Dear Bioconductor Community,

I am trying to do a differential expression analysis between different cell types, where I have four different cell types from two different experiments. Two of the cell types come from one experiment and four cell types come from the other. I have a total of 18 samples. I have also detected that there is a batch effect in the samples coming from the second experiment. How would I do a differential expression analysis when I have a batch effect in only 12 of my 16 samples? Would I make a design matrix that includes the batch effect as well as the experiment number? Below is an example of what I am describing.

cellType <- factor(c("cellType1","cellType2","cellType1","cellType2","cellType1","cellType2",rep("cellType3",3),rep("cellType4",3),rep("cellType5",3),rep("cellType6",3)))
batches2 <- factor(c(0,0,0,0,0,0,1,0,0,1,0,0,1,0,0,1,0,0))
experiment <- factor(c(0,0,0,0,0,0,rep("1",12)))
myDesign <- model.matrix(~0+cellType+experiment+batches2)
colnames(myDesign) <- c("cellType1","cellType2","cellType3","cellType4","cellType5","cellType6","experiment","batch")

Also, if I wanted to get the values of the batch corrected data after doing differential expression analysis would I put the experiment as a covariate or would I include it in the design? Below is an example of both methods.

log2RPKMmat <- matrix(sample(1:16,90,replace=T), ncol=18)
batchVals_Covariate <- removeBatchEffect(log2RPKMmat,batch=batches2,design=model.matrix(~0+cellType),covariates=experiment)
batchVals_noCovariate <- removeBatchEffect(log2RPKMmat,batch=batches2,design=model.matrix(~0+cellType+experiment))

I also looked at the paper "Methods that remove batch effects while retaining group differences may lead to exaggerated confidence in downstream analyses." It says that  a two-way ANOVA model (which I believe I may be describing above) could cause false positives because my study is unbalanced. Are there any other methods you would propose?

Thank you!

Sam

Your design matrix looks fine, though it seems you've mixed up your column names for the batch and experiment factors (not that it really matters, because you're only interested in the cell types). You can then use makeContrasts to construct contrasts to compare any two cell types. As to the paper you're referring to, I've only glanced at it but I believe it describes the case where you remove the batch effects prior to the analysis. If you include the batches as blocking factors in the design matrix, as you have done, there shouldn't be any loss of error control because the uncertainty of estimation of the batch effects will be considered in the significance calculations. Finally, to remove the experiment effect, use the batch2 argument in removeBatchEffect to specify a second blocking factor. Don't put it in the design, as it won't be removed if you do that.