Hi,

I use Limma to assess differential expression of miRNAs. I have 3 donnors, two conditions, and two days of experimentation (D7 and D21), for 361 miRNA.

When i submit the program below to compare miRNAs expression at Day 7, i found that the fit$s2.post was equal to fit$s2.prior for all my miRNAs. so that suppose that the same variance is used whatever the miRNA

for the moderated t-test. What does it mean ?  

best regards,

Julie

#Day 7
donnor <- factor(tableD7$Donnor)
Type <- factor(tableD7$Type, levels=c("Q","SIPS"))

design <- model.matrix(~donnor+Type)

fit <- lmFit(arnEXTD7QvsSIPS, design)
fit <- eBayes(fit)

> fit$s2.prior
[1] 1.786667

> fit$s2.post
  [1] 1.786667 1.786667 1.786667 1.786667 1.786667 1.786667 1.786667 1.786667 1.786667 1.786667 1.786667 1.786667 1.786667 1.786667
 [15] 1.786667 1.786667 1.786667 1.786667 1.786667 1.786667 1.786667 1.786667 1.786667 1.786667 1.786667 1.786667 1.786667 1.786667
 [29] 1.786667 1.786667 1.786667 1.786667 1.786667 1.786667 1.786667 1.786667 1.786667 1.786667 1.786667 1.786667 1.786667 1.786667
 [43] 1.786667 1.786667 1.786667 1.786667 1.786667 1.786667 1.786667....

You shouldn't really need to look at the prior or posterior estimates to use limma. But if you really want to know, the reason that they're the same is because the estimated prior degrees of freedom is very large. In other words, the true variances are very similar across the different miRNAs. This allows limma to perform strong shrinkage of the gene-wise sample variances towards the prior - so strong, in fact, that the shrunken posterior values are effectively equal to the prior value. This is the intended behaviour, as strong shrinkage results in more stable variance estimates which should subsequently increase the power of the moderated t-test.

This kind of strong shrinkage is somewhat unusual for expression data. RNA-seq, for example, tends to have lower prior d.f. estimates and less shrinkage because there's more genes with variable variability. I guess that strong shrinkage may be possible if all your genes are miRNAs, as you might expect that they should all behave similarly in whatever assay you're using. However, I don't have any experience with miRNAs to be sure.

Finally, you should tag your post with the package name by itself, i.e., just "limma". Otherwise, the maintainers will not be informed.

Continuing on from Aaron's answer. What this means is that the estimated variances look less variable than chance, so limma is putting all the variances equal. While it can happen, for example for simulated data, that the true genewise variances are indeed all equal, for miRNA data is it far more likely that there is problem with your data.

The most likely cause is that your experiment has a strong unexplained batch effect, whereby the different donors are not truly comparable in their response to treatment. The donors may have strongly different responses to the treatment in a systematic way across a large proportion of the miRNAs. This will cause the residual variances to be systematically large, driven by unmodeled systematic effects rather than variability, and limma will be forced to set the variances to a consistent large value, which is what you have observed. An alternative explanation is that the design matrix isn't specified correctly. If your data has problems of this sort then it will be obvious from standard diagnostic plots, which I assume you would have already made and looked at.