[BioC] limma: writing down the matrix in an almost (?) factorial design experiment

[Massimo Pinto]

Dear all,

I am writing in relation to some doubts that I have on the
implementation of a design matrix in a factorial design experiment. I
have tried to follow, religiously, the recommendations as at paragraph
23.10 of the R&Bioconductor monography, but have come up with several
afterthoughts.

Here is my experiment. Together with my colleagues, we have taken a human cell
culture, the human lymphoblastoid line TK6, and split it in two
laboratories with
different environmental conditions. Specifically, environmental
background ionizing radiation differs across the labs by a factor of
80. We are asking whether continuous cell culture under reduced
environmental background radiation renders cells more or less tolerant
to acute exposure to genotoxic or cytotoxic agents, a line of research
that the lab in which I am working has been busy for several years.
These two labs, and here is the first factor, are called "ISS" and
"LNGS" in what follows. We have
isolated total RNA samples (all instances contain 4 biological
replicates) from these two cell cultures after they have been
maintained in each laboratory for six months (corresponding to hundreds of cell
generations) since we hypothesized that it took several cell
generations before deviations at the level of the transcriptome may
reveal. Therefore, a second variable (factor) is time, and this has
the values "0" and "6 months".
As you imagine, we have a determination on RNA extracted from the "0"
time sample, which is the 'mother' cell
culture of both "ISS" and "LNGS" (6 months) cultures.
Additionally, to reveal any subtle differences between the two aged
cultures, we have exposed them to an acute dose of ionizing radiation,
which acts as a stressor. Our third variable/factor, therefore, is radiation
Dose, which takes the values "0" and "1 Gy". Accordingly, we have an
RNA extraction and a microarray determination at time = "0" and Dose =
"1Gy", to compare with responses  to radiation after six months in
each laboratory.
Following the BioC Monography, I have applied the model.matrix()
function obtaining
a design matrix with 8 columns. Two such columns, howewer, have no
sense to this particular experiment, since the variable Laboratory
("ISS", "LNGS")
has no meaning unless 6 months have elapsed, since their source is the
same culture, the "0" culture from which the experiment started.
Accordingly, I deleted - by hand - those two columns and obtained the
attached design matrix.
Do you think that this matrix is correct? We have applied it for some
time in our analysis and felt sure it was, but we have come across to
some odd results with respect to all analyses of 1Gy-irradiated
samples and we are now re-evaluating this matrix.

One anchoring point in our reasoning is what follows. The samples
exposed to 1Gy after six months in culture in both labs (ISS, LNGS)
are not directly derived from samples exposed to the same 1Gy dose at
time "0". Those would be survivors to the 1Gy dose delivered 6 months
before, which is not a question being addressed in this experiment
(though a reasonable question). Instead, samples exposed to 1Gy are
always derived from
their unirradiated counterparts at the same time and in the same
laboratory. For example, the LNGS, 6 months, 1Gy-irradiated sample is obtained
from exposure to 1Gy of the sample maintained for six months at LNGS,
again, not by maintaining for six months at LNGS the sample that had been
exposed to 1Gy dose at time "0".

I want to thank you very much in advance for the patience that you
have put in reading all down here and I hope to read any suggestions.

yours,

Massimo P.
-------------- next part --------------
> design
   (Intercept) Dose1Gy Ageing6mo Dose1Gy:Ageing6mo Ageing6mo:LabLNGS Dose1Gy:Ageing6mo:LabLNGS
1            1       0         0                 0                 0                         0
2            1       0         0                 0                 0                         0
3            1       0         0                 0                 0                         0
4            1       0         0                 0                 0                         0
5            1       1         0                 0                 0                         0
6            1       1         0                 0                 0                         0
7            1       1         0                 0                 0                         0
8            1       1         0                 0                 0                         0
9            1       0         1                 0                 0                         0
10           1       0         1                 0                 0                         0
11           1       0         1                 0                 0                         0
12           1       0         1                 0                 0                         0
13           1       1         1                 1                 0                         0
14           1       1         1                 1                 0                         0
15           1       1         1                 1                 0                         0
16           1       1         1                 1                 0                         0
17           1       0         1                 0                 1                         0
18           1       0         1                 0                 1                         0
19           1       0         1                 0                 1                         0
20           1       0         1                 0                 1                         0
21           1       1         1                 1                 1                         1
22           1       1         1                 1                 1                         1
23           1       1         1                 1                 1                         1
24           1       1         1                 1                 1                         1