DESeq2 model design + contrasts (not full rank)

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Hi,

I'm new to this forum and I got a question doe DESeq2 concerning model design and contrast, because my model design is not full ranked. I read multiple threads before and still did not understand how to proceed correctly.

I have 16 samples of single end Illumina reads. With 4 different treatments (group). Per treatment I have 4 biological replicates (indi). Unfortunately, the biological replicates are not evenly distributed across both used flowcells (flow). I am interested in the differences between the different treatments (group) and how to correctly get rid of the batch effect, if thats even possible. I followed the DESeq2 manual for this particular case as follows:

Here my meta matrix for the samples:

group indi flow 
  T1   I1    A 
  T1   I2    A 
  T1   I3    B   
  T1   I4    B    
  T2   I1    A    
  T2   I2    A    
  T2   I3    B    
  T2   I4    B    
  T3   I1    A    
  T3   I2    A    
  T3   I3    B    
  T3   I4    B    
  T4   I1    A    
  T4   I2    A    
  T4   I3    B    
  T4   I4    B

Like in the manual I first built my design matrix like so:

ds_txi <- DESeqDataSetFromTximport(txi = txi_salmon,
                                   colData = meta,
                                   design = ~ indi+group)

ds_txi$indi_n <- c("I1","I2","I1","I2","I1","I2","I1","I2","I1","I2","I1","I2","I1","I2","I1","I2")

meta$indi_n <- c("I1","I2","I1","I2","I1","I2","I1","I2","I1","I2","I1","I2","I1","I2","I1","I2")

meta$indi_n <- as.factor(meta$indi_n)
ds_txi$indi_n <- as.factor(ds_txi$indi_n)

ds_txi <- DESeqDataSetFromTximport(txi = txi_salmon,
                                   colData = meta,
                                   design = ~ flow + flow:indi_n + flow:group)

This workaroud should allow me, to get the differences between treatments within one batch:

dss <- DESeq(ds_txi)
res <- results(dss,contrast=list("flowA.groupT1","flowA.groupT2"), alpha= p_adjust_treshold,  lfcThreshold = L2FC_treshold)

Resulting in a new meta table:

 group indi flow indi_n
  T1	I1    A     I1
  T1	I2    A     I2
  T1	I3    B     I1
  T1	I4    B     I2
  T2	I1    A     I1
  T2	I2    A     I2
  T2	I3    B     I1
  T2	I4    B     I2
  T3	I1    A     I1
  T3	I2    A     I2
  T3	I3    B     I1
  T3	I4    B     I2
  T4	I1    A     I1
  T4	I2    A     I2
  T4	I3    B     I1
  T4	I4    B     I2

But how do I use the contrast, to get the differences between treatment T1 versus T2 with the elimination of the batch effect of the flowcells. Is this possible?

Can I maybe just do something like this:

res <- results(dss,contrast=list(c("flowA.groupT1","flowB.groupT1"),c("flowA.groupT2","flowB.groupT2")), alpha= p_adjust_treshold,  lfcThreshold = L2FC_treshold)