Normalization for cDNA Microarray Data Originally Yee Hwa Yang, Sandrine Dudoit, Percy Luu and Terry Speed. Ho Kim

Normalization To describe the process of removing system variations such as Physical properties of dyes efficiency of dye incorporation Experimental variability in probe coupling and processing procedures Scanner settings

Normalization issues Within-slide Paired-slides (dye swap) What genes to use Location Scale Paired-slides (dye swap) Self-normalization Between slides

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) Methods? Global normalization 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 : when only small portion of gene are expected to be differentially expressed, symmetry is also assumed. Constantly expressed genes (house keeping) : e.g. Beta actin Controls Spiked controls (e.g. synthetic DNA sequences, plant genes) : should have equal red and green intensities Genomic DNA titration series Other set of genes

Experiment KO #8 mRNA samples R = Apo A1 KO mouse liver G = Control (All C57Bl/6) KO #8 Probes: ~6,000 cDNAs, including 200 related to lipid metabolism.

M vs. A M = log2(R / G) : log intensity ratio A = log2(R*G) / 2 : mean log-intensity

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

Nonpapametric Smoothing (1) Consider X Y plot. Draw a regression line which requires no parametric assumptions The regression line is not linear The regression line is totally dependent on the data Two components of smoothing Kernal function : How to calculate weighted mean Bandwidth : width of the window (span), determines the smoothness of the regresssion line; wider > smoother

Nonpapametric Smoothing (2) Uniform Kernel

Nonpapametric Smoothing (3) Triangular Kernel

Nonpapametric Smoothing (4) Normal Kernel

Nonpapametric Smoothing (5) Default Lowess line : Span=0.5

Nonpapametric Smoothing (6) Lowess line : Span=0.2

Nonpapametric Smoothing (7) Lowess line : Span=0.1

Normalization - lowess Global lowess Assumption: changes roughly symmetric at all intensities.

Normalisation - print-tip-group Assumption: For every print group, changes roughly symmetric at all intensities.

M vs. A - after print-tip-group normalization

Effects of Location Normalisation Before normalisation After print-tip-group normalisation

Box Plot IQR=Q3-Q1 Outliers 1.5*IQR Q3 Median(Q2) Q1

QQ-plot : to compare sample distribution with other ones (e.g. normal) T(df=9) vs standard normal

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

Taking scale into account Assumptions: 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 = ai mij Robust estimate of ai is MADi = medianj { |yij - median(yij) | }

Effect of location + scale normalization

Effect of location + scale normalization

Comparing different normalisation methods

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 -> red ctl-> green. Slide 2, ttt -> green ctl->red.

Follow-up Experiment

Paired-slides: dye swap Slide 1, M = log2 (R/G) - c Slide 2, M’ = log2 (R’/G’) - c’ Combine by subtract the normalized log-ratios: [ (log2 (R/G) - c) - (log2 (R’/G’) - c’) ] / 2  [ log2 (R/G) + (log2 (G’/R’) ] / 2  [ log2 (RG’/GR’) ] / 2 = (M-M`)/2 provided c = c’ Assumption: the separate normalizations are the same.

Verify Assumption

Result of Self-Normalization Plot of (M - M’)/2 vs. (A + A’)/2

Summary Case 1: A few genes that are likely to change Within-slide: 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: http://www.stat.berkeley.edu/users/terry/zarray/Html/ Technical Reports from Terry’s group: http://www.stat.Berkeley.EDU/users/terry/zarray/Html /papersindex.html 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 http://lib.stat.cmu.edu/R/CRAN/