Microarray Basics

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Microarray Basics

• Part 2 Data normalization, data filtering,
  measuring variability

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Log transformation of data
Most data bunched in lower left
corner Variability increases with intensity
Data are spread more evenly Variability is more
even
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Simple global normalization to try to fit the data
Slope does not equal 1 means one channel responds
more at higher intensity
Non zero intercept means one channel is
consistently brighter
Non straight line means non linearity in
intensity responses of two channels
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Linear regression of Cy3 against Cy5
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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 issues
Basically a rotation and rescaling of the data
A (log2R log2G)/2
X axis
M log2R-log2G
Y axis
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Scatter plot of intensities
MA plot of same data
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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
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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 axis
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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

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Spatial Bias
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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

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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

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Extremes of distribution
Std Dev of distribution with mean
Extremes of distribution
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Data Scaling

• Makes mean of
• distributions equal
• Subtract mean
• log ratio
• from each log ratio
• Mean of measurements
• will be zero

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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

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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

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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

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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

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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

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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/
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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)

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Filtering based on replicates

• Consider two replicates with dyes swapped
• A1 and B2 B1 A2

• We can calculate ? and eliminate spots with the
  greatest uncertainty ? gt2

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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
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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)-?/?
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Intensity-dependent Z-score
Z gt 2 is at the 95.5 confidence level
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Approaches to using filtering algorithms
qsize
qsignal to noise
qlocal background
qbackground variability
qsaturated
qcom composite quality score based on the
continuous and discrete functions listed above
Taken from Wang et al (2001) NAR 29 e75
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qcom in relation to log ratio plot
Taken from Wang et al (2001) NAR 29 e75
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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

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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

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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

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Calculate mean of each replicate
Calculate the deviation from the mean for each
replicate
Produce MA plots
If needed, can normalize
0
Diff (Rep1)
Calculate std dev of errors
Ch1 ave log intensity
If the error distribution is normal, you
can calculate v
Frequency
Ch1 Difference
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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

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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

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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

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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

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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)

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http//genome-www5.stanford.edu/mged/normalization
.html
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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