Transcript Low-Level Analysis of Affymetrix Data

Low-Level Analysis of
Affymetrix Data
Mark Reimers
National Cancer Institute
Bethesda Maryland
Overview
•
•
•
•
•
the Affymetrix technology
Normalization
Relationships among probes in
Combining Probe Information
Quality Control
®
Affymetrix GeneChip Probe Arrays
Hybridized Probe Cell
GeneChip Probe Array
Single stranded, fluorescently
labeled DNA target
*
*
*
*
*
Oligonucleotide probe
20µm
1.28cm
Each probe cell or feature contains
millions of copies of a specific
oligonucleotide probe
Over 400,000 different probes
complementary to genetic
information of interest
Image of Hybridized Probe Array
Affymetrix Probe Design
Published 5´
Gene Sequence
3´
Multiple (11-20) 25-base
oligonucleotide probes
Perfect Match
Mismatch
PM is exactly complementary to published sequence
MM is changed on 13th base
Affymetrix Image Reading
• About 100 pixels per
probe cell
• Selects 16-25
brightest contiguous
pixels
• Take average of
selected pixels
• Variability in best
pixels ~ 5-20%
Image courtesy of Affymetrix
Normalization Approaches
• Simple: find average of each chip; divide all
values by chip average
• MAS5: fit regression line relative to a reference
chip
• Invariant set: find subset of probes in almost same
rank order as in a reference chip
• Quantile normalization: fit to average quantiles
across experiment
• Others: local loess, local regression.
Comparing Probes on Different Chips
Plots of two Affymetrix chips against the experiment means
MAS 5.0 Normalization
• Plot probes
from each chip
against
common baseline chip
• Fit regression
line to middle
98% of probes
This method fits the ends well,
but seems to miss an important
trend between 1500 and 4000
Invariant Set (Li-Wong) Method
• Select baseline chip X
• For each other chip Y:
• Select probes p1, …, pK, (K ~ 10000), such
that p1 < p2 < …< pK in both chips X and Y
• Fit running median through points
{ (xp1,yp1), …, (xpK, ypK) }
• Subtract fitted value along running meidan
from each y value
Quantile Method (part of RMA)
• Distributions of probe intensities vary
substantially among replicate chips
• This cannot be even approximately resolved by
any linear transformation
• Apply a non-linear transform, based on the idea
that comparable quantiles of the probe distribution
should have comparable values
• This doesn’t wipe out individual gene differences,
although it compresses variation at the high end
Probe Intensities in 23 Replicates
Quantile Distribution
Normalization
of
Reference
Chip Intensities
Distribution
Formula:
xnorm = F2-1(F1(x))
Density
function
Assumes:
gene distribution
changes little
F1(x)
Cumulative
Distribution
Function
F2(x)
a
x
y
After Normalization vs Before: intensity scale
Ratio-Intensity: Before
Ratio-Intensity: After
Quantile normalization works
Quantile normalization .vs. normalization by scaling
2
  quantile
log 2
 
 scale




Methods for computing expression
• Affymetrix MicroArray Suite: v.4, 5
– robust average of probes on one chip
• Linear Model (multi-chip) methods
– dChip: Li and Wong
– Bioconductor affy package (RMA)
• Bolstad, Irizarry, Speed, et al
• Many others published
– Some based on thermodynamic considerations
Probe Variation
• Probes vary by two orders of magnitude on
each chip
Signal from 16 probes for the GAPDH gene on one chip
•Individual probes don’t agree on fold changes
across chips
-Bright probes more often, but not always, more reliable
Probe Variation - II
•Typical probes are two orders of magnitude different!
•CG content is most important factor
•RNA target folding also affects hybridization
3x104
0
Principles of MAS 5 method
First estimate background
•bg = MM (if physically possible)
•log(bg) = log(PM)-log(non-specific proportion)
(if impossible)
•Non-specific proportion = max(SB, e)
•SB = Tukeybiweight(log(PM)-log(MM))
•Signal = Tukeybiweight(log(Adjusted PM))
Critique of MAS 5 principle
• ‘Average’ of different probes isn’t really
meaningful, since probes have intrinsically
different hybridization characteristics
• The MAS5 method doesn’t ‘learn’ based on
cross-chip performance of individual probes
Motivation for multi-chip models:
log(PM)
log(concentration)
Courtesy of Terry Speed
Raw data from a single probe set in a spike-in study;
each color represents a different probe in the probe set;
note the parallel trend across chips of all probes, although
some probe signals depart from the pattern
Linear Models
• Extension of linear regression
• Essential features:
– Measurement errors independent of each other
• ‘random noise’
• Needs normalization to eliminate systematic variation
– Noise levels comparable at different levels of signal
– Small number of factors combine in linear function or
simple algebraic form to give predicted levels
Model for Probe Signal
• Each probe signal is proportional to
– i) the amount of target sample – qi
– ii) the affinity of the specific probe sequence to the
target – fj
Probes
1 2 3
chip 1
q1
chip 2
q2
f1 f2 f3
• NB: High affinity is not the same as specificity
– Probe can give high signal to intended target and also to
other transcripts
Multiplicative Model
• Each gene has a set of probes p1,…,pk
• Each probe pj binds the gene with efficiency
(‘avidity’) fj
• In each sample there is an amount qi of the
target transcript
• In principle, intensity of probe j on chip i –
PMij – should be proportional to fj x qi
• Always some noise; and some outliers!
Robust Statistics
• Outlier: a measure that is far beyond the typical
random variation
– common in biological measures
– 10-15% in Affy probe sets
• Robust methods try to fit the majority of data
points
– Issue is to identify which points to down-weight or
ignore
– iteratively re-weighted least squares
– Median polish
Li & Wong (dChip)
• Model: PMij = qifj + eij
- Original model (dChip 1.0) used PMij - MMij = qifj + eij
by analogy with Affy MAS 4
• Outlier removal:
–
–
–
–
Fitting probes in one set on one chip
Identify extreme residuals
Remove
Re-fit
Iterate until converge
Dark blue: PM values
Red: fitted values
Light blue: probe SD
Critique of Li-Wong model
• Model assumes that noise for all probes has
same magnitude
• All biological measurements exhibit
intensity-dependent noise
Bolstad, Irizarry & Speed – (RMA)
• For each probe set, take the log transform of
PMij = qifj:
log ( PM ij )  log( ai )  log( f j )
• i.e. fit the model:
nlog ( PM ij  bg)  ai  b j  e ij
Where nlog() stands for logarithm after normalization
• Fit this additive model by iteratively re-weighted
least-squares or median polish
Critque of RMA
• Assumes probe noise is homoschedastic
(comparable variances) on log scale
• In fact noise for low signal probes appears
to be much greater
• Depends on normalization & bg
compensation
• Variance-stabilizing transform seems better
in principle; so far not a great deal of
improvement in practice
Comparing Expression Measures
Compare gene abundance estimates based on identical samples
(These were non spike-in genes in the spike-in experiment)
Better performance means variation of estimates should be smaller
The figure shows standard deviations of expression estimates across arra
arranged in four groups of genes by increasing mean expression level
Courtesy of Terry Speed
Green: MAS5.0; Black: Li-Wong; Blue, Red: RMA
Comparison Summary
• Affymetrix Suite gets better every year
– Affymetrix is developing their own multi-chip model
• MAS P & A calls reasonable proxies for confidence
(not gene abundance)
– based on probe-by probe comparison of PM & MM
• MAS 5.0 estimation does a reasonable job on
abundant genes
• dChip and RMA do better on genes that are less
abundant
– Signalling proteins, transcription factors, etc
Model-based QC for Affy Chips
• Outliers from fitted model may show spatial
Portion
of an Affy chip
Pink pixels represent probes that
pattern
do not fit consensus pattern
of relative probe intensities
Image made with dChip
These probes will be
down-weighted or ignored
by a robust multi-chip model.
If non-conforming probes
are numerous and wide-spread
then suspect such a chip
Current Work: Improving the Model
• How to use the MM information profitably
– Combine estimates from PM and MM probes?
• Assessments of probe quality
• Accurate estimates of probe background
• Normalization method based on 2-d loess to
correct spatial inhomogeneity
Relation Between PM and MM
Across One Experiment Set
MM
PM
Colored symbols are one probe
Probe Specific Background
Fitted Data
Probe BG subtracted
Horizontal lines represent probes; colored symbols correspond to arrays
After subtracting individual backgrounds for each probe, the ratios among
corresponding arrays are more consistent between probes
Software for Affymetrix
• MAS provided by Affymetrix
– Current version 6 in beta testing
• dChip from www.dchip.org
• RMA from www.bioconductor.org
– affy package
– Regularly updated
– Version with probe background in September
from my website: reimers.cgb.ki.se