[BioC] Help with limma design and contrasts matrices

[Gordon K Smyth]

This experiment has a deep problem in that there is no replication which replicates the RNA
extraction process.  Your replicates are just aliquots of a single RNA sample or, even worse,
aliquots of a labelled sample.  Hence there is no way to realistically estimate the array to array
variation against which treatment effects can be compared.

By comparison, the batch effect for C is not so important.  The experiment is balanced with
respect to A, B and C and the treatment differences, so any difference between C and the other two
replicates will cancel out.

I think that your only option is to rank genes and forget about format hypothesis testing.  I
guess that if I was analysing this data I would treat the labelled aliquots (A&B) as correlated
blocks and might include a fixed effect for the C vs A,B batch effect.  The block effect would be
included using duplicateCorrelation() with block=c(1,1,2,3,3,4,5,5,6 etc).  However this analysis
will over-state the true level of significance, by an unknown amount, because of the replication
problems already mentioned.  The ranking of the genes will be correct if (i) the measurement error
dominates or (ii) the higher level error components are proportion to the lower.

The section on "Special Designs" in the limma User's Guide at
http://bioinf.wehi.edu.au/limma/usersguide.pdf might be helpful.  You do not make it clear what
documentation you have read or whether you have already tried any possibilities.

Gordon

----------- original message ------------------
Fri Oct 22 06:51:08 CEST 2004
--------------------------------------------------------------------------------

Dear BioC List Members:

I have a data set that I would like to analyze with the limma package.  I am
having trouble figuring out how to make the design and contrasts matrices,
and I was hoping that someone would advise me.  The data set contains the
results from 18 Affymetrix hybridizations.  The table below explains the
experimental design:

  Sample	      RNA aliquot   Labeled sample aliquot	 Dose of Tx1
+/- Tx2
Untreated - A		1	 	   1
0		   -
Untreated - B		1		   2
0		   -
Untreated - C		2		  N/A
0		   -
Tx1 Dose1 - A		1		   1
Dose1	  	   -
Tx1 Dose1 - B		1		   2
Dose1	  	   -
Tx1 Dose1 - C		2		  N/A
Dose1	  	   -
Tx1 Dose2 - A		1		   1
Dose2	  	   -
Tx1 Dose2 - B		1		   2
Dose2	  	   -
Tx1 Dose2 - C		2		  N/A
Dose2	  	   -
Tx2 - A			1		   1
0		   +
Tx2 - B			1		   2
0		   +
Tx2 - C			2		  N/A
0		   +
Tx2 + Tx1 Dose1 - A	1		   1
Dose1	  	   +
Tx2 + Tx1 Dose1 - B	1		   2
Dose1	  	   +
Tx2 + Tx1 Dose1 - C	2		  N/A
Dose1	  	   +
Tx2 + Tx1 Dose2 - A	1		   1
Dose2	  	   +
Tx2 + Tx1 Dose2 - B	1		   2
Dose2	  	   +
Tx2 + Tx1 Dose2 - C	2		  N/A
Dose2	  	   +

Tx = treatment
N/A = not applicable

Note that two types of technical replicates were performed:  samples labeled
with "A" and "B" are replicates at the level of the labeled sample aliquot,
and samples labeled with "C" are replicates that were performed at the level
of the RNA aliquot.  In addition, the "C" replicates were done at a much
later date using a different lot of microarrays, a different lot of
reagents, and a different scanner.  It is not surprising that we are
observing a batch effect in the "C" replicates that is not removed even
after normalization.

Specific questions that I am hoping to have answered:
1. Can I use limma to remove the batch effect that I have observed with the
third replicate?
2. If so, could someone please help me with the creation of the design and
contrasts matrices?  The comparisons that I would like to make are the
following:
     Tx1 Dose1  vs.  Untreated
     Tx1 Dose2  vs.  Untreated
     Tx2  vs.  Untreated
     Tx2 + Tx1 Dose1  vs.  Untreated
     Tx2 + Tx1 Dose2  vs.  Untreated
3. If anyone has any other suggestions for methods other than limma that I
could use to analyze this data set, I would greatly appreciate hearing those
as well.

Thank you,

Jim

_____________________
Jim Breaux, Ph.D.
ViaLogy Corp.
2400 Lincoln Ave.
Altadena, CA 91001
Office: (626) 296-6473
jim.breaux at vialogy.com