1 Pre-processing - Normalization Databases Statistics for Microarray Data Analysis – Lecture 2 The Fields Institute for Research in Mathematical Sciences May 25, 2002

2 Biological question Biological verification and interpretation Microarray experiment Experimental design Image analysis Normalization TestingEstimation Clustering Discrimination Analysis

3 Diagnostic Plots

4 Was the experiment a success? What analysis tools should be used? Are there any specific problems? Begin by looking at the data

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

6 Always log, always rotate log 2 R vs log 2 GM=log 2 R/G vs A=log 2 √RG

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

8 Slide 3 of the swirl data: used in all that follows.

9 MA-plot

10 Spatial plots: background

11 Spatial plots: log ratios (M)

12 Boxplots: Print-tips effects

13 Boxplots: plate effects

14 Time of printing effects

15 Serious time of printing effects Another data set, green channel intensities (log 2 G). Printed over 4.5 days. spot number

16 Normalization

17 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. We find dye biases which vary with overall spot intensity, location on the array, plate origin, pins, scanning parameters,….

18 Self-self hybridizations False color overlay Boxplots within pin-groupsScatter (MA-)plots

19 A series of non self-self hybridizations From the NCI60 data setEarly Ngai lab, UC Berkeley Early PMCRI, Melbourne AustraliaEarly Goodman lab, UC Berkeley

20 Normalization Within-slides -Which genes to use? -Location normalization -Scale normalization Paired-slides (dye-swap) -Self-normalization Between-slides

21 Within-slide normalization

22 Which spots to use? All genes on the array. Constantly expressed genes (housekeeping). Controls -Spiked controls (e.g. plant genes); -Genomic DNA titration series. Rank invariant set.

23 Which spots to use, cont.? 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, we can justify the use of a global LOWESS approach 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. Print-tips-group LOWESS requires stronger assumptions: that one of the above applies within each print-tip-group. The use of other sets of genes, e.g. control or housekeeping genes, involve similar assumptions.

24 log 2 R/G  log 2 R/G - c = log 2 R/ (kG) Standard practice (in most software) c is a constant such as the mean or median log ratio. Our preference c is a function of overall spot intensity A and print-tip group, and possibly other variables. Compute c by robust locally weighted regression of M On these variables. E.g. lowess. Location normalization

25 Location normalization: details a) 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. housekeeping genes). Or, total intensity normalization, where k = ∑R i / ∑G i. b) Intensity-dependent normalization. Here we 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.

26 MA-plot

27 MA-plot

28 Boxplot: print-tip effects remain after global normalization

29 Normalization: details cont. c) 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 artifacts 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.

30 Print-tip normalized data: M vs A plot

31 Print-tip normalized data: spatial and box plots

32 Smoothed histograms of M values Black: unnormalized; red: global median; green: global lowess; blue: print-tip lowess

33 Within-slide Paired slide

34 Follow-up experiment On each slide, half the spots (  8) are differentially expressed, the other half are not.

35 Paired-slides: dye-swap Slide 1, M = log 2 (R/G) - c Slide 2, M’ = log 2 (R’/G’) - c’ Combine by subtracting the normalized log-ratios: [ (log 2 (R/G) - c) - (log 2 (R’/G’) - c’) ] / 2  [ log 2 (R/G) + log 2 (G’/R’) ] / 2  [ log 2 (RG’/GR’) ] / 2 provided c = c’. Assumption: the normalization functions are the same for the two slides.

36 Checking the assumption MA plot for slides 1 and 2: it isn’t always like this.

37 Result of self-normalization (M - M’)/2 vs. (A + A’)/2

38 MSP titration series (Microarray Sample Pool) Control set to aid intensity- dependent normalization Different concentrations Spotted evenly spread across the slide Pool the whole library

39 Yellow: GAPDH, tubulin Light blue: MSP pool / titration Orange: Schadt-Wong rank invariant set Red line: lowess smooth MSP normalization compared to other methods

40 Composite normalization Before and after composite normalization -MSP lowess curve -Global lowess curve -Composite lowess curve (Other colours control spots) c i (A)=  A g(A)+(1-  A )f i (A)

41 Comparison of Normalization Schemes (courtesy of Jason Goncalves) No consensus on best segmentation or normalization method Scheme was applied to assess the common normalization methods Based on reciprocal labeling experiment data for a series of 140 replicate experiments on two different arrays each with 19,200 spots

42 DESIGN OF RECIPROCAL LABELING EXPERIMENT Replicate experiment in which we assess the same mRNA pools but invert the fluors used. The replicates are independent experiments and are scanned, quantified and normalized as usual

43 The following relationship would be observed for reciprocal microarray experiments in which the slides are free of defects and the normalization scheme performed ideally We can measure using real data sets how well each microarray normalization scheme approaches this ideal

44 Deviation metric to assess normalization schemes We now use the mean array average deviation to compare the normalization methods. Note that this comparison addresses only variance (precision) and not bias (accuracy) aspects of normalization.

45 ***

46 Multiple-slide

47 Scale normalization: between slides Boxplots of log ratios from 3 replicate self-self hybridizations. Before normalization After location normalization After scale normalization

48 Before normalization After location normalization After scale normalization

49 One way of taking scale into account 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 MADi = median j { |y ij - median(y ij ) | }

50 Summary of normalization 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 More? Use controls! Normalization introduces more variability Outliers (bad spots) are handled with replication

51 What is missing? Principally, a discussion of data quality issues. Most image analysis programs collect a wide range of measurements associated with each spot: morphological measures such as area and perimeter (in pixels), uniformity measures such as the SD of foreground and background intensities in each channel, and of ratios of intensities (with and without background) across the pixels in a spot; and spot brightness indicators such as the ratio of spot foreground to spot background, and the fraction of pixels in the foreground with intensity greater than background intensity (or a given multiple thereof). From these, further derived measures can be calculated, such as coefficients of variation, and so on. How should we make use of the various quality indicators? Most programs include procedures for flagging spots on the basis of one or more indicators, and users typically omit flagged spots from their primary analyses. “Data filtering” of this kind clearly improves the appearance of the data, but….can we do more? That is a longer story, for another time.

52 Acknowledgments Natalie Thorne (WEHI) Ingrid Lönnstedt (Uppsala) The swirl data were provided by Katrin Wuennenberg-Stapleton from the Ngai Lab at UC Berkeley. The swirl embryos for this experiment were provided by David Kimelman and David Raible at the University of Washington. The self-self data were provided by Vivian Peng from the Ngai Lab at UC Berkeley. Reference: Yang et al (2002) Nucleic Acids Research 30, e15.