A Data Warehousing Approach for Genomics Data Meta-Analysis - Evolving Application Domains of Data Warehousing and Mining - page 141

Comparative Study Example1

1. Sort columns of original matrix:

Here, we compare the RMA-based integration
method proposed above with the CDF reported in
(Jiang et al., 2004). A two-sample Kolmogorov-
Smirnov test is used to compare the distribution
(repartition) of the data combined by CDF and
the data combined by RMA-based procedure
described in the previous subsection. The test
provides the maximal distance between two
samples. In this test, we obtained a distance before
and after combining the data that was around D =
0.07 with p-value< 2.2e -16 . This result demonstrates
similar results between CDF and our RMA-based
procedure on these data. We combined data of
the Affymetrix GSE6475 and GSE9120 series
(described previously in this chapter). Figure 2
that plots intensity densities on two different data
samples, shows three curves for each sample:

ì ü ì ü

ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï

4729
5285
1358
8234

1 224
4235
5358
8789

x = Þ= x sort

í ý í

ý

ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï

î þ î þ

2. Compute row means:

ì ü ì ü

ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï

1 224
4235
5358
8789

225
3

.
.
.
.

50
525
800

x sort = Þ

í ý í ý

ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï

î þ î þ

3. Set mean for all columns:

ì ü ì ü

ï ï ï ï ï ï 225

350
525
800

.
.
.
.

ï ï ï ï ï ï ï ï ï ï ï ï 225 . 2225225 . . 225 . ï ï ï ï ï ï

1. the “ single data via RMA ” curve represents

GSE6475 data transformed via standard
RMA normalization,

350350 . . 350350 . .

'

Þ= x sort

í ý í ý

ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï 525525 . . 525525 . . ï ï ï ï ï ï

2. the “ meta data via RMA ” curve represents

GSE6475 data combined and transformed in
a meta-analysis way with GSE9120 data via
a RMA-based transformation as described
in the previous subsection,

800800 . . 8008 . .00

î þ î þ

4. Unsort columns to original order:

ì ü ì ü

ï ï ï ï ï ï 225225 . . 225225 . . ï ï ï ï ï ï ï ï ï ï ï ï 3 . 50 800225 . . 800 . ï ï ï ï ï ï

3. the “ meta data via CFD ” curve represents

GSE6475 data combined and transformed
in a meta-analysis way with GSE9120 data
via a CFD transformation as described in
the previous subsection on “Procedure of
integration”.

350350 . . 350350 . . 525225 . . 800350 . .

'

x sort = Þ x normalized =

í ý í ý

ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï ï

525525 . . 525525 . . 225525 . . 525525 . .

8000800 . . 800800 . . 800350 . . 350 . 225 .

î þ î þ

This method of distribution transformation is
robust, simple and easy for application. While
other methods only perform the distribution trans-
formation for two datasets, the advantage of RMA
is that it allows combining multiple individual
datasets and normalizing them globally. The fol-
lowing section presents a comparative study that
gives a proof of its efficiency.

We can observe that RMA and CFD transforma-
tions give results very close one to the other.
In fact, the quantile normalization method
used in RMA is a specific case of the CDF trans-
formation zFFx
X

= -1 (()) , where we estimate
F Y by empirical distribution of each array and
F X using the empirical distribution of averaged
sample quantiles. However, our procedure does

Y