Thanks for the answer, Michi.
I do get the differentially expression part, but still not how the time variable helps us in a reliable manner.
As far as I know, there is not a 'turning on' of e.g. cancer genes. E.g. a differentiation process goes through a daily, sometimes weekly process, turning on and off different genes all the time. I do not think that there is a linear phase from 'normal' to 'cancer', or is there? because I think the model is treating the problem like this