sets. The next step is to test the coexpression difference for the
above gene sets in different experiments or conditions by calculat-
ing the pairwise correlation for gene set (sizen) and summarizing
them by t-statistics and sampling n genes randomly from the
expression data and repeating the above step formtimes to form
the distribution oft-statistics. This will be repeated in the other
condition. If thet-statistics is significant in condition 1 and not
significant in condition 2, the gene set will be identified as differen-
tially coexpressed.
For the method DiffCoEx, it provided two types for differential
coexpression that is within-module differential coexpression and
module-to-module differential coexpression. First, build adjacency
matrix by Pearson correlation coefficient, and then compute the
matrix of adjacency coefficient.dij¼ffiffiffi
1
2r
sign c
j 1 j
ij
∗ c
j 1 j
ij 2
sign c
j 2 j
ij
∗ c
j 2 j
ij(^) 2
!β
Then calculate the topological overlap measure to identify
genes that share similar neighbors.
tij¼ 1
P
k
dikdkj
þdij
min
P
k
dik;
P
k
djk
þ 1 dij
And the modules will be identified by the dissimilarity values’
formed matrix. The statistical significance of differential coexpres-
sion can be assessed using a measure of the statistics. This method
can be extended to the study of differential coexpression over more
than two conditions.
DICER detects differentially coexpressed gene sets using a
probabilistic score. First a DC score is defined.
RuD,ivRuD,jvN μiμj;
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
σ^2 iþσ^2 j
q
Then a probabilistic framework will be applied to test the
significance of the difference.
Besides the methods to detect new modules differentially coex-
pressed, there are methods for analyzing modules predefined.
GSCA used the Euclidean distance to measure the difference for
the pairwise correlation coefficient from the given pathway genes
under different conditions. And test the significance of the distance
using a permutation process. The method can be extended to
multiple conditions. Then the GSNCA estimates net correlation
changes by introducing for each gene a weight factor that charac-
terizes its cross-correlations in the coexpression networks and tests
the hypothesis that for a gene set there is no difference in the gene
weight vectors between two conditions.
Differential Coexpression Network Analysis for Gene Expression Data 161