Purcell, S (2002). Variance components models for geneenvironment interaction in twin analysis. Twin Res, 5(6):554-571
– Useful framework: do A/C/E change as a function of a
measured ‘environmental’ variable?
– Often regress out main effects of moderator on trait of interest
Gene effect
Gene-environment interaction
?
Environmental effect
G x E interaction
The environment modifies the effect of a gene
A gene modifies the effect of an environment
S.Purcell ©
Gene effect
Epistasis
Gene effect
Gene × gene interaction
Epistasis: one gene modifies the effect of another
S.Purcell ©
Biometrical G × E model
No
interaction
Genotype
Equivalently…
Interaction
Mean
a
1

2
1
0
1
1
-a
Environment
AA
M
Aa
Environment
aa

-
M
Environment
M
Standard ACE model for twin resemblance
1(MZ) .5(DZ)
1
1
1
1
1
1
1
A
C
E
A
C
E
a
c
e
Twin 1
a

1

c
e
Twin 2
Moderated ACE model for twin resemblance
1(MZ) .5(DZ)
1
1
1
1
1
1
1
A
C
E
A
C
E
a + XM1
c
a + XM2
e
Twin 1
 + mM1
1
 + mM2
c
e
Twin 2
Within-person correlations across age
Single-factor model (r=1)
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
• Red = 1.0 Green = -1.0
Growth Curve Model
VL
VS
r
L
1
1
S
1
2
1
3
1
4
Trait Age 1
Trait Age 2
Trait Age 3
Trait Age 4
e
e
e
e
Enhanced Moderated AE model
1(MZ) .5(DZ)
1
AS
aSM1
r
1
1
1
1
AL
E
AS
aL
Twin 1
e
µ + βmM1
r
aSM2
1
µ + βmM2
1
1
AL
E
aL
e
Twin 2
Two-factor Moderated AE model r=.0 : .9
Enhanced Moderated AE model
Within-person correlations across age
r=1.0 r=.9 r=.6 r=.3
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
Extension for correlated moderator
model: 1 Twin
Perhaps best to integrate
across AC, CC or other
components of variance
Volume controls on Factor or
on T are coherent
Bivariate Moderated AE model: 1 Twin
1(MZ) .5(DZ)
1
1
1
1
1
AM
CM
EM
AST
eTM
aM
cM eM
cTM
r
1
1
ALT
ET
aSM M aLT
eT
aTM
Moderator
µM
1
µT
Trait
Research Design Considerations
1. No variation in Age(M) at measurement
1. Estimation of parameters via mixture modeling (but could be
due to anything)
2. Variation in age, but twins measured once at same time
1. Know variance, MZ and DZ covariance @ different ages
2. Don’t know if same genes/envt at different ages (assume r)
3. Variation in age, twins measured once at different times
1. Know 2.1 plus MZ & DZ covariances as f(Age difference), i.e.,
have pairs concordant & discordant wrt Age
2. Can get A & C factors split into level & slope
4. Longitudinal data, twins possibly measured at different times
1. Can get E factor split (rE) as well
Greg Carey Article
Genotype-Environment Interaction Problems
and a Multivariate Solution
“Please do not cite until I’m certain I got the
whole thing right.”
Definition variables
Conditional Distributions
New Mx script
Necessary background
“For example, if the ACE model in the general
population assumes that A, C, and E are
uncorrelated, then A, C, and E within the poor
environmental group will be usually be
correlated when home environment is
correlated with ASB”
Conditional distributions
Distribution of Phenotype conditional on
Moderator
Pearson-Aitken selection formulae
Pearson Aitken Selection
Pearson Aitken Selection
Careful with measurement!
Example item response probability curves in white
0.5
Response
Probability
0.4
1
0.3
.75
0.2
.5
0.1
.25
N
.0
0
-4
-3
-2
Low Info
-1
0
1
High Info
2
3
4