As shown in ref.51,55, for an association study of N independent samples, the expected χ2 statistic is E[χ2] = 1 + Nlh2GE/M, where l is the LD-score accounting for correlation, M is the number of markers, and h2GE is the variance in trait explained by the imputed expression. We estimated l directly from the genetic values of expression to be close to independence (1.4, 1.5 for METSIM, YFS) allowing us to solve for h2GE from the observed distribution of χ2 (or, asymptotically equivalent Z2) statistics. We did not compute this value for the BMI GWAS because the conservative multiple GC-correction applied in that study would yield a severe downwards bias6.
