Experimental Design, Normalization, and Exploratory Data Analysis

Class web site: http://statwww.epfl.ch/davison/teaching/Microarrays/

Statistics for Microarrays

A B

C

Biological questionDifferentially expressed genesSample 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)

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

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.

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

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

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.

Natural design choice

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 referenceSamples: Different tumor samples.Question: To discover tumor subtypes.

C

T1 T2 T3 T4 T1

Ref

T2 Tn-1 Tn

Treatment vs Control

Two samplese.g. KO vs. WT or mutant vs. WT

T CT Ref

C Ref

Direct Indirect

2 /2 22

average (log (T/C)) log (T / Ref) – log (C / Ref )

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 A = B = C = 2

Ave. variance

One-way layout: one factor, k levels

C B

A

ref

CBA

ref

CBA

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 A = B = C = 2

Ave. variance 1 0.67

One-way layout: one factor, k levels

C B

A

ref

CBA

ref

CBA

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.)

Design I

Design III

A B

C

A

Ref

B C

Illustration from one experiment

Box plots of log ratios: direct still ahead

CTL OSM

EGF OSM & EGF

Factorial experiments

•Treated cell lines

•Possible experiments

Here interest is not in genes for which there is an O or an E (main) effect, but in which there is an OE interaction, i.e. in genes for which log(O&E/O)-log(E/C) is large or small.

Indirect A balance of direct and indirect

I) II) III) IV)

# Slides N = 6

Main effect A

0.5 0.67 0.5 NA

Main effect B

0.5 0.43 0.5 0.3

Int A.B 1.5 0.67 1 0.67

2 x 2 factorial: some design options

C

A.BBA

B

C

A.B

A

B

C

A.B

A

B

C

A.B

A

Table entry: variance (assuming all log ratios uncorrelated)

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?

ctl OSM

EGF OSM & EGF

ctl

OSM EGF OSM & EGF

2

Design A: Design B:

Combining Estimates

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)

How do we combine these?

LL

PPVV

DD

MM

AA

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

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 2 1 2 1 1.5

B) Direct Hybridization 1 1 1 2 2 3 1.67

N=4 C) Common reference 2 2 2 2 2 2 2

D) T1 as common ref + more .67 .67 1.67 .67 1.67 1 1.06

E) Direct hybridization choice 1 .75 .75 .75 1 1 .75 .83

F) Direct Hybridization choice 2 1 .75 1 .75 .75 .75 .83

T2 T3 T4T1

T2 T3 T4T1

Ref

T2 T3 T4T1

T2 T3 T4T1

T2 T3 T4T1

T2 T3 T4T1

Replication

• Why?• To reduce variability• To increase generalizability

• What is it?• Duplicate spots• Duplicate slides

• Technical replicates• Biological replicates

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 1 Data 1

Dat

a 2

Dat

a 3

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)

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

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

(BREAK)

Mini-Review: How to make a cDNA microarray

384 well plate --

Contains cDNA probes

Glass Slide

Array of bound cDNA probes

4x4 blocks = 16 print-tip groups Print-tip group 6

cDNA clones

Spotted in duplicate

Print-tip group 1

Pins collect cDNA from wells

Ngai Lab arrayer , UC Berkeley

Building the chip

Print-tip head

Microarray Experiment

HybridizationBinding cDNA samples (targets) to cDNA probes on

slide

cover

slip

Hybridise for

5-12 hours

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)

Background matters

From Spot From GenePix

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

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

• Was the experiment a success?

• Are there any specific problems?

• What analysis tools should be used?

Preprocessing: Data VisualizationPreprocessing: Data Visualization

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 (http://www.bioconductor.org/)

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 color balance, uniformity of hybridization, spot uniformity, background, and artefactssuch as dust or scratches

Scatterplots: always log, always rotate

log2R vs log2G M=log2R/G vs A=log2√RG

Signal/Noise = log2(spot intensity/background intensity)

Histograms

Boxplots of log2R/G

Liver samples from 16 mice: 8 WT, 8 ApoAI KO

Spatial plots: background from the two slides

Highlighting extreme log ratios

Top (black) and bottom (green) 5% of log ratios

Pin group (sub-array) effects

Boxplots of log ratios by pin groupLowess lines through points from pin groups

Boxplots and highlighting pin group effects

Clear example of spatial bias

Print-tip groups

Lo

g-r

ati o

s

Plate effects

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

Time of printing effects

Green channel intensities (log2G). Printing over 4.5 days.The previous slide depicts a slide from this print run.

spot number

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,….

Self-self hybridizations

False color overlay Boxplots within pin-groups Scatter (MA-)plots

From the NCI60 data set (Stanford web site)

Similar patterns apparent in non self-self hybridizations

From Lawrence Berkeley National Laboratory

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.

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.

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.

Use of Control Slides: M vs A PlotM = log R/G = logR - logG

A = ( logR + logG ) /2

Positive controlsNegative controls

blanks

Lowess curve

Global scale, global lowess, pin-group lowess; spatial plot after, smooth histograms of M after

Normalization makes a difference

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

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

DESIGN OF RECIPROCALDESIGN OF RECIPROCALLABELING EXPERIMENTLABELING 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

Comparison of Normalization Methods - Using 140 19K Microarrays

0.3

0.32

0.34

0.36

0.38

0.4

0.42

0.44

0.46

Pre Normalized Global Intensity Subarray Intensity Global Ratio Sub-Array Ratio Global LOWESS Subarray LOWESS

Normalization Method

Ave

rage

Mea

n D

evia

tion

Val

ue

***

Scale normalization: between slides

Boxplots of log ratios from 3 replicate self-self hybridizations.Left panel: before normalizationMiddle panel: after within print-tip group normalizationRight panel: after a further between-slide scale normalization.

The “NCI 60” experiments (no bg)

Some scale normalization seems desirable

Scale normalization: another data set

Lo

g-r

ati o

s

Only small differences in spread apparent. No action required.

`

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) | }

One way of taking scale into account

A slightly harder normalization problem

Global lowess doesn’t do the trick here

Print-tip-group normalization helps

But not completely

Still a lot of scatter in the middle in a WT vs KO comparison

Effects of previous normalization

Before normalization After print-tip-groupnormalization

Within print-tip-group box plots of M after print-tip-group

normalization

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) | }

Taking scale into account, cont.

Effect of location & scale normalization

Clearly care is needed in making decisions like this

A comparison of three M v A plots

Unnormalized Print-tip normalization Print tip & scale n

The same normalization on another data set

.

Before

After

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

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

= Log2( Red intensity / Green intensity)

slide 1 slide 2 slide 3 slide 4 slide 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.

First Steps: QQ-Plots

Used to assess whether a sample follows aparticular (e.g. normal) distribution (or to compare two samples)

A method for lookingfor outliers when dataare mostly normal

Sam

ple

Theoretical

Sample quantile is 0.125

Value from Normal distribution which yields a quantile of 0.125

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)