data is not due to phenotype or racial/ethnic group (Johnson et al, unpublished observations, 2010); such structure might account for the permutation results from the African American data [28], [29]. Based on statistical considerations, the present analyses are likely to provide many false negative results. The power of each of these samples to detect polygenic influences is moderate. The requirement for convergent identification of the same chromosomal region by data from both samples of the same racial/ethnic background provides a likelihood of even more false negative results. Case vs control allele frequency differences in the NIDA/MNB samples were genotyped using multiple DNA pools and an Affymetrix 6.0 platform, providing t tests that use information about both mean differences and variances. Case vs control differences in the dbGAP samples were assessed using Illumina platform genotyping of individual samples, yielding χ2 results without explicit assessment of variance. The requirement that at least 4 nominally-significant SNPs lie within 10 kb of each other cannot be fulfilled in a number of chromosomal regions or in a number of genes in which the density of SNPs is too low to meet this stringent requirement (see Supplement of [14] for list of the genes that cannot
