DESeq2: likelihood ratio test

Hi,

I just want to make sure that I understand the LRT correctly. My purpose is to test if Gender is a confounder in gene expressions across diseases (control, disease1, disease2). I have this code:

neu.dds <- DESeqDataSetFromMatrix(countData = neuron.counts.data,
  colData = neuron.mapping.data,
  design = ~ Gender+Disease)
neu.dds.LRT <- DESeq(neu.dds,betaPrior=FALSE, test="LRT", full=~Gender+Disease, reduced=~Gender)

The LRT test the full vs reduced model.  So, the null model is reduce and the alternative model is full.  When a gene has a p-value < 0.05, we conclude the gene expression changes at some disease in the presence of gender, while others only affected by Gender only???

Also, since my disease has 3 levels, I noticed that the p-values for disease2 vs control are the same as for disease1 vs control for the LRT, but not the same for the disease2 vs disease1. Specifically, I have 80 genes with padj< 0.05 for D1 vs Con and D2 vs Con, but have 139 genes with padj <0.05 for D2 vs D1.  Why is this the case?

Thanks,
Quynh
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