Statistical Analyses of High Density Oligonucleotide Arrays

Rafael A. IrizarryDepartment 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

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

Probe Arrays

24µm24µm

Millions of copies of a specificMillions of copies of a specificoligonucleotide probeoligonucleotide probe

Image of Hybridized Probe ArrayImage of Hybridized Probe Array

>200,000 different>200,000 differentcomplementary probes complementary probes

Single stranded, Single stranded, labeled RNA targetlabeled RNA target

Oligonucleotide probeOligonucleotide probe

* ****

1.28cm1.28cm

GeneChipGeneChip Probe ArrayProbe ArrayHybridized Probe CellHybridized Probe Cell

Compliments of D. Gerhold

PM MM

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)j=1,…, J (usually 16 or 20)n = 1,…, N (between 8,000 and 12,000)

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 GeneChip’s Software uses

AvDiff as expression measure• Does it work? Can it be improved?

What is the evidence? Lockhart et. al. Nature Biotechnology 14 (1996)

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.

j

jj MMPMdiffAvg )(1.

Competing Measures of Expression

• GeneChip® new version uses something else

with MM* a version of MM that is never bigger than PM.

)}{log( *jj MMPMghtTukeyBiweisignal

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

),0(, 2 NMMPM ijijjiijij

i

Competing Measures of Expression

• Why not stick to what has worked for cDNA?

with A a set of “suitable” pairs.

Aj

j BGPMBGPMAvLog )log(1)(

Features of Probe Level Data

SD vs. Avg of Defective Probes

ANOVA: Strong probe effect5 times bigger than gene effect

Histograms of log2(PM/MM) stratifies by log2(PMxMM)/2 for mouse chip for defective and normal probe

Normalization at Probe Level

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)

Set A: Probe Level Data (12 chips)

What Did We Learn?

• Don’t subtract or divide by MM• Probe effect is additive on log scale• Take logs

Why Remove Background?

Background Distribution

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 < 0 use minimum of positives

divided by 2• Take average

Expression after Normalization

Expression Level Comparison

Spike-In BProbe Set Conc 1 Conc 2 RankBioB-5 100 0.5 1BioB-3 0.5 25.0 2BioC-5 2.0 75.0 4BioB-M 1.0 37.5 4BioDn-3 1.5 50.0 5DapX-3 35.7 3.0 6CreX-3 50.0 5.0 7CreX-5 12.5 2.0 8BioC-3 25.0 100 9DapX-5 5.0 1.5 10DapX-M 3.0 1.0 11

Later we consider 23 different combinations of concentrations

Differential Expression

Differential Expression

Differential Expression

Differential Expression

Observed RanksGene AvDiff MAS 5.0 Li&Wong AvLog(PM-BG)BioB-5 6 2 1 1BioB-3 16 1 3 2BioC-5 74 6 2 5BioB-M 30 3 7 3BioDn-3 44 5 6 4DapX-3 239 24 24 7CreX-3 333 73 36 9CreX-5 3276 33 3128 8BioC-3 2709 8572 681 6431DapX-5 2709 102 12203 10DapX-M 165 19 13 6Top 15 1 5 6 10

Observed vs True Ratio

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

Dilution Experiment Data

Expression and SD

Slope Estimates and R2

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

Observed vs. Model SE

Observed vs. Model SE

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

Acknowledgements

• Gene Brown’s group at Wyeth/Genetics Institute, and Uwe Scherf’s 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)