# GWAS and Statistical theory - does the likelihood of a detectable main effect decrease with complexity?

I've been wondering recently about the difficulty of detecting statistically significant results from, say, genome-wide association studies. In these studies, many - ($10^{8}$) for example- statistical tests on tiny genetic changes are performed in order to detect an association with a trait - say heart disease.

The difficulties are manifold. First, multiple testing. Simple Bonferroni correction for $10^{8}$ tests often leaves these entire experiments labelled "insignificant" if they don't find an association that withstands these mad Bonferroni corrections. (There's probably a case for the "Manhattan" plot being replaced with a Pareto plot, because of the hypothesis generating nature of these studies. It's a cultural issue and a little off my topic).

However, using narrower sets of data and better defined phenotypes we can sometimes detect statistical interactions between particular genotypes which are associated with a particular (endo)phenotype. My questions is: is it in the nature of complex systems that main effects will "cancel out" but that statistical interactions will be more detectable? With many more "true" effects in your system - is it less likely you will detect those effects as main effects without controlling for others? This might be particularly true of the genome, but could be true of other complex systems. I don't really have a good structure in which to think about this problem and I wonder if it has been written about before.

Thanks

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While I agree that GWAS studies involve many statistical tests, how do you get $10^{13}$? There are around $3\times10^9$ base pairs in the human genome, around $10^7$ single nucleotide polymorphisms, and the GWAS studies I'm familiar with genotype $10^5$ to $10^6$ of those. – onestop Jun 29 '12 at 9:42
corrected - but kind of not the point – rosser Jun 29 '12 at 10:12