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Joint analysis of the same effect of two treatments in RNA-seq data

Hi, I have RNA-seq data - two series of paired samples (two treatments), three biological replicates for each treatment (12 samples in total). I need to find gene expression changes associated with a phenotype (considered identical) that is induced by both treatments. I am less interested in treatment-specific changes. I could do separate analyses and search for the intersection, but why not to increase sensitivity by joint analysis? I used DESeq2 with a design formula ~replicate+phenotype on the all-sample series. Is this correct? Can large changes after one treatment "mask" no change after the second? If so, can this be prevented somehow?

rna-seq deseq2 linear model

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