Our study has several limitations. The GWS and other top-ranked findings were identified with imputed SNPs; however, empirically, our results show that the top-ranked SNPs in our study were imputed with excellent quality. Although our strongest results were with imputed SNPs, they are not rare. (Two had MAF=0.08; two, 0.06; and one, 0.03.) The primary concern about rare (MAF<1%) SNPs is the greater rate of false positive results possible due to large effect sizes (i.e., greatly increased risk) derived from small allele frequency differences between cases and controls or genotyping errors. However, studies examining this issue have concluded that nominally significant results occur less frequently than expected, even for low MAF SNPs, provided there is no genotyping or imputation quality bias between cases and controls (37, 38). Moreover, the concern about false positives is substantially less when the results are replicated or supported by evidence from multiple samples, which is the case for the associations that we reported. Also, although our sample size is reasonable, experience has shown that many true associations are detected only in samples or meta-analyses that
