Preprocessing of cDNA microarray dataPreprocessing of cDNA microarray data

Lecture 19, Statistics 246,

April 1, 2004

Was the experiment a success?

What analysis tools should be used?

Are there any specific problems?

Begin by looking at the dataBegin by looking at the data

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 ofhybridization, spot uniformity, background, and artifiactssuch as dust or scratches

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

Boxplots and highlightingBoxplots and highlighting

Clear example of spatial bias (here high is red, low green)

Print-tip groups

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pin group #

Pin group (sub-array) effects

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

Plate effects

KO #8

Probes: ~6,000 cDNAs, including 200 related to lipid metabolism. Arranged in a 4x4 array of 19x21 sub-arrays.

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

NormalizationNormalization

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)

A series of non self-self hybridizations

Early Ngai lab, UC Berkeley

Early Goodman lab, UC Berkeley

From the Ernest Gallo Clinic & Research Center

Early PMCRI, Melbourne Australia

Normalization: methodsNormalization: methods a) 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.

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.

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: methodsNormalization: methods

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.

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.

Which spots to use for normalization?Which spots to use for normalization?

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.

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 spotsUse of control spots

M = log R/G = logR - logG A = ( logR + logG) /2

Positive controls

(spotted in varying concentrations) Negative controls

blanks

Lowess curve

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

MSP titration seriesMSP titration series((Microarray Sample PoolMicroarray Sample Pool))

Control set to aid intensity- dependent normalization

Different concentrations

Spotted evenly spread across the slide

Pool the whole library

Yellow: GAPDH, tubulin Light blue: MSP pool / titration

Orange: Schadt-Wong rank invariant set Red line: lowess smooth

MSP normalization compared to other methods

Composite normalizationComposite normalization

Before and after composite normalization

-MSP lowess curve-Global lowess curve-Composite lowess curve(Other colours control spots)

ci(A)=Ag(A)+(1-A)fi(A)

Comparison of Normalization SchemesComparison of Normalization Schemes(courtesy of Jason Goncalves)(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

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

2.2/1

21.2/1

2 )(log)(log ExpChCh

GeneAExpChCh

GeneA RatioRatio −=

The following relationship would be observedfor 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

2.2/1

21.2/1

2 )(log)(log ExpChCh

GeneAExpChCh

GeneASpot RatioRatioDeviation +=

n

RatioRatioDeviation

ExpChCh

GeneNExpChCh

GeneN

n

geArrayAvera

2.2/1

21.2/1

21

)(log)(log +=∑

Deviation metric to assessDeviation metric to assessnormalization schemesnormalization schemes

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

***

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

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Only small differences in spread apparent. No action required.

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Assumption: All slides have the same spread in M

True log ratio is ij where i represents different slides and j represents different spots.

Observed is Mij, where

Mij = ai ij

Robust estimate of ai is

MADi = medianj { |yij - median(yij) | }

One way of taking scale into accountOne way of taking scale into account

MADi

MADii=1

I∏I

A slightly harder normalization problemA slightly harder normalization problem

Global lowess doesn’t do the trick here.

Print-tip-group normalization helpsPrint-tip-group normalization helps

But not completelyBut not completely

There is still a lot of scatter in the middle in a WT vs KO comparison.

Effects of previous normalisationEffects of previous normalisation

Before normalisation After print-tip-groupnormalization

Within print-tip-group box plots of M afterWithin print-tip-group box plots of M afterprint-tip-group normalizationprint-tip-group normalization

Assumption:

All print-tip-groups have the same spread in M

True log ratio is ij where i represents different print-tip-groups and j represents different spots.

Observed is Mij, where

Mij = ai ij

Robust estimate of ai is

MADi = medianj { |yij - median(yij) | }

Taking scale into account, cont.Taking scale into account, cont.

MADi

MADii=1

I∏I

Effect of location & scale normalizationEffect of location & scale normalization

Clearly care is needed in making decisions like this one.

A comparison of three MA-plots

Unnormalized Print-tip normalization Print tip & scale n.

The same idea on another data setThe same idea on another data set

After print-tip location and scale normalization.

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Print-tip groups

Follow-up experiment

On each slide, half the spots (8) are differentially expressed, the other half are not.

Paired-slides: dye-swapPaired-slides: dye-swap

Slide 1, M = log2 (R/G) - c

Slide 2, M’ = log2 (R’/G’) - c’

Combine by subtracting the normalized log-ratios:

[ (log2 (R/G) - c) - (log2 (R’/G’) - c’) ] / 2

[ log2 (R/G) + log2 (G’/R’) ] / 2

[ log2 (RG’/GR’) ] / 2

provided c = c’.

Assumption: the normalization functions are the same for the two slides.

Checking the assumptionChecking the assumption

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

Result of self-normalizationResult of self-normalization

(M - M’)/2 vs. (A + A’)/2

Summary of normalizationSummary of normalization

— Reduces systematic (not random) effects— Makes it possible to compare several arrays

— Use logratios (MA-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

What is missing?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.

AcknowledgmentsAcknowledgments

Jean Yee Hwa Yang (UCB)

Sandrine Dudoit (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)

Reference: Yang et al (2002) Nucleic Acids Research 30, e15.

Some web sites:

Technical reports, talks, software etc.http://www.stat.berkeley.edu/users/terry/zarray/Html/

Statistical software R (“GNU’s S”) http://www.R-project.org/

Packages within R environment:-- SMA (statistics for microarray analysis) http://www.stat.berkeley.edu

/users/terry/zarray/Software/smacode.html--Spot http://www.cmis.csiro.au/iap/spot.htm