For these analyses, we included all GWAS studies that provided genome-wide results for both the full distribution and tails of BMI, height and WHR. First, we used the results for the full distribution to calculate, for each genotype, the expected number of individuals in the upper and lower 5% tails. We used these values to perform a logistic regression, comparing the upper and lower tails, and obtained the ‘expected beta’ and ‘expected standard error’. Second, we tested the differences between the ‘expected betas’ and the ‘observed betas’ obtained from the meta-analyses of the tails of the distributions. The standard error of the differences was estimated as: sqrt[expected standard error ˆ2 + observed standard error ˆ2 - 2*0.65*(expected standard error* observed standard error)], where 0.65 is the correlation between ‘expected betas’ and ‘observed betas’ obtained from TWINGENE by bootstrapping. Finally, differences between ‘expected betas’ and ‘observed betas’ were meta-analyzed using the inverse variance method in METAL.
