1. Statistics for Microarrays
Experimental Design, Normalization,
and Exploratory Data Analysis A B C
Class web site:

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

3. Some Considerations for cDNA Microarray Experiments (I)
Scientific (Aims of the experiment)
Specific questions and priorities
How will the experiments answer the questions
Practical (Logistic)
Types of mRNA samples: reference, control, treatment, mutant, etc
Source and Amount of material (tissues, cell lines)
Number of slides available

4. Some Considerations for cDNA Microarray Experiments (II)
Other Information
Experimental process prior to hybridization: sample isolation, mRNA extraction, amplification, labelling,…
Controls planned: positive, negative, ratio, etc.
Verification method: Northern, RT-PCR, in situ hybridization, etc.

5. Aspects of Experimental Design Applied to Microarrays (I)
Array Layout
Which cDNA sequences are printed
Spatial position
Allocation of samples to slides
Design layouts
A vs B: Treatment vs control
Multiple treatments
Factorial
Time series
There are two broad aspects of to designing a microarray experiments.
The first part is designing the array. Such as which cDNA sequence to print, what library to spots and what quality controls to include.
This part of design is more of a bioinformatics question. The second aspects is on the allocation of samples to the slides.
This refers to the assignment of dye labels to the samples and to determine which samples should be paried and hyb on the same slides.
Later in the talk, we’ll see the different design choices in each of the different experimental settings.
-- Other general issues to keep in mind which affects design choices are replication. The number and type of replication, this often determines precision and generalizability of your experiments. Extensibility, refers to the ability to compare between essentially arbitrarily many sources of data sets.
-- In the interest of time, I will be focusing on the aspect that illustrate precision of estimates varies in different design layout in 4 different experimental context / setting.

6. Aspects of Experimental Design Applied to Microarrays (II)
Other considerations
Replication
Physical limitations: the number of slides and the amount of material
Sample Size
Extensibility - linking
There are two broad aspects of to designing a microarray experiments.
The first part is designing the array. Such as which cDNA sequence to print, what library to spots and what quality controls to include.
This part of design is more of a bioinformatics question. The second aspects is on the allocation of samples to the slides.
This refers to the assignment of dye labels to the samples and to determine which samples should be paried and hyb on the same slides.
Later in the talk, we’ll see the different design choices in each of the different experimental settings.
-- Other general issues to keep in mind which affects design choices are replication. The number and type of replication, this often determines precision and generalizability of your experiments. Extensibility, refers to the ability to compare between essentially arbitrarily many sources of data sets.
-- In the interest of time, I will be focusing on the aspect that illustrate precision of estimates varies in different design layout in 4 different experimental context / setting.

7. Layout options
The main issue is the use of reference samples, typically labelled green. Standard statistical design principles can lead to more efficient layouts; use of dye-swaps can also help.
Sample size determination is more than usually difficult, as there are 1,000s of possible changes, each with its own SD.

8. Natural design choice T1 T2 T3 T4 T1 Ref T2 Tn-1 Tn C
Case 1: Meaningful biological control (C)
Samples: Liver tissue from four mice treated by cholesterol modifying drugs.
Question 1: Genes that respond differently between the T and the C.
Question 2: Genes that responded similarly across two or more treatments relative to control.
Case 2: Use of universal reference
Samples: Different tumor samples.
Question: To discover tumor subtypes.
In some cases, given the nature of the experiment and the material available, one design stands out as preferable to all others.
For example, if we wish to study mRNA from cells, each treated by a different drug, and the primary comparisons of interest are those of the treated cells versus the untreated cells, then the appropriate design is clear: the untreated cells become a de facto reference, and all hybridizations involve one treated set of cells and the untreated cells.
Remember that in a 2-color microarray system, every thing has to be pairwise comparisons, we can not simply observed the effect of T1, T2 rather we need to observed the relative expression of T1 to something else. In this case, relative expression of T1 to C is a natural choice.
These are examples, where given the nature of the scientific question, you have a natural design choice.
With most experiments, a number of designs can be devised which seem suitable for use, and we need some principles for choosing one from the set of possibilities.

9. Treatment vs Control T C 2 /2 22 Two samples
e.g. KO vs. WT or mutant vs. WT
Direct
Indirect T
Ref T C C
Ref
average (log (T/C))
log (T / Ref) – log (C / Ref )
A very common questions and a active area of discussion among genomics circles.
The heart of the design issue with cDNA microarrays is the decision between direct rather than indirect comparisons, that is, between making expression comparisons within slides rather between slides. We begin by discussing this comparison in the simplest case of treatment T versus control C.
2 /2
22

10. One-way layout: one factor, k levels
I) Common Reference
II) Common reference
III) Direct comparison
Number of Slides
Ave. variance
Units of material
A = B = C = 1
A = B = C = 2
Ave. variance C B A
ref
Here we illustrate how combination of indirect and direct comparisons are often a practical solution.
All pair-wise comparisons are of equal importance
Compare three sources of mRNA….In all the illustration follows, we consider the variance for one gene in a direct hybridization to be sigma.
If the number of slides are the limitation….
If there are no limitations…..compared using the same amount of materials
When k gets large, difficult to do all pairwise comparisons

11. One-way layout: one factor, k levels
I) Common Reference
II) Common reference
III) Direct comparison
Number of Slides
N = 3
N=6
N=3
Ave. variance 2
0.67
Units of material
A = B = C = 1
A = B = C = 2
Ave. variance 1 C B A
ref
Here we illustrate how combination of indirect and direct comparisons are often a practical solution.
All pair-wise comparisons are of equal importance
Compare three sources of mRNA….In all the illustration follows, we consider the variance for one gene in a direct hybridization to be sigma.
If the number of slides are the limitation….
If there are no limitations…..compared using the same amount of materials
When k gets large, difficult to do all pairwise comparisons
For k = 3, efficiency ratio (Design I / Design III) = 3. In general, efficiency ratio = 2k / (k-1). (But may not be achievable due to lack of independence.)

12. Illustration from one experiment
Design I A B C
Ref
Design III A B C
MAD is a robust measure of SD. Since we don’t have enough sample to estimate v for every gene, we use the sample variance of the log-ratios to approximate v.
Box plots of log ratios: direct still ahead

13. Factorial experiments
Treated cell lines
Possible experiments
CTL
OSM
OSM & EGF
EGF
Here interest is not in genes for which there is an O or an E (main) effect, but in which there is an OE interaction, i.e. in genes for which
log(O&E/O)-log(E/C) is large or small.

14. 2 x 2 factorial: some design options
Indirect
A balance of direct and indirect I)
II)
III)
IV)
# Slides
N = 6
Main effect A
0.5
0.67 NA
Main effect B
0.43
0.3
Int A.B
1.5 1 C
A.B B A
Depending on the question of interest:
Interaction only;
Main effect only
A combination of both
Table entry: variance (assuming all log ratios uncorrelated)

15. Some Design Possibilities for Detecting Interaction
Samples: treated tumor cell lines at 4 time points (30 minutes, 1 hour, 4 hours, 24 hours)
Question: Which genes contribute to the enhanced inhibitory effect of OSM when it is combined with EGF? Role of time?
Design A:
ctl
Design B:
ctl
OSM
Design A uses less mRNA (2 units per source, compared to 6), but larger variance 2
OSM & EGF
OSM & EGF
EGF
OSM
EGF

16. Combining Estimates A D M L V P How do we combine these?
Different ways of estimating the same contrast:
e.g. A compared to P
Direct = A-P
Indirect = A-M + (M-P) or
A-D + (D-P) or
-(L-A) - (P-L) M L V P
How do we combine these?

18. Time Course Experiments
Number of time points
Which differences are of highest interest (e.g. between initial time and later times, between adjacent times)
Number of slides available

19. Design choices in time series. Entry: variance
t vs t+1
t vs t+2
t vs t+3
Ave
T1T2
T2T3
T3T4
T1T3
T2T4
T1T4
N=3
A) T1 as common reference 1 2
1.5
B) Direct Hybridization 3
1.67
N=4
C) Common reference
D) T1 as common ref + more
.67
1.06
E) Direct hybridization choice 1
.75
.83
F) Direct Hybridization choice 2 T2 T3 T4 T1
Ref
Generating all possible hybridization patterns is difficult once the number of mRNA sources becomes large

20. Replication Why? What is it? To reduce variability
To increase generalizability
What is it?
Duplicate spots
Duplicate slides
Technical replicates
Biological replicates

21. Technical Replicates: Labeling
3 sets of self – self hybridizations
Data 1 and Data 2 were labeled together and hybridized on two slides separately
Data 3 were labeled separately
Data 3
Data 2
Data 1
Data 1

22. Sample Size Variance of individual measurements (X)
Effect size(s) to be detected (X)
Acceptable false positive rate
Desired power (probability of detecting an effect of at least the specfied size)

23. Extensibility
“Universal” common reference for arbitrary undetermined number of (future) experiments
Provides extensibility of the series of experiments (within and between labs)
Linking experiments necessary if common reference source diminished/depleted

24. Summary Balance of direct and indirect comparisons
Optimize precision of the estimates among comparisons of interest
Must satisfy scientific and physical constraints of the experiment
This is the situation where generating all possible designs combination is not feasible.
Finding an algorithm to estimate the local optimal designs.

25. (BREAK)

26. Mini-Review: How to make a cDNA microarray

27. Pins collect cDNA from wells
384 well plate --
Contains cDNA probes
cDNA clones
Spotted in duplicate
Print-tip group 1
Glass Slide
Array of bound cDNA probes
4x4 blocks = 16 print-tip groups
Print-tip group 6

28. Building the chip
Ngai Lab arrayer , UC Berkeley
Print-tip head

29. Microarray Experiment

30. Hybridization Binding cDNA samples (targets) to cDNA probes on slide
cover
slip
Hybridise for
5-12 hours

32. Quantification of expression
For each spot on the slide we calculate
Red intensity = Rfg - Rbg
fg = foreground, bg = background, and
Green intensity = Gfg - Gbg
and combine them in the log (base 2) ratio
Log2( Red intensity / Green intensity)

33. Background matters
From Spot
From GenePix

34. Quality Measurements Array Correlation between spot intensities
Percentage of spots with no signals
Distribution of spot signal area
Spot
Signal / Noise ratio
Variation in pixel intensities
Identification of “bad spot” (spots with no signal)
Ratio (2 spots combined)
Circularity

35. Affymetrix Oligo Chips
Only one “color”
Different technology, different normalization issues
Affy chip normalization is an active research area – see

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

37. Tools for Microarray Normalization and Analysis
Both commercial and free software
The labs for this course use the R package sma
Upcoming release (29 April 2002) of Bioconductor (

38. Red/Green overlay images
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
Bad: high bg, ghost spots, little d.e.
Good: low bg, lots of d.e.

39. Scatterplots: always log, always rotate
log2R vs log2G
M=log2R/G vs A=log2√RG

40. Histograms
Signal/Noise = log2(spot intensity/background intensity)

41. Boxplots of log2R/G
Liver samples from 16 mice: 8 WT, 8 ApoAI KO

42. Spatial plots: background from the two slides

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

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

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

46. Plate effects

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

48. Time of printing effects
spot number
Green channel intensities (log2G). Printing over 4.5 days.
The previous slide depicts a slide from this print run.

49. 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.
We find dye biases which vary with overall spot intensity, location on the array, plate origin, pins, scanning parameters,….

50. Self-self hybridizations
False color overlay
Boxplots within pin-groups
Scatter (MA-)plots

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

52. From Lawrence Berkeley National Laboratory

53. Normalization Methods (I)
Normalization based on a global adjustment
log2 R/G -> log2 R/G - c = log2 R/(kG)
Choices for k or c = log2k are c = median or mean of log ratios for a particular gene set (e.g. housekeeping genes). Or, total intensity normalization, where
k = ∑Ri/ ∑Gi.
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.
log2 R/G -> log2 R/G - c (A) = log2 R/(k(A)G).
One estimate of c(A) is made using the LOWESS function of Cleveland (1979): LOcally WEighted Scatterplot Smoothing.

54. 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.
log2 R/G -> log2 R/G - ci(A) = log2 R/(ki(A)G),
where ci(A) is the LOWESS fit to the MA-plot for the ith grid only.

55. 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.

56. Use of Control Slides: M vs A Plot
M = log R/G = logR - logG
Lowess curve
blanks
Positive controls
Negative controls
A = ( logR + logG ) /2

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

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

59. 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

60. 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

61. ***

62. 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.

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

64. Scale normalization: another data set
Log-ratios
Only small differences in spread apparent. No action required. `

65. One way of taking scale into account
Assumption: All slides have the same spread in M
True log ratio is mij where i represents different slides and j represents different spots.
Observed is Mij, where
Mij = ai mij
Robust estimate of ai is
MADi = medianj { |yij - median(yij) | }

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

67. Print-tip-group normalization helps

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

69. Effects of previous normalization
Before normalization
After print-tip-group
normalization

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

71. Taking scale into account, cont.
Assumption: All print-tip-groups have the same spread in M
True log ratio is mij where i represents different print-tip-groups and j represents different spots.
Observed is Mij, where
Mij = ai mij
Robust estimate of ai is
MADi = medianj { |yij - median(yij) | }

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

73. A comparison of three M v A plots
Unnormalized
Print-tip normalization
Print tip & scale n

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

75. 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

76. Pre-processed cDNA Gene Expression Data
On p genes for n slides: p is O(10,000), n is O(10-100), but growing,
Slides
slide 1 slide 2 slide 3 slide 4 slide 5 …
Genes 3
Gene expression level of gene 5 in slide 4 =
Log2( Red intensity / Green intensity)
These values are conventionally displayed
on a red (>0) yellow (0) green (<0) scale.

77. First Steps: QQ-Plots Used to assess whether a sample follows a
particular (e.g. normal) distribution (or to compare two samples)
A method for looking
for outliers when data
are mostly normal
Sample
Sample quantile is 0.125
Theoretical
Value from Normal distribution which yields a quantile of 0.125

78. 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)