A FC-GSEA Approach to Identify Significant Gene-Sets Using Microarray Gene Expression Data - Advances in Computational Science and Engineering - page 118

Fig. 2. A typical graphical pattern of the SNR values for the gene-list ordered by SNR-based
gene ranking

() ()

µ i - µ i

A B

SNR( ) i =

(1)

() ()

σ i + σ i

A B

Here the µ A and µ B denote the means of expression intensities of a gene i over sample
group A and sample group B, respectively. The σ A and σ B denote the standard devia-
tions of expression intensities of a gene i over sample group A and sample group B,
respectively. When the SNR is used for gene ranking, the SNR values for the ordered
gene-list typically have such a pattern as shown in Fig. 2. That is, the genes having
higher SNR values (i.e. larger positive SNR values) are more highly ranked and are
located at the front side of Fig. 2. The genes having lower SNR values (i.e. larger
negative SNR values) are more lowly ranked and are located at the rear side of Fig. 2.
From eq. (1), we note that the positive SNR of a gene occurs when the gene has
larger expression intensity in a sample group A than a sample group B, and the nega-
tive SNR of a gene occurs when the gene has smaller expression intensity in a sample
group A than a sample group B.
With the entire gene-list ordered by this SNR ranking statistic and the genes in-
cluded in a specific gene-set, the KS score is computed by employing the empirical
cumulative distribution functions for P hit and P miss shown in eqs. (2).

()

Ej

i

∑

()

Pi =

hit

N

j = 1

H

(2)

( )

()

1 − Ej

i

()

∑

Pi =

miss

N

j

M

() ()

ES = max P i − P i

(3)

hit miss

i = 1, , N

L

Here P hit is the empirical cumulative distribution function of which cumulative sum
becomes 1 when the first i genes in the ordered gene-list completely match the
genes included in a specific gene-set. On the other hand, P miss is the one of which
cumulative sum becomes 1 when there is no match between them. In eqs. (2), E(j) is
the ranking score (i.e. SNR) of the j th gene if the j th gene in the ordered gene-set is
included in a gene-set (i.e. hit ), or is 0 if the j th gene in the ordered gene-set is not