[BioC] Harsh results using limma!

Gordon Smyth smyth at wehi.edu.au
Fri Aug 13 13:56:05 CEST 2004

At 09:14 PM 13/08/2004, michael watson (IAH-C) wrote:
>Firstly, I think limma is excellent and use it a lot, but some recent
>results are a bit, erm, disappointing and I wondered if someone could
>explain them.
>Basic set up was a double dye-swap experiment (4 arrays) involving
>different animals, one infected with one type of bacterium and the other
>a different bacterium, compared to one another directly.  I used limma
>to analyse this and got a list of genes differentially regulated -
>THEN another replicate experiment was performed (so now I have 6 arrays,
>3 dye-swaps), and I re-did the analysis and my set of genes was
>completely different - but that's fine, we can put that down to
>biological variation.  We know limma likes genes which show consistent
>results across arrays, and when I looked at my data, I found that the
>genes in my original list were not consistent across all six arrays.  So
>I am reasonably happy about this.
>My question comes from looking at the top gene from my old list in the
>context of all six arrays.  Here are the normalised log ratios across
>all six arrays (ds indicates the dye-swap):
>Exp1            -5.27
>Exp1ds  6.29
>Exp2            -4.61
>Exp2ds  5.54
>Exp3            -0.2
>Exp3ds  0.2

Changes of +-0.2 are tiny and look like pure noise. So, you can have a gene 
for which only 2/3 of your mice show a difference. Statistical methods 
based on means and standard deviations will always judge this situation 
harshly. If you try an ordinary t-test rather than the limma method, you'll 
find that this gene would be judged much more harshly again.


>Not suprisingly, limma put this as the top gene when looking at the
>first four arrays.  However, when looking across all six arrays, limma
>places it at 230 in the list with a p-value of 0.11 (previously the
>p-value was 0.0004).
>So finally we get to my point/question - does this gene really "deserve"
>a p-value of 0.11 (ie not significant)?  In every case the dye-flips are
>the correct way round, it is only the magnitude of the log(ratio) which
>differs - and as we are talking about BIOLOGICAL variation here, don't
>we expect the magnitude to change?  If we are taking into account
>biological variation, surely we can't realistically expect consistent
>ratios across all replicate experiments??   Isn't limma being a little
>harsh here?  After all the average log ratio is -3.7 (taking into
>account the dye-flips) - and to me, experiment 3's results still support
>the idea of the gene being differentially expressed, and are even
>consistent within that biological replicate.
>Clearly I am looking at this data from a biologists point of view and
>not a statisticians.  But we are studying biology, not statistics, and I
>can't help feel I am missing out on something important here if I
>disregard this gene as not significantly differentially expressed (NB
>this is just the first example, there are many others).
>I should also add that there appears nothing strange about the arrays
>for Experiment 3 - the distribution of log(ratio) for those arrays is
>pretty much the same as the other four, so this is not an array-effect,
>it is an effect due to natural biological variation.
>Comments, questions, criticisms all welcome :-)

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