Twins Studies - GitHub Pages · Twins Studies • Monozygotic (MZ; “identical”) –...
Transcript of Twins Studies - GitHub Pages · Twins Studies • Monozygotic (MZ; “identical”) –...
![Page 1: Twins Studies - GitHub Pages · Twins Studies • Monozygotic (MZ; “identical”) – Fertilization of a single egg by a single sperm ... Twin 1 E C A 1 1 1 Twin 2 A C E 1 1 1 Model](https://reader033.fdocuments.net/reader033/viewer/2022060207/5f03fbd17e708231d40bbd5e/html5/thumbnails/1.jpg)
Twins Studies
• Monozygotic (MZ; “identical”)
– Fertilization of a single egg by a single sperm
– Share 100% of their genetic material.
• Dizygotic (DZ, “fraternal” or “non-identical”)
– Result from the independent fertilization of two
eggs by two sperm
– Share on average 50% of their genes (just like full
siblings).
![Page 2: Twins Studies - GitHub Pages · Twins Studies • Monozygotic (MZ; “identical”) – Fertilization of a single egg by a single sperm ... Twin 1 E C A 1 1 1 Twin 2 A C E 1 1 1 Model](https://reader033.fdocuments.net/reader033/viewer/2022060207/5f03fbd17e708231d40bbd5e/html5/thumbnails/2.jpg)
A Natural Experiment
• Twins reared apart
– They did not experience the same
environment
– Gives a much stronger test of genetic and
non-shared environmental contributions
– But separated MZs are rare
![Page 3: Twins Studies - GitHub Pages · Twins Studies • Monozygotic (MZ; “identical”) – Fertilization of a single egg by a single sperm ... Twin 1 E C A 1 1 1 Twin 2 A C E 1 1 1 Model](https://reader033.fdocuments.net/reader033/viewer/2022060207/5f03fbd17e708231d40bbd5e/html5/thumbnails/3.jpg)
![Page 4: Twins Studies - GitHub Pages · Twins Studies • Monozygotic (MZ; “identical”) – Fertilization of a single egg by a single sperm ... Twin 1 E C A 1 1 1 Twin 2 A C E 1 1 1 Model](https://reader033.fdocuments.net/reader033/viewer/2022060207/5f03fbd17e708231d40bbd5e/html5/thumbnails/4.jpg)
Path Diagram
![Page 5: Twins Studies - GitHub Pages · Twins Studies • Monozygotic (MZ; “identical”) – Fertilization of a single egg by a single sperm ... Twin 1 E C A 1 1 1 Twin 2 A C E 1 1 1 Model](https://reader033.fdocuments.net/reader033/viewer/2022060207/5f03fbd17e708231d40bbd5e/html5/thumbnails/5.jpg)
Path Analysis
• Derive predictions for the variances and covariances of the variables under the specified model– Present relationships between variables using
diagrams– The relationships can also be represented as
structural equations and covariance matrices
– Structural equation modelling (SEM) represents a unified platform for path analytic and variance components models
![Page 6: Twins Studies - GitHub Pages · Twins Studies • Monozygotic (MZ; “identical”) – Fertilization of a single egg by a single sperm ... Twin 1 E C A 1 1 1 Twin 2 A C E 1 1 1 Model](https://reader033.fdocuments.net/reader033/viewer/2022060207/5f03fbd17e708231d40bbd5e/html5/thumbnails/6.jpg)
Maximum Likelihood
Estimation• Likelihood: probability that an observation
(data point) is predicted by specified model
• For MLE, determine most likely values of population parameter value (e.g, µ, σ, β) given observed sample value – define model
– define probability of observing a given event conditional on a particular set of parameters
– choose a set of parameters which are most likely to have produced observed results
![Page 7: Twins Studies - GitHub Pages · Twins Studies • Monozygotic (MZ; “identical”) – Fertilization of a single egg by a single sperm ... Twin 1 E C A 1 1 1 Twin 2 A C E 1 1 1 Model](https://reader033.fdocuments.net/reader033/viewer/2022060207/5f03fbd17e708231d40bbd5e/html5/thumbnails/7.jpg)
Observed Variable
Latent Variable
Causal Path
Covariance Path
Path Diagram Conventions
![Page 8: Twins Studies - GitHub Pages · Twins Studies • Monozygotic (MZ; “identical”) – Fertilization of a single egg by a single sperm ... Twin 1 E C A 1 1 1 Twin 2 A C E 1 1 1 Model](https://reader033.fdocuments.net/reader033/viewer/2022060207/5f03fbd17e708231d40bbd5e/html5/thumbnails/8.jpg)
Path diagram for the effects of genes and environment on phenotype
P
G E
Measured variable
Latent variables
Genotype Environment
Phenotype
h e
r
![Page 9: Twins Studies - GitHub Pages · Twins Studies • Monozygotic (MZ; “identical”) – Fertilization of a single egg by a single sperm ... Twin 1 E C A 1 1 1 Twin 2 A C E 1 1 1 Model](https://reader033.fdocuments.net/reader033/viewer/2022060207/5f03fbd17e708231d40bbd5e/html5/thumbnails/9.jpg)
Variance Components
• Heritability (narrow-sense, A or a2; broad-sense, H or h2): phenotypic variance in a sample that can be attributed to genotypic variance.
• Shared or common environment (C or c2): experiences that makes individuals more similar to one another, regardless of genetic similarity
• Non-shared or Unique environment and Error (E or e2): What is left over
![Page 10: Twins Studies - GitHub Pages · Twins Studies • Monozygotic (MZ; “identical”) – Fertilization of a single egg by a single sperm ... Twin 1 E C A 1 1 1 Twin 2 A C E 1 1 1 Model](https://reader033.fdocuments.net/reader033/viewer/2022060207/5f03fbd17e708231d40bbd5e/html5/thumbnails/10.jpg)
IDENTICAL TWINS
• MONOZYGOTIC:
• Have IDENTICAL genes
(A)
• Come from the same
family (C)
• Have unique experiences
during life (E)
FRATERNAL TWINS
• DIZYGOTIC: Have
DIFFERENT genes (A)
• Come from the same
family (C)
• Have unique experiences
during life (E)
![Page 11: Twins Studies - GitHub Pages · Twins Studies • Monozygotic (MZ; “identical”) – Fertilization of a single egg by a single sperm ... Twin 1 E C A 1 1 1 Twin 2 A C E 1 1 1 Model](https://reader033.fdocuments.net/reader033/viewer/2022060207/5f03fbd17e708231d40bbd5e/html5/thumbnails/11.jpg)
Twin 1
E C A1 1 1
Twin 2
A C E1 1 1
Model for an MZ PAIR
1
1
Note: a, c and e are the same cross twins
e ac a ec
![Page 12: Twins Studies - GitHub Pages · Twins Studies • Monozygotic (MZ; “identical”) – Fertilization of a single egg by a single sperm ... Twin 1 E C A 1 1 1 Twin 2 A C E 1 1 1 Model](https://reader033.fdocuments.net/reader033/viewer/2022060207/5f03fbd17e708231d40bbd5e/html5/thumbnails/12.jpg)
Twin 1
E C A1 1 1
Twin 2
A C E1 1 1
Model for a DZ PAIR
1
.5
Note: a, c and e are also the same cross groups
e ac a ec
![Page 13: Twins Studies - GitHub Pages · Twins Studies • Monozygotic (MZ; “identical”) – Fertilization of a single egg by a single sperm ... Twin 1 E C A 1 1 1 Twin 2 A C E 1 1 1 Model](https://reader033.fdocuments.net/reader033/viewer/2022060207/5f03fbd17e708231d40bbd5e/html5/thumbnails/13.jpg)
Heritability among unrelateds
![Page 14: Twins Studies - GitHub Pages · Twins Studies • Monozygotic (MZ; “identical”) – Fertilization of a single egg by a single sperm ... Twin 1 E C A 1 1 1 Twin 2 A C E 1 1 1 Model](https://reader033.fdocuments.net/reader033/viewer/2022060207/5f03fbd17e708231d40bbd5e/html5/thumbnails/14.jpg)
VP = a2 + c2 + e2
![Page 15: Twins Studies - GitHub Pages · Twins Studies • Monozygotic (MZ; “identical”) – Fertilization of a single egg by a single sperm ... Twin 1 E C A 1 1 1 Twin 2 A C E 1 1 1 Model](https://reader033.fdocuments.net/reader033/viewer/2022060207/5f03fbd17e708231d40bbd5e/html5/thumbnails/15.jpg)
Falconer’s model
Assumes all genetic effects are additive (h2 = a2)
rMZ = a2 + c2
rDZ = 0.5a2 + c2
1.0 = a2 + c2 + e2
![Page 16: Twins Studies - GitHub Pages · Twins Studies • Monozygotic (MZ; “identical”) – Fertilization of a single egg by a single sperm ... Twin 1 E C A 1 1 1 Twin 2 A C E 1 1 1 Model](https://reader033.fdocuments.net/reader033/viewer/2022060207/5f03fbd17e708231d40bbd5e/html5/thumbnails/16.jpg)
Falconer estimates
a2 = 2(rMZ – rDZ)
c2 = 2rDZ – rMZ
e2 = 1 – rMZ
![Page 17: Twins Studies - GitHub Pages · Twins Studies • Monozygotic (MZ; “identical”) – Fertilization of a single egg by a single sperm ... Twin 1 E C A 1 1 1 Twin 2 A C E 1 1 1 Model](https://reader033.fdocuments.net/reader033/viewer/2022060207/5f03fbd17e708231d40bbd5e/html5/thumbnails/17.jpg)
Polderman et al. 2015, Nature Genetics
![Page 18: Twins Studies - GitHub Pages · Twins Studies • Monozygotic (MZ; “identical”) – Fertilization of a single egg by a single sperm ... Twin 1 E C A 1 1 1 Twin 2 A C E 1 1 1 Model](https://reader033.fdocuments.net/reader033/viewer/2022060207/5f03fbd17e708231d40bbd5e/html5/thumbnails/18.jpg)
![Page 19: Twins Studies - GitHub Pages · Twins Studies • Monozygotic (MZ; “identical”) – Fertilization of a single egg by a single sperm ... Twin 1 E C A 1 1 1 Twin 2 A C E 1 1 1 Model](https://reader033.fdocuments.net/reader033/viewer/2022060207/5f03fbd17e708231d40bbd5e/html5/thumbnails/19.jpg)
What about “dominance”* effects?
VP = a2 + d2 + c2 + e2
* Dominance defined statistically as individuals being
more similar on the basis of genetic overlap alone than
would be predicted by a linear model – i.e., any non-
linear genotype “dosage” effects
![Page 20: Twins Studies - GitHub Pages · Twins Studies • Monozygotic (MZ; “identical”) – Fertilization of a single egg by a single sperm ... Twin 1 E C A 1 1 1 Twin 2 A C E 1 1 1 Model](https://reader033.fdocuments.net/reader033/viewer/2022060207/5f03fbd17e708231d40bbd5e/html5/thumbnails/20.jpg)
ACE or ADE
Cov(mz) = a2 + c2 or a2 + d2
Cov(dz) = ½ a2 + c2 or ½ a2 + ¼ d2
VP = a2 + c2 + e2 or a2 + d2 + e2
3 unknown parameters (a, c, e or a, d, e), and only 3 distinctive predicted statistics:
Cov MZ, Cov DZ, Vp)
this model is just identified
![Page 21: Twins Studies - GitHub Pages · Twins Studies • Monozygotic (MZ; “identical”) – Fertilization of a single egg by a single sperm ... Twin 1 E C A 1 1 1 Twin 2 A C E 1 1 1 Model](https://reader033.fdocuments.net/reader033/viewer/2022060207/5f03fbd17e708231d40bbd5e/html5/thumbnails/21.jpg)
Twin 1
E D A1 1 1
Twin 2
A D E1 1 1
ADE Model
1(MZ) / 0.25 (DZ)
1/.5
e ad a ed
![Page 22: Twins Studies - GitHub Pages · Twins Studies • Monozygotic (MZ; “identical”) – Fertilization of a single egg by a single sperm ... Twin 1 E C A 1 1 1 Twin 2 A C E 1 1 1 Model](https://reader033.fdocuments.net/reader033/viewer/2022060207/5f03fbd17e708231d40bbd5e/html5/thumbnails/22.jpg)
Twin Correlations � Sources
of Variance
rMZ > rDZ
rMZ = 2 rDZ
rMZ = rDZ
rMZ < 2 rDZ
rMZ > 2 rDZ
A
only A (no C,D)
only C (no A,D)
A & C
A & D
![Page 23: Twins Studies - GitHub Pages · Twins Studies • Monozygotic (MZ; “identical”) – Fertilization of a single egg by a single sperm ... Twin 1 E C A 1 1 1 Twin 2 A C E 1 1 1 Model](https://reader033.fdocuments.net/reader033/viewer/2022060207/5f03fbd17e708231d40bbd5e/html5/thumbnails/23.jpg)
Classical Twin Study
Assumptions• Equal
means/variances in Twin 1 and Twin 2
• Equal means/variances in MZ and DZ twins
• Random Mating
• Equal Environments of MZ and DZ pairs
• No GE Correlation
• No G x E Interaction
• No Sex Limitation