Biomedical Engineering Reference
In-Depth Information
where g
ij
is the genotype of individual j at SNP i , a
j
is the ancestry (the eigenvec-
tor) of individual j along a given axis of variation and is the regression coefficient
for ancestry predicting genotype across individuals at SNP i . Therefore, computed
association with Armitage chi-square statistics between genotypes and phenotypes,
both before and after PCA correction, results in two chi-square values for each
SNP and relative p values. If we compare the most significantly associated SNPs in
EIGENSTRAT, we observe that the results change if we correct using 3 or 9 PCs
(Table
9.10
), while the results using 9 PCs and 10 PCs (where is 1.000) are the
same.
9.2.2.4
PLINK and CMH
PLINK performs a complete-linkage hierarchical clustering based on genome-wide
identical-by-state (IBS) between any two subjects in order to cluster individuals into
homogeneous subsets using classical multi-dimensional scaling (MDS) to visualize
substructure. The CMH test is used for overall disease/gene association, controlling
for clusters, where the number of clusters is selected by the user. It is a chi-squared
value given by:
X
!
2
X
a
i
A
i
i
D
1
i
D
1
CMH
D
;
(9.4)
X
V
i
i
D
1
where a
i
are the observed count of alles, A
i
are the expected count and V
i
are the
variance.
9.2.3
Genomic Control
GC 11 assumes that, in the presence of population substructure, the standard chi-
squared statistics used in case-control studies is inflated by an estimated inflation
factor () that is proportional to the degree of stratification. Computation of is as
described in Devlin et al. [
11
]:
median.Y
1
;Y
2
;:::;Y
L
/
0:456
O
D
;
(9.5)
where Y
i
represents the chi-squared statistics of Armitage trend test for L unlinked
markers. Then, value represents the median of chi-squared statistics divided by
0.456, the predicted median value of a central chi-squared distribution, A value
above 1 indicates inflation in chi-squared statistics and, by definition, it is not
allowed to be more than 1 in a homogeneous sample.
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