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:: Microarray analysis ::. Data pre-processing Normalization Molecular diagnosis Statistical classification. Florian Markowetz florian@genomics.princeton.edu. From experiment to data. Raw data are not mRNA concentrations. tissue contamination RNA degradation amplification efficiency

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microarray analysis

:: Microarray analysis ::

Data pre-processing


Molecular diagnosis

Statistical classification

Florian Markowetz


raw data are not mrna concentrations
Raw data are not mRNA concentrations

tissue contamination

RNA degradation

amplification efficiency

reverse transcription efficiency

Hybridization efficiency and specificity

clone identification and mapping

PCR yield, contamination

  • spotting efficiency
  • DNA support binding
  • other array manufacturing related issues
  • image segmentation
  • signal quantification
  • “background” correction
quality control noise and reliable signal
Quality control: Noise and reliable signal

Probe level

Array level

Gene level

Arrays 1 ... n

  • Probe level: quality of the expression measurement of one spot on one particular array
  • Array level: quality of the expression measurement on one particular glass slide
  • Gene level: quality of the expression measurement of one probe across all arrays
probe level quality control
Probe-level quality control
  • Individual spots printed on the slide
  • Sources:
    • faulty printing, uneven distribution, contamination with debris, magnitude of signal relative to noise, poorly measured spots;
  • Visual inspection:
    • hairs, dust, scratches, air bubbles, dark regions, regions with haze
  • Spot quality:
    • Brightness: foreground/background ratio
    • Uniformity: variation in pixel intensities and ratios of intensities within a spot
    • Morphology: area, perimeter, circularity.
    • Spot Size: number of foreground pixels
  • Action:
    • set measurements to NA (missing values)
    • local normalization procedures which account for regional idiosyncrasies.
    • use weights for measurements to indicate reliability in later analysis.
spot identification
Spot identification



Individual spots are recognized, size and shape might be adjusted per spot (automatically fine adjustments by hand).

Additional manual flagging of bad (X) or non-present (NA) spots

poor spot quality

good spot quality

Different Spot identification methods: Fixed circles, circles with variable size, arbitrary spot shape (morphological opening)

spot identification7
Spot identification
  • The signal of the spots is quantified.

Histogram of pixel intensities of a single spot


Mean / Median/ Mode/ 75% quantile

local background
Local background




array level quality control
Array level quality control
  • Problems:
    • array fabrication defect
    • problem with RNA extraction
    • failed labeling reaction
    • poor hybridization conditions
    • faulty scanner
  • Quality measures:
    • Percentage of spots with no signal (~30% excluded spots)
    • Range of intensities
    • (Av. Foreground)/(Av. Background) > 3 in both channels
    • Distribution of spot signal area
    • Amount of adjustment needed: signals have to substantially changed to make slides comparable.
gene level quality control
Gene-level quality control
  • Poor hybridization in the reference channel may introduce bias on the fold-change
  • Some probes will not hybridize well to the target RNA
  • Printing problems: such that all spots of a given inventory well have poor quality.

Gene g

  • A well may be of bad quality – contamination
  • Genes with a consistently low signal in the reference channel are suspicious
gene expression data
Gene expression data

mRNA Samples

sample1 sample2 sample3 sample4 sample5 …

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 ...


gene-expression level or ratio for gene i in mRNA sample j

Log2(red intensity / green intensity)

M =

Function (PM, MM) of MAS, dchip or RMA

average: log2(red intensity), log2(green intensity)

A =

Function (PM, MM) of MAS, dchip or RMA



Data (log scale)

Message: look at your data on log-scale!

ma plot
MA Plot

M = log2(R/G)

A = 1/2 log2(RG)

median centering
Median centering

One of the simplest strategies is to bring all „centers“ of the array data to the same level.

Assumption: the majority of genes are un-changed between conditions.

Median is more robust to outliers than the mean.

Divide all expression measurements of each array by the Median.

Log Signal, centered at 0

problem of median centering
Problem of median-centering

Scatterplot of log-Signals after Median-centering

M-A Plot of the same data

Log Red

M = Log Red -Log Green

Log Green

A = (Log Green + Log Red) / 2

Median-Centering is a global Method. It does not adjust for local effects, intensity dependent effects, print-tip effects, etc.

lowess normalization
Lowess normalization

M = Log Red -Log Green

A = (Log Green + Log Red) / 2

Local estimate

Use the estimate to bend

the banana straight

summary i
Summary I
  • Raw data are not mRNA concentrations
  • We need to check data quality on different levels
    • Probe level
    • Array level (all probes on one array)
    • Gene level (one gene on many arrays)
  • Always log your data
  • Normalize your data to avoid systematic (non-biological) effects
  • Lowess normalization straightens banana
from data to knowledge
From data to knowledge

mRNA Samples

sample1 sample2 sample3 sample4 sample5 …

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 ...


Ok, now we made sure that our data is of high quality and systematic, non-biological effects are removed.

The result is a gene expression matrix

Is that already a result? No! It’s just data, not knowledge.

We need to use this data to answer a scientific question.

supervised analysis
Supervised analysis

= learning from examples, classification

  • We have already seen groups of healthy and sick people. Now let’s diagnose the next person walking into the hospital.
  • We know that these genes have function X (and these others don’t). Let’s find more genes with function X.
  • We know many gene-pairs that are functionally related (and many more that are not). Let’s extend the number of known related gene pairs.

Known structure in the data needs to be generalized to new data.

un supervised analysis
Un-supervised analysis

= clustering

  • Are there groups of genes that behave similarly in all conditions?
  • Disease X is very heterogeneous. Can we identify more specific sub-classes for more targeted treatment?

No structure is known. We first need to find it. Exploratory analysis.

supervised analysis21
Supervised analysis

Calvin, I still don’t know the difference between cats and dogs …

Oh, now I get it!!

Don’t worry!

I’ll show you once more:

Class 1: cats

Class 2: dogs

un supervised analysis22
Un-supervised analysis

Calvin, I still don’t know the difference between cats and dogs …

I don’t know it either.

Let’s try to figure it out together …

supervised analysis setup
Supervised analysis: setup
  • Training set
    • Data: microarrays
    • Labels: for each one we know if it falls into our class of interest or not (binary classification)
  • New data (test data)
    • Data for which we don’t have labels.
    • Eg. Genes without known function
  • Goal: Generalization ability
    • Build a classifier from the training data that is good at predicting the right class for the new data.
one microarray one dot
One microarray, one dot

Think of a space with #genes dimensions (yes, it’s hard for more than 3).

Each microarray corresponds to a point in this space.

If gene expression is similar under some conditions, the points will be close to each other.

If gene expression overall is very different, the points will be far away.

Expression of gene 2

Expression of gene 1

support vector machines
Support Vector Machines

Maximal margin

separating hyperplane

Datapoints closest

to separating


= support vectors

how well did we do
How well did we do?

Training error: how well do we do on the data we trained the classifier on?

But how well will we do in the future, on new data?

Test error: How well does the classifier generalize?

Same classifier (= line)

New data from same classes

The classifier will usually perform worse than before:

Test error > training error

cross validation

Training error

Train classifier and test it

Test error



K-fold Cross-validation




Step 1.

Here for





Step 2.




Step 3.

summary ii
Summary II
  • Supervised and un-supervised learning

… are needed everywhere in biology and medicine

  • Microarrays = points in high-dimensional spaces
  • Classifiers = lines (hyperplanes) in these spaces
  • Support Vector Machines use maximal margin hyperplanes as classifiers
  • Classifier performance: Test error > training error
  • Cross-validation is the right way to evaluate classifier performance

Experimental Cycle

Biological question (hypothesis-driven or explorative)

To call in the statistician after the experiment is done may be no more than asking him to perform a post-mortem examination:

He may be able to say what the experiment died of.

Ronald Fisher

Experimental design


Microarray experiment



Image analysis









Biological verification

and interpretation


Terry Speed, „Statistical Analysis of Gene Expression Microarray Data”. Chapman & Hall/CRC

David W. Mount, „Bioinformatics“, Cold Spring Harbor

Giovanni Parmigani et al, „The Analysis of Gene Expression Data“, Springer

Gentleman, Carey, Huber, “Bioinformatics and Computational Biology Solutions Using R and Bioconductor”, Springer

Pierre Baldi & G. Wesley Hatfield, „DNA Microarrays and Gene Expression”, Cambridge

and how do i analyze my own data
And how do I analyze my own data?
  • www.r-project.org
  • www.bioconductor.org
  • Open source
  • Free
  • Easy installation
  • Helpful community
  • High quality standards
  • Regularly maintained and updated
  • Tons of documentation
  • Every package comes with example vignettes to walk you through standard tasks.
  • I ‘borrowed’ slides from:

Tim Beissbarth, Achim Tresch, Wolfgang Huber, Ulrich Mansmann, Terry Speed, Jean Yang, Benedikt Brors, Anja von Heydebreck, Rainer König

  • More info on microarray analysis, lectures, tutorials: