Hello, I have bulk rna-seq data that consist of two conditions (control, treated) tested across three time points (day 0, 1 and 3).  We already observed by simple pair-wise (intra-condition) EdgeR that a big number of genes exhibit a change in expression between each two **adjacent** time points (day 1 vs 0 , then day 3 vs 1). We want to find significant differences INTER-conditions i.e genes whose change  is significantly different in Treated vs Control at day 1 vs 0 , then day 3 vs 1. How could I do this with EdgeR?  I have run EdgeR before but I do not know how to test both influence of treatment and time in one single design formula, and make sure that adjacent time points be tested (and NOT 3 vs 0 for exemple).  I have 3 biological replicates by time-point and condition.  Thanks for any help!
You could use a full-factorial design by combining the time variable and treatment variable like (simplified exampe):

    sample	treatment	time	factorial

    sample1	case	t0	case_t0
    sample2	control	t0	control_t0
    sample3	case	t1	case_t1
    sample4	control	t1	control_t1
    sample5	case	t3	case_t3
    sample6	control	t3	control_t3

and then design as `~factorial` followed by making the desired contrasts. Contrasts could be something like:

`(case_t1 - control_t1) - (case_t0 - control_t0)`

That would test for genes where the difference between case and control is differential between time points. For example a modest change between case and control at t0 that is much greater in t1 would could come out as significant.
This is called an interaction. See e.g. section 3.3 in the manual for more details and examples, https://www.bioconductor.org/packages/release/bioc/vignettes/edgeR/inst/doc/edgeRUsersGuide.pdf
