The genomic control method in association studies was proposed in (Devlin and Roeder, 1999; Bacanu et al., 2000; Devlin et al., 2001) to correct population stratification and “cryptic relatedness” between samples. Despite quantitative differences in the mechanism for correlation, population stratification and family clusters could have similar consequences, and this similarity is exploited in a unified framework for association studies of quantitative traits (Yu et al., 2006). In the genomic control method, neutral markers are used to estimate the variance inflation factor λ, and λ is used to divide the chi-square statistic: Xgc2=X2/λ for a modified test statistic. This can be compared to our formula for an ESS-corrected chi-square test statistic in Eq.(10), Xe2≈αX2 (if the allele counts NA,con,NB,con in control group are not too small). In this approximation, Xe2≈Xgc2 if α = 1/λ.
