Model-based analysis of oligonucleotide arrays, dChip software

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Model-based analysis of oligonucleotide arrays,
dChip software
Cheng Li (Joint work with Wing Wong)

• Statistics and Genomics Lecture 4
• Department of Biostatistics
• Harvard School of Public Health
• January 23-25, 2002

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Source Affymetrix website
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Custom software raw image
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Custom software getting representative value of
a probe cell
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Normalization is needed to minimize
non-biological variation between arrays
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Normalization methods

• Current software uses linear normalization
• Nonlinear curve fitting based on scatter plot is
  still inadequate because 1) effects of
  differentially expressed genes may be
  normalized 2) regression phenomenon and
  asymmetry

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Regression phenomenon and asymmetry
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Invariant set normalization method

• A set of points (xi, yi) is said to be
  order-preserving if yi lt yj whenever xi lt xj
• The maximal order-preserving subset can be
  obtained by dynamic programming
• If a gene is really differentially expressed,
  its cells tend not to be included into an large
  order-preserving subset
• Our method is based on an approximately order
  preserving subset, called Invariant set

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Fig. 2.9 Normalization of a pair of replicated
arrays
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Figure 2.10. Two different samples. The smoothing
spline in (A) is affected by several points at
the lower-right corner, which might belong to
differentially expressed genes. Whereas the
invariant set does not include these points
when determining normalization curve, leading to
a different normalization relationship at the
high end.
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A pair of split-sample replicate arrays
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Source Affymetrix website
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Data for one probe set, one array
PM/MM differences eliminate background and
cross-hybridization signals
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Validation experiments suggest Average
Differences are linear to mRNA concentrations at
certain dynamic range
Lockhart et al. (1996) Nature Genetics, Vol 14
1675-1680
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Data for one gene in many arrays
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Box plot showing array and probe effects
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Modeling probe effects
1) Probes sequence has different hybridization
efficiency 2) cross hybridization, SNP,
alternative splicing 3) Probe position effect, 3
bias Probe effects can dominate biological
variation of interest Previous method use
multiple probes, average to reduce noise Our
methods statistical models for probe effects,
meta-analysis, learning algorithms, estimation
of expression level conditional on knowledge of
probe effect
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Principal component analysis (42 points in
20-space) suggests the data matrix has approx.
rank 1
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Model for one gene in multiple arrays
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Figure 1.1. Black curves are the PM and MM data
of gene A in the first 6 arrays. Light curves are
the fitted values to model (1). Probe pairs are
labeled 1 to 20 on the horizontal axis.
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Using PM/MM Differences

• PM/MM differences eliminate most background and
  cross-hybridization signals
• Affyemtrixs GeneChip software is using average
  differences as basis for determining fold
  changes, and their validation showed average
  differences are linear to mRNA concentrations at
  certain dynamic range

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Model for PM/MM differences (1.2)
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Figure 1.2. Black curves are the PM-MM difference
data of gene A in the first 6 arrays. Light
curves are the fitted values to model (2).
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(No Transcript)
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Residuals of the fitting
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Model fitting amounts to fixing ?s and regress
to estimate ?
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Fig 1.5 Array outlier large standard errors of ?4
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Fig. 1.6 Probe outlier large standard errors of
?17
Also see gene 6898
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Fig. 1.4 Array outlier image shows that the model
automatically handles image contamination
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Compare Model-based expression with Average
Difference

• The array set 5 has 29 pair of arrays replicated
  at split-mRNA level
• The differences between the replicated arrays
  provides a opportunity to assess different
  expression calculation method

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Figure 2.5. Log (base 10) expression indexes of a
pair of replicate arrays (array 1 and 2 of array
set 5) for MBEI method (A) and AD method (B). The
center line is yx, and the flanking lines
indicate the difference of a factor of two.
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(A)
(B)
Figure 2.6. Boxplots of average absolute log
(base 10) ratios between replicate arrays
stratified by presence proportion for (A) MBEI
method, (B) AD method.
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Source Affymetrix website
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Finding Confidence Interval of Fold Change
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Table 2.1 Using expression levels and associated
standard errors to determine confidence intervals
of fold changes
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Resampling hierarchical clustering using standard
errors of model-based expression
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Incorporate biological knowledge and database
when analyzing microarray data
Right picture Gene Ontology tool for the
unification of biology, Nature Genetics, 25, p25
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Functional significant clusters
Found 13 structural protein genes out of a
49-cluster (all 198/2622, PValue 1.00e000)
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Problems with LWR model

• Statistical analysis of high-density
  oligonucleotide arrays a multiplicative noise
  model
• R. Sasik and J. Corbeil (UCSF)

• LWR model
• The expression index can still be negative.
• Genes with negative index can still be classified
  as present.

Slides prepared by Xuemin Fang
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Statistical model

• Based on the same assumption as the LW model,
  that PM intensity is directly proportional to the
  concentration ci of the transcript,
  . Write the relation in the form
• Our model is
• where
• Least squared estimation of the parameters.
• Constraint

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Algorithm -- When analyzing a batch of ns samples

• Normalize all samples to the first one on the
  list by requiring the sum of all PM intensities
  be the same as that of the first sample.
• Select the background probes using Naefs method
  (MM is used in this step).
• Subtract the median of the background probe
  intensity from every PM probe in the array.
• Probes that become negative are eliminated.
• Fit the model and probes contributes most to the
  sum of squares are eliminated.
• Normalize again and repeat 1-5, until the
  distribution of residuals is Gaussian.

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• Bias, variance and fit for three measures of
  expression AvDiff, Li Wong's,
• AvLog (PM -bg)
• Rafael Irizarry, Terry Speed (Johns Hopkins)

Slides prepared by Xuemin Fang
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A background plus signal model

• Here represents
  background signal caused by optical noise and
  non-specific binding.
• The mean background level is represented with
  and the random component with .
• The transcript signal
  contains a probe affinity effect
  , the log expression measures , and an
  error term.
• Both error terms and are
  independent standard normal.

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Expression index

• A naïve estimate of is given by
• with the mode of the log2(MM)
  distribution.
• An estimate of this distribution is obtained
  using a density kernel estimate.

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Acknowledgement
Data source Stan Nelson (UCLA)Sven de Vos
(UCLA) Dan Tang (DFCI)Andy Bhattacharjee
(DFCI)Richardson Andresa (DFCI) Allen Fienberg
(Rockefeller)