Can resemblance e'g' correlations between sib pairs, or DZ twins, be modeled as a function of DNA ma

1
Can resemblance (e.g. correlations) between sib
pairs, or DZ twins, be modeled as a function of
DNA marker sharing at a particular chromosomal
location?
2
Three groups of DZ twins

• IBD 2 (all markers identical by descent)
• IBD 1
• IBD 0
• Are the correlations (in e.g. lipid levels)
  different for the 3 groups?

3
A fully informative mating
mother
father
D
A
B
C
X
Q?
Q?
Q?
Q?
4
Identity By Descent (IBD) status in siblings.
Four parental marker alleles A - B and C - D.
Two sibs can inherit 0, 1 or 2 alleles IBD.
IBD 0 1 2 25 50 25
Derivation of IBD probabilities for one marker
(with and without parental genotypes known) was
given by Haseman and Elston (1972). Applications
affected sib-pair method linkage with
quantitative traits
5
Adult Dutch DZ pairs distribution of pi-hat (p)
at 65 cM (chromosome 19). p IBD/2 all pairs
with p lt0.25 have been assigned to IBD0 group
all pairs with p gt 0.75 to IBD2 group others to
the IBD1 group.
6
Exercise

• Model DZ correlation in LDL as a function of IBD
• Test if the correlations are the same
• Add data of MZ twins
• Test if the correlation in the DZ group with IBD
  2 is the same as the MZ correlation
• Repeat for apoB and ln(apoE) levels
• Does eliminating subjects who are on
  lipid-lowering medication change the results?
• Do cross-correlations (across twins/across
  traits) differ as a function of IBD? (trivariate)

7
Basic script and data (LDL, apoB, apoE)

• Correlation estimation in DZ BasicCorrelationsDZ(
  ibd).mx
• Information on data datainfo.doc
• Datafiles DZ partionedAdultDutch3.dat
• MZ AdultDutchMZ3.dat
• Complete (MZ DZ tests) job
  AllCorrelations(ibd).mx

8
Correlations as a function of IBD IBD2 IBD1 I
BD0 MZLDL 0.81 0.49 -0.21 0.78ApoB 0.64 0
.50 0.02 0.79lnApoE 0.83 0.55 0.14 0.89
9
Correlations as a function of IBDchi-squared
tests all DZ equal DZ(ibd2)MZLDL 21.77 0.
0975apoB 7.98 1.53apoE 12.45 0.576 (df2)
(df1)
10
Can heritability be modeled as a function of DNA
marker sharing at a particular chromosomal
location?
11
DZ twin pairs who are IBD 2 familial and QTL
effects
r 1
E
E
r 1
e
e
F
F
f
f
Q
Q
q
q
DZ 1
DZ 2
12
DZ twin pairs who are IBD 1 familial and QTL
effects
r 1
E
E
r 0.5
e
e
F
F
f
f
Q
Q
q
q
DZ 1
DZ 2
13
DZ twin pairs who are IBD 0 familial effects
r 1
E
E
e
e
F
F
f
f
DZ 1
DZ 2
14
Linkage analysis in DZ twins or sib pairs

• 3 groups IBD2,1,0 (p1, 0.5, 0)
• Model the covariance as a function of IBD
• Allow for background familial variance
• Total variance also includes E
• Covariance pQ F E
• Variance Q F E

15
MZ Twin pairs
rMZ 1
rMZ 1
E
E
rMZ 1
C
C
e
e
A
A
c
c
a
a
Q
Q
q
q
MZ 1
MZ 2
16
rMZ rDZ 1
rMZ 1, rDZ 0.5
E
E
rMZ 1, rDZ 0, 0.5 or 1
C
C
e
e
A
A
c
c
a
a
Q
Q
q
q
Twin 1
Twin 2
4 group linkage analysis (3 IBD DZ groups and 1
MZ group)
17
Exercise

• Fit FQE model to DZ data (i.e. Ffamilial, QQTL
  effect, Eunique environment)
• Fit FE model to DZ lipid data (drop Q)
• Is the QTL effect significant?
• Add MZ data ACQE model (A additive genetic
  effects, Ccommon environment), does this change
  the estimate / significance of QTL?

18
Basic script and data (LDL, apoB, apoE)

• FQE model in DZ twins FQEmodel-DZ.mx
• Information on data datainfo.doc
• Datafiles DZ partionedAdultDutch3.dat
• MZ AdultDutchMZ3.dat
• Complete (MZ data DZ data tests) job
  ACEQ-mzdz.mx

19
Test of the QTL chi-squared test(df 1) DZ
pairs DZMZ pairsLDL 12.247 12.561apoB
1.945 2.128 apoE 12.448 12.292
20
Use pi-hat single group analysis (DZ only)
rDZ 0.5
E
E

rDZ ?
e
e
A
A
a
a
Q
Q
q
q
Twin 1
Twin 2
21
Exercise PiHatModelDZ.mx

• Chi-square (LDL) 12.318

22
rMZ rDZ 1
rMZ 1, rDZ 0.5
E
E

rMZ 1, rDZ ?
C
C
e
e
A
A
c
c
a
a
Q
Q
q
q
Twin 1
Twin 2