I would like advise about how to make a design for my experiment using DEseq2. In principle my question is straightforward, I'd simply like to find differentially expressed genes between two conditions. However, I've noticed that I have a large batch effect (I have two batches) and also large differences due to gender. Thus, I think I should include the two factors in my design:

> dds <- DESeqDataSetFromTximport(txi, sampleTable, ~BATCH + GENDER + Condition)
...
> resultsNames(dds)
[1] "Intercept"                                            "Batch_2_vs_1"
[3] "GENDER_MALE_vs_FEMALE"                                "Condition_T_vs_N"

Q1: if my question is which are the DE genes between conditions taking into account the batch and gender effects, which is the better option:

dds <-DESeq(dds)
res <- results(dds)
summary(res, name="Condition_T_vs_N")

or

dds_LRT <- DESeq(dds, test="LRT", reduced=~BATCH + GENDER)
res_LRT <- results(dds_LRT)
summary(res_LRT)

Q2: if I add an interaction term to the design, to which question am I answering?

dds <- DESeqDataSetFromTximport(txi, sampleTable, ~BATCH + GENDER + Condition:GENDER)

Many thanks for your comments, Cinta

The Wald test and the LRT should give similar (not exactly the same) results. Either is correct as you have it above.

The second design provides an baseline for sex and then two different condition effects, one for M and one for F.