I have RNAseq data for three conditions (A, B, and C) with results from three different batches (PK, GB, and EG) and I am trying to apply batch correction using DeSeq2. I am intersted in contrasting all three condtions (i.e. A vs B, B vs C and A vs C) while taking the batch effect into account. My code is as follow:

# Assign condition and batch
(condition <- factor(c(rep("A", 3), rep("B", 3), rep("C", 3))))
(batch <- factor (c("PK","GB", "EG","PK","GB", "EG","PK","GB", "EG")))

# Analysis with DESeq2 ----------------------------------------------------

library(DESeq2)

# Create a coldata frame and instantiate the DESeqDataSet
(coldata <- data.frame(row.names=colnames(countdata), condition, batch))
dds <- DESeqDataSetFromMatrix(countData=countdata, colData=coldata, design=~batch + condition)

# Run the DESeq pipeline
dds <- DESeq(dds)

When I run this code and then do resutsNames(dds), I get the following:

[1] "Intercept"        "batch_GB_vs_EG"   "batch_PK_vs_EG"   "condition_B_vs_A" "condition_C_vs_A"

However, I am also interested in "conditionAvsC" and I am not sure why this is not being created by this design formula. Also, I am not sure why "batchPKvsGB" is not being created. Is there something wrong with my design formula?

Thanks for your help!

You can extract contrasts of interest using the contrast argument of results. Take a look at the help page:

?results

The answer as to why certain coefficients are listed involves how linear models are represented in R. You can take a look at course material about linear models, for example the course I taught with Rafael Irizarry on Edx has some online material about linear models.