Hi, could someone tell me if I am using the LRT method correctly?

I am analyzing RNA-seq data to study responses to infection. Our data includes 3 timepoints and comes from 4 different animals and we are only interested in changes in expression in response to infection, not differences among the individuals. From PCA plots we generated, it looks like there is a lot of variation among individuals, so I am thinking it might be best to use LRT instead of the Wald test. If I understand correctly, this would allow the model to account for the variation among individuals but focus the hypothesis testing on differences due to the response to infection over time. Is my logic here correct? And is the following code applying the LRT method correctly?

dds <- DESeqDataSetFromMatrix(countData = cts, colData = coldata, design= ~ animal + timepoint)
dds <- DESeq(dds, test = "LRT", reduced = ~ animal)
res <- results(dds, contrast = c("timepoint", "day3", "day0"))

Also, is the lfcShrink function ever applied to a DESeqDataSet object that was generated using the LRT? And if so, would applying lfcShrink to my data possibly be useful?

Take a look at the help in ?results, unless you specify test="Wald" then it is ignoring contrast for the p-value calculation. The p-value only cares about full and reduced (recommend to consult with a statistician on how to set up the two designs to perform an LRT).

If you want to compare two groups, I'd recommend using Wald tests (the default examples in the vignette).