1. Normalization Class web site: http://statwww.epfl.ch/davison/teaching/Microarrays/ETHZ/ Statistics for Microarrays

2. Biological question Differentially expressed genes Sample class prediction etc. Testing Biological verification and interpretation Microarray experiment Estimation Experimental design Image analysis Normalization Clustering Discrimination R, G 16-bit TIFF files (Rfg, Rbg), (Gfg, Gbg)

3. Was the experiment a success? Are there any specific problems? What analysis tools should be used? Preprocessing: Data Visualization

4. Tools for Microarray Normalization and Analysis Both commercial and free software R (use sma package or Bioconductor: http://www.bioconductor.org/) http://www.bioconductor.org/

5. Red/Green overlay images Good: low bg, detectable d.e. Bad: high bg, ghost spots, little d.e. Co-registration and overlay offers a quick visualization, revealing information on color balance, uniformity of hybridization, spot uniformity, background, and artefacts such as dust or scratches

6. Scatterplots: always log*, always rotate log 2 R vs log 2 GM=log 2 R/G vs A=log 2 √RG * O ther transformations can provide improvement

7. Signal/Noise = log 2 (spot intensity/background intensity ) Histograms

8. Boxplots of log 2 R/G Liver samples from 16 mice: 8 WT, 8 ApoAI KO

9. Spatial plots: background from the two slides

10. Highlighting extreme log ratios Top (black) and bottom (green) 5% of log ratios

11. Pin group (sub-array) effects Boxplots of log ratios by pin group Lowess lines through points from pin groups

12. Boxplots and highlighting pin group effects Clear example of spatial bias Print-tip groups Log-ratios

13. Plate effects

14. KO #8 Probes: ~6,000 cDNAs, including 200 related to lipid metabolism. Arranged in a 4x4 array of 19x21 sub-arrays. Clearly visible plate effects

15. Time of printing effects Green channel intensities (log 2 G). Printing over 4.5 days. The previous slide depicts a slide from this print run. spot number

16. Preprocessing: Normalization Why? To correct for systematic differences between samples on the same slide, or between slides, which do not represent true biological variation between samples How do we know it is necessary? By examining self-self hybridizations, where no true differential expression is occurring. There are dye biases which vary with spot intensity, location on the array, plate origin, pins, scanning parameters,…

17. Self-self hybridizations False color overlayBoxplots within pin-groupsScatter (MA-)plots

18. From the NCI60 data set (Stanford web site) Similar patterns apparent in non self-self hybridizations

19. From Lawrence Berkeley National Laboratory

20. Normalization Methods (I) Normalization based on a global adjustment log 2 R/G -> log 2 R/G - c = log 2 R/(kG) Choices for k or c = log 2 k are c = median or mean of log ratios for a particular gene set (e.g. all genes, or control or housekeeping genes). Or, total intensity normalization, where k = ∑R i / ∑G i. Intensity-dependent normalization Here, run a line through the middle of the MA plot, shifting the M value of the pair (A,M) by c=c(A), i.e. log 2 R/G -> log 2 R/G - c (A) = log 2 R/(k(A)G). One estimate of c(A) is made using the LOWESS function of Cleveland (1979): LOcally WEighted Scatterplot Smoothing.

21. Normalization Methods (II) Within print-tip group normalization In addition to intensity-dependent variation in log ratios, spatial bias can also be a significant source of systematic error. Most normalization methods do not correct for spatial effects produced by hybridization artefacts or print-tip or plate effects during the construction of the microarrays. It is possible to correct for both print-tip and intensity- dependent bias by performing LOWESS fits to the data within print-tip groups, i.e. log 2 R/G -> log 2 R/G - c i (A) = log 2 R/(k i (A)G), where c i (A) is the LOWESS fit to the MA-plot for the ith grid only.

22. Normalization: Which Spots to use? The LOWESS lines can be run through many different sets of points, and each strategy has its own implicit set of assumptions justifying its applicability. For example, the use of a global LOWESS approach can be justified by supposing that, when stratified by mRNA abundance, a) only a minority of genes are expected to be differentially expressed, or b) any differential expression is as likely to be up- regulation as down-regulation. Pin-group LOWESS requires stronger assumptions: that one of the above applies within each pin-group. The use of other sets of genes, e.g. control or housekeeping genes, involve similar assumptions.

23. Global scale, global lowess, pin-group lowess; spatial plot after, smooth histograms of M after Normalization makes a difference

24. Normalization by controls: Microarray Sample Pool titration series Control set to aid intensity-dependent normalization Different concentrations in titration series Spotted evenly spread across the slide in each pin-group Pool the whole library

25. Comparison of Normalization Schemes (courtesy of Jason Goncalves) No consensus on best normalization method Experiment done to assess the common normalization methods Based on reciprocal labeling experimental data for a series of 140 replicate experiments on two different arrays each with 19,200 spots

26. DESIGN OF RECIPROCAL LABELING EXPERIMENT Replicate experiment with same mRNA pools but invert fluors (dye swap) Replicates are independent experiments Scan, quantify, normalize as usual

27. ***

28. Scale normalization: between slides Boxplots of log ratios from 3 replicate self-self hybridizations Left panel: before normalization Middle panel: after within print-tip group normalization Right panel: after a further between-slide scale normalization

29. The “NCI 60” experiments (no bg) Some scale normalization seems desirable

30. Scale normalization: another data set Log-ratios Only small differences in spread apparent; no action required. `

31. Assumption: All slides have the same spread in M True log ratio is m ij where i represents different slides and j represents different spots. Observed is M ij, where M ij = a i m ij Robust estimate of a i is MAD i = median j { |y ij - median(y ij ) | } One way of taking scale into account

32. A slightly harder normalization problem Global lowess doesn’t do the trick here

33. Print-tip-group normalization helps

34. But not completely Still a lot of scatter in the middle in a WT vs KO comparison

35. Effects of previous normalization Before normalizationAfter print-tip-group normalization

36. Within print-tip-group box plots of M after print-tip-group normalization

37. Assumption: All print-tip-groups have the same spread in M True log ratio is m ij where i represents different print-tip-groups and j represents different spots. Observed is M ij, where M ij = a i m ij Robust estimate of a i is MAD i = median j { |y ij - median(y ij ) | } Taking scale into account, cont.

38. Effect of location & scale normalization Clearly care is needed in making decisions like this

39. A comparison of three M v A plots Unnormalized Print-tip normalizationPrint tip & scale n

40. The same normalization on another data set. Before After

41. Normalization: Summary Reduces systematic (not random) effects Makes it possible to compare several arrays Use logratios (M vs A plots) Lowess normalization (dye bias) MSP titration series – composite normalization Pin-group location normalization Pin-group scale normalization Between slide scale normalization Control Spots Normalization introduces more variability Outliers (bad spots) are handled with replication

42. Affymetrix Oligo Chips Only one “color” Different technology, different normalization issues Affy chip normalization is an active research area – see http://www.stat.berkeley.edu/users/ terry/zarray/Affy/affy_index.html http://www.stat.berkeley.edu/users/ terry/zarray/Affy/affy_index.html

43. Pre-processed cDNA Gene Expression Data On p genes for n slides: p is O(10,000), n is O(10-100), but growing, Genes Slides Gene expression level of gene 5 in slide 4 = (normalized) log 2 ( Red / Green) slide 1slide 2slide 3slide 4slide 5 … 1 0.46 0.30 0.80 1.51 0.90... 2-0.10 0.49 0.24 0.06 0.46... 3 0.15 0.74 0.04 0.10 0.20... 4-0.45-1.03-0.79-0.56-0.32... 5-0.06 1.06 1.35 1.09-1.09... These values are conventionally displayed on a red (>0) yellow (0) green (<0) scale.

44. Acknowledgments Terry Speed (UCB and WEHI) Jean Yee Hwa Yang (UCB) Sandrine Dudoit (UCB) Ben Bolstad (UCB) Natalie Thorne (WEHI) Ingrid Lönnstedt (Uppsala) Henrik Bengtsson (Lund) Jason Goncalves (Iobion) Matt Callow (LLNL) Percy Luu (UCB) John Ngai (UCB) Vivian Peng (UCB) Dave Lin (Cornell)