Monte Carlo methods allow us to test the probabilities of chance clustering of nominally positive SNPs and the chance of convergence between clusters identified in one sample with clusters identified in other samples. Our Monte Carlo approaches deploy an empirical method that uses the existing dataset as a source for randomly selected SNPs for each Monte Carlo trial. The results of these simulations, supported by data derived from permutation, principal components and other analyses, provide strong overall confidence that these results are not due to chance. By contrast, these approaches provide absolutely unequivocal identification for few individual SNPs. This lack of unequivocal identification of individual SNPs is consistent with the current polygenic working models for the genetic architecture of vulnerability to substance abuse [25], [47].
