The method is built upon the assumption that the reference sample is from the same population as the samples from which the genotype-phenotype associations are estimated, meaning that the LD correlations that are estimated from the reference sample are unbiased. We show by simulation (Supplementary Note) that the P values from our approximate approach are highly consistent with those from the conditional meta-analysis (correlation of >0.99 in 1,000 simulation replicates), given a reference sample of 6,654 individuals (Supplementary Fig. 3 and Supplementary Table 4). The simulation results did not change if the reference sample was independent of the discovery sample, as long as both were sampled from the same general population (Supplementary Fig. 4). We recommend that a reference sample be chosen with a large sample size, so that the LD correlations are estimated with little error17. The simulation results indicate that a reference sample with a size of at least 2,000 is required and that little additional accuracy is gained beyond a sample size of 5,000 (Supplementary Fig. 4). The reference sample needs to be checked for cryptic relatedness
