Evaluating Components of Variance
QTDT can evaluate not only the evidence for association, but
also estimate the significance of individual components of variance.
As you will see, this is useful when evaluating if a candidate
polymorphism is the disease mutation, for example. If you are
not familiar with variance components, you may wish to proceed
to the last section.
To evaluate the significance of one variance component, specify
two alternative variance models using the -w and -v
options. For example, to estimate the heritability of the trait
in the sibs data set run qtdt -d sibs.dat -p sibs.ped -x-99.999
-a- -c- -we -veg. As usual, the -d, -p and -x options
describe the input files. The -a- and -c- options
turn off the association model and covariate, and the -we
and -veg options specify you are comparing a model with
only an environmental variance with a model with polygenic and
environmental variances. Try running the command now...
The following models will be evaluated...
NULL MODEL
Means = Mu
Variances = Ve
FULL MODEL
Means = Mu
Variances = Ve + Vg
Testing trait: Trait
=============================================
Allele df(0) LnLk(0) df(V) LnLk(V) ChiSq p
1 : 198 750.25 197 738.86 22.79 0.0000 (200 probands)
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The results suggest good evidence for a polygenic component.
QTDT places parameter estimates in the regress.tbl file,
to see the size of the estimated polygenic effect sift through
the contents of regress.tbl:
[...ignore the preceding information...]
FULL HYPOTHESIS
---------------
Family #1 var-covar matrix terms [2]...[[Ve]][[Vg]]
Family #1 regression matrix...
[linear] =
[4 x 1] Mu
1.3 1.000
1.4 1.000
1.5 1.000
1.6 1.000
Some useful information...
df : 197
log(likelihood) : 738.86
variances : 40.330 65.786
means : 98.625
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In the FULL HYPOTHESIS section of the regress.tbl file,
parameter estimates are given. Estimates for the means and variances
appear in the same order as in the model description section of
the QTDT output. In this case, the estimate for Ve is 40.330 and
for Vg it is 65.786. The single estimated mean parameter is the
phenotypic mean, in this case 98.625. As usual, estimates for
variance components are quite imprecise in small samples and must
be taken with a grain of salt.
To evaluate the evidence for linkage, run qtdt -d sibs.dat
-p sibs.ped -i sibs.ibd -x-99.999 -a- -c- -weg -vega. This
specifies that environmental and polygenic effects (-weg)
should be included in the default model, but additive major
locus effects should be modelled under the alternative hypothesis
(-vega).
The following models will be evaluated...
NULL MODEL
Means = Mu
Variances = Ve + Vg
FULL MODEL
Means = Mu
Variances = Ve + Vg + Va
Testing trait: Trait
=============================================
Testing marker: SNP_1
---------------------------------------------
Allele df(0) LnLk(0) df(V) LnLk(V) ChiSq p
1 : 197 738.86 196 736.97 3.77 0.0521 (200 probands)
Testing marker: SNP_2
---------------------------------------------
Allele df(0) LnLk(0) df(V) LnLk(V) ChiSq p
1 : 197 738.86 196 736.99 3.73 0.0535 (200 probands)
Testing marker: SNP_3
---------------------------------------------
Allele df(0) LnLk(0) df(V) LnLk(V) ChiSq p
1 : 197 738.86 196 737.01 3.69 0.0546 (200 probands)
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There is weak, but suggestive evidence for linkage at all three
markers (p < .10). To evaluate whether a candidate marker could
be the disease mutation, Fulker et al suggested modelling linkage
and association simultaneously. To do this run qtdt -d sibs.dat
-p sibs.ped -i sibs.ibd -x-99.999 -ao -c- -weg -vega -1. Again
we are evaluating the major locus additive genetic effect (-weg
-vega) but this time association is included in the model
(-ao).
The following models will be evaluated...
NULL MODEL
Means = Mu + B + W
Variances = Ve + Vg
FULL MODEL
Means = Mu + B + W
Variances = Ve + Vg + Va
Testing trait: Trait
=============================================
Testing marker: SNP_1
---------------------------------------------
Allele df(0) LnLk(0) df(V) LnLk(V) ChiSq p
1 : 195 726.68 194 726.16 1.05 ( 164/200 probands)
Testing marker: SNP_2
---------------------------------------------
Allele df(0) LnLk(0) df(V) LnLk(V) ChiSq p
1 : 195 730.21 194 729.86 0.70 ( 152/200 probands)
Testing marker: SNP_3
---------------------------------------------
Allele df(0) LnLk(0) df(V) LnLk(V) ChiSq p
1 : 195 737.05 194 735.35 3.40 0.0654 ( 168/200 probands)
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After modelling association, there is little residual evidence
for linkage at SNP_1 and SNP_2. This suggests they are in strong
disequilibrium with the disease mutation. The evidence for linkage
at SNP_3 is not accounted for by association, and this suggests
that SNP_3 is not the disease mutation.
To evaluate the total evidence for association and to test
for population stratification, proceed to the last
section.
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