Hi all,

I'm working with a multifactorial RNA-seq experiment and analyzing it using DESeq2. I have four factors:

• genotype
• treatment1
• treatment2
• time

I'd like to use the Likelihood Ratio Test (LRT) framework in DESeq2 to evaluate the significance of:

1. treatment1 (main effect)
2. treatment2 (main effect)
3. treatment1:treatment2 (their interaction)

According to the DESeq2 documentation, for two factors (batch, condition), the LRT is used like this:

# Testing interaction:
full:    ~ batch + condition + batch:condition
reduced: ~ batch + condition

# Testing one factor:
full:    ~ batch + condition
reduced: ~ batch

Full model in my case:

I start from a full factorial model with all interactions up to 4-way:

design(dds) <- ~ genotype + treatment1 + treatment2 + time +
                genotype:treatment1 + genotype:treatment2 + genotype:time +
                treatment1:treatment2 + treatment1:time + treatment2:time +
                genotype:treatment1:treatment2 + genotype:treatment1:time +
                genotype:treatment2:time + treatment1:treatment2:time +
                genotype:treatment1:treatment2:time

My questions:

What would the correct reduced models be for testing the following with DESeq() and test = "LRT"?

1. Testing treatment1 (main effect only):

Full: same as above Reduced: remove treatment1 and all interaction terms that include it

reduced <- ~ genotype + treatment2 + time +
            genotype:treatment2 + genotype:time + treatment2:time +
            genotype:treatment2:time

2. Testing treatment2 (main effect only):

Full: same as above Reduced: remove treatment2 and all interaction terms that include it

reduced <- ~ genotype + treatment1 + time +
            genotype:treatment1 + genotype:time + treatment1:time +
            genotype:treatment1:time

3. Testing treatment1:treatment2 (interaction only):

Full: same as above Reduced: remove treatment1:treatment2 and all higher-order interactions that include this term (i.e., 3-way and 4-way interactions that contain both treatment1 and treatment2)

reduced <- ~ genotype + treatment1 + treatment2 + time +
            genotype:treatment1 + genotype:treatment2 + genotype:time +
            treatment1:time + treatment2:time +
            genotype:treatment1:time + genotype:treatment2:time

Would appreciate any feedback on whether this is the correct approach, or if there are caveats I should consider

Thanks!

The reduced model depends on what you want to subject to null hypothesis testing. One idea would be to have ChatGPT explain what each full and reduced model LRT implies.