Biomedical Engineering Reference
In-Depth Information
in each subgroup is used for the third dimension to display the distribution
of two array intensities. When two arrays have comparable intensities, the
2D image plot is likely to show a highly dense thin band along the diag-
onal percentile curve. We use the invariant band to reect the degrees of
consistency between two arrays' intensities.
2.1.2. Invariant Band
To construct an invariant band, we use mx% deviation to build up
a lower boundary curve which is formed by data points (Q
a
; Q
b
) with
ab = mx, and an upper boundary curve formed by data points
(Q
a
; Q
b
) with ba = mx. Here (A; B) represents data position with
A on the x-axis and B on the y-axis. The parameter m is dened as
the number of x% unit to adjust for random variation in the grouped
data with 0 < m < k. For example, when m = 2 and x% = 5%, the
mx%(= 10%) invariant band has a lower boundary curve formed by
(Q
10
; Q
0
); (Q
15
; Q
5
); : : : ; (Q
95
; Q
85
), and (Q
100
; Q
90
), and the upper bound-
ary curve formed by (Q
0
; Q
10
); (Q
5
; Q
15
); : : : ; (Q
85
; Q
95
), and (Q
90
; Q
100
).
A data point, (Q
a
; Q
b
), withjbajmx will be covered by the mx%
invariant band. Since the data point is in the tolerable distance away from
the diagonal percentile curve, Q
a
and Q
b
are considered to be compara-
ble. Therefore, if the majority of intensities between two arrays are located
within the invariant band, both arrays are likely to have comparable inten-
sity. Thus, given the mx% invariant band, we compute the degrees of array
variation by a coverage rate, dened as the number of data points inside
the band divided by the total number of data points. A substantial por-
tion of data points outside the band implies a high degree of inconsistency
between two arrays. Such incomparability deserves further investigation of
data quality before analysis (Figures 2.1-2.2).
2.1.3. A Supplementary Tool for Gene Selection
Microarray data are often normalized prior to data analysis. However, the
methods used for normalization remain debatable because dierent nor-
malization procedures often result in selecting dierent gene lists. Neverthe-
less, dierence in expressions between the two groups can be evaluated in
terms of the relative dierence in the raw data, where the relative dierence
in the raw data refers to the degrees of discrepancy of the gene intensity
between the control arrays and the experimental arrays. If there is no rel-
ative dierence in the raw data, but a large absolute dierence occurs in
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