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Microarray Basics. Part 2: Data normalization, data filtering, measuring variability. Log transformation of data. Most data bunched in lower left corner Variability increases with intensity. Data are spread more evenly Variability is more even. Simple global normalization

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microarray basics

Microarray Basics

Part 2: Data normalization, data filtering, measuring variability

log transformation of data
Log transformation of data

Most data bunched in lower

left corner

Variability increases with


Data are spread more evenly

Variability is more even


Simple global normalization

to try to fit the data

Slope does not equal 1 means one channel responds more at higher


Non zero intercept means one

channel is consistently brighter

Non straight line means non

linearity in intensity responses

of two channels


Linear regression of

Cy3 against Cy5

ma plots
MA plots

Regressing one channel against the other has the disadvantage

of treating the two sets of signals separately

Also suggested that the human eye has a harder time seeing

deviations from a diagonal line than a horizontal line

MA plots get around both these


Basically a rotation and rescaling of the data

A= (log2R + log2G)/2

X axis

M= log2R-log2G

Y axis


Scatter plot of intensities

MA plot of same data

non linear normalization
Non linear normalization

Normalization that takes into account intensity effects

Lowess or loess is the locally weighted polynomial regression

User defines the size of

bins used to calculate the

best fit line

Taken from Stekal (2003) Microarray Bioinformatics


Adjusted values for the x

axis (average intensity for

each feature) calculated using

the loess regression

Should now see the data

centred around 0 and

straight across the horizontal


spatial defects over the slide
Spatial defects over the slide
  • In some cases, you may notice a spatial bias of the two channels
  • May be a result of the slide not lying completely flat in the scanner
  • This will not be corrected by the methods discussed before
regressions for spatial bias
Regressions for spatial bias
  • Carry out normal loess regression but treat each subgrid as an entire array (block by block loess)
  • Corrects best for artifacts introduced by the pins, as opposed to artifacts of regions of the slide
    • Because each subgrid has relatively few spots, risk having a subgrid where a substantial proportion of spots are really differentially expressed- you will lose data if you apply a loess regression to that block
  • May also perform a 3-D loess- plot log ratio for each feature against its x and y coordinates and perform regression
between array normalization
Between array normalization
  • Previous manipulations help to correct for non-biological differences between channels on one array
  • In order to compare across arrays, also need to take into account technical variation between slides
  • Can start by visualizing the overall data as box plots
  • Looking at the distributions of the log ratios or the log intensities across arrays

Extremes of


Std Dev of


with mean

Extremes of


data scaling
Data Scaling
  • Makes mean of
  • distributions equal
  • Subtract mean
  • log ratio
  • from each log ratio
  • Mean of measurements
  • will be zero
data centering
Data Centering
  • Makes means and
  • standard deviations equal
  • Do as for scaling,
  • but also divide by the
  • mean standard deviation
  • Will have means intensity
  • measurements of zero,
  • standard deviations of 1
distribution normalization
Distribution normalization
  • Makes overall distributions identical between arrays
  • Centre arrays
  • For each array, order centered intensities from highest to lowest
  • Compute new distribution whose lowest value is average of all lowest values, and so on
  • Replace original data with new values for distribution
some key points
Some key points
  • Design the experiment based on the questions you want to ask
  • Look at your TIFF images
  • Look at the raw data with scatter plots and MA plots
  • Normalize within arrays to remove systematic variability between channels
  • Scale between arrays prior to comparing results in a data set
data filtering flagging of data
Data Filtering (flagging of data)
  • Can use data filtering to remove or flag features that one might consider to be unreliable
  • May base the filter on parameters such as individual intensity, average feature intensity, signal to noise ratio, standard deviation across a feature
using intensity filters
Using intensity filters
  • Object is to remove features that have measurements close to background levels- may see large ratios that reflect small changes in very small numbers
  • May want to set the filter as anything less than 2 times the standard deviation of the background

If using signal to noise ratio, keep in mind that the numbers

calculated by QuantArray are:

spot intensity/std dev of background

Should see that the

S/N ratio increase

at higher intensity

Taken from DNA Microarray Data Analysis (CSC) http://www.csc.fi/oppaat/siru/

removing outliers
Removing outliers
  • May want to simply remove outliers- some estimates are that the extreme ends of the distribution should be considered outliers and removed (0.3% at either end)
  • Also want to remove saturated values (in either channel)
filtering based on replicates
Filtering based on replicates
  • We expect to see

A1B2 B1 A2

= 1


  • Consider two replicates with dyes swapped

A1 and B2 B1 A2

  • We can calculate  and eliminate spots with the greatest uncertainty:  >2
replicate filtering
Replicate Filtering
  • Plot of the log
  • ratios of 2 replicates
  • Remove the data
  • in red based on
  • deviation of 2
  • st dev

Taken from Quakenbush (2002) Nat Genet Supp 32

z scores
  • The uncertainty in measurements increases as intensity decreases
  • Measurements close to the detection limit are the most uncertain
  • Can calculate an intensity-dependent Z-score that measures the ratio relative to the standard deviation in the data:

Z = log2(R/G)-/

intensity dependent z score
Intensity-dependent Z-score

Z > 2 is at the 95.5% confidence level


Small spots with high intensity penalized

Large spots may be print defects

Signal to noise ratio to define confidence

Degree of local background

Variation from average background

Defined as a threshold, not a continuous function

Approaches to using filtering algorithms


qsignal to noise

qlocal background

qbackground variability


qcom = composite quality score based on the continuous and

discrete functions listed above

Taken from Wang et al (2001) NAR 29: e75


qcom in relation to log ratio plot

Taken from Wang et al (2001) NAR 29: e75

measuring and quantifying variability
Measuring and Quantifying Variability
  • Variability may be measured:
    • Between replicate features on an array
    • Between two replicates of a sample on an array
    • Between two replicates of a sample on different arrays
    • Between different samples in a population
quantifying variables in microarray data
Quantifying variables in microarray data
  • Measured value for each feature is a combination of the true gene expression, and the sources of variation listed
  • Each component of variation will have its own distribution with a standard deviation which can be measured
variability between replicate features
Variability between replicate features
  • Requires that features are printed multiple times on a chip
  • Optimal if the features are not printed side by side
  • Need to calculate this variability separately for the 2 channels

Calculate mean of each replicate

Calculate the deviation from the mean for each replicate

Produce MA plots


If needed, can normalize

Diff (Rep1)

Calculate std dev of errors

Ch1 ave log intensity

If the error distribution

is ~ normal, you can

calculate v


Ch1 Difference

variability between channels
Variability between channels
  • Perform a self to self hybridization
  • Perform all the normalization procedures discussed earlier
  • The variation that is left is going to be due to random variability in measurement between the 2 channels
variability between arrays
Variability between arrays
  • Same samples on different arrays (or just use the common reference sample in a larger experiment)
  • Now are calculating both the variability due to the manufacturing of different arrays, and the variability of different hybridizations- these are confounded variables
why calculate these values
Why calculate these values?
  • Gives an estimate of comparability in quality between experiments
  • Gives an estimate of noise in the data relative to population variation
  • Can be used to track optimization of experiment
variability between individuals
Variability between individuals
  • This is the population variability number that is used in the power calculation
  • Generally will find that this is the largest source of variation and this is the one that will not be decreased by improving the experimental system
how to calculate population variability
How to calculate population variability
  • Calculate log ratio of each gene relative to the reference sample
  • Calculate the average log ratio for each gene across all samples
  • For each gene in each sample, subtract the log ratio from the average log ratio
  • Plot the distribution of deviations and calculate the standard deviation (and v)
part 3 data analysis
Part 3-Data Analysis
  • How to choose the interesting genes in your experiment
  • How to study relationships between groups of genes identified as interesting
  • Classification of samples