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 provide strong overall confidence that these sets of results are not due to chance. By contrast, these approaches alone provide unequivocal identification of few individual SNPs or genes. This lack of unequivocal identification of individual SNPs is consistent with polygenic/allelic heterogeneity current working models for the genetic architecture of vulnerability to substance abuse [14], [34]. However, identification of associations at some loci, such as the CDH13 locus, in many independent samples (see below) makes it very highly unlikely that this locus does not harbor allelic variants that influence interactions between humans and addictive substances.
