I recently wrote a blog post about enrichment analysis: http://blog.nextgenetics.net/?e=94

I went over how a simple hypergeometric distribution works in relation to enrichment analysis. My problem with these methods is that the statistical combinatorial space is not representative of the possible biological combinatorial space.

Most of these enrichment assays works on some kind of: "if I was to randomly pick X items out of this population what is the chance that more than Y items of a certain type will be present in X". A more biological example: "If I was to randomly designate 100 genes to be differentially expressed in my transcriptome, what is the chance that more than 50 genes related to 'cell cycle' will be present in the 100 genes".

The statistical p-value is essentially calculated by: "out of all combinations of X items in the population, how many of those combinations have more than Y in X".

However, is using the combinatorial space of "all combinations of X items in the population" valid? How much of that combinatorial space is actually biologically relevant? Can all possible combinations actually happen in nature? Wouldn't a specific combination kill the organism or will be almost impossible to induce? If we reduce the combinatorial space by looking at only biologically possible cases, our p-value will increase. The question, to me, is how much of the statistical combinatorial space is biologically relevant? If most of it are, then our p-values are good. If not, then our p-values are too low.