Transcript Lecture 4: Normalization

Statistics for Microarrays
Normalization
Class web site:
http://statwww.epfl.ch/davison/teaching/Microarrays/ETHZ/
Biological question
Differentially expressed genes
Sample class prediction etc.
Experimental design
Microarray experiment
16-bit TIFF files
Image analysis
(Rfg, Rbg), (Gfg, Gbg)
Normalization
R, G
Estimation
Testing
Clustering
Biological verification
and interpretation
Discrimination
Preprocessing: Data Visualization
• Was the experiment a success?
• Are there any specific problems?
• What analysis tools should be used?
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
Co-registration and overlay offers a quick
visualization, revealing information on color
balance, uniformity of hybridization, spot
uniformity, background, and artefacts
such as dust or scratches
Good: low bg, detectable d.e.
Bad: high bg, ghost spots, little
d.e.
Scatterplots: always log*, always rotate
log2R vs log2G
M=log2R/G vs A=log2√RG
* Other transformations can provide improvement
Histograms
Signal/Noise = log2(spot intensity/background intensity)
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
Lowess lines through points from pin groups
Boxplots of log ratios by pin group
Boxplots and highlighting pin group
effects
Print-tip groups
Clear example of spatial bias
Plate effects
Clearly visible plate effects
KO #8
Probes: ~6,000 cDNAs, including 200 related to lipid metabolism.
Arranged in a 4x4 array of 19x21 sub-arrays.
Time of printing effects
spot number
Green channel intensities (log2G). Printing over 4.5 days.
The previous slide depicts a slide from this print run.
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
Similar patterns apparent in non
self-self hybridizations
From the NCI60 data set (Stanford web site)
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 intensitydependent 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 upregulation 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.
Normalization makes a difference
Global scale, global lowess, pin-group lowess; spatial plot after, smooth histograms of M after
Normalization by controls:
Microarray Sample Pool titration
series
Pool the
whole library
Control set to aid intensity-dependent normalization
Different concentrations in titration series
Spotted evenly spread across the slide in each pin-group
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 RECIPROCAL
LABELING 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
0.46
0.44
Average Mean Deviation Value
0.42
0.4
0.38
0.36
***
0.34
0.32
0.3
Pre Normalized
Global Intensity
Subarray Intensity
Global Ratio
Normalization Method
Sub-Array Ratio
Global LOWESS
Subarray LOWESS
Scale normalization: between slides
Boxplots of log ratios from 3 replicate self-self
hybridizations
Left panel: before normalization
Middle panel: after within print-tip group normalization
Right panel: after a further between-slide scale
normalization
The “NCI 60” experiments (no bg)
Some scale normalization seems desirable
Scale normalization: another data set
Only small differences in spread apparent; no action
required.
One way of taking scale into account
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) | }
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-group
normalization
Within print-tip-group box plots of
M after print-tip-group
normalization
Taking scale into account, cont.
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) | }
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
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,
Slides
Genes
1
2
3
4
5
slide 1
slide 2
slide 3
slide 4
slide 5
…
0.46
-0.10
0.15
-0.45
-0.06
0.30
0.49
0.74
-1.03
1.06
0.80
0.24
0.04
-0.79
1.35
1.51
0.06
0.10
-0.56
1.09
0.90
0.46
0.20
-0.32
-1.09
...
...
...
...
...
Gene expression level of gene 5 in slide 4
=
(normalized) log2( Red / Green)
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)