Bias, Variance, and Fit for Three Measures of Expression: AvDiff, Li &Wong’s, and AvLog(PM-BG)

1. 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)

2. 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

3. SD vs. Avg of Defective Probes

4. Normalization at Probe Level

5. Expression after Normalization

6. Background Distribution

7. 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

8. 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)

9. Why Remove Background?

10. Probe Level Data (12 chips)

11. What Did We Learn? • Don’t subtract or divide by MM • Probe effect is additive on log scale • Take logs

12. Expression Level

13. Spike-In B Later we consider 24 different combinations of concentrations

14. Differential Expression

15. Observed vs True Ratio

16. 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 R2

17. Dilution Experiment Data

18. Expression and SD

19. Slope Estimates and R2

20. 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

21. Observed vs. Model SE

22. Observed vs. Model SE

23. 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

24. 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)