[BioC] Newbie methylation and stats question

[Gustavo Fernández Bayón]

Hi everybody.

As a newbie to bioinformatics, it is not uncommon to find difficulties in the way biological knowledge mixes with statistics. I come from the Machine Learning field, and usually have problems with the naming conventions (well, among several other things, I must admit). Besides, I am not an expert in statistics, having used the barely necessary for the validation of my work.

Well, let's try to be more precise. One of the topics I am working more right now is the analysis of methylation array data. As you surely now, the final processed (and normalized) beta values are presented in a pxn matrix, where there are p different probes and n different samples or individuals from which we have obtained the beta-values. I am not currently working with the raw data.

Imagine, for a moment, that we have identified two regions of probes, A and B, with a group of nA probes belonging to A, another group (of nB probes) that belongs to B, and the intersection is empty. Say that we want to find a way to show there is a statistically significant difference between the methylation values of both regions. 
As far as I have seen in the literature, comparisons (statistical tests) are always done comparing the same probe values between case and control groups of individuals or samples. For example, when we are trying to find differentiated probes.

However, if I think of directly comparing all the beta values from region A (nA * n values) against the ones in region B (nB * n values) with a, say, t test, I get the suspicion that something is not being done the way it should. My knowledge of Biology and Statistics is still limited and I cannot explain why, but I have the feeling that there is something formally wrong in this approximation. Am I right? 

What I have done in similar experiments has been to find differentiated probes, and then do a test to the proportion of differentiated probes to total number of them, so I could assign a p-value to prove that there was a significant influence of the region of reference. 

Several questions here: which could be a coherent approximation to the regions A and B problem stated above? Is there any problem with methylation data I am not aware of which makes only the in-probe analysis valid? Any bibliographic references that could help me seeing the subtleties around?

As you can see, concepts are quite interleaved in my mind, so any help would be very appreciated.
Regards,
Gustavo




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