To apply this procedure, it is necessary to determine a set of markers for which the inflation in type I error for the chosen test statistic (with or without PC adjustment) can be properly measured. Ideally, to avoid bias, this set of markers should be uncorrelated with the set of markers used for PC detection, and not associated with the disease risk. To such an end, we can identify a large set S (approximately 240,000 SNPs) of genomic control markers that do not exceed a threshold level of LD with any SNPs used in the PCA. Although several disease-related SNPs might be included in this set, their effect on the inflation estimation can be ignored as the vast majority of the SNPs in the set S would not be disease-related. For each genomic control SNP in S, assuming an additive genetic model, a 1-df Wald test can be performed by adjusting any chosen PCs and other covariates. Following Devlin and Roeder [27], the over-dispersion factor can be estimated as the median of Wald test statistics over the set of genomic
