Probe Level Analysis of AffymetrixTM Data

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Probe Level Analysis of AffymetrixTM Data

• Mark Reimers, NCI

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Outline

• Design of Affy probesets
• Background
• Normalization
• Non-specific hybridization
• Estimation
• Comparison of Methods

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Affymetrix GeneChip Probe Arrays
Single stranded, fluorescently labeled DNA target
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Affymetrix Probe Design
PM is exactly complementary to published
sequence MM is changed on 13th base
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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

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Chip Nomenclature

• HGU133A - Human Genome Unigene build 133, first
  chip
• PM - perfect match
• MM - mismatch
• Control sequence
• sequence from unrelated organism
• Signal - intensity
• Doesnt translate directly to abundance
• Cross-hybridization
• Binding of sequences other than target

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Affymetrix Background Adjustment and Normalization
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Whats 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

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Probe Intensities in 23 Replicates
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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

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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

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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

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Probes on Different Chips
Plots of two Affymetrix chips against the
experiment means
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MAS 5.0

• Plot probes from each chip against common
  base-line chip
• Fit regression line to middle 98 of probes

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Invariant Set (Li-Wong) Method

• Select baseline chip X
• For each other chip Y
• Select probes p1, , pK, (K 10000), such that
  p1 lt p2 lt lt pK in both chips
• Fit running median through points
• (xp1,yp1), , (xpK, ypK)
• Repeat

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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

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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
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Ratio-Intensity Before
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Ratio-Intensity After
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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 wont be equal
• Better to let higher end be roughly linear
• Requires much memory - could be implemented
  differently

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Model-based Estimates for Affymetrix Raw Data
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Many Probes for One Gene
How to combine signals from multiple probes into
a single gene abundance estimate?
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Probe Variation

• Individual probes dont 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
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Competing Models 2005

• GCOS (Affymetrix MicroArray Suite 5.0)
• Manufacturers 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,

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Probe Measure Variation

• Typical probes are two orders of magnitude
  different!
• CG content is most important factor
• RNA target folding also affects hybridization

3x104
0
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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))

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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

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Motivation for multi-chip models

• Probe level data from spike-in study ( log scale
  ) note parallel trend of all probes

Courtesy of Terry Speed
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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

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Model for Probe Signal

• 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 1 2 3
chip 1
a1
a2
chip 2
f1 f2 f3
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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!

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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

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Robust Linear Models

• Criterion of 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

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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

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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
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Critique of Li-Wong model

• Model assumes that noise for all probes has same
  magnitude
• All biological measurements exhibit
  intensity-dependent noise

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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
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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
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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

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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
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Expression Comparison 2 MAS 5
t-scores
changed genes
Theoretical t-distribution
Courtesy of Terry Speed
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Expression Comparison 3 Li-Wong
Courtesy of Terry Speed
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Expression Comparison 4 - RMA
Courtesy of Terry Speed
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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

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Mix and Match Methods in affy

• Background rma, mas
• Normalization quantile, constant,
• PM-correction none,
• Model median polish, mas
• Estimates lt- expresso( cel.data, bgcorrect.method
  mas, normalization.method quantiles,

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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