Statistical Analyses of High Density Oligonucleotide Arrays

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Statistical Analyses of High Density
Oligonucleotide Arrays

• Rafael A. Irizarry
• Department of Biostatistics, JHU
• (joint work with Bridget Hobbs and Terry Speed,
  Walter Eliza Hall Institute of Medical Research
  and Francois Collin,Gene Logic)
• http//biosun01.biostat.jhsph.edu/ririzarr

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Summary

• Review of technology
• Data exploration
• Probe level summaries (expression measures)
• Normalization
• Evaluate and compare through bias, variance and
  model fit to 4 expression measures
• Use Gene Logic spike-in and dilution study
• Conclusion/future work

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Probe Arrays
Hybridized Probe Cell
GeneChip Probe Array
Single stranded, labeled RNA target
Oligonucleotide probe
24µm
Millions of copies of a specific oligonucleotide
probe
1.28cm
gt200,000 different complementary probes
Image of Hybridized Probe Array
Compliments of D. Gerhold
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PM MM
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Data and Notation

• PMijn , MMijn Intensity for perfect/mis-match
• probe cell j, in chip i, in gene n
• i 1,, I (ranging from 1 to hundreds)
• j1,, J (usually 16 or 20)
• n 1,, N (between 8,000 and 12,000)

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The Big Picture

• Summarize 20 PM,MM pairs (probe level data) into
  one number for each gene
• We call this number an expression measure
• Affymetrix GeneChips Software uses AvDiff as
  expression measure
• Does it work? Can it be improved?

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What is the evidence?

• Lockhart et. al. Nature
  Biotechnology 14 (1996)

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Competing Measures of Expression

• GeneChip software uses Avg.diff
• with A a set of suitable pairs chosen by
  software.
• Log ratio version is also used.
• For differential expression Avg.diffs are
  compared between chips.

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Competing Measures of Expression

• GeneChip new version uses something else
• with MM a version of MM that is never bigger
  than PM.

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Competing Measures of Expression

• Li and Wong fit a model
• Consider expression in chip i
• Efron et. al. consider log PM 0.5 log MM
• Another is second largest PM

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Competing Measures of Expression

• Why not stick to what has worked for cDNA?
• with A a set of suitable pairs.

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Features of Probe Level Data
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SD vs. Avg of Defective Probes
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ANOVA Strong probe effect5 times bigger than
gene effect
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Histograms of log2(PM/MM) stratifies by
log2(PMxMM)/2 for mouse chip for defective and
normal probe
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Normalization at Probe Level
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Spike-In Experiments

• Set A 11 control cRNAs were spiked in, all at
  the same concentration, which varied across
  chips.
• Set B 11 control cRNAs were spiked in, all at
  different concentrations, which varied across
  chips. The concentrations were arranged in 12x12
  cyclic Latin square (with 3 replicates)

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Set A Probe Level Data (12 chips)
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What Did We Learn?

• Dont subtract or divide by MM
• Probe effect is additive on log scale
• Take logs

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Why Remove Background?
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Background Distribution
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Average Log2(PM-BG)

• Normalize probe level data
• Compute BG background mean by estimating the
  mode of the MM distribution
• Subtract BG from each PM
• If PM-BG lt 0 use minimum of positives divided by
  2
• Take average

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Expression after Normalization
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Expression Level Comparison
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Spike-In B
Later we consider 23 different combinations of
concentrations
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Differential Expression
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Differential Expression
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Differential Expression
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Differential Expression
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Observed Ranks
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Observed vs True Ratio
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Dilution Experiment

• cRNA hybridized to human chip (HGU95) in range of
  proportions and dilutions
• Dilution series begins at 1.25 ?g cRNA per
  GeneChip array, and rises through 2.5, 5.0, 7.5,
  10.0, to 20.0 ?g per array. 5 replicate chips
  were used at each dilution
• Normalize just within each set of 5 replicates
• For each probe set compute expression, average
  and SD over replicates, and fit a line to
• log expression vs. log concentration
• Regression line should have slope 1 and high R2

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Dilution Experiment Data
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Expression and SD
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Slope Estimates and R2
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Model check

• Compute observed SD of 5 replicate expression
  estimates
• Compute RMS of 5 nominal SDs
• Compare by taking the log ratio
• Closeness of observed and nominal SD taken as a
  measure of goodness of fit of the model

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Observed vs. Model SE
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Observed vs. Model SE
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Conclusion

• Take logs
• PMs need to be normalized
• Using global background improves on use of
  probe-specific MM
• Gene Logic spike-in and dilution study show all
  four expression measures performed very well
• AvLog(PM-BG) is arguably the best in terms of
  bias, variance and model fit
• Future better BG robust/resistant summaries

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Acknowledgements

• Gene Browns group at Wyeth/Genetics Institute,
  and Uwe Scherfs Genomics Research Development
  Group at Gene Logic, for generating the spike-in
  and dilution data
• Gene Logic for permission to use these data
• Ben Bolstad (UC Berkeley)
• Magnus Åstrand (Astra Zeneca Mölndal)
• Skip Garcia, Tom Cappola, and Joshua Hare (JHU)