Normalization of Microarray Data

1
Normalization of Microarray Data

• - how to do it!

Henrik Bengtsson (hb_at_maths.lth.se) Terry Speed
(terry_at_stat.berkeley.edu)
2
Outline

• The X Data Set
• (R,G) ? (M,A) Transformation
• Background correction or not?
• Within slide normalization
• Across slide normalization
• Identifying differentially expressed genes
• The X2 Data Set

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The X Data Set
Slide Title Name
1 Mutant (a) vs. Reference (a) dUDG558
2 Mutant (a) vs. Reference (a) dUDG409
3 Mutant (a) vs. Reference (a) dUDG405
4 Mutant (b) vs. Reference (b) dUDG411
5 Mutant (b) vs. Reference (b) dUDG412
6 Mutant (b) vs. Reference (b) dUDG414
7 Mutant (c) vs. Reference (c) dUDG413
8 Mutant (c) vs. Reference (c) dUDG415
9 Mutant (c) vs. Reference (c) dUDG813

• All slides are replicates and contains 5184
  spots/genes. Three identical RNA preparations
  were done (a) was hybridized to slide 1-3, (b)
  to slide 4-6, and (c) to slide 7-9.
• All data is collected by GenePixTM Scanner and
  Software. The following analysis was done using
  R and the sma library by Terry Speed Group.

4
(R,G) ? (M,A) Transformation

• Observed data (R,G)n1..5184
• R red channel signal
• G green channel signal
• (background corrected or not)

Transformed data (M,A)n1..5184 M log2(R/G)
(ratio), A log2(RG)1/2 1/2log2(RG)
(intensity) ? R(22AM)1/2, G(22A-M)1/2
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Background correction or not?

• Decision 1 No background correction

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Within Slide Normalization

• Question What kind of normalization should be
  applied
• No normalization, or
• Global (lowess) normalization, or
• Print-tip normalization, or
• Scaled print-tip normalization?

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No Normalization

• Non-normalized data (M,A)n1..5184
• M log2(R/G)

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Global (lowess) Normalization

• Global normalized data (M,A)n1..5184
• Mnorm M-c(A)
• where c(A) is an intensity dependent function.

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Print-tip Normalization
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16

• Print-tip normalized data (M,A)n1..5184
• Mp,norm Mp-cp(A) pprint tip (1-16)
• where cp(A) is an intensity dependent function
  for print tip p.

Print-tip layout
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Scaled Print-tip Normalization

• Scaled print-tip normalized data
  (M,A)n1..5184
• Mp,norm sp(Mp-cp(A)) pprint tip (1-16)
• where sp is a scale factor for print tip p
  (Median Absolute Deviation).

After print-tip normalization
After scaled print-tip normalization
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Spatial Effects

No normalization
Global normalization
Scaled Print-tip normalization
Print-tip normalization
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Another Quick Example

Scaled print-tip normalization
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Within Slide Normalization Summary

• Question What kind of normalization should be
  applied
• No normalization, or
• Global (lowess) normalization, or
• Print-tip normalization, or
• Scaled print-tip normalization?
• Decision 2 Scaled print-tip normalization.

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Across Slides Normalization

Scaled print-tip normalization
Median Absolute Deviation (MAD) Scaling
Averaging
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Average Over All Slides

The average slide
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Cutoff by M values

Top 5 of the absolute M values (M gt 0.56)
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Cutoff by T values

Top 5 of the absolute T values (Tgt8.6) s.t.
SE(M) gt 0.03
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SE Cutoff Level

In this data set, the number of genes found is
insensitive to the SE cutoff level. About 1000 of
the genes with smallest SE can be cutoff before
it affects the final results.
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103 Differentially Expressed Genes

Top 5 of the absolute T values (Tgt8.6) s.t.
SE(M) gt 0.03, and top 5 of the absolute M values
(Mgt0.56)
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Location of Differentially Expressed Genes

Location of the 4x4 grid sized microarray
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25 Differentially Expressed Genes

Gene Mavg Aavg T SE 1 -2.26 9.9 -18.0 0.125
2 -1.97 10.3 -14.5 0.136 3 -1.50
9.6 -14.7 0.102 4 -1.47 9.8 -12.2 0.121 5
-1.40 9.3 -11.9 0.118 6 -1.30 9.9 -14.4 0.090
7 -1.29 9.7 -14.6 0.088 8 -1.28 10.0 -12.7 0.10
1 9 -1.27 9.2 -13.6 0.094 10 -1.19 10.7 -13.7 0
.087 11 -1.18 9.8 -11.4 0.103 12 -1.17
9.9 -20.7 0.057 13 1.12 11.3 13.5 0.083
14 -1.07 11.4 -13.3 0.080 15 -1.05
9.6 -12.8 0.081 16 -1.02 9.9 -12.0 0.085
17 -1.01 9.3 -11.8 0.086 18 -0.99 11.0 -13.6 0.
073 19 -0.99 9.8 -11.4 0.087 20 -0.97 10.5 -13.
8 0.070 21 -0.96 9.6 -12.5 0.077 22
0.95 11.5 11.6 0.082 23 -0.94 10.3 -25.0 0.038
24 -0.93 9.8 -13.5 0.068 25 -0.90 11.6 -12.0 0.
075
Top 2 of the absolute T values (Tgt11) s.t.
SE(M) gt 0.03 and top 2 of the absolute M values
(Mgt0.9)
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The X2 Data Set
Slide Title Name
1 Mutant (a) vs. Reference (a) dUDG816
2 Mutant (a) vs. Reference (a) dUDG817
3 Mutant (b) vs. Reference (b) dUDG818
4 Mutant (b) vs. Reference (b) dUDG820
5 Mutant (c) vs. Reference (c) dUDG821
6 Mutant (c) vs. Reference (c) dUDG822

• All slides are replicates and contains 5184
  spots/genes. Three identical RNA preparations
  were done (a) was hybridized to slide 1 2, (b)
  to slide 3 4, and (c) to slide 5 6.

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93 Differentially Expressed Genes

Top 5 of the absolute T values (Tgt5.6) s.t.
SE(M) gt 0.03) and top 5 of the absolute M values
(Mgt0.38)
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25 Differentially Expressed Genes

Gene Mavg Aavg T SE 1 1.97 12.5 8.3 0.237 2 1
.27 9.7 18.2 0.070 3 1.23 13.2 7.5 0.164
4 1.12 12.3 19.2 0.058 5 0.93 14.2 7.7 0.122
6 0.86 13.7 10.2 0.085 7 -0.86
12.5 -8.1 0.106 8 -0.85 13.0 -17.0 0.050
9 -0.81 12.7 -16.3 0.050 10 -0.75 11.1 -8.6 0.0
88 11 -0.72 11.4 -11.4 0.063 12 -0.71
13.9 -15.6 0.045 13 0.66 10.0 9.4 0.071 14
0.66 10.8 9.2 0.072 15 -0.64 12.5 -15.2 0.042
16 0.64 9.6 7.9 0.081 17 -0.61
12.5 -7.5 0.081 18 -0.60 12.8 -18.2 0.033
19 0.59 11.4 8.3 0.071 20 -0.59
13.7 -8.3 0.071 21 -0.58 10.5 -7.2 0.081
22 -0.56 12.0 -12.5 0.045 23 0.55 11.7
9.1 0.061 24 -0.54 12.6 -7.6 0.071 25 0.53
11.2 9.5 0.056
Top 2 of the absolute T values (Tgt7.1) s.t.
SE(M) gt 0.03 and top 2 of the absolute M values
(Mgt0.53)
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Acknowledgement

• Thanks to
• Jean Yee Hwa Yang
• R Software (free)
• http//www.r-project.org/
• The Statistical Microarray Analysis (sma) library
  (free)
• http//www.stat.berkeley.edu/users/terry/zarray/So
  ftware/smacode.html