Normalization

Class web site:

http://statwww.epfl.ch/davison/teaching/Microarrays/ETHZ/

Statistics for Microarrays

Biological questionDifferentially expressed genesSample class prediction etc.

Testing

Biological verification and interpretation

Microarray experiment

Estimation

Experimental design

Image analysis

Normalization

Clustering Discrimination

R, G

16-bit TIFF files

(Rfg, Rbg), (Gfg, Gbg)

• Was the experiment a success?

• Are there any specific problems?

• What analysis tools should be used?

Preprocessing: Data VisualizationPreprocessing: Data Visualization

Tools for Microarray Normalization and Analysis

• Both commercial and free software

• R (use sma package or Bioconductor: http://www.bioconductor.org/)

Red/Green overlay images

Good: low bg, detectable d.e.Bad: high bg, ghost spots, little d.e.

Co-registration and overlay offers a quick visualization, revealing information on color balance, uniformity of hybridization, spot uniformity, background, and artefactssuch as dust or scratches

Scatterplots: always log*, always rotate

log2R vs log2G M=log2R/G vs A=log2√RG

* Other transformations can provide improvement

Signal/Noise = log2(spot intensity/background intensity)

Histograms

Boxplots of log2R/G

Liver samples from 16 mice: 8 WT, 8 ApoAI KO

Spatial plots: background from the two slides

Highlighting extreme log ratios

Top (black) and bottom (green) 5% of log ratios

Pin group (sub-array) effects

Boxplots of log ratios by pin groupLowess lines through points from pin groups

Boxplots and highlighting pin group effects

Clear example of spatial bias

Print-tip groups

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Plate effects

KO #8

Probes: ~6,000 cDNAs, including 200 related to lipid metabolism. Arranged in a 4x4 array of 19x21 sub-arrays.

Clearly visible plate effects

Time of printing effects

Green channel intensities (log2G). Printing over 4.5 days.The previous slide depicts a slide from this print run.

spot number

Preprocessing: Normalization• Why?

To correct for systematic differences between samples on the same slide, or between slides, which do not represent true biological variation between samples

• How do we know it is necessary? By examining self-self hybridizations,

where no true differential expression is occurring.

There are dye biases which vary with spot intensity, location on the array, plate origin, pins, scanning parameters,…

Self-self hybridizations

False color overlay Boxplots within pin-groups Scatter (MA-)plots

From the NCI60 data set (Stanford web site)

Similar patterns apparent in non self-self hybridizations

From Lawrence Berkeley National Laboratory

Normalization Methods (I)• Normalization based on a global adjustment

log2 R/G -> log2 R/G - c = log2 R/(kG)

Choices for k or c = log2k are c = median or mean of log ratios for a particular gene set (e.g. all genes, or control or housekeeping genes). Or, total intensity normalization, where k = ∑Ri/ ∑Gi.

• Intensity-dependent normalization Here, run a line through the middle of the MA plot,

shifting the M value of the pair (A,M) by c=c(A), i.e. log2 R/G -> log2 R/G - c (A) = log2 R/(k(A)G).

One estimate of c(A) is made using the LOWESS function of Cleveland (1979): LOcally WEighted Scatterplot Smoothing.

Normalization Methods (II)• Within print-tip group normalization In addition to intensity-dependent variation in log

ratios, spatial bias can also be a significant source of systematic error.

Most normalization methods do not correct for spatial effects produced by hybridization artefacts or print-tip or plate effects during the construction of the microarrays.

It is possible to correct for both print-tip and intensity-dependent bias by performing LOWESS fits to the data within print-tip groups, i.e.

log2 R/G -> log2 R/G - ci(A) = log2 R/(ki(A)G),

where ci(A) is the LOWESS fit to the MA-plot for the ith grid only.

Normalization: Which Spots to use?

The LOWESS lines can be run through many different sets of points, and each strategy has its own implicit set of assumptions justifying its applicability.

For example, the use of a global LOWESS approach can be justified by supposing that, when stratified by mRNA abundance, a) only a minority of genes are expected to be differentially expressed, or b) any differential expression is as likely to be up-regulation as down-regulation.

Pin-group LOWESS requires stronger assumptions: that one of the above applies within each pin-group.

The use of other sets of genes, e.g. control or housekeeping genes, involve similar assumptions.

Global scale, global lowess, pin-group lowess; spatial plot after, smooth histograms of M after

Normalization makes a difference

Normalization by controls:Microarray Sample Pool titration

series

Control set to aid intensity-dependent normalization

Different concentrations in titration series

Spotted evenly spread across the slide in each pin-group

Pool the whole library

Comparison of Normalization Schemes

(courtesy of Jason Goncalves)

• No consensus on best normalization method

• Experiment done to assess the common normalization methods

• Based on reciprocal labeling experimental data for a series of 140 replicate experiments on two different arrays each with 19,200 spots

DESIGN OF RECIPROCALDESIGN OF RECIPROCALLABELING EXPERIMENTLABELING EXPERIMENT

• Replicate experiment with same mRNA pools but invert fluors (dye swap)

• Replicates are independent experiments

• Scan, quantify, normalize as usual

Comparison of Normalization Methods - Using 140 19K Microarrays

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Pre Normalized Global Intensity Subarray Intensity Global Ratio Sub-Array Ratio Global LOWESS Subarray LOWESS

Normalization Method

Ave

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Mea

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Val

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Scale normalization: between slides

Boxplots of log ratios from 3 replicate self-self hybridizationsLeft panel: before normalizationMiddle panel: after within print-tip group normalizationRight panel: after a further between-slide scale normalization

The “NCI 60” experiments (no bg)

Some scale normalization seems desirable

Scale normalization: another data set

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Only small differences in spread apparent; no action required.

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Assumption: All slides have the same spread in M True log ratio is mij where i represents different

slides and j represents different spots.

Observed is Mij, where

Mij = ai mij

Robust estimate of ai is

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

One way of taking scale into account

A slightly harder normalization problem

Global lowess doesn’t do the trick here

Print-tip-group normalization helps

But not completely

Still a lot of scatter in the middle in a WT vs KO comparison

Effects of previous normalization

Before normalization After print-tip-groupnormalization

Within print-tip-group box plots of M after print-tip-group

normalization

Assumption: All print-tip-groups have the same spread in M True log ratio is mij where i represents

different print-tip-groups and j represents different spots.

Observed is Mij, where

Mij = ai mij

Robust estimate of ai is

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

Taking scale into account, cont.

Effect of location & scale normalization

Clearly care is needed in making decisions like this

A comparison of three M v A plots

Unnormalized Print-tip normalization Print tip & scale n

The same normalization on another data set

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Before

After

Normalization: Summary

• Reduces systematic (not random) effects• Makes it possible to compare several arrays

• Use logratios (M vs A plots)• Lowess normalization (dye bias)• MSP titration series – composite normalization• Pin-group location normalization• Pin-group scale normalization• Between slide scale normalization

• Control Spots• Normalization introduces more variability• Outliers (bad spots) are handled with replication

Affymetrix Oligo Chips

• Only one “color”

• Different technology, different normalization issues

• Affy chip normalization is an active research area – see http://www.stat.berkeley.edu/users/terry/zarray/Affy/affy_index.html

Pre-processed cDNA Gene Expression Data

On p genes for n slides: p is O(10,000), n is O(10-100), but growing,

Genes

Slides

Gene expression level of gene 5 in slide 4

= (normalized) log2( Red / Green)

slide 1 slide 2 slide 3 slide 4 slide 5 …

1 0.46 0.30 0.80 1.51 0.90 ...2 -0.10 0.49 0.24 0.06 0.46 ...3 0.15 0.74 0.04 0.10 0.20 ...4 -0.45 -1.03 -0.79 -0.56 -0.32 ...5 -0.06 1.06 1.35 1.09 -1.09 ...

These values are conventionally displayed on a red (>0) yellow (0) green (<0) scale.

Acknowledgments

Terry Speed (UCB and WEHI)

Jean Yee Hwa Yang (UCB)Sandrine Dudoit (UCB)Ben Bolstad (UCB)Natalie Thorne (WEHI)Ingrid Lönnstedt

(Uppsala)Henrik Bengtsson (Lund)

Jason Goncalves (Iobion)

Matt Callow (LLNL)Percy Luu (UCB)John Ngai (UCB)Vivian Peng (UCB)

Dave Lin (Cornell)