Hello,

My data consist of RNA counts  from 4  phenotypes  with biological replicates. The phenotypes are the combination of 2  genotypes R and A.  The four groups are  wild type, R, A and RA. 

I am looking for DE genes between groups. I am wondering what model is the best for these data: one factor with 4 levels + contrast or glm  (2 variables with interaction). 

Thank you for your help in advance.

Anita 

I agree with James. It appears you have a one-way layout with four groups. The simplest approach, then, would be to just parameterize the design matrix using these four groups. For example, if you have two replicates in each group, you can do:

grouping <- c("WT", "WT", "R", "R", "A", "A", "RA", "RA")
design <- model.matrix(~0+grouping)

This approach will be the easiest to interpret, as you can formulate the contrasts to compare between your groups.

If you want an genetic interaction model (e.g., to consider epistasis), then you might do something like this. I'll reuse the example above, and assume that R and A are mutations in separate genes. We can then do:

is.a <- c(0,0,0,0,1,1,1,1)
is.r <- c(0,0,1,1,0,0,1,1)
design <- model.matrix(~factor(is.a)*factor(is.r))

If you drop the fourth coefficient, you're testing the interaction between genotypes R and A, i.e., your null hypothesis is that the combined effect of genotype RA is equal to the sum of the individual effects for genotypes R and A. Rejection may indicate epistasis (where the combined effect is less than the predicted additive effect) or synergy (if the combined effect is greater).

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Edit: Mind you, the results from the second approach can be quite difficult to interpret. You'll need to look at the signs of the second and third coefficients to figure out what's going on. For example, if both the A and R mutations result in a 2-fold increase over WT, then a positive value for the RA interaction term might represent synergy. On the other hand, if both single mutations result in a 2-fold decrease against WT, then a positive value for the RA interaction term might represent epistasis (as additional decreases are not observed). One could also imagine a bunch of strange scenarios; for example, if A results in a 2-fold increase and R results in a 2-fold decrease, then a positive RA interaction term might represent some dominance effect of A over R.

Dear Anita,

Aaron has already given you a complete answer, but I think that you might not have got the main point yet, which is that it doesn't matter which design matrix you use, whether you define a factorial model or a one-way layout. They both give exactly the same result.

However I strongly, strongly, recommend that you use the one-way layout, because it is much easier to work with. The factorial model is only for statistical experts and even then only for particular purposes.

Thank you for your responses. I should have made it clear from the beginning . They are animal models of mutation(s).  Based on your responses I guess I perform one-way layout with four groups  since we are looking for DE genes between groups. 

Dear Dr.Smyth, 

Thank you very much for your answer.  It is completely clear now. 

Thanks once again.

Anita