I'm currently analysing an microarray experiment including 2 genotype, 2 treatment, 2 time point and 2 expression levels with three biological replicates (48 samples). When I treat each factor independently, I could find gene affacted by each factor separately. Since my result indicated one factor is strongly afffected by the other, now I would like to also check the interaction between each factor pair on gene expression. But I don't know how to build model in Limma to solve my problem. Anyone could help? Thanks.

Bing

Ph.D

Wageningen University

Hi Aaron,

I would like to know your interpretation for the gene list produced from the formula (T_Cor_D24 - T_Water_D24) - (T_Cor_ND24 - T_Water_ND24). Basically is the interaction between the Cor/water effect and D/ND effect at 24 hours. This fomular produced two gene lists up- (1) and down (-1) regulated. I explained as the positively and negative effect of Cor on the difference between D and ND. Does that mean the up list is the genes that increased the difference between D and ND by Cor and the down list is the genes reduced the difference between D and ND by Cor? what's your explanation. Thanks

Bing

Each of the contrasts you've specified will test for a differential effect between P and T, i.e., whether the effect of treatment/time/whatever for factor P is the same as that for factor T. This represents the interaction between the P/T factor and another factor, depending on the exact contrast you're looking at.

If you want to test for a three-factor interaction, that's a bit more complicated. To illustrate, let's use an example:

A <- rep(c("A", "a"), each=4)
B <- rep(c("B", "b"), 4)
E <- rep(rep(c("E", "e"), each=2), 2)
grouping <- factor(paste(A, B, E, sep="."))
design <- model.matrix(~0+grouping)
colnames(design) <- levels(grouping)

Let's treat the lower case as the "baseline", and the upper case as the "treatment" for each factor. Assume that we want to find the three-way interaction effect in the sample with all three treatments, i.e., A.B.E. This is done with:

con <- makeContrasts(A.B.E - a.b.e # effect of triple treatment
     - ((A.b.e - a.b.e) + (a.B.e - a.b.e) + (a.b.E - a.b.e)) # "main effects"
     - (((A.B.e - A.b.e) - (a.B.e - a.b.e))   # interaction effect between A and B
      + ((A.b.E - A.b.e) - (a.b.E - a.b.e))   # interaction effect between A and E
      + ((a.B.E - a.B.e) - (a.b.E - a.b.e))), # interaction effect between B and E
     levels=design)

The null hypothesis here is that the effect of the triple treatment is equal to the sum of the main effects of the individual treatments and the interaction effects of the pairwise treatments.

Hi Aaron,

Thanks for this. Indeed the contrast I made is to look at P/T interactions. I also have the interactions contrast for other factors. However, this way of contrast will only compare the sample with the interacted factors in the different level of the third factors separately. for example

(P_Water_D6-P_Water_ND6)-(T_Water_D6-T_Water_ND6): for looking at P/T interaction at 6 hours in water

(P_Water_D24-P_Water_ND24)-(T_Water_D24-T_Water_ND24): for looking at P/T interaction at 24 hours in water

While in comparison of 4 way anova, it will take into account of all the P sample and T samples regardless of other factors for P/T interactions.

I'm not so sure which is the best way to look for P/T interaction. Do you recommend multi-factor ANOVA (MANOVA) for this specific question? and what is the best tool for this. Thanks.

Cheers

Bing