I have already discussed in the past this experimental design in which I deal with three factors (inoc: Bact or Mock; tissue: IN or OUT and hpi: 0,1,2,4 and 6h). Indeed, I am interested in the triple interaction, written on edgeR as:
((Bact.IN.Tx - MOCK.IN.Tx) – (Bact.IN.T0 - MOCK.IN.T0)) –
((Bact.OUT.Tx- MOCK.OUT.Tx) - (Bact.OUT.T0- MOCK.OUT.T0))
Now, I am aware that when all fitted counts on one side of the contrast are 0, then the contrast itself will be non-significant because of the indetermination of the zero on zero likelihood. I can circumvent this in the case of a double interaction. Let’s say I am looking at the double interaction between inoc and time. A given gene has 0 counts at T0, whatever Bact or Mock, but not at Tx. Hence, the double interaction is non-significant. However, I may say that, biologically, it makes sense to consider this gene in interaction if there is not inoc effect at T0 (obvious in this case) AND there is a significant inoc effect at Tx. Does this make sense to you?
Well, if that approach with the double sounded reasonable, when dealing with the triple interaction this may get trickier. The question would be: which contrasts should be considered to be taken separately at T0 and Tx when the statistical triple interaction gives non-significance because of the all-zeros at T0? The double interactions at Tx maybe?
Thanks a lot for your help.