Notably, the common SNPs did not follow all of the patterns seen here for low-frequency SNPs (see File S3.) A cosmopolitan reference panel produced high imputation accuracy in both frequency classes, but the accuracy at common SNPs came almost entirely from the most closely related panels. For example, the maximum accuracy at common SNPs in TSI was attained with a TSI+CEU reference panel, and the addition of other panels neither increased nor decreased the accuracy. Hence, our results confirm that cosmopolitan reference panels are benign for imputing common variants, while showing that such panels can be positively helpful for imputing low-frequency variants. This difference can be understood in terms of the representation of the minor allele in the reference panel: common alleles are usually well-represented in population-matched panels of nontrivial size, whereas low-frequency alleles may be present in only a few copies or absent entirely, depending on allele frequency, SNP ascertainment scheme, and the number of reference haplotypes. Additional copies of these alleles (and their associated haplotype backgrounds) may sometimes be found in other populations, which explain why a cosmopolitan reference panel can improve imputation accuracy at low-frequency variants. These statements are supported by the results in File S2.
