Retrieving and interpreting specific contrast results from an interaction experiment in DESeq2

Question

[fr]

I have an experiment with 2 different groups, and several different time points (for simplicity, let's say it is 2 time points), and I'm trying to find the best way to model both group and time effects. Note that time is a categorical variable.

# in
dds <- makeExampleDESeqDataSet(n=100,m=32)
dds$time <- factor(rep(rep(c("T1","T2"),each=8),2)) 
dds$group = factor(rep(rep(rep(c("Ct","Tr"),each=4),2),2))
design(dds) <- ~ time + group + time:group
dds <- DESeq(dds)

colData(dds)

# out
DataFrame with 32 rows and 4 columns
         condition    group sizeFactor replaceable
          <factor> <factor>  <numeric>   <logical>
sample1          A       Ct   1.080654        TRUE
sample2          A       Ct   1.009824        TRUE
sample3          A       Ct   1.035633        TRUE
sample4          A       Ct   0.953337        TRUE
sample5          A       Tr   1.060243        TRUE
...            ...      ...        ...         ...
sample28         B       Ct    1.22126        TRUE
sample29         B       Tr    1.04888        TRUE
sample30         B       Tr    1.09366        TRUE
sample31         B       Tr    1.11761        TRUE
sample32         B       Tr    1.23430        TRUE

We can also see the factors that were computed:

# in
resultsNames(dds)

# out
[1] "Intercept"      "group_Tr_vs_Ct" "time_T2_vs_T1"  "groupTr.timeT2"

Modeling these means we are doing

(Equation 1) y = alpha + beta1 time + beta2 group + beta3 group time

Or using the levels above, the following beta coefficients are defined:

(Equation 2) y = intercept + time_T2_vs_T1 time + group_Tr_vs_Ct group + groupTr.timeT2 group time

Given the reference levels are Ct and T1 (which I am assuming will be encoded as 0 by the model), I'd like to confirm if my interpretation of the following effects makes sense:

• Effect of Tr group (for T1):

    group_Tr_vs_Ct`
  

• Effect of T2 time (for Ct):

    time_T2_vs_T1`
  

• Effect of Tr group (for T2):

    group_Tr_vs_Ct + groupTr.timeT2`
  

• Effect of T2 time (for Ct and Tr), i.e. regardless of group or (Tr.T2 - Tr.T1) - (Ct.T2 - Ct.T1):

    (group_Tr_vs_Ct + groupTr.timeT2 - group_Tr_vs_Ct) - (time_T2_vs_T1 - 0) = groupTr.timeT2 - time_T2_vs_T1
  

• Effect of Tr group (for T1 + T2), i.e. regardless of time or (Tr.T2 - Ct.T2) - (Tr.T1 - Ct.T1):

    (group_Tr_vs_Ct + groupTr.timeT2 - time_T2_vs_T1) - (group_Tr_vs_Ct - 0) = groupTr.timeT2 - time_T2_vs_T1
  

I've been checking a few posts with similar questions that have been quite helpful (example, example and especially here), but I'm uncertain of the interpretation of more complex comparisons. So my questions are:

1. Does the interpretation of the effects above make sense?
2. How to retrieve the final contrast above?
3. Why is it that intercept is not considered for any of the above, in the documentation and posts? Given Equation 1, one would think the intercept would be added to each of the terms above.

Answer 1

[swbarnes2]

Using interactions is not the easiest way to do a lot of these comparisons. It's often simpler, and way more readable, to make a new column with both condition and group concatenated, and contrast with that.

http://bioconductor.org/packages/devel/bioc/vignettes/DESeq2/inst/doc/DESeq2.html#interactions

I think to get all the A's versus B's it's simpler to make your design ~ condition + group, and then just do A vs B.

[fr]

Thanks for your comment @swbarnes2, I agree with you that it becomes quite complex. My question is how to specify the contrasts for multiple columns in that situation? For the last example, and considering your approach, I would get coefficients for each of the four factors Ct.Tr1, Ct.Tr2, Tr.T1 and Tr.T2. I see it is straightforward to contrast a pair of these (e.g. c( group, Tr.T2, Tr.T1)), but how to find a condition contrast regardless of time in this case (i.e. (Tr.T2 - Ct.T2) - (Tr.T1 - Ct.T1))?

edit: would such conditions be given as a vector of numbers based on the order of resultsNames( )? For instance

# in
resultsNames(dds)

# out
[1] "Intercept"      "Ct.T1" "Ct.T2" "Tr.T1" "Tr.T2"

I could retrieve the appropriate contrasts as follows

# for Ct.T2 vs Ct.T1, or (Ct.T2 - Ct.T1):
results(dds, contrast=c(0,-1, 1, 0, 0))

# for group difference irrespective of time, i.e. (Tr.T2 - Ct.T2) - (Tr.T1 - Ct.T1):
results(dds, contrast=c(0,1, -1, -1, 1))

Would this make sense?