Hi,

I am carrying out a multifactorial analysis on edgeR according to the experimental design shown at the end of this message (which I called design.all).

My reference genotype being "Col", I created the following model matrix and its subsequent glmFit model, in order to see for expression modulation according to genotype, time, as well as their interaction:

matrix.all<- model.matrix(~gtype*time, data=design.all)
colnames(matrix.all)
# [1]
"(Intercept)""gtypeOE1""gtypeR24""gtypeX710""timeT1.5""timeT3""timeT6"
"gtypeOE1:timeT1.5"

# [9] "gtypeR24:timeT1.5""gtypeX710:timeT1.5"
"gtypeOE1:timeT3""gtypeR24:timeT3""gtypeX710:timeT3""gtypeOE1:timeT6""
gtypeR24:timeT6""gtypeX710:timeT6"
fit.all <- glmFit (dge.all, matrix.all)

Following the 3.3.4 section of the user guide, I carried on as follows:

lrt.all.gtype <- glmLRT(fit.all, coef=2:4)
lrt.all.time<- glmLRT(fit.all, coef=5:7)
lrt.all.inter <- glmLRT(fit.all, coef=8:16)

Which leaves me with two questions that remain unclear to me: 1-Section 3.3.4. of the user guide states that coefficients 3 and 4 of the depicted example correspond to "the effects of the placebo at 1 hour and 2 hours". Why just placebo? Does not it include the "Drug". In my case, do coefficients 5 to 7 hence refer to "Col" at different times? Do they not include the other genotypes at the corresponding times? 2-Concerning the interaction, why does neither "Col" nor "T0" appear on the coefficients? Should not they be part of the comparison? Do I not need them to follow the difference between genotypes in time? Section 3.3.4.states that "(coef=5:6)...detects genes that respond differently to the drug, relative to the placebo, at either of the times (i.e.1h and 2h)

I thank you any help you could provide me on this. Thank you for your work.

Kind regards,
David Rengel

           gtype time
Col.T0.R2    Col   T0
Col.T0.R3    Col   T0
Col.T1.5.R1  Col T1.5
Col.T1.5.R2  Col T1.5
Col.T1.5.R3  Col T1.5
Col.T3.R1    Col   T3
Col.T3.R2    Col   T3
Col.T3.R3    Col   T3
Col.T6.R1    Col   T6
Col.T6.R2    Col   T6
Col.T6.R3    Col   T6
OE1.T0.R2    OE1   T0
OE1.T0.R3    OE1   T0
OE1.T1.5.R1  OE1 T1.5
OE1.T1.5.R2  OE1 T1.5
OE1.T1.5.R3  OE1 T1.5
OE1.T3.R1    OE1   T3
OE1.T3.R2    OE1   T3
OE1.T3.R3    OE1   T3
OE1.T6.R1    OE1   T6
OE1.T6.R2    OE1   T6
OE1.T6.R3    OE1   T6
R24.T0.R2    R24   T0
R24.T0.R3    R24   T0
R24.T1.5.R1  R24 T1.5
R24.T1.5.R2  R24 T1.5
R24.T1.5.R3  R24 T1.5
R24.T3.R1    R24   T3
R24.T3.R2    R24   T3
R24.T3.R3    R24   T3
R24.T6.R1    R24   T6
R24.T6.R2    R24   T6
R24.T6.R3    R24   T6
710.T0.R2   X710   T0
710.T0.R3   X710   T0
710.T1.5.R1 X710 T1.5
710.T1.5.R2 X710 T1.5
710.T1.5.R3 X710 T1.5
710.T3.R1   X710   T3
710.T3.R2   X710   T3
710.T3.R3   X710   T3
710.T6.R1   X710   T6
710.T6.R2   X710   T6
710.T6.R3   X710   T6

Dear David,

1-Section 3.3.4. of the user guide states that coefficients 3 and 4 of the depicted example correspond to "the effects of the placebo at 1 hour and 2 hours". Why just placebo? Does not it include the "Drug".

Because that is how factorial models are defined in R by default. The main effect for a factor is always relative to the treatment condition with all factors at their base levels. For the example in the User's Guide, the base levels are "Placebo" and "0h". So the Time main effect changes the Time while keeping Drug at the Placebo level. And the Drug effect changes the Drug while keeping Time at the 0h level.

In my case, do coefficients 5 to 7 hence refer to "Col" at different times? Do they not include the other genotypes at the corresponding times? 2-Concerning the interaction, why does neither "Col" nor "T0" appear on the coefficients?

Because they are the base levels, and all coefficients are relative to them.

Should not they be part of the comparison?

Well, it depends on what question you want to answer.

Do I not need them to follow the difference between genotypes in time? Section 3.3.4.states that "(coef=5:6)...detects genes that respond differently to the drug, relative to the placebo, at either of the times (i.e.1h and 2h)

I am a bit unclear as to what questions you are trying to answer about your data. I don't want to give a long tutorial on factorial models, because model.matrix() is a part of the standard installation of R rather than part of edgeR and because I don't recommend factorial models.

If you are not familiar with factorial models in R, then it better not to use them. (Actually I don't recommend factorial models for genomic experiments, even if you are an expert on them.)

You have a 4x4 factorial model with 3 replicates per combination. I recommend that you setup a single factor representing all 16 possible conditions, then use contrasts to make the comparisons you want to make. This approach is outlined in Section 3.3.1 of the User's Guide. This gives identical results to the factorial model, but allows you to make the comparisons you want to make in a more explicit way, so that you actually know what you are testing.

Best wishes
Gordon