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Normalization for cDNA Microarray Data. Yee Hwa Yang, Sandrine Dudoit, Percy Luu and Terry Speed. SPIE BIOS 2001, San Jose, CA January 22, 2001. Normalization issues. Within-slide What genes to use Location Scale Paired-slides (dye swap) Self-normalization Between slides.

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Normalization for cdna microarray data

Normalization for cDNA Microarray Data

Yee Hwa Yang, Sandrine Dudoit, Percy Luu and Terry Speed.

SPIE BIOS 2001, San Jose, CA

January 22, 2001

Normalization issues
Normalization issues


  • What genes to use

  • Location

  • Scale

    Paired-slides (dye swap)

  • Self-normalization

    Between slides

Within slide normalization
Within-Slide Normalization

  • Normalization balances red and green intensities.

  • Imbalances can be caused by

    • Different incorporation of dyes

    • Different amounts of mRNA

    • Different scanning parameters

  • In practice, we usually need to increase the red intensity a bit to balance the green


log2R/G -> log2R/G - c = log2R/ (kG)

Standard Practice (in most software)

c is a constant such that normalized log-ratios have zero mean or median.

Our Preference:

c is a function of overall spot intensity and print-tip-group.

What genes to use?

  • All genes on the array

  • Constantly expressed genes (house keeping)

  • Controls

    • Spiked controls (e.g. plant genes)

    • Genomic DNA titration series

  • Other set of genes


mRNA samples

R = Apo A1

KO mouse liver

G = Control

mouse liver

(All C57Bl/6)

KO #8

Probes: ~6,000 cDNAs, including 200 related to lipid metabolism.

M vs a
M vs. A

M = log2(R / G)

A = log2(R*G) / 2

Normalization median
Normalization - Median

  • Assumption: Changes roughly symmetric

  • First panel: smooth density of log2G and log2R.

  • Second panel: M vs. A plot with median set to zero

Normalization lowess
Normalization - lowess

  • Global lowess

  • Assumption: changes roughly symmetric at all intensities.

Normalisation print tip group
Normalisation - print-tip-group

Assumption:For every print group, changes roughly symmetric

at all intensities.

Effects of location normalisation
Effects of Location Normalisation

Before normalisation

After print-tip-group


Within print tip group box plots for print tip group normalized m
Within print-tip-group box plots forprint-tip-group normalized M

Taking scale into account
Taking scale into account


  • All print-tip-groups have the same spread.

    True ratio is mij where i represents different print-tip-groups, j represents different spots.

    Observed is Mij, where

    Mij = aimij

    Robust estimate of ai is

    MADi = medianj { |yij - median(yij) | }

Follow up experiment
Follow-up Experiment

  • 50 distinct clones with largest absolute

    t-statistics from the first experiment.

  • 72 other clones.

  • Spot each clone 8 times .

  • Two hybridizations:

    Slide 1, ttt -> redctl-> green.

    Slide 2, ttt -> greenctl->red.

Paired slides dye swap
Paired-slides: dye swap

  • Slide 1, M = log2 (R/G) - c

  • Slide 2, M’ = log2 (R’/G’) - c’

    Combine bysubtract the normalized log-ratios:

    [ (log2 (R/G) - c) - (log2 (R’/G’) - c’) ] / 2

     [ log2 (R/G) + (log2 (G’/R’) ] / 2

     [ log2 (RG’/GR’) ] / 2

    provided c = c’

    Assumption: the separate normalizations are the same.

Result of self normalization
Result of Self-Normalization

Plot of (M - M’)/2 vs. (A + A’)/2


Case 1: A few genes that are likely to change


  • Location: print-tip-group lowess normalization.

  • Scale: for all print-tip-groups, adjust MAD to equal the geometric mean for MAD for all print-tip-groups.

    Between slides (experiments) :

  • An extension of within-slide scale normalization (future work).

    Case 2: Many genes changing (paired-slides)

  • Self-normalization: taking the difference of the two log-ratios.

  • Check using controls or known information.

Technical Reports from Terry’s group:



  • Comparison of Discrimination Methods for the Classification of Tumors Using Gene Expression Data

  • Statistical methods for identifying differentially expressed genes in replicated cDNA microarray experiments.

  • Comparison of methods for image analysis on cDNA microarray data.

  • Normalization for cDNA Microarray Data

    Statistical software R


Terry Speed

Sandrine Dudoit

Natalie Roberts

Ben Bolstad

Matt Callow (LBL)

John Ngai’s Lab (UCB)

Percy Luu

Dave Lin

Vivian Pang

Elva Diaz