Bias, Variance, and Fit for Three Measures of Expression: AvDiff, Li

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Bias, Variance, and Fit for Three Measures of
Expression AvDiff, Li Wongs, and AvLog(PM-BG)

• Rafael A. Irizarry
• Department of Biostatistics, JHU
• (joint work with Bridget Hobbs and Terry Speed,
• Walter Eliza Hall Institute of Medical Research)

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Summary

• Summarize the expression level of a probe set by
  Average Log2 (PM-BG)
• PMs need to be normalized
• Background makes no use of probe-specific MM
• Evaluate and compare through bias, variance and
  model fit to AvDiff and the Li Wong algorithm
• Use Gene Logic spike-in and dilution study
• All three expression measures performed well
• AvLog(PM-BG) is arguably the best of the three

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SD vs. Avg of Defective Probes
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Normalization at Probe Level
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Spike-In Experiments

• Add concentrations (0.5pM 100 pM) of 11 foreign
  species cRNAs to hybridization mixture
• 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
Probe Set Conc 1 Conc 2 Rank
BioB-5 100 0.5 1
BioB-3 0.5 25.0 2
BioC-5 2.0 75.0 4
BioB-M 1.0 37.5 4
BioDn-3 1.5 50.0 5
DapX-3 35.7 3.0 6
CreX-3 50.0 5.0 7
CreX-5 12.5 2.0 8
BioC-3 25.0 100 9
DapX-5 5.0 1.5 10
DapX-M 3.0 1.0 11
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
Gene AvDiff MAS 5.0 LiWong AvLog(PM-BG)
BioB-5 6 2 1 1
BioB-3 16 1 3 2
BioC-5 74 6 2 5
BioB-M 30 3 7 3
BioDn-3 44 5 6 4
DapX-3 239 24 24 7
CreX-3 333 73 36 9
CreX-5 3276 33 3128 8
BioC-3 2709 8572 681 6431
DapX-5 2709 102 12203 10
DapX-M 165 19 13 6
Top 15 1 5 6 10
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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
  three 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
• Francois Collin (Gene Logic)
• Ben Bolstad (UC Berkeley)
• Magnus Åstrand (Astra Zeneca Mölndal)