Hi, I am a bit confused with what design matrix to use to test for differential expression. I've used two examples of design matrix for time course analyzis with many time points of two conditions, and I get different results when using voom. For design1 I got 884 genes with adjusted p-value <0.05 while for design 2 I got 146 genes with adjusted p-value<0.05. The code I used was: 

> counts <- read.delim("counts.txt", row.names=1, stringsAsFactors=FALSE, header=TRUE)
> y <- DGEList(counts=counts)
> A <- aveLogCPM(y)
> y2 <- y[A>1,]
> y2 <- calcNormFactors(y2)
> library(splines)
> targets <- read.delim("targets.txt",header=TRUE)
> X <- ns(targets$Time, df=5)
> Group <- factor(targets$Group)
> design1 <- model.matrix(~Group+Group:X)
> v1 <- voom(y2, design1, plot=TRUE)
> fit1 <- lmFit(v1, design1)
> fit1 <- eBayes(fit1)
> toptable_voomd1 <-topTable(fit1, coef=ncol(design1), number=30000, adjust="BH")
> write.table(toptable_voomd1, file="DE voom timecourse different trend design1.txt", sep="\t", quote=FALSE)

> design2 <- model.matrix(~Group*X)
> v2 <- voom(y2, design2, plot=TRUE)
> fit2 <- lmFit(v2, design2)
> fit2 <- eBayes(fit2)
> toptable_voomd2 <-topTable(fit2, coef=ncol(design2), number=30000, adjust="BH")
> write.table(toptable_voomd2, file="DE voom timecourse different trend design2.txt", sep="\t", quote=FALSE)

Design1 column names are:

[1] "X.Intercept."    "GroupControl"    "GroupAA.X1"      "GroupControl.X1" "GroupAA.X2"      "GroupControl.X2"
[7] "GroupAA.X3"      "GroupControl.X3" "GroupAA.X4"      "GroupControl.X4" "GroupAA.X5"      "GroupControl.X5"

Design2 column names are:

 [1] "X.Intercept."    "GroupControl"    "X1"              "X2"              "X3"              "X4"             
 [7] "X5"              "GroupControl.X1" "GroupControl.X2" "GroupControl.X3" "GroupControl.X4" "GroupControl.X5"

Is the result in voom showing different trends in time between group1 and group 2?

Which design is more suitable to find the different trends in time?

Below are the top ten genes obtained for each design with voom, and the targets description:

Thank you, 

Camila 

Despite having the same name, the last coefficients of your two design matrices represent different things.

Let's have a look at the coefficients of design1:

• The intercept, representing the log-expression in the AA group.
• The GroupControl coefficient, representing the log-fold change in Control over AA.
• The GroupAA:X1-X5 coefficients, representing the spline fit to the AA group against time.
• The GroupControl:X1-X5 coefficients, representing the spline fit to the Control group against time.

Now, let's have a look at the coefficients of design2:

• The intercept and GroupControl coefficient, same interpretation as before.
• The X1-X5 coefficients, representing the spline fit to the AA group against time. This is despite the fact that they do not have "AA" in their column names, which stresses the need to actually look at the design matrix.
• The GroupControl:X1-X5 coefficients, which now represent the difference in the spline fits between the AA and Control groups. This can be interpreted as the effect of time on the log-fold change between groups.

So, the GroupControlX5 coefficient does not have the same meaning between design1 and design2. In the first design, it represents (part of) the effect of time on expression in the control group, whereas in the second design, it represents the effect of time on the log-fold change between the control and AA groups. Little wonder, then, that you get different results.

That said, it's rarely sensible to drop individual spline coefficients. They are not easily interpreted by themselves, as the piecewise spline functions are constructed from all coefficients. If you want to test for a time effect, you should drop all 5 spline coefficients together.

I guess you want to find genes for which the time trend is different between the two conditions. In that case,

topTable(fit2, coef=8:12)

will give you what you want.

You could conduct the same test using the first design matrix, but you would need to extract contrasts. For this test, the second design matrix is simpler.