Hello,

First of all I would like to apologise if this is a straight forward question/ similar to another thread.

I have been given some RNA-seq data to do my dissertation (i say this as there is no possibility for more sequencing!), and have assembled a de novo transcriptome. Now I want to look at differentially expressed genes. 

Unfortunately, there are no replicates, and nestedness within the design. 

There are 6 individuals- normal male, infected male (intersex1), infected male (intersex2), normal female, normal female infected, infected female (intersex3). From this I want to look at the differences between males/females, infected/uninfected and normal males/females/intersex1/2/3. However, I also have 4 different tissue types, from each of these individuals which I also want to compare.

So my question is, what would be the best way to approach such analysis?

I can't really remove any explanatory factors, as they are all important- and even then i still probably do not have enough replicates. I am not entirely sure what a 'reasonable' dispersion value would be, as this is not a controlled experiment (environmental samples). So perhaps the method which appeals to me most would be to identify the non DE genes and calculate the dispersion value from that? 

Any advice/ suggestions would be greatly appreciated! 

Many thanks, 

Hazel

Your idea of using non-DE genes is circular. To determine whether a gene is DE or not, you need an estimate for the dispersion, so you're back to the same problem as before. While you could do this in iterations (i.e., identify non-DE genes using an initial value for the dispersion, re-estimate the dispersion from the non-DE genes, and repeat using the new value), there's no guarantee that those iterations would converge to any sensible value for the dispersion. In fact, some back-of-the-envelope calculations suggest that they probably don't.

Anyway, I assume you've read the relevant section of the edgeR user's guide on this topic. The idea of dropping the least-important explanatory factors is only to estimate the dispersion; you still use the full design matrix to fit your GLM and to do your contrasts. If the dropped factor is important, then your dispersion will be overestimated (due to hidden DE inflating the variability between "replicates") and you'll be more conservative. This is probably the lesser of the two evils, with the alternative being that you detect a whole lot of false positives.

Really, though, if I got this data set, I would complain loudly to the person who gave it to me, and then refuse to do anything more than a descriptive analysis of the log-fold changes. Why should I have to suffer due to someone else's bad experimental design?