I have a set of data that I'm having trouble setting up the design.

At time 0, each subject underwent a procedure that generated three regions of samples (groups?); Experimental tissue 1, Experimental tissue 2, and a control tissue.  We want to see what happens to the genes at four time points after that.  Mostly tissue 1 vs control, but 1v2 and 2vC would also be useful.

One issue is that there's multiple data for each time point and they're all from different subjects.  There's from two to five subjects at each time point. There's also baseline data from time point 0 before the procedure that could I suppose be applied to be the baseline of all three experimental groups.

Here is the code I have so far, based off the limma user's guide 9.6

targets <- readTargets("AllTimePointFiles.csv",path=datadir,sep=",",row.names="filename")
data <- ReadAffy(celfile.path=datadir)
eset <- affy::rma(data)

X <- ns(targets$TimeType,df=2)   # the number of days since day 0.
Group <- factor(targets$RegionType) # group number, 1, 2, or 3.
design <- model.matrix(~0+Group*X)
fit <- lmFit(eset, design)
fit <- eBayes(fit)

topTableF(fit,number = 29000,adjust="BH")

Even just trying to do region 1 vs control (omitting region 2 from the file), I'm getting every single gene as being significant, wildly so, like 10^-57 to 10^-11.

The other weird thing is that I suspected it was a problem with not setting the coef correctly, but I cannot set the coef to anything.  Every single thing I choose, I get an error message

"Error in topTableF(fit, coef = 2, number = 29000, adjust = "BH") : 
  unused argument (coef = 2)"

Traceback() is no help.

Any help you can give would be greatly appreciated.  Thank you. 

A cursory scan of the documentation would reveal that topTableF has no coef argument. Moreover, without an intercept, it doesn't make sense to use topTableF. Your null hypothesis would be that all groups and timepoints have an average-log expression of zero, which is a silly thing to test.

The more interesting tests would be whether the spline coefficients for each tissue are non-zero, to determine if there is a time effect for each tissue; or whether the spline coefficients for one tissue are different to those of the other tissues, to determine if there is a tissue-specific time effect. The first case would require use of topTable with coef set appropriately, while the second case would require contrasts.fit.

In any case, you should also be accounting for the fact that each triplet of samples come from the same patient. You would probably need to use duplicateCorrelation for this; blocking on patient in the design matrix would not allow you to compare across timepoints within a single tissue.