# 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.

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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

Expression after Normalization

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

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)

Why Remove Background?

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

Expression Level

Spike-In B GeneConc 1Conc 2Rank BioB-51000.51 BioB-30.525.02 BioC-52.075.03 BioB-M1.035.74 BioDn-31.550.05 DapX-335.73.06 CreX-350.05.07 CreX-512.52.08 BioC-325.01009 DapX-55.01.510 DapX-M3.01.011 Later we consider 24 different combinations of concentrations

Differential Expression

Observed vs True Ratio

Dilution Experiment cRNA hybridized to human chip (HGU_95) 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)

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