Im running DESeq2 on RNAseq data and my experimental design has 2 factors, A and B. A is categorical and has 4 different levels, B is categorical and has 2 different levels

I ran DE with the following design: ~ A + B + A:B I am interested solely in the effect of B, I want to extract genes with a significant effect of B but NO EFFECT of the interaction A:B. I wonder if this is what would report a LRT with the reduced design ~ A + A:B or would it be better to check the output of the lfcShrink for the specific contrast of B I want to look at (i.e. do the significant genes in this output are significant only for the effect B but not for the other variables?)

Testing ~ A + B + A:B vs ~ A + A:B can be misleading in the following sense. The software, whatever it is, can code the A:B term differently depending on whether A and B are present in the model. E.g. if in ~ A + B + A:B design the rank of A:B term is k, then it can be greater than k in ~ A + A:B. It means in the latter design A:B is not "pure" interaction, but it also contains (some of) factor B main effect.