1. Probe Level Analysis of AffymetrixTM Data
Mark Reimers, NCI

2. Outline Design of Affy probesets Background Normalization
Non-specific hybridization
Estimation
Comparison of Methods

3. Affymetrix GeneChip® Probe Arrays
Each probe cell or feature contains
millions of copies of a specific
oligonucleotide probe
Image of Hybridized Probe Array
Over 400,000 different probes
complementary to genetic
information of interest
Oligonucleotide probe *
1.28cm
GeneChip Probe Array
Hybridized Probe Cell
Single stranded, fluorescently
labeled DNA target

4. Affymetrix Probe Design
Published
Gene Sequence
Multiple (11-20) 25-base oligonucleotide probes
Perfect Match
Mismatch 5´ 3´
Multiple 25-mer oligo probes are synthesized that represent the transcript. The probes are synthesized in pairs a ‘Perfect Match’, complementary to the target and a ‘Mismatch’ in which the 13th base is changed. The probes tend to be biased toward the 3’ end and vary in number from 11 to more than 20 per transcript. They are arranged as a perfect match with a corresponding homomeric mismatch. The individual probe pairs which represent a transcript are distributed about the array.
PM is exactly complementary to published sequence
MM is changed on 13th base

5. Chip Layout
Typical chips are square: 640x640 (U95A), 712x712 (U133) or 1042x1042 (Plus2)
Older chips placed all probes for one gene in a row
Modern chips distribute probes according to sequence, not gene

6. Chip Nomenclature
HGU133A - Human Genome: Unigene build 133, first chip
PM - ‘perfect match’
MM - ‘mismatch’
Control sequence
sequence from unrelated organism
Signal - intensity
Doesn’t translate directly to abundance
Cross-hybridization
Binding of sequences other than target

7. Affymetrix Background Adjustment and Normalization

8. What’s the Issue?
Background: some Affy chips show consistently higher values for the lowest signals (presumably absent) than others
Background may vary over a chip
Normalization: Distribution of probe signals may differ between chips, independent of background adjustment
PM and MM may be shifted differently

9. Probe Intensities in 23 Replicates

10. Approaches to Background
Subtract common estimate of background
Fit local background across chip and subtract - MAS 5.0
Consider background as random variable
Use statistical theory to derive background correction

11. RMA ‘Bayesian’ BG Correction
Each S = BG + Intensity + e
BG randomly sampled from Normal distn
Intensity randomly sampled from exponential distribution
Estimate mean and SD of BG distn by fitting values below mode of signal distn
Estimate Intensity, conditional on S, by integrating over possible values of BG

12. Approaches to Normalization
Simple: find average of each chip; divide all values by chip average
MAS5: trimmed mean
Invariant set: find subset of probes in almost same rank order in each chip
Quantile normalization: fit to average quantiles across experiment

13. Probes on Different Chips
Plots of two Affymetrix chips against the experiment means

14. MAS 5.0 Plot probes from each chip against common base-line chip
Fit regression line to middle 98% of probes

15. 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
Fit running median through points
{ (xp1,yp1), …, (xpK, ypK) }
Repeat

16. Quantile Method (RMA)
Distributions of probe intensities vary substantially among replicate chips
This cannot be even approximately resolved by any linear transformation
Drastic solution: ‘shoehorn’ all probe intensities into same distribution
Ideal distribution is taken as average of all

17. Quantile Normalization
Distribution of
Chip Intensities
Reference
Distribution
Formula:
xnorm = F2-1(F1(x))
Density
function
Assumes:
gene distribution
changes little
F1(x)
F2(x)
Cumulative
Distribution
Function a x y

18. Ratio-Intensity: Before

19. Ratio-Intensity: After

20. Critique of RMA Normalization
Distribution of signals looks more like exponential on log scale
No allowance for regional biases in BG
Quantile normalization is very strong: highly expressed genes won’t be equal
Better to let higher end be roughly linear
Requires much memory - could be implemented differently

21. Model-based Estimates for Affymetrix Raw Data

22. Many Probes for One Gene
Sequence
Multiple oligo probes
Perfect Match
Mismatch 5´ 3´
Multiple 25-mer oligo probes are synthesized that represent the transcript. The probes are synthesized in pairs a ‘Perfect Match’, complementary to the target and a ‘Mismatch’ in which the 13th base is changed. The probes tend to be biased toward the 3’ end and vary in number from 11 to more than 20 per transcript. They are arranged as a perfect match with a corresponding homomeric mismatch. The individual probe pairs which represent a transcript are distributed about the array.
How to combine signals from multiple probes
into a single gene abundance estimate?

23. Probe Variation Individual probes don’t agree on fold changes
Probes for one gene may vary by two orders of magnitude on each chip
CG content is most important factor in signal strength
Signal from 16 probes
along one gene on
one chip

24. Competing Models 2005 GCOS (Affymetrix MicroArray Suite 5.0) dChip
Manufacturer’s software
dChip
Li and Wong, HSPH
Bioconductor: affy package (RMA)
Bolstad, Irizarry, Speed, et al
Variants such as gcRMA, vsn
Probe-level analyses
affyPLM, logit-t, …

25. Probe Measure Variation
Typical probes are two orders of magnitude different!
CG content is most important factor
RNA target folding also affects hybridization
3x104

26. 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))

27. Critique of MAS 5 principle
Not clear what an average of different probes should mean
Tukey bi-weight can be unstable when data cluster at either end – frequently the conditions here
No ‘learning’ based on cross-chip performance of individual probes

28. Motivation for multi-chip models:
Probe level data from spike-in study ( log scale ) note parallel trend of all probes
Courtesy of Terry Speed

29. 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 give predicted levels
combine in linear function or simple algebraic form

30. Model for Probe Signal chip 1 a1 a2 chip 2 Probes 1 2 3 f1 f2 f3
Each probe signal is proportional to
i) the amount of target sample – a
ii) the affinity of the specific probe sequence to the target – f
NB: High affinity is not the same as Specificity
Probe can give high signal to intended target and also to other transcripts
Probes
chip 1 a1 a2
chip 2
f1 f2 f3

31. Multiplicative Model For each gene, a set of probes p1,…,pk
Each probe pj binds the gene with efficiency fj
In each sample there is an amount qi.
Probe intensity should be proportional to fjxqi
Always some noise!

32. 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
Median is very robust – but inefficient
Trimmed means are almost as robust and much more efficient

33. Robust Linear Models Criterion of fit Method for finding fit
Least median squares
Sum of weighted squares
Least squares and throw out outliers
Method for finding fit
High-dimensional search
Iteratively re-weighted least squares
Median Polish

34. Why Robust Models for GeneChips?
10% - 15% of individual signals in a probe set deviate greatly from pattern
Often outliers lie close together
Causes:
Scratches
Proximity to heating elements
Uneven fluid flow

35. Fitting probes in one set on one chip
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:
Identify extreme residuals
Remove
Re-fit
Iterate
Fitting probes in one set on one chip
Dark blue: PM values
Red: fitted values
Light blue: probe SD

36. Critique of Li-Wong model
Model assumes that noise for all probes has same magnitude
All biological measurements exhibit intensity-dependent noise

37. Bolstad, Irizarry, Speed – (RMA)
For each probe set, take the log transform of
PMij = qifj:
i.e. fit the model:
Fit this additive model by iteratively re-weighted least-squares or median polish
Where nlog() stands for logarithm after normalization
Critique: assumes probe noise is
constant (homoschedastic) on log scale

38. Comparison of Methods Green: MAS5.0; Black: Li-Wong; Blue, Red: RMA
20 replicate arrays – variance should be small
Standard deviations of expression estimates on arrays
arranged in four groups of genes
by increasing mean expression level
Courtesy of Terry Speed

39. Steady Improvement Affymetrix improves their model
PLIER is a multi-chip model
MAS P & A calls reasonable
MAS 5.0 estimation does a reasonable job on probe sets that are bright
Abundant genes
dChip and RMA do better on genes that are less abundant
Signalling proteins, transcription factors, etc

40. Expression Comparison 1 – MAS 4
Ratio-Intensity Plot
comparing two chips
from spike-in
experiment
White dots represent
unchanged genes
Red numbers flag
spike-in genes
Courtesy of Terry Speed

41. Expression Comparison 2 – MAS 5
t-scores
changed
genes
Theoretical
t-distribution
Courtesy of Terry Speed

42. Expression Comparison 3 – Li-Wong
Courtesy of Terry Speed

43. Expression Comparison 4 - RMA
Courtesy of Terry Speed

44. Comparison on Real Data
These results are based on samples with 14 spike-ins - not realistic complexity
Choe et al (Genome Biology 2005) produced a spike in data set with realistic complexity - found MAS5 PM correction worked well
Comparisons of biological variation vs technical variation in replicated samples suggest RMA defaults work best

45. Mix and Match Methods in affy
Background: rma, mas
Normalization: quantile, constant, …
PM-correction: none,
Model: median polish, mas
Estimates <- expresso( cel.data, bgcorrect.method = mas, normalization.method = quantiles, …

46. gcRMA: Estimating Non-specific Hybridization
Each probe has its own characteristic cross-hybridizations (NSH)
Mismatch is not a good estimate of NSH
GC content may predict NSH reasonably well