Hi everyone,

I know related questions about this topic has been asked, but I still have an important doubt about the difference of interpretation of DESeq2 if it is used with Wald test or with Likelihood Ratio Test . (I also asked few days ago a very complex question, but this time i can be more concise).

Provided that Wad test and LRT are two different tests, the p-value obtained has two different interpretations. However, in 2 condition's comparison they bring similar results. Furthermore, if instead of 1 v 1 comparison, we have more than 2 class, and we want to conduct pairwise comparisons, how will be the interpretation of the p-value be in case of LRT? Since the way of assigning p-value will depend on the comparison of the full model against the model without "condition" and "condition" will have 4 class, I cannot clearly see how can i interpret p-value, and if it is valid and appropriate to use LRT if pairwise comparison are wanted to be conducted. Will the interpretation in that case be bias because it is summed up as "if it is found to be significant in ANY class, then the p-value will be significant"? Will in that case work anyways as I am also considering Genes significant by log2foldchange threshold as well?

Thanks for your time, any comment on that will be super welcomed!

Eric.

The difference between a Wald test and an LRT is not specific to DESeq2. If you fit a full and reduced model and then compute a likelihood ratio test, you are testing if the full model fits the data better than the reduced model. It's an omnibus test that tells you that at least one coefficient is significant, much like an F-test in a conventional linear regression. If you get a small enough p-value then you have evidence that one or more coefficients are significant, but you don't know which. As you note, if you have only one coefficient, then the LRT and Wald will produce similar results.

The Wald tests are specific to a given contrast. You are specifically asking if there is evidence that the coefficient comparing two groups is larger than zero, and if so, you have some evidence that the two groups are different. I would imagine that the vast majority of people use Wald tests exclusively, as they are mostly wanting to make specific comparisons. And if they do an LRT first, they have to come back and do the Wald anyway, so why not just skip the first step?