Transcript Section 3 - Applying statistical Tests to Microarray Data

Applying statistical tests
to microarray data
Introduction to filtering
• Recall- Filtering is the process of deciding
which genes in a microarray experiment have
significantly varying expression across
conditions (and removing from gene
expression matrix those that don’t).
• So how do we decide whether a gene
varies significantly?:
– Hard problem & active area of research (1st use of
microarray only in mid-1990s); no fixed protocol for
analysis.
– Most initial studies simply demanded that intensity
ratios should exceed/fall short of a threshold, eg.
2-fold increase or decrease in intensity between
two conditions.
– More sophisticated approach- apply statistical tests,
such as those that we have just discussed.
Approaches to filtering
 xCy 5 
• ‘Old’ approach: if log 2 
  c, label the gene x
 xCy 3 
as interesting and keep it (where xCy5 is the
background-subtracted intensity of the red
dye on the spot corresponding to gene x, xCy3
the same for green and c is a threshold,
typically c=1)
– here we are comparing 2 samples on the same chip
– In the yeast experiments we discussed earlier- genes
were identified which had 2-fold increases/
decreases.
Approaches to filtering
• ‘Statistical approach’: Perform repeat
experiments- eg. 5 target samples
obtained from yeast grown under
identical conditions and 5 target
samples under a different condition and
perform eg. T test or ANOVA.
• We will go through some concrete
examples of application of statistical
techniques from last section soon, but
first
– we motivate this and
– discuss some choices that must be made
before applying filtering techniques.
Advantages of statistical
approach
• Performing replicate experiments reduces
variability in the summary statistics.
• Data from replicate experiments can be
analysed using formal statistical methods.
• This has the big advantage that you can
establish significance of estimates, ie. know
how confident you are that genes do not just
vary in their intensity values through random
effects or inconsistency in the arrays/ dyes,
but actually vary in their expression.
Issues in filtering
• Preprocessing: Do we use
– Logs or not
– Ratios or raw intensity measurements
– normalized data or not?
• Experiment design: Do we want to
– compare many samples to a reference and obtain
from these expression data which is ratios from that
reference
or
– compare samples of interest directly to each other?
• These issues do not appear to be fully
resolved in the literature. However we will
discuss preprocessing issues after a discussion
of how to apply the statistical tests from the
last section to filtering microarray data.
Design of experiments
• Main issue in design is to decide
which samples to compare on the
same slide.
• Commonly use reference design
for multiple slide comparisons
– ie. have a target sample which is
divided up to be used as “green
sample” on all of the arrays.
Design of experiments
Tests for differential gene
expression in
normal/mutant mice
• For now, assume that we are going to
consider
– log2 expression ratios
– reference design
• So we have a set of values in our gene
expression matrix with entries, Mij
which correspond to
 intensity gene i in test sample j 
log 2 

 intensity gene i in reference sample 
• [See handout]
Normalization & filtering
• Normalization: Identify & remove
sources of systematic variation in
measured intensities other than
differential expression, eg.
– different labelling efficiencies of dyes
– different amounts of RNA in the red and
green samples
• Necessary for within and between slides
comparisons of expression
• Filtering is generally to get rid of
‘random’ variation- use repeat
experiments to see how much a gene’s
expression varies anyway without
change in condition.
Self-self hybridization
• Need for normalization seen in self-self
hybridizations in which the same mRNA
sample is labelled red & green:
Ratios/ raw intensities
• A reason for using ratios is reverse transcriptional
bias- not all mRNAs reverse transcribe with the same
efficiency, so it is not possible to directly compare the
gene expression of two genes on an array.
• Reverse transcriptional bias doesn’t affect
comparison of the same gene between chips.
• But if we have a sufficiently sophisticated statistical
model and we have several arrays with different
conditions and several replicates of each experiment
(same conditions) then it may be possible to estimate
the component of differential intensity due to reverse
transcriptional bias and that due to different gene
expression- see Kerr et al (homework).
• Clearly have more data for estimation if consider red
and green measurements separately.
Logs versus
straightforward ratios
•
Whether we want to use log-transformed
data to perform our statistical analyses
depends on
1.
2.
•
•
On how close the intensity values/ log values are
to a normal distribution with constant variance for
whatever you wish to compare (usually a single
gene across conditions)
Whether factors that we wish to eliminate are
additive or multiplicative (see Kerr et al- homewk)
It is argued that log-transformed data is
closer to normal and that most unwanted
factors (eg. dye affinity) have multiplicative
effect.
Therefore log data is probably better.
Normalization versus not
• Some systematic errors (eg. dye affinity) can
be got rid of by normalization.
• Essentially it makes sense to do this before
filtering for interesting genes, if you cannot do
sufficiently many control replicates to estimate
those errors directly.
• Straightforward normalization saves you
from doing extra experiments eg. dyeswap to separate out dye effects from
genuine expression ratio changes.
Conclusions
• Filtering is the process of deciding
which genes are expressed at
significantly different levels across the
different conditions in your microarray
experiment and getting rid of the other
genes from your expression matrix
before you do other types of analysis
(eg. clustering).
• Old approach: select by demanding
log ratio of intensities exceed threshold.
• Statistical approach: use hypothesis
tests to determine significant variation.
Conclusions
• Can apply T test to work out if the
mean of data is same or different
between two conditions.
• Can apply ANOVA to work out if the
mean of data is same or different
across two or more conditions.
• There are several issues to consider
before applying these statistical
“filtering” techniques eg.
– Should you take logs of data first?
– Should you use raw data / ratios?
– Should you normalize the data first?
References
• Web-based lecture notes by Robert
Gentleman, Harvard
[http://biosun1.harvard.edu/~rgentlem/
Wshop/lect1b.pdf]