Hi, with this post I want to make sure whether I do things correctly.

I am analyzing RNA-Seq data with the following experimental design - a time series study where each sample was grown with and without albumin, and in the presence/absence of host cells. My colData looks like:

Time    Albumin Interaction
0h  No_albumin  Host
0h  With_albumin    Host
0h  No_albumin  Plastic
0h  With_albumin    Plastic
24h No_albumin  Host
24h With_albumin    Host
24h No_albumin  Plastic
24h With_albumin    Plastic
3h  No_albumin  Host
3h  With_albumin    Host
3h  No_albumin  Plastic
3h  With_albumin    Plastic
0h  No_albumin  Host
0h  With_albumin    Host
0h  No_albumin  Plastic
0h  With_albumin    Plastic
24h No_albumin  Host
24h With_albumin    Host
24h No_albumin  Plastic
24h With_albumin    Plastic
3h  No_albumin  Host
3h  With_albumin    Host
3h  No_albumin  Plastic
3h  With_albumin    Plastic
0h  No_albumin  Host
0h  With_albumin    Host
0h  No_albumin  Plastic
0h  With_albumin    Plastic
24h No_albumin  Host
24h With_albumin    Host
24h No_albumin  Plastic
24h With_albumin    Plastic
3h  No_albumin  Host
3h  With_albumin    Host
3h  No_albumin  Plastic
3h  With_albumin    Plastic

I would like to get the DE genes for the following comparisons:

1. For each time point, the DE genes due to presence of albumin, controlling for the effect of "Interaction"
2. For each time point, DE genes due to the "Interaction", controlling for the effect of albumin.
3. DE genes across time points (3h vs 0h, and 24h vs 0h), controlling for both the effect of "Interaction" and presence of albumin.

For 1., I concatenate Albumin and Time columns, run DESeq2 controlling for Interaction, and get the comparisons using contrasts:

pre_dds <- DESeqDataSetFromMatrix(yeast, colData, design = ~Interaction+Time_Alb)
dds <- DESeq(pre_dds)
resultsNames(dds)
results(dds, contrast=c("Time_Alb", "0h_With_albumin", "0h_No_albumin"))

Do I interpret it correctly the the last line retrieves the fold changes due to presence of albumin at 0 time point, controlling for the effect of Interaction?

For 2., I do the same but concatenating Time and Interaction columns, and controlling for Albumin column.

For 3., I concatenate Albumin and Interaction columns, and use this new column as a blocking factor in formula design i.e. ~Albumin_Interaction+Time. Then I retrieve time point comparisons with contrasts.

I would greatly appreciate if someone can comment whether these approaches are adequate for the comparisons I want to get, Thanks

For questions about how to design the statistical analysis and interpret the results, I recommend collaborating or consulting with a statistician or someone familiar with linear models in R. I have to reserve my time on the support site for software related questions.