Hi,

I am dealing with continuous covariate in my design matrix as well. I am using edgeR, I have created a following design matrix:

design1 <- model.matrix(~groups+groups:age)

where there are four different groups. 

So, colname(design1) would give:

(Intercept) group2 group3 group4 group1:age group2:age group3:age group4:age

If I were to do a comparison such as: lrt <- glmLRT(fit, coef=2), what am I comparing? Am I merely comparing group1 and group2? From what reading through forum questions/answers, it seems like this comparison is affected by the age covariate included in the design matrix.

But if I were to create a design matrix: design2 <- model.matrix(~group), and perform the same comparison between group1 and group2, would that give a same result?

Also, using design1 again, if I were to compare group2:age with intercept (coef=6), would that be testing for age effect on group2? And comparing group1:age and group2:age would be testing for the differences in age effect between group1 and group2?

Lastly, if I were to include another continuous variable(s) as covariates into the design matrix such that:

design3 <- model.matrix(~groups+groups:age+continuous1+continuous2)

in order to adjust for the covariates continuous1 and continuous2, other than being adjusted for them, would they affect how the above comparisons turn out.

My apologies for asking a lot of questions. I am quite confused by the usage of design matrix, especially with continuous variables interaction. If there is any confusion regarding the questions I ask, please tell me. Thank you.

Let's have a look at what design1 is actually doing. For each gene in each group, imagine fitting a line to the log-expression values against the age for all samples of that group. The gradient of this line for group X is the groupX:age term, while the intercept of this line is (Intercept) for group 1 and (Intercept) + groupX for every other group. So, if you drop the second coefficient, you'll be testing for the same intercept between groups 1 and 2, i.e., your null hypothesis is that groups 1 and 2 have the same expression at an age of zero. This doesn't really seem very sensible to me - babies aside, would the behaviour of zero-age samples be particularly interesting? The more relevant comparisons would be:

con1 <- makeContrasts(group1_age - group2_age, levels=design1)
con2 <- makeContrasts(group1_age - group2_age, group2, levels=design1)

... assuming that you've replaced the colons with underscores in colnames(design1). The first contrast tests for a differential response to age between groups 1 and 2, while the second contrast tests for any differences in expression between groups 1 and 2 (as the first contrast will not reject the null hypothesis if the gradient is the same between groups).

Now, for design2, the interpretation of the coefficients is different. The (Intercept) will represent the average log-expression in group 1, while each groupX coefficient will represent the log-fold change of group X over group 1. Dropping coef=2 will do a straight-up, no-frills test for any DE between groups 1 and 2. This is unlikely to give the same result as coef=2 with design1; for starters, you're not accounting for age, which means that there's no comparable concept of "age of zero". The most similar contrast would probably be con2, but that is still likely to be different because your variances will change with the different design matrices.

Moving on; if you drop coef=6, then yes, you will be testing for the age effect in group 2. Similarly, the comparison between group1:age and group2:age (as done in con1) will test for a differential age response between groups.

Finally, it's hard to say how the addition of continuous variables will affect the results in design3. In general, I'd expect a decrease in the sample variance as you're increasing the complexity of the model to account for more sources of variability. However, this will come at the cost of a decrease in power, as you're using up more information to estimate the corresponding coefficients. Whether this is offset by the smaller variance depends on your data, so if you want to know the effect, you'll have to try it with and without the covariates. The more concerning issue is if either of the continuous covariates are confounded with age; if so, then this will also compromise detection of the age response, as any genuine increase in expression due to age can be absorbed into the covariate's coefficient and lost.