[Bioc-devel] Appropriate linear model analysis for microarray time course comparison

[Stephen Park]

Dear Bioconductor users,

I'm looking to use linear modelling in Limma (all new to me) to identify
genes responding differently to infection in two different cattle breeds,
and would welcome advice on the correct model to use.

Our experiment took eight animals from each of two genetically distinct
breeds of cattle varying in susceptibility to a parasite and infected them
with the parasite. RNA was isolated pre-infection and at five time-points
post-infection and hybridised to two-colour oligo arrays. A common reference
RNA obtained by pooling samples from both breeds and all timepoints was
labelled with the second dye and hybridised to each array.

We're interested in seeing which genes respond differently to infection in
the different breeds. I believe the model we should be using is something
like 
Gene expression level = intercept + (breed effect) + (time effect) + (time *
breed interaction effect)

Assuming this is the appropriate model, I would like to correct for innate
pre-infection differences between breeds and effects due to infection that
are common to both breeds so that I can find those genes that respond
differently to infection between breeds, either at a given time-point or
across the entire timecourse. 

I'd like to know if I ought to set up a different design matrix from that
generated automatically using the modelMatrix function on my targets and
identifying the reference 

i.e. modelMatrix(targets,ref="Ref")

which generates

		T0_B1	T0_B2	...	T0_B2	...
T0_B1_A1	1	0	...	0	...
T0_B1_A2	1	0	...	0	...
...
T1_B1_A1	0	1	...	0	...
...
T0_B2_A9	0	0	...	1	...
....

where T=time, B=breed, A=animal


If this is OK, am I right in thinking that contrasts 
(T1_B1 - T0_B1) - (T1_B2 - T0_B2)
will remove both the breed component of the model for each breed (within
brackets) and the component due to infection common to both breeds, leaving
me with the interaction component?

Alternatively, should the design matrix contain additional coefficients to
account for time, breed and interaction components?

I'd be very grateful for any advice you could offer.

Thanks,

Stephen 

------------------------------------------------------   
Dr. Stephen Park   
Animal Genomics Lab   
School of Agriculture, Food Science & Vet. Medicine   
University College Dublin   
Dublin 4   
Ireland   
   
Tel: +353 (0)1 716 7767   
Fax: +353 (0)1 716 1103   
Mob: +353 (0)87 7666850   
E-mail: stephen.park at ucd.ie   
Web: http://animalgenomics.ucd.ie/sdepark/