Bias, Variance, and Fit for Three Measures of Expression: AvDiff, Li &Wong’s, 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)

Summary Summarize the expression level of a probe set by Average Log 2 (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

SD vs. Avg of Defective Probes

Normalization at Probe Level

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)

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 Log 2 (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 B Probe SetConc 1Conc 2Rank BioB BioB BioC BioB-M BioDn DapX CreX CreX BioC DapX DapX-M Later we consider 23 different combinations of concentrations

Differential Expression

Observed Ranks GeneAvDiffMAS 5.0Li&WongAvLog(PM-BG) BioB BioB BioC BioB-M30373 BioDn DapX CreX CreX BioC DapX DapX-M Top

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 R 2

Dilution Experiment Data

Expression and SD

Slope Estimates and R 2

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

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

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 Francois Collin (Gene Logic) Ben Bolstad (UC Berkeley) Magnus Åstrand (Astra Zeneca Mölndal)